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Inflation Instruments and Strategies EDITED BY STEFANIA PERRUCCI AND BRICE BENABEN Sensitive Assets

Inflation Sensitive Assets

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Inflation

Instruments and Strategies

EdItEd by StEfanIa PErruccI and brIcE bEnabEn

Sensitive assets

Inflation Sensitive assets

Edited by Stefania Perrucci and brice benaben

The real impacts of inflation and its most extreme form – hyperinflation – are known only too well: they erode value, unbalance economies and destroy wealth. In the wake of the financial crisis a huge monetary overhang threatens the major developed economies. The iron laws of economics have no respect for modern semantic niceties of “quantitative”, “credit” or “monetary” easing: these policies all portend of inflation that must work its way out of the system. As a result markets have focused attention on assets that protect the investor from loss of purchasing power. Inflation-sensitive assets – including commodities, equities, infrastructure and real estate investments, and inflation-linked securities – have in fact become a new asset class. Many institutional investors controlling trillions of dollars’ worth of assets are allocating an increasing weight to the sector as an alternative and complement to other traditional assets.

In Inflation-Sensitive Assets: Instruments and Strategies, Stefania Perrucci and Brice Benaben blend insights and experiences from market participants including investment bankers, asset and pension fund managers and central bankers to guide the reader through this emerging sector.

This book, for the first time, addresses the commodities and inflation markets together, providing a holistic treatment from an inflation perspective. Inflation-Sensitive Assets provides the reader with a deep understanding of the drivers of inflation, the assets which can be used to hedge it and how investors can formulate strategies when managing assets and liabilities in an inflation-sensitive environment. Designed for practitioners, the book includes important academic contributions, and will be of interest to portfolio managers, risk managers, plan sponsors and researchers alike. “This book provides an essential resource for investors, consultants and service providers keen to preserve wealth”MIhIr WorAh, Managing Director, head of real return Portfolio Management, PIMCo

PEFC Certified

this book has been produced entirely from sustainable papers that are accredited as PEfc compliant.

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Inflation-Sensitive Assets

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Inflation-Sensitive AssetsInstruments and Strategies

Edited by Stefania Perrucci and Brice Bénaben

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Published by Risk Books, a Division of Incisive Media Investments Ltd

Incisive Media32–34 Broadwick StreetLondon W1A 2HGTel: +44(0) 20 7316 9000E-mail: [email protected]: www.riskbooks.com

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© 2012 Incisive Media

ISBN 978-1-906348-62-5

British Library Cataloguing in Publication DataA catalogue record for this book is available from the British Library

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Warning: the doing of any unauthorised act in relation to this work may result in both civiland criminal liability.

Every effort has been made to ensure the accuracy of the text at the time of publication, thisincludes efforts to contact each author to ensure the accuracy of their details at publicationis correct. However, no responsibility for loss occasioned to any person acting or refrainingfrom acting as a result of the material contained in this publication will be accepted by thecopyright owner, the editor, the authors or Incisive Media.

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To the memory of our fathers, Bernard Bénaben and Pietro Perrucci

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Contents

About the Editors ix

About the Authors xi

Foreword xixMihir WorahPIMCO

Acknowledgements xxi

PART I INTRODUCTION: MARKETS AND INSTRUMENTS 1

1 Inflation-Sensitive Assets 3Stefania A. PerrucciNew Sky Capital

2 Investable Commodity Indexes and Inflation: A Brief History 13Bob GreerPIMCO

3 Commodities, Inflation and Growth: Implications for Policyand Investments 25Ric Deverell, Kamal NaqviCredit Suisse

4 Inflation and Real Estate Investments 43Brad Case; Susan M. WachterNational Association of Real Estate Investment Trusts(NAREIT); The Wharton School, University of Pennsylvania

5 Infrastructure Assets and Inflation 69Gerald Stack, Dennis Eagar, Kris WebsterMagellan Group

6 Equity Investments and Inflation 79Steven Bregman, Murray StahlHorizon Kinetics LLC

7 Inflation-Linked Markets 103Gang Hu; Stefania PerrucciCredit Suisse; New Sky Capital

8 Understanding and Trading Inflation Swaps and Options 137Brice Bénaben; Hervé Cros; Franck TriolaireNew Sky Capital; BNP Paribas; Morgan Stanley

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PART II RESEARCH AND MACRO PERSPECTIVE 177

9 The Role of Models in Modern Monetary Policy 179Stefania A. Perrucci and David VavraNew Sky Capital; OGResearch

10 Term Structure of Interest Rates and Expected Inflation 209Olesya V. Grishchenko; Jing-Zhi HuangFederal Reserve Board; Penn State University

11 Monetary Policy, Inflation and Commodity Prices 255Frank Browne, David CroninCentral Bank of Ireland

12 Inflation and Asset Prices 277John A. TatomIndiana State University

13 Inflation and Equity Returns 299Jeffrey OxmanUniversity of St Thomas

14 Inflation Hedging through Asset and Sector Rotation 325Alexander Attié, Shaun RoacheInternational Monetary Fund

PART III PRACTICAL INSIGHTS FROM MARKET PARTICIPANTS 349

15 Practical Models for Inflation Forecasting 351Nic JohnsonPIMCO

16 Protecting Insurance Portfolios from Inflation 369Ken Griffin and Edward Y. YaoConning Asset Management

17 Inflation, Pensions and Liability-Driven Investment Solutions 389Markus AakkoPIMCO

18 Ultra-High-Net-Worth Investors and the Real Asset Value Chain 423Ian BarnardCapital Generation Partners

19 Inflation Markets: A Portfolio Manager’s Perspective 435Stefania A. PerrucciNew Sky Capital

20 Inflation Indexation and Products in Emerging Markets 479Brice Bénaben, Stefania A. PerrucciNew Sky Capital

Index 507

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About the Editors

Stefania Perrucci is the founder and CEO of New Sky Capital, anindependent investment and advisory firm with offices in Philadel-phia and London. She has 15 years of investment experience, span-ning both traditional and alternative asset classes. Before foundingNew Sky, she was a portfolio manager at Morgan Stanley, where sheconsistently ranked among the top-quartile performers. Her flagshipfund was the recipient of a Lipper FundsAward in 2008 (based on topthree-year trailing performance). Before joining Morgan Stanley, shewas a risk management specialist at the IFC, part of the World BankGroup. Stefania has established herself as a recognised thought-leader and independent-minded investor. In 2006, she was one of thefew buy-side voices advocating a long insurance position to protectagainst the effects of an imminent collapse in house prices. She isthe author of several proprietary models, with one patent awardedand another pending. She has published cutting-edge research onseveral market topics, and speaks regularly at industry conferencesaround the globe. She is the editor and author of Mortgage and RealEstate Finance. Stefania received her PhD in theoretical physics fromthe University of Virginia, and a Laurea Summa Cum Laude fromthe University of Modena, Italy. She has held academic positionsat universities in both the US and Europe, receiving more than adozen awards, in recognition of outstanding academic and teachingachievement.

Brice Bénaben is a managing director and head of inflation researchat New Sky Capital. He has 15 years of investment experience. Pre-viously, he held positions as managing director and global head ofproperty derivatives and inflation trading at Deutsche Bank, deputyhead of inflation at Citibank, head of inflation structuring at ABNAMRO, head of fixed income and portfolio strategy at Credit Agri-cole Indosuez and portfolio manger/trader at the IFC (World BankGroup). Brice is the editor and author of Inflation-Linked Products,co-editor and author of Inflation Risks and Products, and co-authored“Real Estate Indexes and Property Derivative Markets” in Mortgageand Real Estate Finance. He is a graduate of the University of Oxford,where he studied applied mathematics.

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About the Authors

Markus Aakko is an executive vice president at the Pacific Invest-ment Management Company (PIMCO), working with pension plansand institutional clients. Prior to joining PIMCO in 2010, he was amanaging director and portfolio manager in global portfolio solu-tions within Goldman Sachs Asset Management (GSAM). His priorexperience with GSAM includes roles as head of risk managementand head of fixed income for manager selection. Before joiningGSAM, Markus worked with the International Finance Corporationat the World Bank.

Alexander P. Attié is a senior financial officer with the InternationalMonetary Fund (IMF). He works on the design and implementationof investment strategies for the IMF’s reserves and for assets of trustfunds that support concessional lending. Prior to joining the IMF in2005, he worked for Banque de France as a fixed-income portfoliomanager for eight years. He graduated from the Institut d’ÉtudesPolitiques de Paris in 1993 with a major in economics.

Ian Barnard is a founding partner and chief investment officer ofCapital Generation Partners LLP. Ian is a regular speaker at con-ferences and has contributed articles to the general and more spe-cialised press. He has advised on structured finance, and mergersand acquisitions at Smith Barney, completed an MSc in managementat London Business School and, from Geneva, advised a family-owned investment group on direct and portfolio investments. Ianalso served in HM Diplomatic Service, both in London and abroad,concentrating on the Middle East, as well as serving briefly in theBritish Army.

Steven Bregman is the portfolio manager of Horizon’s core valuestrategy and was a co-founder of the firm. He serves on the invest-ment committee and the board and is a senior member of Hori-zon Kinetics’ research team, with oversight responsibilities for allresearch reports produced by the firm. Previously, he was a seniorinvestment officer in the private bank at the Bankers Trust Company(1985–94), where he was a member of the institutional/individualgroup responsible for the bank’s larger individual relationships and

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for setting equity investment guidelines for the private bank. Stevenalso served as a member of the special situations equity strategygroup, and in a variety of new product development projects. Hehas a BA from Hunter College and gained a CFA in 1989.

Frank Browne is senior advisor to the Governor, Central Bank of Ire-land. He previously worked as senior economist at the OECD (1988–92), as deputy head of Stage 3 (EMU) Division at the European Mon-etary Institute (1994–8) and as advisor to the research directorate atthe European Central Bank (1998–2000). He has been a member ofthe ECB Monetary Policy Committee and the ECB Bank SupervisionCommittee. Frank’s research has been published in European Eco-nomic Review, Review of Economics and Statistics and The ManchesterSchool.

Brad Case is senior vice president of the research and industry infor-mation group for the National Association of Real Estate InvestmentTrusts (NAREIT). His research has been published in Review of Eco-nomics and Statistics, Real Estate Economics, the Journal of Real EstateFinance and Economics, Journal of Portfolio Management and other aca-demic and industry publications. He is the co-inventor of PureProp-erty indexes of commercial property values as well as “backward–forward” trading contracts. Brad earned his BA at Williams College,his MPP at the University of California at Berkeley, and his PhD ineconomics at Yale University.

David Cronin is senior economist at the Central Bank of Ireland.He has represented the Bank at various European System of CentralBanks committees and at other forums. He has published articles injournals such as Journal of Economics and Business, Empirica and TheCato Journal, among others.

Ric Deverell is a managing director and head of the commodi-ties research team at Credit Suisse. He previously spent 10 yearsat the Reserve Bank of Australia, holding several senior positionsincluding deputy head of economic analysis and chief manager ofinternational markets and relations. During the 1990s, Ric worked inthe Department of the Prime Minister and the Australian Treasury,where he was head of the Asian section during the Asia crisis. Hisresearch interests include analysis of the global business cycle, the

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ABOUT THE AUTHORS

emergence of the Asian economies and developments in commod-ity markets. Ric is a graduate in economics from the University ofTasmania.

Dennis Eagar manages global listed infrastructure investment port-folios for Magellan Asset Management on behalf of retail and whole-sale investors. The team is regarded as expert in the investmentanalysis and valuation of infrastructure assets and has more than50 years’ collective experience in infrastructure investment. Theteam has advised on investment in airports, ports, toll roads, com-munications infrastructure, pipelines, electricity distribution andtransmission, and water and waste water treatment and distribution.

Robert J. (Bob) Greer is an executive vice president and managerof real return products at the Pacific Investment Management Com-pany (PIMCO). He managed commodity index business for DaiwaSecurities, Chase Manhattan Bank and JP Morgan. Bob developedone of the two common methods of explaining sources of commodityindex returns and has spoken on this asset class in college lectures,on national television, and at industry conferences and trade meet-ings. He has published in The Journal of Portfolio Management and TheJournal of Derivatives, among others. He has consulted on commodi-ties for the CIA, the Bank of England and the New York Fed. Bob isthe author of The Handbook of Inflation Hedging Investments. He hasa Bachelor’s degree in mathematics and economics from SouthernMethodist University and an MBA from Stanford Graduate Schoolof Business.

Ken Griffin is a managing director at Conning, where he headsthe life and health advisory team that is responsible for providingasset–liability and integrated risk management advisory services tolife and health insurance company clients. He also serves as a leadconsultant for various capital management and investment-relatedprojects involving global life and property and casualty insurancecompanies. Prior to joining Conning in 2001, Ken held various posi-tions within Swiss Re Investors’ ALM unit. He has been involved inproduct development, insurance securitisations, ALM and invest-ment portfolio management for insurance companies since 1997. Heis a graduate of the University of North Carolina at Chapel Hill witha BA in Economics.

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Olesya V. Grishchenko is an economist in the monetary affairs divi-sion of the Board of Governors of the Federal Reserve System, con-ducting research and policy work related to the term structure ofinflation expectations, inflation uncertainty, deflation probabilitiesand on the term structure models of real interest rates. She has aPhD in finance from the Stern School of Business of New York Uni-versity, and previously worked as an assistant professor of financein the Smeal College of Business, Penn State University. Olesyais a visiting assistant professor of finance at the New EconomicSchool of Moscow, with research interests in empirical asset pricing,consumption-based modelling and computational methods. She haspublished in the Journal of Economics and Business and Journal of Busi-ness and Economic Statistics and is a member of the American FinanceAssociation and the European Finance Association.

Gang Hu is a managing director of Credit Suisse in the fixed incomedivision, based in London. Within the fixed-income division he isthe global head of inflation, responsible for the US, UK, EU anddeveloped Asia in linear and non-linear inflation business. He joinedCredit Suisse in July 2011 from PIMCO, where he was an execu-tive vice president in the real return team, co-managing the largestinflation fund group in the world. Prior to that, Gang worked atDeutsche Bank, running the US inflation business. He has 11 years’experience in the banking industry and holds a BAin applied mathe-matics from Tsinghua University and a PhD in applied mathematicsfrom California Institute of Technology.

Jing-Zhi (Jay) Huang is a McKinley Professor of business and asso-ciate professor of finance at the Smeal College of Business, PennState University. His research interests include derivatives mar-kets, credit risk, fixed-income markets, mutual funds and hedgefunds. His papers have been published in The Journal of Finance,Economic Theory, Journal of Derivatives, Journal of Fixed Income, Journalof Real Estate Finance and Economics and Review of Derivatives Research,among others. He won the Best Paper Awards at the Financial Man-agement Association and the Eastern Finance Association Meetings,and NYU’s Stern School Club 6 Teaching Award. He received hisPhD in physics from Auburn University, and his PhD in financefrom New York University.

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ABOUT THE AUTHORS

Nicholas Johnson is an executive vice president and portfolio man-ager at the Pacific Investment Management Company (PIMCO),where he focuses on commodities and inflation. He previouslymanaged the portfolio analysts group. Prior to joining PIMCO in2004, he worked at NASA’s Jet Propulsion Laboratory, developingMars missions and new methods of autonomous navigation. He haseight years of investment experience and holds a master’s degreein financial mathematics from the University of Chicago and anundergraduate degree from California Polytechnic State University.

Kamal Naqvi is a managing director of Credit Suisse in the invest-ment banking division, based in London, where he is the head ofinstitutional commodity sales. He has over 15 years’ experience inthe resources industry. He joined Credit Suisse in July 2007 after fouryears at Barclays Capital, where he was responsible for coverage ofhedge funds and institutional clients across commodity products,after previously being a director in the commodity research team.Prior to that, he was a commodities analyst with Macquarie Bankin London, after having worked for CRU International in Londonas part of both the lead/zinc and precious metals teams. Kamalbegan his career as a project manager/economist for the miningand mineral processing division of the Tasmanian State GovernmentDepartment of Development and Resources. He holds degrees (withhonours) in law and in economics from the University of Tasmania.

Jeffrey Oxman is an assistant professor of finance in the Opus Col-lege of Business at the University of St Thomas in Minneapolis,MN, USA. His research has been published in the Review of Deriva-tives Research and Economics Letters. His research interests includeinflation, value investing and corporate finance. He holds a PhD infinance from Syracuse University in New York.

Shaun K. Roache is an economist in the Western Hemisphere depart-ment of the IMF. He has worked in various countries, includingBrazil and China, contributing to the IMF’s analysis of global com-modity markets, and worked as part of the team managing the IMF’sinvestments. Previously, Shaun worked for 10 years as a global finan-cial market strategist, for companies including ING Barings andCitigroup. He holds a PhD in economics from Birkbeck College,University of London and is a CFA charterholder.

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Gerald Stack manages global listed infrastructure investment port-folios for Magellan Asset Management on behalf of retail and whole-sale investors. The team is regarded as expert in the investmentanalysis and valuation of infrastructure assets and has more than50 years’ collective experience in infrastructure investment. Theteam has advised on investment in airports, ports, toll roads, com-munications infrastructure, pipelines, electricity distribution andtransmission, and water and waste water treatment and distribution.

John A. Tatom is director of research at Networks Financial Insti-tute and associate professor of finance at Indiana State University.From 2000 to 2005, he was an adjunct professor in the economicsdepartment at DePaul University in Chicago, and during 2003–4 hewas also a Senior Fellow at the Tax Foundation in Washington, DC.From 1995 to 2000, John was with UBS in Zurich in various positions,including executive director and head of country research and limitcontrol, and chief economist for emerging market and developingcountries. From 1976 until 1995, he was a research official and policyadviser at the Federal Reserve Bank of St Louis. He has taught atseveral colleges and universities and holds a PhD from Texas A&MUniversity.

Franck Triolaire is an executive director at Morgan Stanley. He hascovered global inflation products since 1999 and is the head of infla-tion trading for Europe and Asia. He started on the buy-side inSinopia, trading inflation products and derivatives. Franck joinedBNP Paribas in 2004 as an inflation trader, took over the euro flowfranchise in 2005 and put BNP Paribas on the top of the rankingswith issuers and customers. He is highly connected in the inflationspace and has managed several government inflation linked bondissues for France, Germany and Italy. He became co-head of inflationtrading for Europe and Asia in 2008 and head in 2010, promotinginflation products on cash, derivatives, volatility and structures.

David Vavra runs a consultancy specialising in macroeconomicmodelling and forecasting, helping the pricing of financial instru-ments in currencies with shallow local markets. He also works asconsultant for the IMF, doing research and applied work on mon-etary and other issues in a number of countries. David assistedthe National Bank of Serbia in implementing its inflation-targeting

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ABOUT THE AUTHORS

regime and helped to develop forecast-based decision-making sys-tems in the central banks of Colombia, the Czech Republic, Croatia,Turkey and Peru. He was associated with the Czech National Bank,leading the macroeconomic modelling and forecasting division andadvising the Governor.

Susan M. Wachter is the Richard B. Worley Professor of financialmanagement, professor of real estate and Finance at The WhartonSchool, University of Pennsylvania. She is also the co-director of thePenn Institute for Urban Research. From 1998 to 2001 she servedas Assistant Secretary for Policy Development and Research at theUS Department of Housing and Urban Development. She was theeditor of Real Estate Economics from 1997 to 1999 and serves on theeditorial boards for several real estate journals. She is the author ofmore than 100 scholarly publications.

Kris Webster manages global listed infrastructure investment port-folios for Magellan Asset Management on behalf of retail and whole-sale investors. The team is regarded as expert in the investmentanalysis and valuation of infrastructure assets and has more than50 years’ collective experience in infrastructure investment. Theteam has advised on investment in airports, ports, toll roads, com-munications infrastructure, pipelines, electricity distribution andtransmission, and water and waste water treatment and distribution.

Edward Y. Yao is a vice president at Conning, where he is responsiblefor providing advisory services to property and casualty insurancecompany clients with respect to strategic asset allocation and inte-grated asset–liability risk management. Prior to joining Conning in2008, he was a pricing actuary with Travelers Insurance Co. Edwardhas provided actuarial consulting services to a variety of clients since2000. He holds a degree in economics from Qingdao University,China, and master’s degrees in economics and computer sciencefrom Vanderbilt University.

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Foreword

Inflation ranks among the most insidious and destructive of eco-nomic forces.

At the extreme, hyperinflation – as seen in Germany during theWeimar Republic in the 1920s, when prices doubled every few days,or Hungary in 1946, when prices doubled every 15 hours – candestroy the value of paper money and social cohesion. Even moder-ate inflation can pick the pockets of savers, erode the competitive-ness of industries and nations and wreak havoc with investmentportfolios designed to preserve purchasing power.

Since Paul Volcker broke the back of the Great Inflation in the early1980s, the US has enjoyed three decades of uninterrupted, low infla-tion. In fact, in the aftermath of the financial crisis of 2008, deflation,not inflation, has seemed the larger risk.

Nonetheless, the outlook for inflation has grown more uncertain,the investment challenges and opportunities more immense. A mixof unconventional monetary policy and massive fiscal stimulus hassaddled the US with an unsustainable debt load, leaving few solu-tions: faster economic growth, higher taxes, reduced spending orinflation. Among these, inflation is the easiest, at least in politicalterms, and the most likely: no act of Congress is required.

Moreover, if the Federal Reserve wants to engineer inflation tolower the nation’s debt-to-GDP ratio, as it did in the years afterWorld War II, it will have plenty of help from secular trends. Indeveloping nations, which over the past 20 years have exerted disin-flationary pressure through exports of low-cost goods and services,nearly 2 billion people are likely to join the middle class over the nexttwo decades – moving from huts to concrete apartments, mopeds tosedans – and putting upward pressure on prices for food, crudeoil, copper and other essential commodities. A slowdown in pro-ductivity improvement in emerging economies also could translateinto higher production costs and, ultimately, higher export prices.Although aggressive inflation of the sort seen in the 1970s appearsunlikely, investors should remain vigilant: history shows that pricespikes can come abruptly, with little warning (think of the Arab oil

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embargoes of the 1970s). Indeed, its structural roots are so deep thatinflation can make us feel as helpless as individuals against the tide.

Yet it need not be so. Armed with an understanding of the factorsthat drive inflation, and the way inflation-sensitive asset classes per-form and correlate with each other, it is possible to prepare for andmanage a variety of inflationary scenarios. Inflation does not alwaysneed to be pernicious; it can also be propitious. What is needed is adynamic portfolio of inflation-sensitive assets.

This book provides an essential resource for investors, consultantsand service providers keen to preserve wealth. Essays from a widerange of experts and “thought leaders”, including some of my col-leagues at PIMCO, explore the risk factors that drive inflation andthe tools and vehicles investors can use to realise attractive potentialreturns in a variety of inflation scenarios.

Part I examines the building blocks, and related derivatives, ofwhat should be viewed as a new asset class of inflation-sensitiveassets, including investable commodity indexes, real estate, infra-structure and inflation-linked bonds. Part II moves to a more theoret-ical level, exploring: models used to forecast inflation and termstructures of interest rates; the interaction of monetary policy, infla-tion and commodity prices; theories of inflation and its impact onequities, fixed income and other asset classes; and ways to hedgeinflation through asset and sector rotation. Part III provides practi-cal guidance to investors, with chapters on: strategies for liability-and real-asset management for insurance, pension and ultra-highnet-worth portfolios; trading tactics; and inflation-linked markets inemerging countries.

I hope these insights give you new ways to think about inflationand practical tools for preserving your purchasing power.

Mihir WorahManaging Director,

Head of Real Return Portfolio Management,PIMCO

May 2012

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Acknowledgements

Many people had an important role in the successful completion ofthis volume. First in line, our excellent contributing authors: thanksfor your dedication, your hard work and for making this project thegreat book it has become.

Over the past year, the team at Risk Books has provided muchneeded guidance, enthusiasm and support. It has been a pleasure towork with them.

Last but not least, to the team at New Sky Capital, and to ourfamilies and friends, thanks for your patience and support duringthe creation of this volume.

Stefania A. PerrucciBrice Bénaben

Philadelphia, June 2012

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Part I

Introduction:Markets and Instruments

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1

Inflation-Sensitive Assets

Stefania A. PerrucciNew Sky Capital

In this chapter, we discuss how inflation should be analysed andmanaged as a key portfolio risk. We also discuss the birth of anew asset class, composed of inflation sensitive assets, that has nowgained explicit stand-alone classification and allocation by severallarge institutional investors, including pension funds and insurancecompanies.

The first section introduces the concept of inflation risk. We thenanalyse some macro issues affecting inflation and asset prices. Thisprovides a natural introduction to why inflation-sensitive assets,and not just inflation-linked products, should be viewed as a sepa-rate asset class and should receive consideration in any diversifiedinvestment strategy.

INFLATION RISK AND EVALUATING INVESTMENTS IN REALSPACEAlthough most commonly used investment metrics measure nom-inal risk and returns, a more rational approach calls for evaluat-ing investments on a real, ie, inflation-adjusted, basis, as investorsshould be concerned about preserving or, even better, increasingtheir purchasing power.

This is not an academic distinction, but a very consequential one.In fact, historic episodes, for example, stagflation in the 1970s andthe “lost decade” in Japan, show the damaging impact that bothhigh inflation and deflation can have on investment portfolios andasset prices. Despite this, inflation remains an often mismanaged,if not completely disregarded, portfolio risk. Indeed, this is partic-ularly worrisome at this junction, after almost 30 years of secular

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Figure 1.1 Annual inflation rates

30

25

20

15

10

5

0

–5

USGermanyGreat BritainJapan

1960

1970

1980

1990

2010

2000

1965

1975

1985

1995

2005

‘‘Great Moderation’’ %

Source: New Sky Capital.

bull bond market, and the generally successful anchoring of infla-tion within a small range. After the “Great Moderation” in the 1980sonwards, and an orderly downward convergence of global inflationrates (Figure 1.1), we are seeing a divergence between developed ver-sus emerging markets, with both deflationary and inflationary forcesat play. As a result of this dichotomy, the necessity to understand andmanage inflation risk is greater than ever.

Policymakers, in particular, will have to design and implementthe right exit strategies, in order to moderate easy monetary stancesin developed countries without choking growth or to control over-heating emerging economies without triggering a collapse in assetprices. It is a delicate balance, as even small shocks to money sup-ply or real growth can have a large effect on medium-term infla-tion, while a loss of confidence in central banks and policymakerscan undermine the long-term anchoring of inflation expectations.Because of these inherent sensitivities, there is little room for error.

Of course, inflation represents not just a risk but also an invest-ment opportunity. We shall expand on this in greater detail inChapter 19.

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Figure 1.2 US CPI-U weights of major components (as of December2011)

Other services20%

Shelter31%

Food15%

Core goods24%

Energy9%

Values have been rounded. Source: Bureau of Labor Statistics, New Sky Capital.

INFLATION: BASIC CONCEPTS

For the purpose of this chapter, we shall happily gloss over the dif-ferent definitions of inflation and the inherent biases of the method-ologies used to measure it, as well as the never-ending discussionsamong different schools of economics on the topic, and simply defineinflation as a rise in the cost of living.

Several indexes and various methodologies are used to measureinflation, generally relying on a defined basket of goods and ser-vices whose price is monitored over time. These indexes are typi-cally published monthly, with a delay, and often seasonally adjusted.For example, the US CPI-U (Consumer Price Index for All UrbanConsumers) is the key measure of US headline inflation, publishedmonthly by the Bureau of Labor Statistics,1 usually around the mid-dle of the following month. See Figure 1.2 for an illustration of theweights of the major components in the US CPI-U.

Intuitively, price inflation arises when too much money is chasingtoo few goods. Money is defined as the legally accepted mediumof exchange for goods and services. This is more than currency,and might include on-demand deposits (which can be readily con-verted into cash, in essence what is typically referred to as the “M1aggregate”) or extend to saving and money market accounts, ie, M2.2

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Figure 1.3 US money and banking system

$$$

$$$ $$$ $$$

$$$ $$$

$$$ $$$

$$$

$$$

Goodsproducer

Good

US Govt

FederalReserve

Bank

Bankloans9 × 1

9 × 1

Treasurybond

Deposit into bank

US governmentpays for goods

The Federal Reservecredits the US

Treasury moneyin exchange

for debtBank credit

Source: New Sky Capital.

This relation is obviously dynamic, as both money and goodsare created/produced and destroyed/consumed over time. There-fore, inflation cannot be understood without an understanding of themechanics of the real economy, the banking system and how mon-etary policy works. Specifically, in the US, money is synonymouswith debt (Perrucci 2011a): the government finances its expendituresthrough the issuance of Treasury securities (bought by investorsand/or the Federal Reserve), while the private sector gets financingthrough the extension of bank credit (fractional system); the mech-anism is illustrated in Figure 1.3. Consequently, both fiscal policy(driven by the US Government) and monetary policy (driven bythe Federal Reserve) are key determinants of money as well as theeconomy.

A MACRO APPROACH:THE DIFFERENT CAUSES OFINFLATION

Several macroeconomic and policy factors influence the path of infla-tion. As a consequence, inflation risk cannot be managed in isolation.A macro approach is crucial, and so is an understanding of the inter-actions with other traditional factors affecting the value of both real

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Figure 1.4 Expectation-augmented Phillips curve

Infla

tion

Unemployment

Source: New Sky Capital.

and financial assets (real and nominal rates, liquidity spreads, creditspreads and equities, commodities, real estate, volatility, foreignexchange rates, etc).

One of the most well-known macro models of inflation is thePhillips curve (Phillips 1958). This describes the inverse relationshipbetween inflation and unemployment observed in many countries,for example, in the UK and the US. Among other things, this rela-tion poses a difficult trade-off for policymakers, who need to balanceprice stability with full employment. However, models based on thePhillips curve were questioned in the 1970s, when many countries,including the US, experienced stagflation, ie, high inflation in themidst of stagnant growth. If, at times, inflation and employment donot move along the Phillips curve, the obvious solution is to movethe curve itself.

Accordingly, new models came about where the relation betweeninflation and unemployment (or alternative measures of real eco-nomic activity, eg, capacity utilisation) became a dynamical feature.In these models, inflation and unemployment could move alongthe usual Phillips/demand-pull curve, while the curve itself couldbe subjected to up or down moves in response to cost shocks (eg,commodities price spikes) or change in inflation expectations (asobservable in inflation surveys or the inflation linked market). Fig-ure 1.4 shows a schematic representation of expectation-augmentedPhillips curve models.

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In expectation-augmented Phillips curve models, inflation canarise as a result of

• supply/demand imbalance (demand-pull or cost-push infla-tion),

• a change in inflation expectations.

In turn, supply/demand of goods and money, as well as changes ininflation expectations, can arise for a variety of reasons, includingchange in money supply, fiscal/monetary policies (and their credi-bility), exogenous shocks (such as commodity and currency spikes),changes in competitive landscape and global trade effects.

The underlying cause of inflation is of critical importance forinvestment decisions, as, although the end result might be the samein terms of inflation print, the effect on different asset classes (or sub-sectors within the same asset class) will be quite different. For exam-ple, without entering into the details of the relationship betweenequity returns and inflation (a topic explored in later chapters),demand-pull inflation is typically more equity friendly than cost-push inflation, although both shocks might have a similar effect oncommodity prices.

INFLATION AND ASSET RETURNS

In the previous section, we explained that not all inflation is cre-ated equal, as the underlying causes can be different, and thus affectdifferent asset classes in distinct (or even opposite) ways.

Unfortunately, studying the effect of inflation on different invest-ments is not as straightforward as it might seem to be. Traditionalhistorical studies often suffer from several biases. Thus, care mustbe taken to interpret (or extrapolate) their results, as the latter mighthide rather than reveal the true underlying dynamics at play. Wegive some specific examples below.

• In historical analysis, broad sector indexes are most oftenused, and general conclusions are drawn. However, equityor commodity indexes might behave quite differently fromspecific subsectors (cyclical versus non-cyclical equities, divi-dend stocks, commodity-linked stocks, energy versus food orindustrial commodities).

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• Furthermore, market prices embed expectations about futuremacroeconomic conditions; thus, asset returns are often notcoincident but might anticipate future realisation (so lagsshould be considered in the analysis). For example, equity andindustrial commodity prices embed forecasts of future growth(among other things), and thus tend to anticipate (correctly ornot) real GDP. Ditto for the slope of the yield curve, with a flat/inverted curve being a recession signal.

• In addition, traditional historical studies often do not dis-criminate among the different underlying causes of inflation.Thus, historical data might not be relevant going forward; pastepisodes of high (low) inflation might not provide a mean-ingful comparison with the next inflation (deflation) shock,with different underlying causes or a different mix of economicconditions.

In the author’s experience, it is crucial to go beyond historical stud-ies of asset returns or average correlations, and to understand themacro-drivers behind those returns and correlations and how thesemight play at different stages of the business cycle. The ability to doso has a huge impact on the risk–return trade-off of any successfulreal return strategy. This topic will expanded upon in Chapter 19.

A NEW ASSET CLASS: INFLATION-SENSITIVE ASSETS

When considering inflation as a risk to be managed, the first assetclass that comes to mind is that comprised of inflation-linked bondsand derivatives. Indeed, these instruments are most directly andtransparently linked to inflation (in a formulaic way), and they havehad tremendous growth in sophistication and liquidity since theirintroduction (Chapters 7 and 8). Obviously, inflation-linked instru-ments provide attractive investment opportunities (Perrucci 2010)as well as diversification benefits to traditional portfolio allocation.

However, inflation-linked products are not the only inflation-sensitive instruments available to the real return manager. Indeed,especially for actively managed strategies, it is important to deter-mine whether a particular view is most efficiently implementedusing inflation-linked products directly, or other inflation sensi-tive assets (such as commodities, equities, real estate assets, infra-structure investments, etc). Coincidentally, this is consistent a global

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trend, with several pension funds, insurance funds, and even wealthfunds, changing their traditional asset allocation to include a new“inflation-sensitive” sector, along with the more traditional equity,fixed income and credit sectors. The newly defined asset class hassteadily gained weight in portfolio allocations from several institu-tional investors. The shift is of monumental importance in the assetmanagement industry, as these institutions control trillions of USdollars of capital in the space.

There are tangible benefits in defining “inflation-sensitive assets”to include other instruments in addition to inflation-linked cash andderivative securities.

• Diversification: these instruments have distinct return distri-bution characteristics and macroeconomic drivers, thus pro-viding diversification in real return space. For example, sev-eral analytical studies show how portfolios should allocateto inflation-linked securities at low/moderate return targets,while other inflation-sensitive assets such as commodities orequities gain a higher weight as the risk–return target of theportfolio is increased along the efficient frontier. Notably, stud-ies made in real (rather than nominal) return space reach evenstronger conclusions in regard to this point (Perrucci 2011b).

• Pricing: often a similar macro/inflation view is priced acrossdifferent asset classes, but to a different degree (because ofeach asset’s distributional characteristics, timing or other fac-tors). This might at times provide an alternative to leveragewhen trying to achieve target returns. For example, deflationwas priced in US Treasury Inflation Protected Securities (TIPS)inflation break-evens when headline CPI plunged in autumn2008; clearly oil futures provided a directionally similar tradewith no need for leverage.

• Different risk premiums in different securities: for example,there is an inflation risk premium to buying insurance directlyin inflation-linked instruments (whether in the cash or deriva-tive markets). This is a consequence of the fact that, for a USinvestor, TIPS might be considered the closest thing to a risk-free asset class (if held to maturity, and putting lags and basketdefinition aside). Note, however, that bond break-even infla-tion levels contain both a liquidity and an inflation-insurance

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risk premium, with the latter often dominating the former(with several important exceptions, for example, the autumn2008/spring 2009 liquidity crisis/deflation scare). Anotherinvestor might be considering hedging a possible negative realgrowth/deflation shock to the economy. While buying infla-tion floors might be one implementation, the investor mightnotice that inflation implied volatility is at high levels relativeto realised, the inflation market usually being short volatilityand might then consider buying out-of-the-money equity puts(or a short inflation floor/long equity put relative value trade).

• Niche opportunities: at times attractive opportunities can occa-sionally be found and/or structured in niche markets whereprofit margins are still high. The author has seen severalsuch opportunities, one example being in infrastructure andinflation-linked investments.

In summary, inflation-sensitive assets provide diversification ben-efits beyond linkers, and the ability to implement hedging or relativevalue trades in the sector(s) where conditions are most favourable(because of valuations, risk, leverage, etc).

CONCLUSIONSIn this chapter, we have discussed inflation as a key portfolio risk.After an analysis of the underlying causes of inflation, we arguedfor the tangible benefits of defining “inflation-sensitive assets” as abroad investment class, which should include commodities, equi-ties, real estate and infrastructure assets in addition to inflation-linked cash and derivative securities. This is consistent with a globaltrend, with several pension funds, insurance funds, and even wealthfunds, changing their traditional asset allocation to include thenewly defined inflation-sensitive sector, along with the more tra-ditional equity, fixed income and credit sectors. As such institutionstogether control trillions of US dollars of capital in the space, thisshift is of monumental importance to any portfolio manager as wellas to the whole asset management industry.

1 See http://www.bls.gov/.

2 See http://www.federalreserve.org/ for a more detailed explanation of monetary aggregates.

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REFERENCES

Perrucci, S., 2010, “Inflation-Sensitive Assets: Portfolio Benefits and Opportunities”, URL:http://www.newskycapital.com.

Perrucci, S., 2011a, “Inflation, Money and Debt”, URL: http://www.newskycapital.com.

Perrucci, S., 2011b, “Efficient Frontier and Optimal Portfolios in Real vs Nominal Space”,URL: http://www.newskycapital.com.

Phillips, A. W., 1958, “The Relationship between Unemployment and the Rate of Changeof Money Wages in the United Kingdom 1861–1957”, Economica 25(100), pp. 283–99.

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2

Investable Commodity Indexes andInflation: A Brief History

Bob GreerPIMCO

In this chapter, we present a brief history of investable commod-ity indexes, and discuss the link between inflation and commodityprices.

The first section covers the 1970s, and the effect of energy and foodprice spikes on inflation and traditional asset classes. Commodityfutures are discussed next, as well as the author’s work in buildingthe first investable commodity index. A brief recap of the evolutionin commodity indexing and investment vehicles until the presentday1 follows. We then conclude with a discussion of commoditiesas an inflation hedge.

COMMODITIES SHOCKS AND INFLATION

Awareness of the relationship between commodities and inflationwas heightened during the 1970s. Oil price shocks, at the height ofthe OAPEC embargo in 1973–4,2 and during the Iran Revolutionin 1979, drove prices of petroleum and the cost of other productsup. Several crop failures and supply shortages in some grains (suchas the one originating from the “Russian wheat deal” of 1972 (Lut-trell 1973), where about 30% of US annual wheat production wassold to Russia, with taxpayer-paid government subsidies going toUS grain exporters) drove up agricultural prices as well. PresidentNixon’s attempts at controlling inflation, through price and wagerestrictions, were unsuccessful, and only distorted markets further.

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Despite these events highlighting the importance of the link be-tween commodities and inflation, investors did not have an effec-tive way to get exposure to commodity prices in order to hedgeinflation. Some tried to purchase natural resource stocks, but thoseinvestments carried other risks as well, in particular a significantcorrelation to the overall equity market, with movements in the lat-ter often overshadowing changes in commodity prices themselves.Other institutional investors, who had very long investment hori-zons, tried to purchase real commodity-producing assets, such asfarmland. But, besides being illiquid, these investments were alsoexposed to other non-essential risks, on both the operational andfinance sides (weather, government regulations, political risk, etc).All of this set the perfect stage for the developments that followed.

COMMODITY PRICE INDEXES AND FUTURESThere has been interest in commodity prices, and indexes of thoseprices, for a very long time. Until the late 1970s, the available indexestypically referred to prices of physical commodities. Some of theseearly indexes were published by Reuters, the Financial Times andThe Economist, among others. They comprised a broad range of com-modities, including some for which there were futures markets, aswell as others that had no futures equivalent. There was also a vari-ety of other indexes of cash prices for specific industries within thecommodity asset class, including livestock, energy products andmining products. Both Dow Jones and the Commodity ResearchBureau published indexes which used the current or spot monthprice from commodity futures markets as a surrogate for cash mar-kets, partly because this information was readily available. But, likethose other early price indexes, those based on futures prices werealso not investable, because they could not be replicated. That is,they simply reported the spot month price as a surrogate for cashprices, without accounting for the fact that an investor would haveto “roll” their exposure from a nearby contract to a distant contractbefore expiry, which can affect returns, sometimes dramatically. Thatis because those early index calculators only wanted a measure of thelevel of cash prices; the concept of actually investing in commodityfutures had not yet been considered.

During the inflation and related shortages of several commodi-ties in the 1970s, the interest in commodities as investments began

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to take root. Although the impact of higher commodity prices oninflation was well understood, the possibility of hedging againstthis, via a systematic investment in a basket of commodities, was notappreciated. No investors were getting exposure to anything like abroad-based index of commodity prices. This began to change whencommodity futures gained acceptance in the investment community,as a surrogate for ownership of physical commodities.

Interestingly enough, the mid 1970s were also a time when thefirst stock index fund3 was offered (of course, there had been stockprice indexes for many, many years before). This development inthe equity market inspired the author to find an analogous wayfor investors to gain exposure to commodities as well. What mightseem a natural idea today was actually quite original in the 1970s, ascommodities were viewed as a very high-risk speculative instru-ment, and thus quite different from investing in the shares of acompany. In reality, the price of an individual commodity, such aswheat, for example, was typically no more volatile than the priceof a single stock, such as IBM. Furthermore, while companies cango bankrupt, cattle cannot. Even in the 1956 debacle in the onionfutures market4, the price of the contract did not go to zero (it wentto 10 US cents, which was about the cost of the bags in which theonions were stored).

The reasons why commodities were thought of as being so riskyare twofold. First, since physical ownership of the underlying com-modity is typically not practical, most investors traded in the futuresmarkets, and often used a large amount of leverage. This leveragewas possible because the market participant did not actually buy, orsell, a physical commodity on a cash basis. Instead, they just made acommitment to buy, or sell, a commodity in the future. As long as theparticipant closed their position before they were contractually obli-gated to take (or give) delivery of the physical commodity, they onlyhad to deposit sufficient margin to ensure that they could performon that future commitment. This margin would of course change inline with the price of the futures contract. This allowed the marketparticipant to control a large notional amount, with only a small cap-ital commitment. Hence, small adverse movements in the price ofcommodities could (and sometimes did) entirely wipe out the capitalof this leveraged investor. The margin deposit might be thought ofas being similar to the earnest money deposit that is typically made

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by a buyer of a house, when that house is put under contract. Thefull amount of the purchase price is required only at time of contractsettlement. This leads to the second reason that commodity invest-ment was misunderstood. Many investors did not understand thevery nature of a futures contract. They equated having a long posi-tion in a commodity futures market with outright ownership of thecommodity itself.

Of course, it is possible to fully collateralise a long commodityfutures contract, and thus take leverage out of a commodity invest-ment. For example, if a live cattle contract (40,000 lb) were tradingat 50 US cents per pound, the notional value of the contract wouldbe US$20,000. Instead of making a minimum margin deposit of, say,US$1000, the investor could allocate a full US$20,000 of their port-folio to support a single long contract in cattle. The investor thuswould have the capital to actually purchase the cattle if they choseto do so and, no matter how low the price of cattle might fall, theinvestor would have money to meet any margin call. In this strategy,the investor’s total return is the return on collateral, plus or minusthe change in the price of the cattle futures contract. Note, however,that full collateralisation can only take place with long futures posi-tions, as we cannot determine how much collateral is required tosupport a short position, since there is no way of knowing the max-imum size of an adverse move. But, if we are hedging against highinflation, the investor would not be short commodities anyway.

As for the complications of delivery of the physical commodity,the investor can overcome these by rolling their future position for-ward before the delivery date. For example, before the first deliveryday for the October contract, they would sell the October future, andbuy a December contract. This way, the investor maintains expo-sure to the rising price of cattle, while still earning interest on thecollateral.

Finally, but not least, through futures we can not only gain expo-sure to commodities, and resolve the issues of leverage and delivery,but also benefit from a standardised, transparently priced, liquidmarket, all of which are important considerations for any investor.

THE FIRST INVESTABLE COMMODITY INDEXAn investor worried about high inflation would want exposure notto a single subsector or futures contract, but to a broad-based set of

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commodities, in order to get more thorough and diversified priceexposure. The first step is to identify the many commodities thathave a sufficiently liquid futures market, and establish a weightingprocedure based on relative economic importance, in terms of eitherworld trade or impact on inflation.

In his early work, the author chose two indexes to measure relativeeconomic importance: one was the Reuters–Commodity ResearchBureau Price Index, which is weighted by relative volume of worldtrade in each commodity; the other was the US Consumer Price Index(CPI), which measures how both goods and services affect overallprice levels. The process required some ingenuity (and imagination),given that not all index components of the commodity index mightbe mapped to liquid future contracts and, even more challenging, away had to be found to deal with the services’ contribution to the CPI(Greer 1978). An average of the two weighting sets resulting fromthese mapping processes, summing to 100%, was taken to build thecommodity futures index.

The next step was to select the collateral to be used to back thecommodity futures index. Greer (1978) chose 90-day bank certifi-cates of deposits (CDs),5 since he wanted to simulate a high-qualityinvestment, with negligible interest rate risk. To calculate returns,the CD rate was applied to 90% of the collateral, assuming a 10%margin requirement.

Finally, historical returns (from 1960 to 1978) for both the futuresindex and the collateral were calculated at six-month intervals,6 withthe futures index rolled forward and rebalanced semi-annually.A1%annual transaction fee7 was also assumed. Recognising that com-modities should be evaluated in the context of their impact on atotal portfolio, Greer next calculated the returns of a portfolio thatwas 50% equities and 50% commodities, rebalanced semi-annually.For 1960–78, the average six-month return for this balanced portfoliowas 4.2%, compared with 2.3% for stocks alone.

Note that although methodologies and computing power haveevolved since then, modern investable indexes still incorporate thekey principles established by Greer’s original work. In particular,investable commodity indexes are typically characterised by

• long-only, and fully collateralised, positions,

• weights that reflect the relative economic importance of thevarious components,

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• transparent methodology for return calculation, as well asspecific rules for rolling and rebalancing the index.

THE EVOLUTION OF COMMODITY INDEXESAlthough there was some additional academic research on commod-ity index investing in the 1980s and early 1990s (see, for example,Bodie and Rosansky 1980;Ankrim and Hensel 1993), investors’ inter-est was minimal. Either they did not understand the nature of futurescontracts or were sceptical about the (then) novel idea of indexing.Some might have been simply enamoured by the stocks in theirportfolios, and reluctant to venture into an area where no institu-tions had yet ventured. Furthermore, there was no straightforwardmechanism, such as a commodity mutual fund, which would enableindividual investors to get commodity index exposure in a practicalmanner.

In fact, it was only in 1991 that the industry saw the first com-mercially available index, supported by a major institution, with thelaunch of the Goldman Sachs Commodity Index (GSCI). In 2007,Goldman sold its index business to Standard & Poor’s, so theirindex is now called the Standard & Poor’s Goldman Sachs Com-modity Index (SPGSCI). The GSCI was soon followed by indexessupported by other investment banks. Bankers Trust began market-ing the Bankers Trust Commodity Index (BTCI). Merrill Lynch beganmarketing the Merrill Lynch Energy and Metals Index (ENMET).JP Morgan started publishing the JP Morgan Commodity Index(JPMCI). And Daiwa Securities worked with Greer to resurrect hisoriginal index, refined to become the Daiwa Physical CommodityIndex (DPCI). The DPCI was later sold to Chase Manhattan Bank(now JP Morgan Chase), to become, first, the Chase Physical Com-modity Index, and then, the JP Morgan Commodity Futures Index(JP Morgan, however, stopped calculating this particular index in2000). The American International Group (AIG) also came to marketwith its own version of a commodity index, the AIGCI (renamedDJAIGCI after Dow Jones became the calculation agent). This indexwas sold to UBS in 2009, after AIG’s downfall, and is now offeredas the Dow Jones UBS Commodity Index (DJUBSCI). In 2009, CreditSuisse used Greer’s established methodology, adapted to currentmarket conditions, to bring to market the Credit Suisse CommodityBenchmark (CSCB).

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Despite the proliferation of commodity indexes in the 1990s, pro-viders mainly sought institutional investors, who might enter intoover-the counter (OTC) swaps to get exposure to their index ofchoice. Then, in 1997, the industry saw the first vehicle by which bothinstitutional and retail investors could get commodity index expo-sure, when Oppenheimer Funds launched the Oppenheimer RealAsset Fund (now renamed the Oppenheimer Commodity StrategyTotal Return Fund), benchmarked to the GSCI.

Meanwhile, research efforts to define the characteristics of com-modities as a distinct asset class, and to educate investors, were alsoongoing. Several papers were published in this period (see, for exam-ple, Greer 1997 and references therein), highlighting the differencebetween traditional asset classes (such as stocks and bonds) andcommodities. The first are capital assets, which generate a streamof cashflows and can be valued using net present value analysis. Incontrast, commodities, albeit investable, do not generate a stream ofcashflows. Their value derives from the fact that they can be con-sumed, and value analysis is driven mainly by supply and demand,including estimates of future supply and demand.

Despite these efforts, commodity index investing remained some-what limited to investment banks’ desks, and did not achieve main-stream status in the investment community. However, there are someexceptions worthy of mention. There were a few early adopters ofcommodities index investing, which included the Harvard endow-ment, the Ontario Teachers’ Pension Plan and two of the largestpension funds in the Netherlands, PGGM and ABP.8 The Govern-ment Investment Company of Singapore also entered this market inthe late 1990s. However, up to the start of the 21st century, it is esti-mated that only about US$10 billion in capital (most of which wasinstitutional money, given the very few retail vehicles available) wasinvested in commodity indexes.

COMMODITY INVESTING BECOMES MAINSTREAMIn the first decade of the 21st century, demand for commodityindex investment surged, accompanied by several new investmentvehicles being offered in the market. This was partly due to thelosses that equity investors suffered in 2000, making them eagerto find another area for investment. In addition, the asset classwas slowly becoming better understood, as commodity indexes

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generally had shown themselves to be a mechanism for portfoliodiversification and inflation hedging. The growth in index invest-ments occurred at the same time that supply–demand factors weredriving commodity prices higher in several markets. This cre-ated a positive feedback loop where the satisfaction of some ofthe early adopters influenced more investors to enter the market.Because of the confluence of these factors, there was a tremen-dous growth in capital allocated to commodity investing, whichBarclays Capital estimated to be about US$300 billion by summer2008.

As mentioned before, several new investment vehicles, includingmutual funds, institutional investment accounts and exchange-traded funds, were also created and received widespread accept-ance.9 Some of these had broadly diverse exposure; others trackedindividual commodities or specific subsectors, and some evenowned physical commodities, most notably gold and silver.

At the same time, the growth in investments also led to a pro-liferation of new commodity indexes, several of which sprangfrom the commodity desks of investment banks. This new set ofindexes is often referred to as “second generation”, compared tothe “first generation” represented by indexes such as the SPGSCIand DJUBSCI. These second-generation indexes share many keycharacteristics with the ones launched in the previous decades.In particular, they include long-only, fully collateralised positions;weights reflect the relative economic importance of the various com-ponents; they have a specific methodology and rules for rolling,rebalancing and return calculations. However, there are also differ-ences, as the second-generation indexes tend to have more com-plex rules, often based on mathematical algorithms, which mightdetermine in a dynamic fashion how to roll positions forward, orhow to spread exposure across several contracts on the futurescurve.

There are also some products now offered in the market whichcall themselves indexes, but in fact might better be considered astrading strategies. These products follow predefined rules, so thattheir calculation is transparent, but they generally include both longand short positions in futures markets. Such a strategy may indeedhave merit as an investment, but it may lose the inherent bene-fits of diversification and inflation hedging, which the asset class

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is designed to provide. In other words, even when these strate-gies have attractive diversification and hedging characteristics inhistorical backtests (as they often do), it is doubtful whether theseresults can be relied on going forward unless there is a solid fun-damental explanation behind those returns. Consequently, theselong/short commodity indexes are more similar to hedge fundstrategies, seeking to produce absolute returns in the commodityspace.

COMMODITY INDEX INVESTING AS AN INFLATION HEDGE

The link between inflation and commodities is clear, as the latter havetraditionally been an important component of the basket of goodsand services used to measure inflation. In the US, for example, foodand energy comprise almost 25% of the CPI,10 and they account foran even larger share, about 75%, of its volatility. Since it is “changes”in inflation, more than absolute levels, which affect stock and bondprices, this volatility is a major concern for investors. For instance, astable, predictable and relatively high rate of inflation might not bebad for bonds, as they might still provide a nominal yield in excess ofthat (the latter being a function of credit quality and other features).But what can be devastating is an unexpected move from a low to ahigh inflation regime. And in turn, material changes in inflation canbe strongly affected by commodity prices. Inflation and commodityprices are important not only to investors but to consumers and, thelatter being voters, to politicians as well. This is especially true offood and energy prices, which are the most visible, and politicallysensitive, component of inflation, as they can be experienced everyday at the petrol pump, and on the grocery shelf.11

Commodity index investing provides two sources of inflationprotection. One is the underlying collateral, typically invested inshort-term T-bills (providing a nominal yield spread for expectedinflation), or inflation-protected securities (guaranteeing a fixed realreturn at maturity). The second is the futures index, which pro-vides diverse exposure to changes in commodity price expectations,including those caused by unexpected supply–demand shocks.

The fact that a commodity index strategy might be employedto provide inflation-hedging benefits is also apparent from many

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research studies (see, for example, Cavalieri et al 2010) based on his-torical data. Furthermore, the fundamental link between commodi-ties and traditional metrics of inflation (for example CPI) suggeststhat these benefits should continue in the future, at least as long asthe underlying drivers of higher inflation are rooted in commodityprices.

Of course, commodity index returns can be affected by manyfactors, at times dramatically; this happened in the second half of2008, when a deep global recession triggered a significant collapsein prices. This highlights the added value that skilful managementcan bring to commodity investing, whether in its own right, orfor inflation-hedging purposes. Clearly, dynamic markets cannot beoptimally managed, and the full diversification and hedging ben-efits delivered, by simply employing a mostly static index-basedstrategy. Nevertheless, indexes remain an effective and transparentway to gain exposure to commodities, as well as benchmarks of assetclass returns.

CONCLUSIONS

Commodities are key price inputs in the basket of goods and servicesused to measure inflation. This relationship was brought into focusin the 1970s, a decade during which the investment community grewdeeply aware of the negative effects inflation can have on traditionalcapital assets, such as bonds and stocks.

This relationship, and the successful introduction of indexing inequity funds, prompted the author to develop the first investablecommodity index in 1978. Investors’ interest, however, dwindled forquite some time, and it was only in 1991 that the first commerciallyavailable commodity index was launched. Over time, others fol-lowed, and a few pooled vehicles were also established in the space,albeit the capital committed to commodity strategies remained quitelimited until the turn of the century. It was only in the next decadethat commodity investing became mainstream, with a considerableproliferation of new indexes and investment vehicles and a virtuouscycle of positive performance (which was interrupted, if only briefly,by the global recession of 2008).

Since inflation remains one of the most debated issues at the timeof writing, a discussion of whether a commodity index strategy

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INVESTABLE COMMODITY INDEXES AND INFLATION: A BRIEF HISTORY

might provide inflation hedging is a very topical one. Indeed, com-modity index investing provides two sources of inflation protection:the underlying collateral and the futures index itself. These hedgingproperties are supported by historical data, and may continue in thefuture, at least as long as the underlying drivers of higher inflationare rooted in commodity prices.

Past performance is not a guarantee or a reliable indicator of futureresults. All investments contain risk and may lose value. Com-modities contain heightened risk including market, political, reg-ulatory and natural conditions, and may not be suitable for allinvestors. This material contains the current opinions of the authorbut not necessarily those of PIMCO and such opinions are sub-ject to change without notice. This material has been distributedfor informational purposes only and should not be considered asinvestment advice or a recommendation of any particular security,strategy or investment product. Statements concerning financialmarket trends are based on current market conditions, which willfluctuate. Information contained herein has been obtained fromsources believed to be reliable, but not guaranteed.

1 That is, the time of writing in autumn 2011.

2 The Organization of Arab Petroleum Exporting Countries (OAPEC) is a multi-governmentalorganisation, with headquarters in Kuwait, which coordinates energy policies between oil-producing Arab nations. In 1973 it resolved to cut oil production in response to the US decisionto resupply the Israeli military during the Yom Kippur War. While many members of OAPECare also members of the Organization of Petroleum Exporting Countries (OPEC), the twoorganisations are separate.

3 This was the First Index Investment Trust launched on December 31, 1975, now known as theVanguard 500 Index Fund.

4 This in turn resulted in the passage of Onion Futures Act of 1958 (7 USC Chapter 1, Section 13-1), banning the trading of futures contracts on onions.

5 In most modern indexes, the collateral is assumed to be invested in 90-day US Treasury bills,but the guiding principles are analogous.

6 Because personal computers had not yet been invented, the gathering of data (often by handfrom microfilmed copies of The Wall Street Journal) and calculation of returns were quitelaborious, especially by modern standards.

7 Modern index methodologies typically assume no transaction fees.

8 PGGM stands for Pensioen V/d Gezondheid, Geest and Maatsch Belangen. ABP is the abbre-viation for Stichting Pensioenfonds ABP, the pension fund for employers and employees inservice of the Dutch government and educational sector.

9 One of the largest mutual funds of this sort is the PIMCO CommodityRealReturn Strat-egy Fund, which invests mainly in commodity futures exposure and uses US TreasuryInflation Protected Securities (TIPS), rather than T-bills, as collateral. The fund had aboutUS$27.6 billion in assets as of September 2011.

10 In some other countries, especially emerging economies, food and energy are an even largerpart of the total index than in the US.

11 In contrast, other factors, such as the price of shelter, may be a larger component of the CPI,but they are not as obviously felt, or reported on, every day.

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REFERENCES

Ankrim, E. M., and C. R. Hensel, 1993, “Commodities in Asset Allocation: A Real-AssetAlternative to Real Estate?”, Financial Analysts Journal 9(3), pp. 20–9.

Bodie, Z., and V. Rosansky, 1980, “Risk Return in Commodity Futures”, Financial AnalystsJournal 36, pp. 27–39.

Cavalieri, J. R., R. J. Greer and E. Urbano, 2010, “Commodities as an Effective InflationHedge”, PIMCO Viewpoints, October.

Greer, R. J., 1978, “Conservative Commodities: A Key Inflation Hedge”, The Journal ofPortfolio Management 4(4), pp. 26–9.

Greer, R. J., 1997, “What Is an Asset Class, Anyway?”, The Journal of Portfolio Management23(2), pp. 86–91.

Luttrell, C. B., 1973, “The Russian Wheat Deal: Hindsight vs Foresight”, Federal ReserveBank of St Louis Review, October, pp. 2–9, URL: http://www.research.stlouisfed.org/publications/review/article/743.

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3

Commodities, Inflation and Growth:Implications for Policy and

Investments

Ric Deverell, Kamal NaqviCredit Suisse

In this chapter, we discuss the link between commodity prices, infla-tion and real economic growth. We start with a review of the effectcommodity prices have on inflation, comparing and contrastingdeveloped and emerging markets, and analysing 2008 as a detailedcase study. Next, we discuss how higher commodity prices influ-ence monetary policy, and compare different policy approaches fromthree major central banks (the US Federal Reserve, the EuropeanCentral Bank and the People’s Bank of China). A section discussingthe relationship between commodity prices and economic growthfollows; the key mechanisms through which commodities influencethe real economy are introduced, and the effect of growth imbalancesbetween developed and emerging markets is explained. Finally, wediscuss how commodity investments might be used, either to hedgehigher inflation or to lower growth. A summary section concludesthe chapter.

COMMODITIES AND INFLATION

The impact of commodities on inflation continues to be a hot topicamong academic economists and policymakers alike.1 However,while it is clear that large movements (note that it is the changenot the level that matters most) can have a significant impact on“headline” consumer price inflation (CPI), there is little consensus

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Table 3.1 Commodity prices and inflation (first half of 2008, annualised)

Non-food,Food Energy non-energy

Headline ︷ ︸︸ ︷ ︷ ︸︸ ︷ ︷ ︸︸ ︷inflation Wt Contrib. Wt Contrib. Wt Contrib.

Mature 3.7 13.3 0.7 7.7 1.4 79.0 1.6economies

Emerging 8.1 29.5 3.8 7.7 0.9 62.8 3.4economies

Wt, weight; Contrib, contribution.Source: BIS, OECD, Credit Suisse.

on the ultimate impact on growth and “core” inflation,2 or on howpolicymakers should react.

When thinking about the impact of movements in commodityprices on CPI, it is useful to consider the first round impact, andthen to assess the likely flow through to other prices, or to so-called“core inflation”. Or to use the framework set out by Cecchetti andMoessner (2008), whether headline inflation tends to revert to coreinflation, or vice versa.

The first round impact of commodity price increases on inflation isheavily dependent on which commodity prices are increasing andthe stage of development of individual countries. In general, themost significant impact is felt through increases in food and energyprices, both of which form a sizeable component of CPI baskets.While increases in basic material prices are also significant, the directimpact on CPI inflation is more muted, as these commodities are notdirectly represented in CPI baskets.3

Cecchetti and Moessner (2008) estimate the average weightsof food and energy prices in CPI in both mature and emergingeconomies. As Table 3.1 shows, the first round impact of food infla-tion falls disproportionately heavily on emerging market economies,with the weight of food in the average CPI basket for emergingeconomies around 29.5%, more than double than the average of13.3% for mature economies.

In addition, the impact of food commodity prices on CPI foodinflation is more muted in mature economies, where a greater shareof the food sold is processed, and thus less sensitive to changes in

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input commodity prices (the latter representing only a fraction ofconsumer food prices). This means that, for any given increase inraw commodity prices, the increase in CPI food inflation will be fargreater in emerging market countries than in developed economies(this is why the contribution of food price increases to emergingeconomies inflation is on average more than five times that formature economies: 3.8% versus 0.7%).

In contrast to food prices, the average weight of energy in theconsumer basket is roughly the same for both emerging and matureeconomies (around 7.7%). However, while a given increase in inputfood prices has a larger impact on emerging markets’ inflation, thisrelationship is reversed with energy (compare the 1.4% for matureeconomies with the 0.9% for emerging economies), as many emerg-ing market economies subsidise energy prices to consumers. Note,however, that these subsidies decreased in many economies in theearly 2000s, and other effects such as taxes might act in the oppositedirection (for example, in developed economies such as the euro-zone, where taxes are such a high percentage of final gasoline pricesthat the relative impact of raw commodities spikes is diminished).

The impact of commodities on core (ie, the CPI basket excludingfood and energy, the last two columns in Table 3.1) inflation is morecontroversial. Much of the debate has focused on whether commod-ity price inflation should be viewed as a one-off price change or assomething that is likely to continue for some time. Of course, thechallenge is that it is not possible to tell which of these possibilitieswill play out ex ante, although the state of the economy is one keyconsideration, with the impact on consumer inflation likely to bemore pronounced when there is little economic spare capacity in thesystem.

A simple way of assessing the impact of commodities on non-food and energy inflation is to calculate the correlation betweenmovements in a broad-based commodity index and movementsin core inflation. To this end, in early 2011, Credit Suisse’s ChiefEconomist, Neal Soss, together with Jay Feldman, assessed the cor-relation between annual percentage changes in the CommodityResearch Bureau (CRB) Index against the US core CPI (Soss andFeldman 2011). They concluded that if the question is whether his-torically commodity price hikes have had an impact on core inflationin the US, the answer over the past quarter century is unequivocally

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Figure 3.1 US core inflation and commodity prices

1988 1991 1994 1997 2000 2003 2006 2009 20120

1

2

3

4

5

6

US

cor

e C

PI –

YoY

cha

nge

(%)

50403020100

–10–20–30–40–50C

CI (

CR

B)

Inde

x –

YoY

cha

nge

CCI (CRB) Index

US Core CPI

Sources: CRB, US Bureau of Labor Statistics, Credit Suisse.

Figure 3.2 European core inflation and commodity prices

1991 1994 1997 2000 2003 2006 2009 20120

1

2

3

4

5

euro

cor

e C

PI –

YoY

cha

nge

(%)

50403020100

–10–20–30–40–50

CC

I (C

RB

) In

dex

– Yo

Y c

hang

e

CCI (CRB) Index

US Core CPI

Sources: CRB, Eurostat, Credit Suisse.

“no”. Indeed, as Figure 3.1 demonstrates, the correlation coefficientfor data going back to 1985 is negative, at−37%. And a positive cor-relation does not emerge even by using the CRB Index to predictcore inflation in future periods (ie, using a lagged response). Sossand Feldman go on to note that

in today’s less cartelized, less unionized, more globally exposedeconomy, increases in oil and food usually manifest as “relativeprice” shocks, not generalised inflation. When prices of essentialslike food and gas go up, households are left with less free cash tospend on other things, tending to restrain other (core) prices.

While this conclusion would not be too surprising to many in theUS, with its fabled non-unionised and deregulated labour market,

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Figure 3.3 China: non-food inflation and commodity prices

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

0

1

2

3

4

US

cor

e C

PI –

YoY

cha

nge

(%)

50

40

30

20

10

0

–10

–20

–30

–40

–50

CC

I (C

RB

) In

dex

– Yo

Y c

hang

e

–1

–1

–3

CCI (CRB) IndexChina non-food CPI

Sources: CRB, Chinese National Bureau of Statistics, Credit Suisse.

it is also interesting that in the eurozone area, where labour mar-kets generally remain more heavily unionised and regulated, sim-ilar conclusions can also be reached. In fact, since 1991, when theEuropean Union started publishing combined eurozone inflationdata, the correlation between annual changes in the CRB Index andeurozone core (again excluding food and energy) inflation has beennegative, in this case−0.27%, suggesting that, as in the US, commod-ity price spikes negatively affect relative prices in other consumersectors, rather than permanently increasing overall inflation by rais-ing inflation expectation, wages and other non-commodity prices(Figure 3.2).

This analysis suggests that, while large movements in commodityprices can have a significant impact on headline inflation in the shortrun, there is little clear evidence of significant sustained (long-term)impact on either core or non-core inflation in the US and Europe, atleast in recent history. This is in line with Cecchetti and Moessner(2008), who also conclude that4

in recent years, core inflation has not tended to revert to headline,which suggests that higher commodity prices have generally notspawned strong second-round effects.

While the results of correlation analysis in mature economies areunequivocal, there is considerable divergence in the results for some

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Figure 3.4 Correlation of core inflation with commodity prices

–60

–40

–20

0

40

20

80

60Yo

Y C

orre

latio

n w

ith C

CI (

CR

B)

and

Cor

e C

PI (

%)

Kor

ea

Pol

and

Chi

le

Cze

ch R

ep US

Indo

nesi

a*

Eur

ozon

e

Bra

zil

Indi

a**

Chi

na**

*

∗Indonesia from 2003, interpolating June 2008 to November 2008; ∗∗India usingWPI; ∗∗∗China using non-food CPI (see also endnote 5).Sources: CRB, Press Information Bureau of India, Eurostat, US Bureau of LaborStatistics, NBS, Credit Suisse.

emerging economies, with China and India (Figures 3.3–3.4) show-ing a relatively high positive correlation between movements in theCRB Commodity Index and core inflation since around 2009.5

This suggests that the impact of higher commodity prices on coreinflation is substantially higher in some cases, or, using Cecchetti’s(2008) framework, that core inflation has tended to revert to headlineinflation in economies such as China and India. However, note that,in the case of China, the positive correlation might be overstated,given that the short sample period is dominated by the global reces-sion of 2008–9, when most prices moderated substantially. In thefollowing section, we shall elaborate on these points and analysewhat happened in 2008, and give potential explanations for thesepositive correlations.

WHAT HAPPENED IN 2008?In the 18 months from January 2007 to June 2008, the US dollar priceof oil increased by 135%, while the price of food (as measured bythe United Nations Food and Agriculture World Food Price Index)increased by 65%. In the 12 months from July 2007 to June 2008, theaverage US dollar price of oil increased by 95%, while food pricesincreased by 44%. The direct impact of food inflation was greaterthan that of energy in both emerging and mature economies. It is

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Figure 3.5 Food and energy contribution and share of CPI (first half of2008, annualised)

Matureeconomies

Emergingeconomies

Matureeconomies

Emergingeconomies

9

8

7

6

5

4

3

2

1

0

908070605040302010

0

100

% %

Food Non-food and non-energyEnergy

Sources: BIS, Credit Suisse.

striking, however, that food contributed significantly more to infla-tion in emerging economies than that in mature economies. It is alsonotable that despite being the same weight in CPI baskets, energyprices had a far larger impact on CPI inflation in mature economiesthan that in emerging economies.

Figure 3.5 shows clearly that in mature economies 55% of theincrease in inflation in this period was attributable to food andenergy prices (the key commodity drivers), with only 45% aris-ing from “core” inflation. For emerging markets, 57% of inflationcomes from food and energy, and 43% from core inflation. Thisshould not be terribly surprising given the far greater weight of foodand energy components in the average CPI basket in the emergingmarkets (nearly 40%) compared with about 20% on average acrossmature economies (Table 3.1). Notably, while food and energy pricesmade a significant contribution to inflation in emerging economies,the contribution from “core inflation” was much higher in theseeconomies. These findings, coupled with the higher correlationbetween commodity prices and core inflation, suggest that commod-ity price inflation is more of an issue for emerging economies thandeveloped ones.

For emerging (but not for mature) markets, empirical evidenceshows that commodity prices, and food in particular, have had animpact on core inflation. However, even in those cases, the increase

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has not been structural in nature (at least since 1998) as higher coreinflation has reverted to previous (lower) levels in line with thesubsequent stabilisation (or fall) in commodity prices.

INFLATION AND MONETARY POLICYWhen assessing the likely monetary policy response, a key questionis whether commodity price inflation is mainly driven by supply(like the oil crisis in the 1970s) or demand shocks. For example, in thecase of food prices, the predominant cause has typically been sup-ply disruptions,6 due to droughts, floods and crop diseases. Whilethese disruptions can affect food prices for some time, they generallyself-correct in the medium to long run. Instead, in the first decadeof the 21st century, much of the increase in oil prices was driven bystronger than anticipated demand, although supply shocks (such asthe one experienced in early 2011) remain a real risk, particularly inthe light of political turmoil in producing countries in North Africaand the Middle East. For basic materials, the predominant cause ofprices trending up (35% for copper and 100% for iron over the firstdecade of the 21st century) was stronger than anticipated demand,driven by China and other countries. Such demand-side fundamen-tals are likely to remain the main driver of basic metals prices forthe foreseeable future. In summary, commodities price movementsin the first decade of the 21st century have often had very differentdrivers from the oil supply shock of the 1970s.

An important question is whether the increase in prices is likelyto be permanent or temporary (such as a one-off price adjustment),although in practice it is difficult to assess which one of these will beex ante. To the extent that changes are driven primarily by temporaryfactors (such as most supply shocks), many central banks would beexpected to “look through” the impact when setting monetary pol-icy. This is partly because monetary policy has very little impacton factors such as food prices. But it is also because, by the timemonetary policy can reasonably have begun to affect broader prices(given the long and variable lags), the price change is already likelyto have reversed. The objective of monetary policy is not to controlshort-term inflation fluctuations but to make sure that, on average,inflation remains within an acceptable range. On the other hand,when changes in commodity prices are driven by a demand shock,they are likely to prove more resilient, increasing the likelihood that

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policymakers will indeed intervene. Given the difficulties in assess-ing the effects of all of these factors, several central banks tend tofocus on inflation expectations. If the latter remain well anchored,there is scope for monetary policy to “look through” a (likely) tem-porary period of higher inflation, primarily because firms and con-sumers are doing the same. This said, and for a variety of reasons(some related to differences in the specific country’s inflation pro-cess, and some related to cultural and historical norms), it is clearthat there are significant differences in how the major central banksassess inflation and react to a change in commodity prices. For exam-ple, at least historically, the US Federal Reserve has not been overlyconcerned about the effect of higher commodity prices on head-line inflation, as long as core inflation remained well behaved. Thisstance is likely to be reaffirmed, given the relatively low level of coreinflation and large output gap (extra capacity in the economy) at thetime of writing. In contrast, the European Central Bank (ECB), andbefore that the Deutsche Bundesbank, has had an explicit headlineinflation target. The ECB will tighten monetary policy if headlineinflation moves above its target because of commodity prices, evenif the move is likely to be transitory. The People’s Bank of China hasgenerally adopted a flexible and pragmatic approach, using mone-tary policy in order to ensure that commodity price inflation (partic-ularly food inflation) does not unduly affect core prices and inflationexpectations.

COMMODITIES AND GROWTHAs with inflation, the impact of commodity prices on the macroeco-nomy, and real growth in particular, has been the subject of muchacademic research. However, while there are many articles on thetopic, most of the literature is heavily focused on oil and the impacton the US economy.7 As Rasmussen and Roitman (2011) point outin a recent IMF working paper, there has been “much less work onother countries and very little of that on developing economies”.In addition, most of the research focuses exclusively on the impactof oil.

There are two key mechanisms that are discussed when assessingthe impact of commodities inflation on economic growth. The firstis that an increase in commodity prices can lead to higher inflationand therefore result in tighter monetary policy than would otherwise

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have been the case. This would in turn reduce the pace of economicgrowth. The second is that higher commodity prices can act as atax on consumers and business, lowering profits and reducing con-sumption and investment. While there is merit in both arguments,as often in economics, both rely on strong assumptions, which arenot likely to hold consistently over time.

On the first point, while there is no doubt that rapid increases incommodity prices can result in higher inflation, the policy response,if any, is likely to vary significantly depending on the stage in theeconomic cycle, and each specific country’s approach to monetarypolicy. For example, in 2011 the increase in commodity prices provedfar more problematic for emerging economies, where the commod-ity weight in inflation baskets is larger and where there is little sparecapacity. In contrast, in mature economies such as the US, commod-ity inflation has been fairly inconsequential for policymakers, inview of the large output gap and slow economic growth.

On the second point, while there is much focus on higher com-modity prices being a tax on consumers, this effect has been mostrelevant in developed markets, and in the US in particular. From aglobal perspective, movements in commodity prices are by defini-tion a zero-sum game, with some countries (or corporations) benefit-ing from higher revenues, while others face the opposite side of thecoin. While there will be frictional issues, as the negative effect onconsumers will manifest in less time than is required for the benefi-ciaries of higher prices (be they corporations or countries) to translatehigher incomes into higher investments and growth, the ultimateimpact at the global level should be one of distribution rather thancreation or destruction of wealth. Therefore, it is a mistake to focusonly on the cost-side impact of higher commodity prices, especiallyin an increasingly globalised economy. For example, while highercommodity prices might indeed impact negatively on consumersand producers in G7 economies, many of those same consumersmay own shares in multinational commodity companies, and maystand to benefit directly from higher equity valuations and higherdividend payments.

As the global economy continues to recover from the “Great Reces-sion” of 2008–9, the distributional issues related to higher commod-ity prices in the macroeconomy are likely to be more pronouncedthan normal. In simple terms, many of the countries that benefit

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most from higher commodity prices are emerging markets (SaudiArabia, Brazil, etc; Canada and Australia are notable exceptions),and their economic growth has rebounded strongly following theGreat Recession. Given that these economies have little spare capac-ity, local monetary authorities have generally tightened policy byraising interest rates to avoid inflationary pressures, as there is littlescope for output to expand further. In contrast, many of the countrieswhere economies remain fragile, primarily Japan, EU member statesand the US, have experienced the negative impact of higher prices.In these countries, the severe recession was followed by disappoint-ingly anaemic growth. This in set the stage for an environmentwhere higher prices (oil in particular) have had the most negativeimpact on consumers’ behaviour and curbed both spending and eco-nomic growth significantly. In other words, the imbalance betweengrowth in emerging and developed economies has increased theimpact of higher commodity prices on global growth to more thanjust a distributional issue. Emerging markets have already grownclose to or exceeded capacity and have been trying to slow theireconomies in the face of higher commodity prices and the threatof inflation. Developed markets face the negative impact of higherprices on top of fragile economies, with few tools in the policyarsenal to boost growth, as interest rates are already at historicallows and quantitative easing measures have had only a temporaryeffect.

In regard to the impact of higher energy prices, Rasmussen andRoitman suggest that

the negative impact of oil price increases depends to a large extenton, first, how dependent countries are on oil imports, and, second,how strong are their links to oil exporters and the rest of the world.

Interestingly, the US appears to be an outlier, with the real economyrelatively sensitive to movements in oil prices despite the fact that oilimports are relatively small. This is likely to be due to lower gasolinetaxes in the US than most other advanced economies, which meansthat movements in oil prices affect the retail price of gasoline muchmore substantially.Also, because the gasoline price is typically lowerin the US than in most developed countries, such as EU memberstates, the average American consumes far more gasoline per capitathan their European counterpart and thus is more directly affectedby higher prices.

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Figure 3.6 Mining investments in Australia as a percentage of GDP

1860 1880 1900 1920 1940 1960 1980 20000

2

4

8

10

6

Min

ing

as s

hare

of G

DP

(%

)

Forecast

Sources: Reserve Bank of Australia, Credit Suisse.

As mentioned before, there are also beneficiaries of higher com-modity prices. Some examples are the oil-exporting countries andAustralia. The latter is an interesting case, with higher commodityprices resulting in a massive surge in mining investment (Figure 3.6),which is likely to continue. The interesting thing is that this sort ofinvestment is capital and import intensive, and our ballpark estimateis that approximately half of the value added will be from imports.Consequently, while the impact from higher commodity prices isa tax on consumers in the US, many American companies will beclear beneficiaries from greater exports, which will support mininginvestments in Australia.

The behaviour of oil exporters such as Saudi Arabia will also bekey for the net global impact of higher commodity prices on growth.In the five years from 2003 to 2008, the massive increase in oil rev-enues to the Middle East and North Africa (MENA) was primar-ily reinvested in the US bond market, contributing to the low-ratesconundrum during the period. In this case, higher capital from oilrevenues was not spent on goods and services but invested in USbonds. In other words, investment of MENA oil revenues in the USbond market flattened the yield curve and resulted in looser creditconditions than would otherwise have been the case. Given the sig-nificant political unrest in the MENA region in 2011, the more likelyoutcome is that the countries from the region will spend a larger

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proportion of oil revenues on building infrastructure and support-ing social programmes domestically. In turn, this may still bene-fit other countries, since imports of both consumer and investmentgoods from developed markets into MENA are likely to increasesubstantially.

Another key factor when considering the impact of higher com-modity prices on the real economy is the underlying cause of theincrease in prices. If commodity prices are rising because of strongerdemand, as is the case for most non-corn agricultural commodities, itis unlikely for economic growth to slow substantially. If, on the otherhand, higher prices are the result of a supply shock (as occurred inthe 1970s and early in 2011), the impact on growth is likely to bemore substantial.

COMMODITIES INVESTINGAs highlighted above, commodity prices are affected by and have aneffect on both inflation and real economic growth. In the following,we shall briefly explore how commodity investments can be used toexploit these relationships with inflation and real economic growth.

Commodity investments and inflationThe market for inflation protection has grown markedly.As an exam-ple, the inflation-linked bond market has reached a notional size ofover US$1.5 trillion, and other inflation sensitive assets such as prop-erty, infrastructure and commodities have all attracted investors’attention specifically due to their inflation-hedging characteristics.

Despite the evidence that it is emerging markets investors thathave the most to gain from an investment in commodities as ahedge to inflation, it has been developed market investors that havemost commonly cited inflation as the basis for their investment incommodities. This may be in part a reflection of different invest-ment approaches, with emerging market investors typically havingan absolute return objective, and developed market institutionalclients typically following a more diversified portfolio approach.For the latter, indexes consisting of commodity futures, such as theStandard & Poor’s Goldman Sachs Commodities Index (SPGSCSI),Dow Jones UBS Commodities Spot Index (DJUBSCI) or Credit SuisseCommodity Benchmark (CSCB), have become the most commonlyused investment vehicles to gain exposure to commodities. Such

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indexes use liquid, transparently priced futures contracts and fol-low a specific weighting and trading methodology. Importantly, theycan be back-tested: for example, the SPGSCI has been tradeable since1992, although in academic studies researchers have reconstructedthe index going back to 1959 (Chapter 2).

Commodity indexes saw significant evolution in the early 2000s,and at the time of writing a range of them incorporate featuressuch as yield optimisation, thematic weighting or dynamic activeelements. These indexes are also highly customisable, conditionalon the liquidity of the underlying commodities, with country orregional inflation weighting being offered by several banks. As anexample, Credit Suisse has built and traded an index, the CreditSuisse Commodity Benchmark China Index, of those commodi-ties that are most sensitive to commodity demand from China.There are, of course, other ways in which commodity exposure canbe obtained. An investor may choose to trade commodity futuresdirectly, although this requires knowledge of both the fundamen-tals and technical characteristics of each specific commodity sector.More commonly, investors (and retail investors in particular) takeexposure to a customised commodity basket, through a structureproviding derivative exposure to specific commodities over a setperiod of time (and sometimes capital protection). Although thesestructured investments can be tailored to the specific investor, theytend to be significantly less liquid and lack the transparency of aplain vanilla commodities index.

There is an active debate about whether to invest in commodity-related equities or directly in the underlying commodities. This isnot a black-and-white debate, as there will be certain situationswhen one or the other will be the better choice. That said, over thefirst decade of the 21st century, the rise in extraction and develop-ment costs, widespread geopolitical risks, the popularity of resourcenationalism and a raft of natural disasters have demonstrated thatthe ability of a resources company to grow profitability consistentwith rising gross revenue from higher commodity prices is debat-able. In turn, this has resulted in a shift towards direct commodityinvestments.

This shift has been aided by the development of Exchange TradedProducts (ETPs) offering commodity exposure. These vehicles haveallowed a much wider cross-section of investors to gain commodity

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exposure as effortlessly as buying an exchange-traded stock. Indeed,by mid 2011, SPRD Gold Shares,8 an exchange-traded fund (ETF)backed by gold, had become the largest exchange-traded fund, sur-passing more conventional ETFs tracking equity indexes such as theS&P 500. The trend towards direct commodity investing has becomefirmly established in North America and Europe, but this remains arelatively new development in the Middle East, South America andAsia. Given the key impact of commodity prices in these economies,interest for commodities has grown substantially. In our opinion,there is considerable potential for growth in commodities investingin these emerging markets, although investors are likely to adopt amore regional focus, investing in local commodities, conditional ontheir liquidity.

Lastly, a discussion on commodity investing and inflation isnot complete without an explicit mention of gold. Gold has seenrenewed interest as an investment asset in its own right in the early2000s, with inflation expectations often being cited as one of themajor drivers for such interest. Although empirical evidence in sup-port of gold as an inflation hedge is not that strong, gold is generallyperceived as a defensive asset. Whether its hedging characteristicswill be reaffirmed by future performance remains to be seen, espe-cially in light of the volatile and uncertain market environment weare likely to experience in the foreseeable future.

Commodity investments and growthIn addition to the traditional role of commodity investments as infla-tion hedges, a trend has emerged in which investors take commodityexposure as a way of hedging negative shocks to economic growththat might result from higher commodity prices (oil in particular).For example, out-of-the-money calls on oil have been employed inthis capacity, as a way to acquire protection against such tail events.The realisation that commodity prices may be not only a beneficiaryof growth but also a risk to growth has significantly expanded thenumber of potential investors in commodities, a trend that is likelyto continue thanks to persistent market volatility. As noted before,supply-type shocks are more likely to negatively affect growth, andthus produce scenarios where even commodity-related equities maynot provide an effective hedge to higher prices (and lower growth).

As explained before, the impact of commodities on growth iscountry specific, and differs for emerging and developed markets.

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Other, more subtle, factors are also important. For example, in theUS, oil might be a greater challenge to growth (and equity prices),while in China agricultural prices might pose the greatest risk. Thus,it is unlikely that any global commodities index will provide thebest solution for all. Rather, the appropriate vehicle (be it a specificcommodities basket or some other commodity derivative structure)needs to be tailored to the specific needs and views of the investor.

CONCLUSIONS

In this chapter, we have analysed the connection between commod-ity prices, inflation and economic growth. We discussed the differentfactors influencing developed and emerging markets, in particularthe effect of food and energy prices on headline inflation and thecorrelation between commodity prices and core inflation, and howthese depend on the underlying cause of commodities inflation, ie,whether the price change results from a supply or demand shock. Wealso discussed the likely monetary response. Finally, we discussedcommodity investments either as a way to hedge shocks in overallprices, ie, inflation, or for economic growth.

1 See, for example, Cecchetti and Moessner (2008), Fry et al (2009), Hobijn (2008) and Lipskey(2008).

2 In this chapter, we generally use the exclusion method when calculating “core inflation”,which simply excludes energy and food from the basket of services and goods. However,this is done for simplicity, given that other statistical measures such as trimmed mean andweighted median generally give a better feel for the underlying tendency of inflationarypressures.

3 The direct first-round impact of commodity price changes on most finished goods is generallysmall. For example, for laptop computers and mobile telephones it is a tiny fraction, while forUS-made cars it is less than 10% of final sale price (pension obligations, in contrast, account foras much as 25%). For residential apartments, the total cost of raw materials (steel, aluminium,copper, etc) is generally less than 10% of the cost of construction, and an even smaller fractionof sale price (developer margins are generally greater than raw material costs).

4 Similar conclusions are drawn for Australia in a 2010 study conducted by Norman andRichards (2010), who “find little evidence that either commodity prices or the growth rateof money directly influence Australian underlying inflation”.

5 Note that there are some limitations on data. China has published a core measure of inflationonly since 2006, while India does not publish a CPI. We have therefore used the WholesalePrice Index for India.

6 While supply disruptions have been the predominant short-term cause of spikes in food pricesin the early 2000s, it is possible that over time increased demand from emerging markets couldslow or even halt the long-term downwards trend in food prices evident at least since thebeginning of the 20th century. In addition, government policies can have an impact. Forexample, the introduction of ethanol mandates in the US has directly contributed to thedoubling of global corn consumption growth, from 0.8% per year in the period 1975–2003, to1.6% per year since then. This policy is likely to lead to higher food prices over coming years(all other things being equal).

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7 See, for example, Hamilton (1983, 1996, 2005, 2009), Bernanke et al (1997) and Blanchard andGalí (2007).

8 See http://www.spdrgoldshares.com (ticker: GLD).

REFERENCES

Bernanke, B., M. Gertler and M. Watson, 1997, “Systematic Monetary Policy and theEffects of Oil Price Shocks”, Brookings Papers on Economic Activity 28(1), pp. 91–157.

Blanchard, O., and J. Galí, 2007, “The Macroeconomic Effects of Oil Price Shocks: Whyare the 2000s So Different from the 1970s?”, NBER Working Paper 13368.

Cecchetti, S., and R. Moessner, 2008, “Commodity Prices and Inflation Dynamics”, BISQuarterly Review, December, pp. 55–66.

Fry, R., C. Jones and C. Kent (eds), 2009, “Inflation in an Era of Relative Price Shocks”,in Proceedings of Reserve Bank of Australia Conference 2009, Kirribilli, NSW, URL: http://www.rba.gov.au/.

Gorton, G., and K. Rouwenhorst, 2005, “Facts and Fantasies about Commodity Futures”,Working Paper 04-20, Yale Information Center for Finance.

Hamilton, J., 1983, “Oil and the Macroeconomy since World War II”, Journal of PoliticalEconomy 91(2), pp. 228–48.

Hamilton, J., 1996, “This Is What Happened to the Oil Price/Macroeconomy Relation”,Journal of Monetary Economics 38(2), pp. 215–20.

Hamilton, J., 2005, “Oil and the Macroeconomy”, in S. Durlaf and L. Blume (eds), The NewPalgrave Dictionary of Economics, Second Edition (London: MacMillan).

Hamilton, J., 2009, “The Causes and Consequences of the Oil Shock of 2007–08”, NBERWorking Paper 15002.

Hobijn, B., 2008, “Commodity Price Movements and PCE Inflation”, Federal Reserve Bankof New York Current Issues in Economics and Finance 14(8), pp. 1–7.

Lipskey, J., 2008, “Commodity Prices and Global Inflation”, Speech to International Mon-etary Fund, May, URL: http://www.imf.org/external/nap/speeches/2008/050808.htm.

Norman, N., and A. Richards, 2010, “Modeling Inflation in Australia”, Discussion PaperRDP 2010-03, Economics Analysis Department, Reserve Bank of Australia, Sydney.

Rasmussen, T., and A. Roitman, 2011, “Oil Shocks in a Global Perspective:Are They ReallyThat Bad?” Working Paper WP/11/194. International Monetary Fund.

Soss, N., and J. Feldman, 2011, “Commodities and Core CPI: As Dead as Disco”, USEconomics Digest, February 17.

Stevens, G., 2008, “Commodity Prices and Macroeconomic Policy: An Australian Perspec-tive”, Reserve Bank of Australia Bulletin, June, URL: http://www.rba.gov.au/.

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4

Inflation and Real Estate Investments

Brad Case; Susan M. WachterNational Association of Real Estate Investment Trusts (NAREIT);

The Wharton School, University of Pennsylvania

In this chapter we analyse the inflation sensitivity of real estate in-vestments, comparing them to other inflation-sensitive assets. Themost transparent source of real estate investment returns comesfrom publicly traded stocks of real estate investment trusts (REITs).We examine the available return data, with an emphasis on theirrelationship to US inflation, although our conclusions may applyelsewhere as well.

Consumer price inflation (CPI) in the US was 13.5% during 1979,the worst year since 1947. Dividend income from REITs tradedthrough the stock exchange averaged 21.2% that year, and totalreturns amounted to 24.4%, not only preserving but increasing forREIT investors the purchasing power that they had lost to inflation.Inflation averaged 11.6% per year during 1978–80, the worst three-year period in six decades; again, however, publicly traded equityREITs outpaced inflation, with income and total returns averaging12.2% and 23.1% per year, respectively. The period 1974–81 was themost inflationary eight years in the history of the Consumer PriceIndex at 9.3% per year, but equity REIT returns easily preserved pur-chasing power, with income and total returns averaging 10.2% and16.3% per year.

During the first eight months of 2011, annualised consumer priceinflation was 5.1%. Again, equity REIT returns protected purchas-ing power, with annualised total returns averaging 8.4%. However,dividend income, during a period of extraordinary weakness in realestate operating fundamentals, fell short of inflation at 3.4% per year.

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The rate of growth of equity REIT dividend payments averaged7.71% per year from the beginning of 1978 up to and includingAugust 2011, while consumer price inflation over the same periodaveraged just 3.92%, and equity REIT dividend income exceeded theinflation rate in 306 of the 404 individual months during that histor-ical period. Thus, over this entire period, REIT returns preservedpurchasing power. This of course raises the question of how wellREITs hedge inflation during sub-periods and in comparison withother assets.

In the analysis that follows, we compare real estate investmentsto other inflation-sensitive assets, and point out that the com-mon approach to evaluating sensitivity, by computing correlationbetween asset returns and inflation, fails to address directly thequestion of whether returns from a given asset actually protect con-sumers from loss of purchasing power. The relevance of this factstems from the observation that many investors do not hedge theirexposure to inflation formally by computing the optimal hedge ratioand acquiring long or short positions to implement the hedge; rather,they typically rely on some informal combination of strategic andtactical asset allocation, deploying capital into asset classes that areexpected to perform well during inflationary regimes, and doing somore aggressively when high inflation is anticipated.1

In response to this observation, we employ a direct measureof the effectiveness of the passive inflation protection providedby a given asset. We also note that, given the difference in assetreturns in high- versus low-inflation periods, choosing a tacticalasset allocation specific to a high-inflation regime exposes investorsto considerable directional risk. A balanced approach that pro-vides similar risk-adjusted returns in both low- and high-inflationregimes may be preferable for investors who do not possess superiorinflation-forecasting abilities.

In addition to investing in commercial real estate through own-ership of stock in publicly traded equity REITs, investors can alsoinvest in illiquid real estate assets such as shares in private equityreal estate investment funds (including non-listed equity REITs) ordirect ownership of properties. In this chapter we note the sub-stantial pitfalls of using return estimates based on appraised prop-erty values for evaluating inflation sensitivity of illiquid assets, andreview the available evidence on illiquid real estate as an inflation

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hedge. Finally, we consider why certain property types may be moresensitive to inflation than others, and review evidence on inflationsensitivity by property type.

REAL ESTATE AS A HEDGE AGAINST INFLATIONWe begin by considering conceptually the extent to which real estatecan be expected to hedge against inflation. The Gordon growthmodel suggests that real estate can be considered a perfect hedgeagainst inflation (unlike, for example, most fixed-income products)because real estate is a long-lived asset with income that adjusts toinflation (Gordon 1962). The model, despite its obvious limitations,2

clearly illustrates this relationship. Real estate asset prices (and, sim-ilarly, REIT equity prices) are given by the net present value (NPV)of the future rent cashflow stream, which is assumed to grow indef-initely at a constant rate g and is discounted by the appropriatenominal rate r

real estate price = NPV(future rent income)

= next period rentr − g

REIT equity price = NPV(future dividends)

= next period dividendr − g

Assuming no change in the real economy,3 inflation will affect thediscount rate r and the rent (equity dividend) growth rate g inequal measure, and thus will have no impact on capitalisation ratesin inflation-adjusted terms, or on real estate asset values. In otherwords, the inflation-adjusted return from holding real estate assetsis invariant to inflation, at least in this simple model. Of course, mod-els aside, the question needs to be tested, and settled, by empiricalevidence, which we shall do in the following sections.

Real estate prices may, of course, change in response to several fac-tors other than inflation itself, and these may be difficult to isolatein the empirical analysis. Most notably, exogenous supply/demandshocks (as well as endogenous cycles within the real estate market)will affect asset prices as well as imputed rents (or, equivalently,the growth rate g) differently. Specifically, positive demand shockswill tend to increase real estate asset prices and rents, while pos-itive supply shocks (which increase costs) will act in the opposite

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direction. For example, as discussed below, energy-related supply-shock inflation episodes such as the oil shocks of the 1970s will affectreal estate returns differently from demand shock inflation derivingfrom either monetary or fiscal policy. Moreover, over the real estatecycle, the inflation-adjusted return of real estate assets will increasewhen real estate assets are in demand, and decrease when supply isplentiful.

In practice, although many REITs have contractually specifiedstep-up clauses, actual responsiveness of rents, especially to short-run and intermediate-run effects associated with shocks and cycles,tends to be dampened by the use of leases.4 As typical lease struc-tures differ by property type, the dampening effect on rent adjust-ments will also differ: a topic that will be investigated empiricallylater in the chapter.

Another conceptual issue that we briefly consider here relates tothe debt structure of real estate investments. It is plausible to assumethat, if an asset were to be financed with long-term fixed-rate debt,higher inflation would be beneficial to the liabilities of the real estateowner, as the loss to the debt investor is mirrored as a gain to the bor-rower. This suggests an empirically testable hypothesis: REITs hold-ing relatively large amounts of long-term fixed-rate debt will tendto have stronger returns than REITs holding small amounts of long-term fixed-rate debt, during periods of high inflation. Unfortunately,while data on total debt is readily available through sources such asSNL Financial,5 data on the composition of debt (long-term versusshort-term, and fixed-rate versus variable-rate) is more difficult tocollect consistently, which is why we have only briefly examinedthis here.

As a proxy for detailed information on REIT use of debt, we iden-tified 41 equity REITs that generally used relatively high leverageand 41 that generally used relatively low leverage, and comparedtheir returns during months of high versus low inflation during theperiod 1991–2010, where high-inflation months were identified rela-tive to the median monthly CPI over the study period. The empiricaldata supports the hypothesis, though not strongly enough to rejectthe null: the median monthly total return of high-leverage REITs(1.26%) exceeded that of low-leverage REITs (1.16%) during monthsof higher-than-median inflation, but fell short (1.05% versus 1.76%)during months of lower inflation.6

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Having considered conceptually how real estate can be thoughtof as a hedge against inflation, in the remainder of this chapter wedevelop empirical techniques for analysing the inflation sensitivityof real estate assets.

HEDGE EFFECTIVENESS AND INFLATION SENSITIVITYAn approach to evaluating the relationship between investmentsand inflation that is fairly standard in the investment community(although less so in the academic literature) is to compute the con-temporaneous correlation between inflation (eg, change in consumerprice inflation, available monthly) and asset returns at the same fre-quency (cf. Bhardwaj et al 2011; Lomelino et al 2011; Ralls 2010). Acorrelation approaching 100% is considered a sign of high sensitivityto inflation, and therefore of an asset with good inflation-hedgingproperties.

There are three problems with this standard approach, as appliedby investors and investment advisers (many of whom do not hedgebut rather use strategic and tactical asset allocation to protect againstinflation). First, the correlation coefficient gives equal weight to allhistorical periods without regard to whether inflation was high orlow in those periods, whereas many investors seek inflation pro-tection specifically during periods of high inflation. Possible solu-tions to this problem include computing a semi-correlation coef-ficient using data from only those months in which inflation wasrelatively high, or weighting each month according to the level ofinflation during that month.

Second, use of the contemporaneous correlation implies that onlythose assets whose returns respond to inflation during the samemonth are of value to investors as inflation protection. Returns ofsome assets, though, may be sensitive to inflation with a lag, espe-cially when inflation is unexpected. For example, even US TreasuryInflation Protected Securities (TIPS), which provide income explic-itly linked to realised inflation through a monthly adjustment to thebond principal, have a two-to-three month lag in their indexationto CPI.7 Note, however, that the market price of TIPS will respondin synchronicity with changes in relevant market variables, mostnotably (real) interest rates (which in general will display correla-tion with inflation). Because of this, the investor’s horizon remains arelevant empirical issue in the study of inflation sensitivity; ways to

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address this issue include computing the correlation between assetreturns and lagged inflation, developing a distributed-lag model ofthe relationship between inflation and asset returns and estimatinga vector autoregression (VAR) model of the same relationship.

Third, the correlation coefficient is a measure of co-movementbut not a measure of whether returns preserve purchasing poweror provide what we term here an “effective” inflation hedge. Thatis, correlation measures whether asset returns move in the samedirection as inflation, but to establish an effective inflation hedgethe correlation coefficient needs to be used as an input, along withthe volatilities of different asset returns, to compute the appropriatehedge ratio.8 In practice, the stability of the correlation coefficient isoften the most challenging aspect in determining the optimal hedgeratio and employing a hedge strategy.

As an alternative to the optimal hedge ratio, then, investorsmay consider other forms of inflation protection. One approachis to establish a strategic portfolio allocation with significant posi-tions in assets that preserve purchasing power during high-inflationregimes; in the next two sections we introduce a direct measureof inflation-protection dependability based on the success rate ofa given asset in accomplishing this goal, and test the findingsfor robustness. A strategic allocation appropriate to high-inflationregimes, however, may produce poor returns during low-inflationregimes. In the following sections, we consider the opportunities andrisks inherent in a strategy of shifting tactically between portfoliosoptimised for high- and low-inflation scenarios, and suggest anapproach towards developing a strategic portfolio balanced betweenoptimal performances in both inflation regimes.

EFFECTIVENESS OF TACTICAL ASSET SELECTION FORINFLATION PROTECTIONA fundamental problem with using correlation to evaluate the infla-tion protection provided by an investor’s choice of asset classes isthat the correlation coefficient measures whether asset returns co-move with inflation (and therefore its value as an input in devel-oping an optimal inflation hedge), not whether they protect directlyagainst inflation, in the sense of protecting against purchasing powerloss. In order to develop a direct measure of inflation protection, wepropose the following process.

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Figure 4.1 Distribution of annualised six-month CPI rates

10

0

30

20

50

40

70

60

90

80

100

Num

ber

of o

bser

vatio

ns

Inflation rate bucket (%)

<0 1–2 3–4 5–6 7–8 9–10 11+

16 18

51

8783

53

26

157 5 6

1418

Source: US Bureau of Labor Statistics data.

(i) Define the investment horizon over which inflation protectionis desired: in our analysis, a six-month period. Our study cov-ers the window from January 1978 to August 2011, thus includ-ing 399 overlapping9 semesters summarised in Figure 4.1.Among the 399 observations in our sample, the median annu-alised inflation rate was 3.2%. In the following section, weshall also consider how the results change if inflation protec-tion is measured at different horizons (monthly, bi-monthly,annually).

(ii) Specify the inflation scenarios under which protection issought. Our analysis focuses on high-inflation periods, definedas semesters during which annualised inflation exceeded 3.2%,our sample’s median. By construction, half of the observa-tions in our data set satisfy this criterion; of course, otherdemarcation lines are possible, as discussed in the followingsection.

(iii) Define how to measure the effectiveness of inflation protec-tion. We use the “success” rate: that is, the relative frequencywith which returns equalled or exceeded inflation duringthe 199 semesters of high inflation in our sample, therebyaccomplishing the usual goal of protecting purchasing power.

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Table 4.1 Inflation protection success rate (%)

Success rate (%)

REITs 65.8Commodities 70.4Stocks 60.8TIPS 53.8Gold 43.2

Source:FTSE NAREIT All Equity REITs Index, S&P Goldman Sachs Com-modity Index, Ibbotson Associates US TIPS, Barclays Capital US TreasuryTIPS Index, S&P 500 Index, S&P GSCI Gold Index.

Table 4.1 presents the proposed measure of inflation protec-tion using six-month periods constructed from monthly data for aselection of five asset classes:

1. publicly traded equity REITs, measured by the FTSE NAREITAll Equity REITs Index;

2. commodities, measured by the S&P Goldman Sachs Commod-ity Index (GSCI);

3. TIPS as measured by the IbbotsonAssociates synthetic US TIPSseries, which is equal to the Barclays Capital US Treasury TIPSIndex from January 1997 onwards, but is backfilled by Ibbotsonprior to that;10

4. US equities, as measured by the S&P 500 Index;

5. gold as measured by the S&P GSCI Gold Index.11

All indexes measure total returns (ie, income plus price apprecia-tion).

As Table 4.1 shows, the two assets providing the most dependableinflation protection (by our measure) were commodities and equityREITs, with commodities providing total returns that equalled orexceeded inflation during 70.4% of high-inflation semesters andequity REITs close behind at 65.8%. Stocks and TIPS provided some-what weaker inflation protection by this measure, with stocks pro-tecting purchasing power during 60.8% of high-inflation six-monthperiods and TIPS even lower at 53.8%. By our measure, the weak-est inflation protection among this group of assets was provided bygold, which successfully protected purchasing power during only43.2% of high-inflation six-month periods.12

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As a note of caution in interpreting these results going forward,we stress that one key issue to choosing an asset class for tactical pro-tection against inflation is not just forecasting correctly high (or low)periods of inflation, but having insight on the specific cause drivingprices higher (or lower). For example, if inflation is caused by higherenergy costs through an oil supply shock, it is plausible that energycommodities will be the winning sector in terms of tactical alloca-tion (and later be the losers when the price spike corrects itself). Thismight not be true in the case of a dis-anchoring of inflation expec-tations driven by ineffective monetary or fiscal policies. This caveatapplies, of course, to any historical study of inflation sensitivity ofdifferent asset classes, given that high-inflation periods in the USfrom the 1970s onwards have been mostly commodity driven.

ROBUSTNESS OF TACTICAL ASSET SELECTION FORINFLATION PROTECTION

There are four main modelling decisions that may affect the empir-ical results shown in Table 4.1:

1. the six-month investment horizon chosen to measure inflation-protection effectiveness;

2. the definition of “high-inflation” semesters as those duringwhich annualised inflation exceeded the sample’s median;

3. the choice of the S&P GSCI to measure commodity returns;

4. the use of the Ibbotson Associates synthetic US TIPS series.

The choice of six months as the investment horizon was motivatedby the observation that TIPS adjust explicitly to the inflation ratebut pay interest only every six months. A shorter investment hori-zon can generally be expected to favour those assets whose returnsrespond most quickly to unexpected inflation, while a longer invest-ment horizon should favour those assets whose returns most closelytrack expected inflation.

Surprisingly, row 1 of Table 4.2 shows that, when the analysisis conducted using returns in the same month as inflation (that is,no acceptable delay in asset responsiveness to inflation), the successrates of the assets included in the comparison differ only slightly: thebest-performing inflation protector remains commodities at 55.4%followed by stocks at 53.0%, REITs at 51.5%, TIPS at 51.0% and

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Table 4.2 Inflation-protection success rates (%) under differentmodelling decisions

REITs Commod. Stocks TIPS Gold

Base scenario (Table 4.1) 65.8 70.4 60.8 53.8 43.2

1 1 month 51.5 55.4 53.0 51.0 50.02 2 months 58.2 61.7 56.2 50.2 44.83 12 months 68.9 75.5 71.4 56.6 46.4

4 67th percentile = 4.29 59.4 70.7 54.9 42.9 46.65 80th percentile = 4.89 55.0 66.3 50.0 41.3 52.56 90th percentile = 8.65 65.0 55.0 55.0 27.5 60.0

7 S&P GSCI Energy Index 75.38 S&P GSCI Non-Energy Index 61.09 Barclays Capital TIPS Index 56.3

Source:FTSE NAREIT All Equity REITs Index, S&P Goldman Sachs Com-modity Index, Ibbotson Associates US TIPS, Barclays Capital US TreasuryTIPS Index, S&P 500 Index, S&P GSCI Gold Index, S&P GSCI EnergyIndex, S&P GSCI Non-Energy Index.

gold at 50.0%. As row 2 shows, however, the assets differ muchmore substantially over two-month periods of relatively high infla-tion: the most dependable inflation protection has been provided bycommodities (61.7%) followed by equity REITs (58.2%) and stocks(56.2%), with TIPS (50.2%) lagging slightly. Gold (44.8%) success-fully protected purchasing power in fewer than half of high-inflationtwo-month periods.

A longer investment horizon should favour assets with strongerexpected returns that are more sensitive to expected inflation. Row 3of Table 4.2 shows that, during 12-month periods of relatively highinflation, the most dependable inflation protection was providedby commodities (75.5%), stocks (71.4%) and equity REITs (68.9%),with TIPS (56.6%) somewhat weaker; again, gold (46.4%) historicallyhas covered the inflation rate in fewer than half of high-inflation12-month periods.

The “high-inflation” scenarios were defined for Table 4.1 as thosesemesters during which inflation exceeded the annualised median3.2% of the 399 observations in the sample period. As noted, how-ever, inflation during the 1970s and early 1980s reached muchgreater severity, up to a maximum of 16.26% during the first sixmonths of 1980. Rows 4–6 of Table 4.2 summarise the inflation

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protection provided by each asset class during progressively moresevere inflationary environments: the 67th percentile (correspond-ing to an annualised inflation rate of 4.3% in our sample), 80th per-centile (that is, a 4.9% annualised inflation rate) and 90th percentile(8.7% annualised inflation). The numbers indicate that commodi-ties and TIPS are progressively less likely to provide returns cover-ing the inflation rate during more severe inflationary periods. Onlygold provides monotonically more dependable inflation protectionduring progressively more severe inflationary environments; thesuccess rates of REITs and stocks change non-monotonically withrespect to the severity of the inflation regime. For those periodswhen inflation exceeded its 90th percentile, a condition last expe-rienced during June–November 1981, returns on gold equalled orexceeded inflation 60.0% of the time, while returns on REITs per-formed even better, with a 65.0% success rate. It is important toremember, of course, that the statistical relevance of these resultsdecreases both with the number of applicable sample points (infla-tion was higher than the 90th percentile during only 40 semestersout of the total 399 in our sample) and with the possibility thata regime change since 1981 may have rendered the older dataobsolete.

Commodity returns were measured using the S&P GSCI, forwhich data is available over the full historical period but which isdominated by energy prices; in contrast, other indexes such as theDow Jones–UBS commodity index attach significantly less weightto energy prices but are available over a much shorter historicalperiod. To investigate the differential contributions of energy andnon-energy commodities, rows 7 and 8 of Table 4.2 summarise theinflation-protection dependability of the GSCI Energy Index and theGSCI Non-Energy Commodities Index over the period since Febru-ary 1983 during which both have been available. The numbers showthat, in the sample considered, energy investments provided muchmore dependable inflation protection than non-energy commodi-ties, with returns that equalled or exceeded inflation in 75.3% of high-inflation six-month periods compared to just 61.0% for non-energycommodities.

Finally, US TIPS have been available only since January 1997, sothe performance of TIPS in providing inflation protection cannotbe evaluated using actual returns during the inflationary periods

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of the 1970s and early 1980s. The analysis shown in Table 4.1 usedthe synthetic TIPS return series estimated by Ibbotson Associates,while row 9 of Table 4.2 tests the robustness of the TIPS results byreporting the inflation-protection dependability computed using analternative synthetic TIPS return series estimated by Barclays Cap-ital. As the numbers show, the results are not very sensitive to theTIPS return series used, with the Barclays Capital synthetic TIPSIndex returns equalling or exceeding inflation in 56.3% of the 199high-inflation periods in our sample, comparable to the 53.8% com-puted using the Ibbotson synthetic TIPS Index. The fact that thetwo synthetic indexes show similar results does not, of course, ruleout the possibility that both indexes may be affected by commonmethodological biases in backfilling historical returns.

USING TACTICAL PORTFOLIO ALLOCATION FOR INFLATIONPROTECTIONMany investors may choose to shift asset class selections tacticallyover time, based on their outlook on inflation and other relevantvariables. The asset classes considered display substantial differ-ences in returns during high- versus low-inflation periods, makingthis tactical asset selection option both valuable and risky. In otherwords, correct insight on future inflation (and its root causes) cangreatly enhance investment returns, while mistakes in forecastingcan prove costly. During the overlapping six-month periods that wehave identified as high-inflation semesters, the average annualisedrate of inflation was 6.1%, compared to 1.8% during low-inflationsemesters.

As Table 4.3 shows, during high-inflation semesters, commoditiesprovided by far the strongest average annualised returns at 19.2%per year. This should not be surprising, as commodities not onlyaccount for a substantial share of the CPI but also have been a driverof short-term inflation spikes13 in the historical window of our study.Equity REITs and stocks also provided strong returns, averaging12.3% per year for equity REITs (with income-only returns averaging8.6%) and 10.2% per year for stocks. The average return on TIPSbarely beat the inflation rate at 6.9%, while gold fell short of theinflation rate at 6.0%.

How much the ability to discern between high- and low-inflationregimes affects the outcome is clear by comparing the previous

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Table 4.3 Average annualised returns in high-inflation semesters

Average annualisedreturn (%)

CPI 6.1Commodities 19.2Equity REITs 12.3

Equity REITs (income only) 8.6Stocks 10.2TIPS 6.9Gold 6.0

Source:FTSE NAREIT All Equity REITs Index, S&P Goldman Sachs Com-modity Index, Ibbotson Associates US TIPS, Barclays Capital US TreasuryTIPS Index, S&P 500 Index, S&P GSCI Gold Index.

Table 4.4 Average annualised returns in low-inflation semesters

Average annualisedreturn (%)

CPI 1.8Equity REITs 13.7

Equity REITs (income only) 6.9Stocks 13.0TIPS 9.2Gold 7.2Commodities −2.4

Source:FTSE NAREIT All Equity REITs Index, S&P Goldman Sachs Com-modity Index, Ibbotson Associates US TIPS, Barclays Capital US TreasuryTIPS Index, S&P 500 Index, S&P GSCI Gold Index.

results with the average returns in low-inflation periods (Table 4.4).During the latter, equity REITs and stocks provided the strongestannualised returns, averaging 13.7% and 13.0% respectively. (REITincome-only returns averaged 6.9% per year, far more than the aver-age inflation rate.) The returns on TIPS and gold, too, exceeded theinflation rate at 9.2% and 7.2% per year, respectively.

By far the worst performing asset class is commodities, with totalreturns averaging −2.4% per year during low-inflation regimes:again, not surprising given the share of commodities in the CPI.Clearly, the large variance in commodity returns is, in part, the con-sequence of the high-volatility and self-corrective nature of energy

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price spikes (for example, oil supply shocks), which are virtuallyimpossible to predict but whose effects tend to average out overlonger investment horizons.

These results (as shown in Table 4.4), if taken at face value, suggestthat, at least in the historical period considered, the winning alloca-tion strategy would have been to shift the portfolio aggressively intocommodities during periods of high inflation, shifting back to assetsthat fulfil other investment goals (eg, income, risk-adjusted returns,diversification), such as equity REITs or TIPS, during periods of lowinflation. Of course, the difficulty with successfully implementingsuch a strategy rests in the ability to predict the inflation regimeduring the next several months; the consequences of being wrongare eloquently showcased by the variance in asset class returns thatcharacterises different inflation regimes.

Although investors typically focus on the risk of high infla-tion, low inflation (or even deflation) can be equally insidious forthe returns of a portfolio. While insightful asset allocation by theactive investor has the potential to enhance portfolio returns ineither regime considerably, the objective of a strategic asset allo-cator or hedger is not to select each period’s best performing assetclass but, quite to the contrary, to build effective protection againstboth inflation and deflation shocks, thus minimising or eliminatingany reliance on the difficult and risky task of correctly forecastinginflation going forward.

A BALANCED APPROACH TO THE INFLATION-PROTECTEDPORTFOLIOThe fact that various assets respond differently to inflation suggeststhat a blended portfolio of assets with differing inflation-protectionproperties may provide a better bulwark against inflation than anyasset in isolation. To illustrate this point, Figure 4.2 summarises theresults of a Markowitz (1952, 1959) mean–variance portfolio opti-misation exercise conducted using historically realised real returns(that is, returns in excess of inflation) for the five inflation-sensitiveassets considered during the 199 high-inflation semesters in our datasample.

Each point in Figure 4.2 shows an optimal asset allocation, fromthe minimum-variance portfolio at the left edge (annualised aver-age real return 3.6%, volatility 9.4%, Sharpe ratio14 0.31) to the

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Figure 4.2 Optimal portfolio allocation and success rates inhigh-inflation semesters

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Figure 4.3 Optimal portfolio allocation in low-inflation semesters

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maximum-return portfolio at the right edge (annualised average realreturn 16.1%, volatility 27.9%, Sharpe ratio 0.55).

The jagged line in Figure 4.2 (right-hand axis) shows the successrate for each portfolio: that is, the relative frequency with which thenominal returns on each portfolio equalled or exceeded the inflationrate during high-inflation semesters in our historical sample. Forexample, a portfolio comprising a 55.1% allocation to commoditieswith 39.1% invested in equity REITs, 4.6% in TIPS and 1.2% in stocks

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(with no gold) would, over the historical period of our analysis,have generated nominal returns equalling or exceeding the inflationrate during 77.9% of the 199 high-inflation semesters, substantiallyoutpacing the most dependable asset in isolation, commodities, atjust 70.4%.

Maintaining such a maximum-effectiveness (as per our defini-tion) portfolio as a strategic asset allocation, however, would haveexposed the investor to considerable directional risk to inflation. AsTable 4.5 reports, the average annualised real return during high-inflation periods was 12.3% over the historical period, with volatil-ity of 18.0% and a Sharpe ratio of 0.65. During low-inflation periods,however, the portfolio would have generated significantly lower realreturns (8.2% on average) with significantly higher volatility (23.2%),for a Sharpe ratio of just 0.27.

Over the entire historical period (encompassing both low-in-flation and high-inflation periods) the maximum success rate port-folio would have generated real returns averaging 10.2% per yearwith 20.9% volatility for a Sharpe ratio of 0.43. The explanation forthis directional risk can be seen by comparing Figure 4.2 with Fig-ure 4.3, which summarises the results of an equivalent Markowitzmean–variance portfolio optimisation exercise conducted using his-torical real returns during the 200 low-inflation semesters in ourdata sample.

During high-inflation periods (Figure 4.2), the largest roles inoptimised portfolios are played by commodities, TIPS and REITs,with optimal allocations to TIPS declining as portfolio return andvolatility increase, while optimal allocations to both commoditiesand REITs increase. Stocks and gold have very small (and declin-ing) allocations in portfolios optimised over high-inflation histor-ical periods. In contrast, during low-inflation periods the largestroles in optimised portfolios are played by TIPS, REITs and stocks;commodities play no role in portfolios optimised over low-inflationperiods except at the lowest levels of portfolio volatility, whilegold accounts for small allocations throughout the risk–returnspectrum.

In short, portfolios that include substantial allocations to com-modities have historically provided dependable protection againstinflation during high-inflation periods, but have exposed investorsto substantial directional risk. In contrast, the historical data suggests

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Table 4.5 Historical performance of optimised investment portfolios

Period(s) Ann. Ann. SuccessOrigination of return volatility Sharpe ratecriterion inflation (%) (%) ratio (%)

Maximum High 12.3 18.0 0.65 77.9success rate Low 8.2 23.2 0.27(high-inflation All 10.2 20.9 0.43periods)1

Maximum High 5.6 10.5 0.48 74.9Sharpe ratio Low 9.5 12.4 0.60(all periods)2 All 7.5 11.7 0.54

Maximum High 12.8 18.8 0.65 75.9Sharpe ratio Low 8.2 24.3 0.26(high-inflation All 10.5 21.9 0.42periods)3

Maximum High 2.4 9.8 0.19 57.8Sharpe ratio Low 9.0 8.9 0.79(low-inflation All 5.7 9.9 0.45periods)4

Minimum High 3.1 9.6 0.25 67.3variance Low 7.6 8.3 0.67(all periods)5 All 5.3 9.3 0.44

Minimum High 3.6 9.4 0.31 69.3variance Low 8.3 9.0 0.70(high-inflation All 5.9 9.5 0.49periods)6

Minimum High 2.0 10.0 0.14 59.8variance Low 7.7 8.1 0.71(low-inflation All 4.9 9.5 0.38periods)7

Equal Sharpe High 6.0 10.4 0.52 75.4ratios in Low 8.3 12.0 0.52high- and low- All 7.1 11.3 0.52inflation periods8

1Allocation: 55.1% commodities, 39.1% REITs, 4.6% TIPS, 1.2% equi-ties, 3.3% gold. 2Allocation: 48.9% TIPS, 16.9% REITs, 14.6% commodi-ties, 13.9% equities, 5.8% gold. 3Allocation: 58.1% commodities, 41.3%REITs, 0.5% equities, 0% gold. 4Allocation: 78.7% TIPS, 10.8% equities,5.4% gold, 5.0% REITs, 0% commodities. 5Allocation: 80.9% TIPS, 8.4%commodities, 5.8% gold, 4.9%, 0% REITs. 6Allocation: 73.3% TIPS, 8.6%commodities, 8.4% equities, 5.0% gold, 4.8% REITs. 7Allocation: 90.4%TIPS, 5.3% gold, 2.6% commodities, 1.7% equities, 0% REITs.8Allocation:54.1% TIPS, 21.8% commodities, 14.5% REITs, 6.4% equities, 3.3% gold.Source:FTSE NAREIT All Equity REITs Index, S&P Goldman Sachs Com-modity Index, Ibbotson Associates US TIPS, Barclays Capital US TreasuryTIPS Index, S&P 500 Index, S&P GSCI Gold Index.

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Figure 4.4 Optimal portfolio allocation: all semesters

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Portfolio expected inflation-adjusted return (%)5.3 6.1 6.8 11.4 12.1 12.97.6 8.4 9.1 9.9 10.6

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that TIPS and equity REITs play important roles in optimisedportfolios during both low- and high-inflation periods.

Indeed, as Figure 4.4 shows, TIPS and REITs together account forhalf or more of the optimised investment portfolio over nearly everypart of the risk–return spectrum in a Markowitz mean–varianceoptimisation conducted using real returns for the entire historicalperiod included in the analysis, with TIPS especially important inlow-volatility portfolios and REITs playing the dominant role inhigh-return portfolios.

For investors seeking to reduce directional risk associated with therealised inflation rate, an alternative to the effectiveness-maximisinginvestment strategy presented earlier, under which directional risk isconsiderable, might be to select the strategic asset allocation that gen-erated the strongest risk-adjusted returns over the entire historicalperiod.

Table 4.5 identifies this portfolio as being composed of 48.9%TIPS, 16.9% equity REITs, 14.6% commodities, 13.9% stocks and5.8% gold: this portfolio generated historical real returns averag-ing 7.5% per year, with an 11.7% volatility and a Sharpe ratio of 0.54.Moreover, this portfolio was quite successful in protecting againstinflation, providing nominal returns that equalled or exceeded theinflation rate in 74.9% of high-inflation six-month periods. While thisportfolio is not as effective as the maximum success rate portfolio(77.9%), its effectiveness is superior to the best asset in isolation, ie,commodities at 70.4%.

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Investors using the maximum Sharpe ratio asset strategic allo-cation, however, would still have been exposed to directional riskrelated to the inflation rate (Table 4.5). During low-inflation peri-ods, this strategic asset allocation would have generated real returnsaveraging 9.5% per year, with volatility of 12.4% and a Sharperatio of 0.60. During high-inflation periods, however, the maximumSharpe ratio allocation would have produced substantially lowerannualised average real returns (5.6%), with only moderately lowervolatility (10.5%) and a Sharpe ratio of 0.48.

Investors seeking to eliminate directional risk altogether (at leaston an expected basis) could have instead chosen a portfolio com-prising a 54.1% allocation to TIPS along with 21.8% in commodities,14.5% in equity REITs, 6.4% in stocks and 3.3% in gold. Across theentire historical period, this portfolio would have generated realreturns averaging 7.1% per year with 11.3% volatility, for a strongSharpe ratio of 0.52; the portfolio would also have provided verydependable protection against inflation, with nominal returns cover-ing the inflation rate in 75.4% of high-inflation periods. Moreover, therisk-adjusted returns of this portfolio would not have depended onthe inflation rate: during high-inflation periods real returns wouldhave averaged 6.0% with 10.4% volatility (Table 4.5), while duringlow-inflation periods both real returns (8.3%) and volatility (12.0%)would have been commensurately higher, resulting in no differencein returns on a risk-adjusted basis (ie, Sharpe ratios).

INFLATION SENSITIVITY OF DIFFERENT PROPERTY TYPES

The value of income-producing real estate in protecting against infla-tion arises from the adjustment process by which lease rents respondto changes in inflation. Different types of property, however, are char-acterised by significant differences in lease provisions, and these giverise to differences in their inflation sensitivity.

Perhaps the most important provisions for inflation sensitivity arethe lease term and, consequently, the frequency of lease turnoverand negotiation. At one extreme, hotels have typical lease terms ofonly one night, or a few nights, implying that rents can be adjustedalmost continuously in response to changes in inflation, as well asother factors. Rental apartments typically employ 12-month leases,

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Table 4.6 Inflation protection success rates by property type

Success ratio (%)

Self-storage 81.0Residential 77.8Shopping centres 73.0Equity REITs 71.4Industrial 71.4Office 69.8Regional malls 69.8Lodging 68.3Health care 68.3Free-standing retail 61.9Commodities 81.0TIPS 63.5Equities 58.7

perhaps with monthly lease extensions after the first year, imply-ing that rents can be adjusted annually, if not monthly; self-storagefacilities typically have similarly short lease terms.

For hotel, apartment and self-storage properties, the fact that leaserents are typically fixed during the entire duration of the contractterm is mitigated by the fact that contract terms are typically short,potentially enabling property owners to adjust rents in response toinflation. Other property types may employ automatic adjustmentsto changes in inflation, whether explicit or implicit. For example,many retail leases specify monthly rental payments as a function ofthe sale revenues generated by each store; thus, as inflation affectsthe sale prices of consumer goods, it affects lease rents as well.

In some cases, especially with tenants that are government agen-cies, office leases may include an explicit adjustment in response toinflation; in these cases, office property returns may be sensitive toinflation even with long lease terms. A slightly different mechanismmay affect lease rents for health-care properties, including long-termcare facilities: if health-care reimbursement rates are regulated, theninflation may be accounted for in determining payments for vari-ous health-care services, and therefore pass through to owners ofhealth-care properties.

Table 4.6 presents the same analysis of the inflation-protectioneffectiveness shown in Table 4.1, but focuses on publicly traded

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equity REITs across different sectors over the historical period fromJanuary 1994 to August 2011 for which data is available.15 AsTable 4.6 shows, the two property sectors that provided the mosteffective inflation protection, with returns greater than or equal toinflation during high-inflation semesters, were self-storage (81.0%)and residential (77.8%), that is, two of the property types charac-terised by short lease terms, and therefore frequent lease turnoverand renegotiation. Lodging, however (the third property type char-acterised by short leases), demonstrated a success rate of just 68.3%,less than the equity REIT industry as a whole (71.4%). Shoppingcentres, too, provided inflation-protection dependability above thatof the industry as a whole, at 73.0%, but the other two retail prop-erty types, regional malls (69.8%) and especially free-standing retail(61.9%), fell short of the industry average, as did other propertytypes including office (69.8%) and health care (68.3%).16

INFLATION HEDGING WITH ILLIQUID REAL ESTATEINVESTMENTS

We have measured real estate investment returns using the returnson publicly traded equity REITs, but several other real estateindexes are available, including the NCREIF Property Index (NPI) ofunleveraged core property returns published by the National Coun-cil of Real Estate Investment Fiduciaries, the Open-End DiversifiedCore Equity (ODCE) Fund Index, also published by NCREIF, andindexes of private equity real estate fund investments publishedjointly by NCREIF and The Townsend Group.17 All of these indexesmeasure the returns of illiquid investments, either in commercialproperties themselves (held directly or through separate accountswith investment managers) or in non-traded shares of private equityreal estate funds.

The illiquidity of such real estate investments means that theirperiodic returns, unlike the returns of publicly traded REIT equities,cannot be measured directly on the basis of price discovery fromactual transactions.18 Instead, returns on unlisted real estate invest-ments are appraisal based, ie, appraisals are conducted (whetherinternally or externally) and used to periodically (typically quar-terly) estimate the capital appreciation component of total returns.For the purpose of evaluating non-traded real estate holdings as an

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Table 4.7 Correlations of private real estate return measures withinflation

Correlation withReturn component Measure quarterly CPI (%)

Capital appreciation NPI 31ODCE 31

Income return NPI 17ODCE 27

Total return NPI 32ODCE 33

TBI 10

Source: NCREIF Property Index, Open-End Diversified Core Equity FundIndex, Transaction Based Index.

inflation hedge, this introduces a critical problem, as current or esti-mated inflation is a typical input in the appraisal process, or in theextrapolation between appraisals. Thus, comparing appraisal-basedreturns with inflation as a means of analysing sensitivity to inflationbecomes tautological.19

Circumstantial evidence for this problem can be seen in Table 4.7,which shows the correlation between quarterly inflation and quar-terly capital appreciation and income returns on illiquid real estate,as measured by the NPI and the ODCE. For both indexes, correla-tion between capital appreciation and inflation (31%) is greater thancorrelation between income and inflation (27% from the ODCE, andjust 17% from the NPI). This suggests that the appraisal-based val-ues of commercial properties fluctuate more strongly in responseto inflation than does the quarterly income produced by the sameproperties (as measured by actual rents received).

Additional evidence is uncovered by comparing correlationscomputed from appraisal-based total returns with correlations com-puted from actual transaction values. Table 4.5 also shows the corre-lations of quarterly inflation with quarterly total returns measuredby the NPI, the ODCE and the Transaction Based Index (TBI) cal-culated until recently by the Center for Real Estate at the Mas-sachusetts Institute of Technology. The TBI is computed using all thetransactions of properties that are also in the database used to com-pute the NPI, which itself has substantial overlap with the databaseused to compute the ODCE, implying that differences among the

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assets underlying the three indexes are slight. The computed cor-relations, however, are different: just 9.8% using actual transactionvalues as measured by the TBI, compared with 32% using appraisedvalues from the NPI, and 33% using appraised values from theODCE.

To summarise, we caution against the use of appraisal-based esti-mates to evaluate the sensitivity of asset returns to inflation. Whilethe evidence reviewed here is specific to the real estate asset classin the US, the conclusion seems equally applicable to other illiq-uid assets whose values and returns are estimated by appraisal. Ifvaluations are influenced in part by the appraiser’s awareness ofcurrent or expected inflation, then evaluating inflation sensitivitymay amount to tautology.

CONCLUSIONS

According to the Gordon growth model, real estate can be considereda perfect hedge against inflation, under the strong assumption thatfuture rent growth and discount rates move in line with expectedand actual inflation rates. In this chapter, we have examined thehistorical performance of real estate as an inflation hedge from 1978to 2011, and compared it with other inflation-sensitive asset classes.

In the historical sample, looking at single asset classes first, com-modities provide the best inflation protection, as per the measureof hedge effectiveness adopted here, with an overall success rate of70% in high-inflation semesters (75% for energy commodities and61% for non-energy commodities). These results are only slightlysensitive to differences in the time horizon used to calculate returns,the demarcation line used to define high-inflation periods and thechoice of synthetic TIPS return series.

During low-inflation periods, however, commodities generatedthe lowest returns of any asset class considered. This large perfor-mance difference highlights the utility of constructing a balancedportfolio if performance in both high- and low-inflation regimes isthe goal.

Historically, a Markowitz mean–variance optimisation suggeststhat a blended portfolio, invested 49% in TIPS, 17% in equity REITs,15% in commodities, 14% in stocks and 6% in gold, achieves the

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maximum Sharpe ratio (0.54) across all semesters in our sample. Thesuccess rate of this multi-asset-class portfolio is quite high (75%), butit also has considerable directional risk.

To mitigate the latter, historically, slightly more could have beeninvested in TIPS (54%) and commodities (22%), and slightly lessin equity REITs (14%), stocks (6%), and gold (3%). Historically, thisportfolio has provided not only a similar success rate (75%) in high-inflation semesters, but also a similar Sharpe ratio (0.52), with theadvantage that the latter is identical in both high- and low-inflationperiods.

Finally, investors seeking to maximise the success rate in high-inflation semesters, without regard to directional risk, would havechosen a more aggressive portfolio, with 55% in commodities, 39%in REITs, 5% in TIPS, 1% in stocks and no gold holdings. Historically,this portfolio has a success rate of 78% in high-inflation semesters,but considerable directional risk.

Different property types provide different levels of inflation pro-tection, depending on the extent to which rents adjust to infla-tion. The property types expected to provide the strongest inflationprotection are those characterised by short-duration leases, or byrents linked to revenues. Empirical data generally supports theseexpectations, with self-storage, residential properties and shoppingcentres having a success rate ranging from around 75% to 80%in high-inflation semesters (Table 4.6), higher than the industryaverage (71%).

Although we have used publicly traded equity REIT returns, sim-ilar empirical analysis could in principle be conducted using returnson illiquid investments, ie, properties themselves or private equityreal estate investment funds. Unfortunately, the latter are typicallyestimated by appraisals, which are linked to inflation, thus makingan analysis of their price sensitivity to inflation amount to tautology.

The empirical evidence examined in this chapter suggests that avariety of assets have inflation-protecting characteristics. Real estate,considered a strong inflation hedge on conceptual grounds, has infact performed as well as, or better than, other inflation-sensitiveassets in the historical sample considered, and has not exposedinvestors to significant directional inflation risk. Indeed, basedon both empirical results and theoretical arguments, real estate,accessed through publicly traded equity REITs, provides attractive

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return characteristics and deserves consideration in diversifiedinflation-protected portfolios.

Dr Susan Wachter acknowledges assistance from the ResearchSponsors Program of the Zell/Lurie Real Estate Center at Wharton.

1 Strategic asset allocation is the choice of a set of portfolio weights that are not expected tochange in response to market conditions, requiring only that the portfolio be rebalanced peri-odically to the strategic weights. Tactical asset allocation is the choice of portfolio weights inresponse to current market conditions, overweighting assets or asset classes that are expectedto outperform, while underweighting those expected to underperform.

2 Discussing the limitations of this simple valuation model is outside the scope of this chapter.For a discussion with reference specifically to real estate and REITs, see Geltner et al (2007).

3 Clearly, this is a very strong assumption that may not generally hold in reality, but it is auseful baseline for illustrating the relevant issues.

4 Demand shocks also affect real interest rates in the short run.

5 See http://www.snl.com.

6 If the analysis is restricted to the historical period from January 1990 to September 2008,thereby excluding the liquidity crisis of 2008–9, then during months of higher-than-medianinflation the median return of high-leverage REITs (1.14%) is slightly less than the medianreturn of low-leverage REITs (1.17%); during months of lower-than-median inflation, returnsto high-leverage REITs were more markedly less than returns of low-leverage REITs (1.34%versus 1.92%).

7 That is, month n principal is linked to an interpolated value of the CPI published in monthsn− 1 and n− 2, which measure inflation in months n− 2 and n− 3, respectively. Moreover,TIPS income is paid only every six months, a consideration relevant to some retail investors.

8 For example, we might define the most effective hedge as the one that minimises the varianceof the overall position. In this case, if series Y and X have correlation ρ and volatilities σYand σX , respectively, the optimal hedge ratio is given by h = ρσX/σY , which means that toobtain the optimal (minimum variance) hedge we need to sell h units of asset Y for each unitof X.

9 Note that the observations are not statistically independent.

10 January 1978 is the first date for which the S&P GSCI Gold Index is available. Data for theother assets is available from January 1972 (the starting date of the FTSE NAREIT EquityREITs Index); over the longer historical period the success rate was about 67% for both REITsand commodities, and about 55% for both stocks and TIPS.

11 Although TIPS income return is linked to, and thus increases with, inflation, the TIPS Indexalso has real rate duration, ie, its price decreases with an increase in real rates. This effectis especially important before TIPS first issuance, where real rates have no observable mar-ket dynamics, and are reconstructed by subtracting realised inflation to market-observablenominal rates. Since nominal rates typically increase more than one-to-one with inflation,these historically backfilled synthetic real rates will also tend to increase with inflation anddecrease with index price, thus underestimating the hedging performance of the asset classin high-inflation scenarios.

12 This ranking may seem intuitive given that higher-volatility, higher-return assets such ascommodities, REITs and equities will have a greater chance to satisfy our inflation-protectioncriterion during high-inflation periods. As noted in the next section, however, this intuitiondoes not hold firmly. The reader should bear in mind that the measured performance of TIPSmay be sensitive to the methodology used to construct a synthetic TIPS return index forperiods preceding TIPS issuance (ie, before 1997), as discussed in the next section.

13 This is mirrored by the fact that commodities become the worst performing asset in low-inflation months.

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14 The Sharpe ratio is defined as the ratio of portfolio return in excess of the risk-free rate toportfolio volatility. In the analysis, the monthly risk-free rate is given by the return on theCitigroup BIG 1-month US Treasury Bill Index.

15 The historical period for the analysis of inflation-protection dependability by property typebegins in January 1994, the inception date for the FTSE NAREIT family of property-typeindexes.

16 Other property types for which separate historical data is not available include timberlandand specialised data centres.

17 See http://www.ncreif.org.

18 Transaction-based indexes of commercial property values and returns do exist, including theTBI employed later in this section. Several researchers, including Lin and Vandell (2007),Cheng et al (2010) and Bond and Slezak (2010), however, have noted that transaction-basedindex methodologies applied to illiquid assets provide biased measurements of both theaverage and the volatility of returns or changes in value.

19 The same, or an analogous, problem may affect the backfilling of returns on TIPS prior toDecember 1997.

REFERENCES

Bhardwaj, G., D. J. Hamilton and J. Ameriks, 2011, “Hedging Inflation: The Role ofExpectations”, Report ICRUIHE 042011, Vanguard Group, URL: https://www.vanguardinvestments.de/content/documents/Articles/Insights/hedging-inflation.pdf.

Bond S. A., and S. L. Slezak, 2010, “The Optimal Portfolio Weight for Real Estatewith Liquidity Risk and Uncertainty Aversion”, Working Paper, URL: http://ssrn.com/abstract=1691503.

Cheng, P., Z. Lin and Y. Liu, 2010, “Illiquidity and Portfolio Risk of Thinly Traded Assets”,Journal of Portfolio Management 36(2), pp. 126–38.

Geltner, D. M., N. G. Miller, J. Clayton and P. Eichholtz, 2007, Commercial Real Estate:Analysis and Investments, Second Edition (Mason, OH: Thomson South-Western).

Gordon, M. J., 1962, The Investment, Financing and Valuation of the Corporation (Homewood,IL: Irwin).

Lin, Z., and K. Vandell, 2007, “Illiquidity and Pricing Biases in the Real Estate Market”,Real Estate Economics 35(3), pp. 291–330.

Lomelino, D., K. Gillett and M. Komarynsky, 2011, “Inflation Hedging with Inflation-Linked Bonds”, Report, Towers Watson, URL: http://www.towerswatson.com/assets/pdf/4125/1101-TIPS-FIN.pdf.

Markowitz, H., 1952, “Portfolio Selection”, The Journal of Finance 7(1), pp. 77–91.

Markowitz, H., 1959, Portfolio Selection: Efficient Diversification of Investments (New York:John Wiley and Sons).

Ralls, B., 2010, “Inflation or Deflation: Prepare for Either”, Fidelity Investments, URL:https://guidance.fidelity.com/viewpoints/inflation-vs-deflation.

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5

Infrastructure Assets and Inflation

Gerald Stack, Dennis Eagar, Kris WebsterMagellan Group

The aim of this chapter is to define the infrastructure asset class,and to explain how each different segment within the infrastructureclass is linked to inflation. In fact, for infrastructure to be considereda separate asset class, it must generate returns that are different fromother asset classes. Indeed, infrastructure provides a unique and dis-tinct investment opportunity, as companies often operate in a quasi-monopolistic environment where demand is fairly price inelastic.Because of this, and because their earnings are structurally linked toinflation, infrastructure companies can generate remarkably stablereal (ie, inflation-adjusted) returns over the business cycle.

INFRASTRUCTURE DEFINED

The term infrastructure can be used to express a multitude of mean-ings. For the purposes of this chapter, an asset is taken to be aninfrastructure asset if

• it provides a service that is essential for the efficient functioningof a community, and hence faces reliable demand irrespectiveof underlying economic conditions,

• the cashflows it generates are not affected by external variables,such as competition, technology obsolescence or commodityprice risk,1

• the earnings generated by the asset are structurally linkedto inflation (for assets that meet this definition, the financialreturns will be robust across economic cycles and protectedfrom inflation).

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The primary sectors falling within our definition of infrastructureare energy and water utilities, tollroads and airports. Each of thesesectors exhibits different investment characteristics, and is affecteddifferently by inflation.

Clearly, there are a number of assets commonly referred to asinfrastructure that fail the definition outlined above. For example,merchant power generators (ie, power generators that sell their out-put at prevailing market rates) provide an essential service, but theprice they receive for the power they generate fluctuates over time.In fact, since their output is relatively constant, demand and priceswill fluctuate along with the prevailing economic conditions. As aresult, their cashflows are neither stable nor structurally linked toinflation, and consequently they are not considered infrastructurefor our purposes.

THE IMPACT OF INFLATION ON INFRASTRUCTURE ASSETS

A sustained increase in inflation has several effects on a typical com-pany. First, input costs will generally increase; in addition, higherinterest rates will increase borrowing costs,2 as well as reduce thediscounted net present value of future revenues generated by thecompany. In such a scenario, companies can be expected to respondby raising prices. However, to the extent that a company is unable topass through increases in input or borrowing costs without affect-ing demand or market share, inflation will negatively affect earningsand, consequently, returns to shareholders. The size of the impactwill be determined by the company’s pricing power, competitiveposition and debt structure, as well as the price elasticity of demandfor its products and services. In practice, very few companies operat-ing in competitive markets will not suffer some diminution in valueif inflation increases.

While the average company struggles to deal with the effectsof inflation, the impacts upon infrastructure assets are relativelybenign, and can even be positive for earnings and underlying value.3

The ability of infrastructure assets to mitigate the effects of infla-tion hinges on the highly inelastic demand for their services, whichenables infrastructure assets to pass on an increase in inflation withlimited, if any, impact on underlying demand.

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As mentioned above, there are three separate segments that fit ourdefinition of infrastructure assets. We will discuss each of these, andtheir unique features, in the following.

ENERGY AND WATER UTILITIES

Utilities that meet our previously stated definition of infrastructureinclude the following:

• utilities that engage in transmission and distribution4 of elec-tricity; these companies are responsible for either the trans-port of electricity from power generators to communities onhigh-voltage power lines or for electricity distribution withincommunities on low-voltage power lines;

• utilities that engage in the transmission and distribution of gas;these entities use pipelines to transport gas from natural gasbasins to the ultimate end-users, such as households;

• utilities that supply water and/or treat waste water.

Because of the vital public and safety service provided, these com-panies have a natural monopoly and are generally heavily regulated,with the government monitoring and controlling the price chargedfor their services. In essence, the relevant government regulatorgrants the privilege (and responsibility) to deliver reliable, qualityservice and, in exchange, it sets a pricing mechanism to secure a fairrate of return for the utility company.

The price-setting process requires the regulator to take intoaccount the impact of several effects, including higher interest rates(which, as mentioned before, affect the cost of debt and equity cap-ital) and higher inflation (which increases operating costs and con-struction costs on new assets built, as well as the value of the assetsalready owned). As a consequence, the value of an efficiently reg-ulated utility company, as measured by the net present value ofits cashflows, should be relatively stable, irrespective of economicconditions, and inflation in particular.5

In practice, the protection to earnings from inflation depends uponthe frequency of the price-setting process, which usually includes aperiod of public consultation, and therefore an often sizeable “reg-ulatory” time lag. Although the latter varies according to differentjurisdictions, price reviews are generally conducted annually, at the

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Table 5.1 Price–demand inelasticity on the Eastern Distributor tollroad,Australia

Traffic growth (%)Date of Toll ︷ ︸︸ ︷increase increase (%) Quarter Year

July 2001 17.0 +9.2 +15.6April 2003 14.0 +5.8 +5.0October 2004 13.0 +5.5 +4.8March 2008 8.6 +2.5 +0.4September 2010 8.6 +2.3 +2.5

Source: Magellan Asset Management, Transurban Group.

request of either the utility company or community groups. Thus,the utility company is afforded a high level of protection from theeffects of inflation.

TOLLROADS

Around the world, the standard business model for a tollroad isthat a government agency enters into a concession agreement thatentitles the tollroad company to collect tolls for a defined period,and increase those tolls on a regular basis,6 in a contractually definedway. At the end of the concession, the road needs to be handed backto the government, in a good state of repair.

In most markets, the tollroad is not the only road route availableto motorists (water crossings like bridges being an exception). Con-sequently, the tollroad is not a pure monopoly. However, some of thereasons why it is built in the first place might be because the alterna-tive routes are not suitable for high-speed or long-distance travel,7 orare highly congested and operating at, or close to, capacity. The open-ing of a new tollroad inevitably reduces traffic on the alternative toll-free routes, at least in the short run. Over time, however, any growthin traffic will plausibly increase flow in the free roads first, until thelatter are soon again operating at capacity, after which the tollroadwill effectively behave much like a monopoly, with the company incharge benefiting from considerable price-setting power (althoughthe government usually monitors and controls the price-setting pro-cess, through terms specified in the concession agreement). As anexample, Table 5.1 shows our analysis of the impact of toll increases

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Table 5.2 Tollroad price concession agreements

Basis ofAsset Location toll increases Frequency

407 ETR Canada At operator’sdiscretion

Discretionary

APRR France 85% of CPI AnnuallyAtlantia Italy 70% of CPI AnnuallyBrisa Portugal 90% of CPI AnnuallyChicago Skyway US Greater of

2%, CPI ornominal GDPper capita

Annually

CityLink Australia Greater of4.5% or CPIto 2015 thenCPI

Quarterly

Eastern Distributor Australia Greater of4.1% orbasket of 67%averageweeklyearnings and33% CPI

In A$0.50increments∗

Indiana Toll Road US Greater of2%, CPI ornominal GDPper capita

Annually

M5 Australia CPI Annually

M6 Toll UK At operator’sdiscretion

Discretionary

Western Harbor Hong Kong CPI AnnuallyTunnel

CPI denotes Consumer Price Inflation, as measured by the index specifiedin the contract. GDP denotes Gross Domestic Product. ∗The formula isapplied to a theoretical toll each quarter, but tolls only increase whenrounding takes it to the next A$0.50 increment.Source: Magellan Asset Management, underlying operators.

on demand for the Eastern Distributor, a tollroad located in Sydney,Australia, over the first decade of the 21st century. As can be seen,demand has been very price inelastic, as traffic has kept increasingdespite higher tolls.

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As mentioned above, the basis on which tolls are increased is con-trolled by the terms of the concession agreement. There are onlythree toll roads of any significance in the Western world where theconcessionaire has full discretion on toll increases: the M6 Toll inthe UK, the 407 ETR in Canada and the South Bay Expressway inCalifornia. All other tollroad operators have to follow specific for-mulas, which are generally linked to inflation. Table 5.2 providesan illustrative cross-section. As can be seen, the pricing mechanismfor these tollroads picks up any increases in inflation, with minimallag. Consequently, the majority of tollroad operators have the abil-ity to respond quickly to any spike in inflation. And as the data inTable 5.1 highlights, tollroad concessionaires can expect that therewill be minimal, if any, disruption in demand as tolls are increased,so revenues, which are the product of toll price and traffic volume,will fully offset the inflationary impact.

Of course, the other key area where inflation can have an impactis on capital expenditures. With most tollroads, however, capitalexpenditures are minimal, and generally limited to keeping theroads in good operating conditions, by resurfacing, replacing ageingcrash barriers, etc, as needed. Consequently, for this infrastructuresegment, inflation has very little material effect when it comes tocapital expenditures. Another crucial aspect is that tollroads, likemost infrastructure assets, are generally more highly leveraged thanaverage industrial companies. The impact of higher inflation on debtcosts is important, and it is covered later in the chapter.

AIRPORTSAirports involve two separate businesses, ie, airside and landsideoperations.

Airside operations encompass the management of the aeronauti-cal aspects, such as the operation and maintenance of the runwaysand taxiways of the airport. The majority of airside revenue is gen-erated by a charge levied on passenger movements (ie, passengerarrivals and/or departures), a charge levied on each aircraft move-ment or a combination of both. In most jurisdictions, the onus is onthe airport to negotiate appropriate charges with the airlines, withsome form of regulation as a fall-back position. This componentof the airport’s operations therefore behaves much like a regulatedutility, with increases in inflation leading to increases in charges in

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order to ensure the airport earns a fair rate of return on the capitalinvested.

Landside operations involve the remainder of the airport, and fallinto three primary areas: retail operations, car parking and generalproperty development. Most airports do not directly run the retailoutlets. Instead, they act as the lessor and receive a guaranteed mini-mal rental, normally indexed to inflation, along with a share of sales.Hence, a spike in inflation will lead to an increase in nominal retailsales (assuming static demand), and the airport will benefit from theinflation protection of these revenues.

The car parking operations at the airport generally behave like amonopoly, although there is some substitution threat, ie, the poten-tial for travellers to park off airport, or to use alternatives, such astaxis or public transportation. However, the level of substitutionthreat is generally weak, and thus the airport has significant pricingpower that can be used to offset inflationary spikes.

As for property development, there is a range of businesses thatseek to be located on or close to airports, including the airlinesand freight forwarders, along with the customs and immigrationofficials. Accordingly, airport operators typically invest in propertyassets and act as the lessor, receiving a rental stream that is indexedto inflation, thus offering protection against rises in price levels.

Airports incur the highest level of capital expenditures amongthe infrastructure segments. Airside capital expenditures includewidening and extension of runways and taxiways, and are gener-ally undertaken after consultation and agreement with the airlinesas well as the relevant regulatory authorities. Airside charges aretypically increased to recover these development and maintenancecosts over time. Landside capital expenditures are often incurredto increase the retail or parking space available, or other propertyleasing facilities. Higher inflation may affect the financial viability ofsuch capital expenditure, but it is expected that the airport operatorwill be rational and elect not to proceed with such expansion projectsif the project is not expected to yield a reasonable real rate of return.In other words, if project and revenue planning is done correctly,inflation will increase the cost of capital expenditures and yet havea minimal impact on the value of the airport asset as a whole.

When considering an airport asset as an investment, there are sev-eral issues that need to be carefully considered, as they contribute

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to the operational efficiency of the infrastructure asset. For example,airports in certain countries might find it more challenging to man-age the cost base of their workforce because of existing labour laws,thus making the infrastructure asset more vulnerable to inflationspikes, all other things being equal.8

IMPLICATIONS OF HIGH LEVERAGE ON INFRASTRUCTUREASSETS

Due to the relatively robust long-term revenues produced by infra-structure assets, many companies are able to obtain relatively cheaplong-term debt, by comparison with the average industrial company.And because leverage levels are generally high by industrial com-pany standards (the capital structure of a typical regulated utilitycomprises approximately 50–60% debt, and the remaining 40–50%equity), the structure of debt is of significant importance to infra-structure companies, and generally very carefully managed, bothin terms of cashflows and overall value. In fact, during the tur-moil in the global credit markets experienced in 2008 and 2009, veryfew infrastructure companies experienced problems in meeting theirpre-existing debt obligations, or even funding new debt. This was indistinct contrast to other highly leveraged businesses, such as banksand real estate investment trusts.

As discussed before, utilities have the ability to recover the costincreases related to an inflationary spike through a periodically reg-ulated price-adjustment mechanism. The latter generally includesspecific allowance for an increase in financing costs, and thus expo-sure to interest rates will be limited to the length of time betweenreset periods, and the “regulatory” time lag. Provided the utilitycompany hedges its residual interest exposure due to these fre-quency/lag effects, cashflow management is pretty straightforward,and the net present value of earnings should be fairly insensitive tomovements in interest rates.

Airports and tollroads do not enjoy the automatic linkages toincreased borrowing costs that utilities do and, while their rev-enue streams enjoy inflation linkages, there are few mechanismsto recover increased borrowing costs. Because of this, most com-panies swap their floating-rate debt into fixed-rate debt; by doingso, they usually incur an interest rate term risk premium, but they

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simplify their cash-management position, as they will be able to ser-vice their debt with stable fixed-rate outflows, even if interest ratesrise. In addition, the net-present value of their long-term fixed-rateliabilities will decrease if interest rates and inflation increase, thusoffsetting, at least in part, the imperfect inflation-linkages on therevenue side.

CONCLUSIONSAlthough infrastructure is a relatively new asset class for manyinvestors, it is increasingly seen as an attractive substitution alter-native in the context of a diversified portfolio. When it comes toinflation protection in particular, several characteristics provide anattractive platform for investors seeking a “safe haven”, includingthe fact that infrastructure revenues are typically structurally linkedto inflation and relatively high levels of debt are generally managedprudently in order to minimise, or even benefit from, interest ratemovements.

1 Although commodity price risk is definitely a cause of earnings volatility, the link betweencommodity prices and inflation is weak at best. This is why, in the example that follows, wedo not consider merchant power generators to be infrastructure assets, as their earnings arebusiness cyclical, and yet not structurally linked to inflation.

2 Here we assume the debt is floating rate and resets periodically. Note that, in this case, ifinflation and interest rates rise, the cashflow outlays required to service the debt will increase,but the debt’s net present value will remain unchanged.

3 This depends on the price-transferring mechanisms, the structure of operating costs and thenature of liabilities.

4 Transmission refers to the transport of the commodity from source to the distribution hub, eg,from the electricity generation plant to an electricity sub-station in a community. Distributionis the transport of the commodity from the distribution hub to the point of use, ie, homes,offices, factories, etc.

5 In other words, for the value of an infrastructure asset to be stable, earnings should grow withinflation, so that their net present value remains unchanged.

6 Toll increases usually occur in sizeable increments and in a highly publicised manner for theEastern Distributor (Table 5.1), as tolls are paid in cash. Fully electronic tollroads, like theCityLink in Melbourne (Australia), the Westlink M7 in Sydney (Australia) and the 407 ETRin Toronto (Canada) have tolls regularly increased by lower increments, with little fanfare,and no impact on demand.

7 This is the case for many European highways.

8 This is true for several airports in Europe, while the issue is typically not present in Australiaand New Zealand.

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6

Equity Investments and Inflation

Steven Bregman, Murray StahlHorizon Kinetics LLC

Unlike a stock market crash, inflation erodes wealth insidiously andcovertly. Given the unprecedented amount of stimulus provided bythe US Government between 2008 and 2011, the utmost vigilanceis required to protect the real value of assets from the effects ofinflation. In this chapter we shall discuss some investment strate-gies that can help to achieve this objective. Traditional methods ofacquiring inflation protection, such as purchasing physical gold orother commodities, might not be the most effective, as better andless speculative alternatives exist. In particular, there are businessmodels, and thus equity securities, which benefit during periods ofinflation yet do not necessarily depend upon inflation in order toprosper. In addition, under certain conditions, some fixed-incomesecurities, such as convertibles, can also offer inflation protection. Inthis chapter we shall cover such equity strategies and examine theirmore salient characteristics.

INFLATION AND EQUITY PRICES

The complexities of inflation and how certain equity investmentsmight mitigate its effects are not always as obvious as they mayseem. It can be most challenging to discern the diverse ways inwhich inflation affects different assets, as well as the reactions ofmarket participants, and thus the impact on prices. While equityprices are generally thought to incorporate an inflationary compo-nent, as both output and input prices incurred by businesses aredirectly affected, the process of exploiting this relationship can oftenprove counterintuitive.

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Table 6.1 Carmike Cinemas, Inc: price changes versus consumer priceinflation (1992–2010)

Average price per patron︷ ︸︸ ︷Admission Concessions Total

Year (US$) (US$) (US$)

1992 3.47 1.28 4.752010 6.85 3.43 10.28

Annualised price change (%) 3.9 5.6 4.4CPI annualised change∗ (%) 2.5

∗CPI, All Urban Consumers, US City Average (all items); not seasonallyadjusted.Source: data from Department of Labor, Bureau of Labor Statistics.

We shall illustrate this point by using Carmike Inc as the busi-ness model typical of cinema chains (Table 6.1).1 Historically, cine-mas have had sufficient pricing power to raise ticket and concessionprices at rates exceeding general inflation price indexes. This pric-ing power has persisted even though this particular business sectorexperienced some degree of saturation during the period consid-ered, when the market might have been expected to revert to a price-competitive system (cinema attendance in North America peaked in2002).

Even modest pricing power (Table 6.2) is important, as it canbe leveraged against a relatively fixed cost structure, resulting ina meaningfully greater expansion in net income (which, simply put,means that if most of your costs are fixed, but you can increase yourprices, then net income (revenue minus costs) will increase). A cin-ema chain is a good example of a high-fixed-cost, low-marginal-costbusiness. Some 85% of the operating expenses of a cinema are rela-tively fixed: basic operating expenses such as rent and film exhibitioncosts. Costs that might be considered more variable with respect topatronage volumes, administrative expense and the cost of operat-ing the food concessions amount to only about 3% each. Revenuesfrom the food concessions, though, comprise about one-third of rev-enues, the balance being ticket sales.Accordingly, the change in oper-ating costs between a cinema operating at 50% of capacity and 95%of capacity is virtually nil (the same rent must be paid, the same

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Table 6.2 Carmike Cinemas, Inc: growth in income margin (2001–4)

Total Annualisedchange change

2001 2004 (%) (%)

Avg ticket price (US$) 4.83 5.17 7.0 2.3Avg concession sales 2.10 2.33 10.9 3.5

per patron (US$)Total attendance (mn) 64.261 63.260 (1.6) (0.5)

Revenue (US$ mn) 457.0 494.5 8.2Operating costs∗ (US$) (420.8) (423.6) 0.7Operating income (US$) 36.2 70.9 95.9Interest expense (US$) (9.1) (26.1) 186.8Pre-tax income (US$) 27.1 44.8 65.3

Pre-tax income margin (%) 5.9 9.1

∗Operating costs exclude impairment of long-lived assets and gains onsales of property and equipment; pre-tax income excludes loss on extin-guishment of debt.Source: Carmike Cinemas, Inc. 10-K.

minimal staffing is required for the ticket line and concession stands,and so forth) so that the earnings are highly sensitive to capacity utili-sation. The alluring income margin growth rate reported in this tableshould not be misinterpreted as representative of the company’s (orthe cinema industry’s) long-term results, since the 2001–4 periodwas selected specifically to illustrate this form of operating lever-age. From this example, it can be seen that, even with slightly lowerattendance at cinemas, a modicum of pricing power, of the orderof 3% per annum, was sufficient to raise pre-tax income by 65.3%(Table 6.2).

All else being equal, an increase in ticket and concession pricing,since it requires no increase in operating cost, amounts to a pureincrease in operating profit. If the initial profit margin is relativelylow (in this case about 6%), then pricing power of merely 2–3% peryear can be sufficient to increase the profit margin by around 50%or more in a very few periods.

Therefore, equities as a class do have the ability to mitigatethe impact of inflation on purchasing power through the earningsleverage of a business. Unfortunately, this does not mean that aninvestor can automatically capture the inflation effects on earningsas reported in a company’s income statement. Even specific equity

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sectors popularly identified as inflation beneficiaries, the earningsof which are particularly sensitive to price levels and expand alongwith inflation, do not necessarily provide the presumed benefitsduring the inflationary periods for which they were acquired. Thereasons for this are discussed in the following.

The impact of rising interest rates and operating costs

To illustrate one of the challenges, imagine that you had the oppor-tunity to be transported back to 1970, yet retain your general his-torical knowledge of that era. At that time, the price of gold wasapproximately US$35 per ounce and, with the advantage of hind-sight, we know that 1970s were characterised by intense inflationarypressure. In particular, it is well known that gold appreciated to wellover US$500 per ounce by the beginning of the 1980s. Cognisant ofthese information advantages, should you, desiring to hedge againstimpending inflation, have bought Newmont Mining (“Newmont”),a gold mining company, in 1970?

The short answer is no. Newmont would not have been as remu-nerative as we might have expected, despite the extraordinary risein the price of gold. At year-end 1969, Newmont traded at a price-to-earnings (P/E) ratio of 12.5.2 The inverse of the P/E ratio, theearnings yield (1/12.5 = 8.0% for Newmont), is more relevant (inthe sense that it can be compared with the yield on other assets) andis an indication of the amount of earnings we receive for the price of ashare. This can be directly compared with the yield on fixed-incomesecurities and interest rates in general. For example, in December1969, the 10-year US Treasury yielded 7.7%, which was similar tothe earnings yield of Newmont stock.

During the following decade, the price of gold rose dramatically,and Newmont’s earnings rose at a 10.8% annualised rate. However,in response to inflationary pressure, the 10-year Treasury rate alsorose to 10.4% by December 1979. Similarly, the earnings yield ofNewmont increased as well: in this instance to 17.9%, which impliesthat its P/E ratio contracted to 5. 6. In other words, even though theprice of gold and Newmont’s earnings increased dramatically, themultiple that investors were willing to pay for this earnings streamdeclined throughout the decade. The increase in earnings was alsolimited by the fact that Newmont, in order to replace its deplet-ing gold reserves, had to acquire new properties at a cost that also

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rose with inflation, thereby limiting the potential for margin expan-sion. During the period, Newmont’s share price only increased byan annualised 2.2% in nominal terms, for a negative return in infla-tion adjusted terms (annualised consumer price inflation was 7.4%in the decade from 1970 to 1979).

The key variable in this example was the rising earnings yield forshares driven by rising interest rates, among other factors, as wellas the negative effect on operating margin due to higher replace-ment costs. Similar counter-intuitive examples can be found in oilexploration and drilling companies during periods of rising oilprices.

The impact of expectations on pricesAnother important element is that, in addition to inflation and inter-est rates, market prices embed expectations about future earningsand other cashflow streams, and these expectations, whether con-firmed by future economic realisation or not, powerfully influencewhere stocks trade, over longer periods of time than we have beentaught to believe.

To illustrate this point, we shall examine how Newmont stock per-formed from 1996 to 2010, again using the literary conceit of perfectforesight. Say that it could have been known in 1996 that gold priceswould more than triple over the ensuing 14 years (from an aver-age price of US$388 per ounce in 1996 to US$1,216 per ounce in May2010, for an annualised appreciation rate of 8.5%). As a counterpointto the preceding example, though, it is also known that consumerprice inflation would average a mere 2.4%, lower than any year dur-ing the prior decade, and that interest rates would actually decline.Nevertheless, Newmont stock, which traded at US$60.25 per share inMay 1996, was lower, at US$53.82 per share, in May 2010. Therefore,a seemingly obvious investment in Newmont would have resultedin a loss in nominal terms and, more importantly, a substantial neg-ative real rate of return over the period considered, despite muchhigher gold prices and lower interest rates.

In this example, the limiting variable on the share price was notinflation or higher interest rates and, consequently, a lower P/E ratio(higher required earnings yield). Rather, in the 1990s, gold min-ing companies did not produce significant earnings, so investorstended to value them based on net asset value. This involves estimat-ing production over the life of the mine (several decades forward),

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projecting the prices at which gold will be sold in the future and sub-tracting the estimated cost of production to derive the prospectiveannual payment streams. A net-present-value calculation is appliedto each of those payment streams, the sum of which would equal,after allowance for net cash or debt, the net asset value of the com-pany. Using that methodology, at a gold price of US$388, investorsconcluded, in aggregate, that fair value in 1996 was US$60 a share.Yet, by 2010, when mining companies were producing substantialincome, they came to be valued on a price-to-earnings basis, asopposed to a net-asset-value basis, by which approach investorsconcluded that the value of the company’s stock was still roughlyUS$60, despite gold prices being dramatically higher.

The lesson to be learnt is that even when the earnings of companiesbenefit from inflation, if too many investors anticipate a positivecase outcome, that outlook will be largely discounted in their stockprices, the result being a poor inflation hedge. If the initial valuationof such a company is too high, there is hardly a realistic level of rapidearnings growth, even a decade of such growth, that will suffice toovercome the momentary change in clearing prices that can occurwhen investors’ outlooks change.

In addition, many are the complexities of stock and company val-uation. For example, in the period considered, the value of Newmontas a company, that is, its market capitalisation, did indeed increaseat a double-digit rate. However, this was because of the issuanceof new shares to raise capital. This financing actually diluted theprice per share, which is the only relevant measure to an investor,contributing to the poor performance outlined above.

The example above highlights how it is not just (inflation) fore-casts that count, but their relation to future scenarios embedded inshare prices. Therefore, the true analytical challenge is not merelyfinding a company (or type of company) for which a good forecastcan be produced, but finding one that can produce a good forecastand for which no one else is desirous of, or interested in provid-ing, a good forecast. In other words, the best positioned and bestmanaged inflation-beneficiary company, if recognised as such anddesired by investors, will paradoxically be priced with a sufficientpremium so as to produce a disappointing return; we must locate aninflation-beneficiary company whose shares incorporate little or noexpectation of a satisfactory return, because returns are made not on

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paper but in the marketplace, where the attitudes of other investorsaffect clearing prices.

In contradistinction, consider Archer Daniels Midland Company(ADM), a company that performed much better during the period inquestion, even though (or perhaps because) it was not considered anobvious inflation beneficiary. ADM is a processor of commodities,specifically food products (it mills wheat into flour, corn into corn-meal, etc). The company operates with a very narrow margin of theorder of 2.5% of the value of the commodities processed. Therefore,on a bushel of wheat valued at US$1, the company might make 2.5¢.At US$2 per bushel, though, it might earn closer to 5¢. At higherprices, the company can make substantially more money, even if themargin remains fixed.

At the beginning of the 1970s, ADM’s P/E ratio was about 10,equivalent to an earnings yield of 10%, and it was the same at thebeginning of the 1980s.3 In other words, the ADM share price did notsuffer from the contraction of valuation multiple that afflicted New-mont, and as its earnings increased (at an average of about of 20%per annum) its share price rose as well, and its market capitalisationrate remained about the same in spite of generally higher interestrates (which increased over the period).4 Though perhaps not obvi-ous from the conventional view of what constitutes a good inflationhedge, ADM was a much more successful investment than New-mont. The heuristic “gold company equals good inflation hedge”did not provide the returns that Newmont shareholders expectedduring the high-inflation period in question.

The lesson of Newmont and ADM should not be lost on theinvestor: inflation and its effects on each individual company’s shareprice are complex and difficult to ascertain, even if the future rateof inflation, interest rates and commodity prices were known inadvance, which of course is not the case.

A SENSIBLE APPROACH TO EQUITY INVESTING ANDINFLATIONIt is our view that basing investment decisions on future forecasts ofinflation is fraught with danger. First, the confidence we can have insuch a market forecast is limited; second, as illustrated by the twoexamples in the previous section, an investor might get the forecastright, yet still get the investment vehicle wrong.

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One approach towards managing the risk of inflation is to makeinvestments that do not necessarily rely on a specific inflation rateto be remunerative, but that will benefit if inflation were indeed tooccur. In this way, the expected outcome is not a binary event. Thisapproach hinges on a company’s ability to produce an adequatereturn on its capital irrespective of the inflationary environment,while maintaining a positive correlation with general price levels.In the following, we shall analyse several equity sectors that mightprovide such attractive characteristics.

Royalty companies

Aprime example of companies that incorporate this dynamic are pre-cious metals royalty companies such as Franco-Nevada and RoyalGold. These companies are, essentially, unleveraged finance busi-nesses that engage in very particular types of transactions with goldproducers and, to a lesser extent, with oil exploration companies.They do not conduct mining operations themselves, nor do theymake conventional equity investments. This form of business wasborn of the distinct project-financing challenges faced by extractioncompanies. In fact, even if there is certainty of the future productivityof an undeveloped deposit, a gold miner cannot typically afford totake on too much debt, because the capital costs can be substantial,and a very long time is generally required to reach the stage whencommercial production can start. During this time, output pricesand input costs can vary dramatically enough to threaten a debt-financed miner. Likewise, if the share price is too low, issuing newequity is excessively dilutive.

Royalty companies devised an elegant solution for the specificproject-financing needs of these resource extraction companies.In simple terms, a royalty company purchases a revenue streamderived from the sale of the precious metal or oil to be extracted bythe company (eg, gold in the case of Newmont). Consequently, therevenues from these contracts are independent of either the prof-itability or the share price of the miner, as long as the underly-ing commodity is extracted and sold. Specifically, the royalty com-pany pays today the net present value of the commodity to be pro-duced by the extraction company at some time in the future. Asa hypothetical example, Franco-Nevada might agree to pay New-mont the prevailing price of gold at the time of writing in 2011:5

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Table 6.3 Franco-Nevada and Newmont equity prices versus gold price

Franco-Nevada Newmont GoldMining Corp∗ Mining (per oz)

(US$) (US$) (US$)

Dec 30, 1983 0.20 4.23 382.40Dec 28, 2001 23.10 17.71 278.95

Annualised change (%) 30.2 8.3 −1.7

∗This is the “old” Franco-Nevada, for which the earliest share price avail-able is in October 1983, and which was acquired in February 2002 by New-mont Mining. Franco-Nevada became public again in December 2007.Source: Bloomberg.

US$1,500 per ounce (to use a round figure), discounted at a fixedinterest rate, say 10%. Thus, the first year production is sold todayat US$1,363 = US$1,500/1.1; the second year production is sold atUS$1,240 = US$1,500/(1.1)2, and so on. For the 30th year’s output,Franco-Nevada will have paid, in advance, only 5.7% of the cur-rent market price of that gold. Accordingly, if the price of gold doesnot change in the future, and the gold mining company producesthe expected amount of gold (even if at break-even or a loss), therate of return the royalty company would realise would be the dis-count rate applied to the original investment, which in this exampleis 10%. Contrast this with purchasing gold outright, either throughan exchange-traded fund (ETF) or the physical commodity itself.Whereas a flat gold price would produce a zero return in a directpurchase of the commodity, the royalty company would still gener-ate a return equivalent to the discount rate. If the price of gold wereto rise, a holder of physical gold would receive a return equivalentto the rate of appreciation on the commodity. However, assumingno hedges are in place, the royalty company would receive the rateof return on the underlying commodity on top of the original dis-count rate. Of course, this can go both ways, but note that if a royaltycompany purchases production at a discount of 10% over 30 years, itcan actually sustain a 10% decline in gold prices each and every yearover a 30-year period without incurring a capital loss. This is sim-ply not possible through a direct investment in the precious metal,or in a mining company (or in virtually any other industry, for thatmatter).

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Finally, it is not unusual for these financing contracts to includea rate adjustment linked to the price of the underlying commod-ity, such that the royalty company can receive incremental royaltyincome should the sales price of the mining company’s ore rise abovecertain predetermined benchmarks.6 Table 6.3 shows the impressivereturn of Franco-Nevada’s share price over a period of almost twodecades. This exceptional performance occurred in spite of declin-ing gold prices (the point-to-point decline was 26%, as displayed inTable 6.3, and the average year-end gold price from 1983 to 2001,inclusive, was US$354, or 7% lower than the 1983 price),7 and wasbased on the discount rates on the financing contracts offered toNewmont.

Spread-based companies

Another sector that can prosper in an inflationary environment iscomprised of companies that are able to pass through the costs ofinflation via a spread-based business by charging a fixed percent-age fee for their products and/or services. Companies such as theaforementioned ADM and MasterCard belong to this sector.

The case of MasterCard is interesting because this company isoften (erroneously) categorised as a financial institution, similar tobanks and other companies that lend money. In reality, MasterCard issimply a processor; it does not issue credit cards, it simply processesthe transactions made on credit cards bearing its brand. The com-pany’s revenues derive from two sources: a fixed US dollar fee pertransaction, and a small percentage fee based upon the transaction’sUS dollar value.

For illustrative purposes, let us say that MasterCard’s percentagefee amounts to 1% of the US dollar value of each transaction, so thata purchase of US$100 would generate a fee of US$1 (in reality, Mas-terCard’s percentage fee averages a small fraction of 1%, applied totrillions of US dollars in transactions). If a product’s price were toincrease by, say, 10%, care of inflation, the total value of the pur-chase would be US$110, with a proportionate increase in the fee toUS$1.10. Accordingly, a company such as MasterCard, which oper-ates a spread-based business, is somewhat immunised from infla-tion. Indeed, it might actually benefit from a general rise in the priceof goods and services. In this much simplified example, the 10%

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Table 6.4 Wilshire US Real Estate Securities Index versus S&P 500period return (June 2007 to June 2011)

Wilshire US Real Estate S&P 500Securities Index Index

Period return (%) 2.6 −4.1

increase in revenue requires no direct increase in the number of per-sonnel, computer processing capacity, office space or other expensesand thus should be particularly profitable.

Real estate companies

Although the real estate industry experienced much distress duringthe 2008–9 financial and housing crisis, this episode has not invali-dated real estate as an inflation beneficiary. Indeed, from the begin-ning of that period up to and including June 2011, real estate stocksdid not underperform broad stock indexes, irrespective of their moredramatic interim decline. Table 6.4 shows a comparison of returnsbetween the general US equity market as measured by the S&P 500Index and the Wilshire US Real Estate Security Index8, which is acomposite of publicly traded Real Estate Investment Trusts (REITs)and Real Estate Operating Companies (REOCs).

There is a certain structural limitation to the ability of REITs tocompound their per-share value, since by regulation they must dis-tribute as dividends substantially all of their income. As a result,they must issue additional shares in order to acquire new prop-erties, and there are periods when the cost of new equity capitalwill be disadvantageous. Non-REIT real estate companies can rein-vest their income and are less dependent upon the public marketfor growth capital. Therefore, we might be better advised to concen-trate on select commercial real estate companies, with strong balancesheets and unique income-producing properties. Aside from theirfundamental investment merits, these companies provide inflation-hedging benefits through multiple modalities. First, inflation typ-ically increases the value of the underlying real estate properties,so that such a company’s net asset value tends to rise in inflation-ary periods. Second, as their commercial leases approach renewal,higher prices can be charged to reflect the effects of inflation onprevailing rental rates. Finally, real estate companies typically use

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leverage to purchase their properties. To the extent that the mort-gage payments are fixed, their liabilities will decrease in real termsbecause of higher inflation. In this sense, leveraged companiesin general can benefit an investment portfolio during inflationaryperiods.

Leveraged companies and deleveraging mechanisms

Leverage is an important element when evaluating an equity invest-ment. In this section, we shall explain how changes in leverage canaffect the value of a company and thus its stock price. The first mech-anism is directly related to inflation and the operational leverage (ie,higher operating margin) that comes with higher output price levelsrelative to a fixed cost structure. The next mechanism is linked notto inflation per se or to a higher operating margin, but to the expan-sion in earnings that results from deleveraging, ie, paying down thedebt and reducing interest costs. There is also a market-based mech-anism, whereby a company’s stock market valuation can rise as adirect function of its paying down debt. All three mechanisms areimportant and can be present at the same time; thus, they are coveredin this section.

We have already discussed how inflation and higher outputprices (versus a fixed cost structure) can result in considerablyhigher income margins (Table 6.1). In essence, rising sale pricesprovide a form of operating leverage, as they do not require addi-tional resources (such as sales personnel, manufacturing capacityor other production inputs), and thus do not increase variable costs(as opposed to rising unit sales). This effect can be amplified bythe presence of fixed-rate leverage as well, since inflation favoursthe fixed-rate debtor over the creditor. In that relationship, eachyear’s interest payment remains constant, even as sales revenueand, presumably, earnings rise in concordance with rising pricelevels.

The fact that inflation favours the fixed-rate debtor, due to thefact that the interest is fixed in the face of overall rising prices, is atheme that applies beyond publicly traded equities. In fact, one ofthe most effective inflation hedges during the inflationary decadesof the 1970s and 1980s was the 30-year fixed-rate home mortgage.Specifically, from 1973 to 1982, a mortgagor’s fixed-rate paymentcheapened by 8.7% per annum in inflation-adjusted terms (using the

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average Consumer Price Index (CPI) inflation rate over the period).9

In other words, by the end of the 10-year period, a homeowner wouldhave been making mortgage payments at 45 = 1/(1.087)10 cents onthe dollar in real terms. In addition, over the same period, they wouldhave received higher wages and a higher value for their house, insympathy with other price levels.

Although fixed-rate leverage amplifies the positive effects onoperating margin of higher output prices, it is the deleveraging ofa company that often offers attractive investment opportunities. Inparticular, a company with a high level of fixed-rate leverage, butin the process of entering a deleveraging phase, might offer the bestof both worlds, ie, attractive performance prospects combined withprotection from rising price levels.

Take the example of a company with a stable business, whichemploys its earnings to reduce its debt (through plainly using thecompany’s earnings to pay down its debt, in the same way thatan individual might use their salary to pay down their credit carddebt).

Initially, we shall assume zero revenue growth (Table 6.5) anda constant operating margin (no operating leverage) to isolate theeffect of debt reduction. As liabilities are paid down each year,the interest expense associated with debt is also extinguished. Thisleaves more after-tax income available the next year, so that a yetlarger amount of debt may be paid down. This process createsan increase in net income, which compounds over time (for anannualised rate of 4.9% in the decade considered).

Table 6.6 presents an additional example, this time with a mod-est rate (3% per annum) of revenue expansion, but still no operatingleverage (the operating margin is constant at 20%), for an annualisedincome growth of 12.7% over the period. In practice, few companiessustain a linear path of any sort for a whole decade, but the pre-vious examples serve to illustrate the degree to which merely thetwo factors of persistent interest expense reduction and the operat-ing leverage of price-inflated revenues can serve the cause of valuecreation in a leveraged company.

However, a third and probably the most powerful equity valuecreation dynamic from the deleveraging process is expressed bythe Miller–Modigliani invariance theorems (Modigliani and Miller1958). These state, in part, that the enterprise value of the firm (that

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Table 6.5 The effects of deleveraging with no revenue growth/no operating leverage

IncomeOperating Interest Pre-tax net Interest

Revenue income expense income of tax Debt coverageYear (US$ mn) (US$ mn) (US$ mn) (US$ mn) (US$ mn) (US$ mn) ratio

0 1,000 200 (150) 50 33 2,000 1.331 1,000 200 (148) 52 34 1,968 1.362 1,000 200 (145) 55 36 1,933 1.383 1,000 200 (142) 58 37 1,898 1.414 1,000 200 (140) 60 39 1,860 1.435 1,000 200 (137) 63 41 1,821 1.466 1,000 200 (133) 67 43 1,780 1.507 1,000 200 (130) 70 45 1,736 1.548 1,000 200 (127) 73 48 1,691 1.589 1,000 200 (123) 77 50 1,643 1.62

10 1,000 200 (120) 80 52 1,594 1.67

Annualised change (%) 0.0 0.0 (2.2) 4.9 4.9 (2.2)

We make the following assumptions. Revenue growth: 0%. Operating margin: 20%. Debt interest rate: 7.5%. Income tax rate: 35%.

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Table 6.6 The effects of deleveraging with modest revenue growth/no operating leverage

IncomeOperating Interest Pre-tax net Interest

Revenue income expense income of tax Debt coverageYear (US$ mn) (US$ mn) (US$ mn) (US$ mn) (US$ mn) (US$ mn) ratio

0 1,000 200 (150) 50 33 2,000 1.331 1,030 206 (148) 58 38 1,968 1.402 1,061 212 (145) 67 44 1,930 1.473 1,093 219 (141) 77 50 1,886 1.554 1,126 225 (138) 87 57 1,836 1.645 1,159 232 (133) 98 64 1,779 1.746 1,194 239 (129) 110 72 1,715 1.867 1,230 246 (123) 123 80 1,643 2.008 1,267 253 (117) 136 88 1,563 2.169 1,305 261 (111) 150 98 1,475 2.36

10 1,344 269 (103) 166 108 1,377 2.60

Annualised change (%) 3.0 3.0 (3.7) 12.7 12.7 (3.7)

We make the following assumptions. Revenue growth: 3%. Operating margin: 20%. Debt interest rate: 7.5%. Income tax rate: 35%.

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is, the sum of its debt and equity) is invariant (under certain assump-tions) to the capital structure of the firm. This presumes that com-panies are valued in the marketplace on an enterprise value basis,irrespective of the distinction between debt and equity. Accordingly,if a company has a low stock market capitalisation in relation to itsdebt, and if it uses its cashflow to reduce debt, the equity valueshould increase by a like amount such that the total enterprise valueremains unchanged. As a conceptual test, were this not so, then ahighly leveraged company that repays debt would find its enterprisevalue contracting, which is to say that investors would penalise thecompany for reducing its financial risk.

In our experience, deleveraging companies exhibit such distinc-tive characteristics that they deserve their own sector classification.In other words, companies in separate sectors yet with commonbalance-sheet structures and debt reduction strategies will sharegreater return commonalities than many companies in the samesector but with different balance-sheet arrangements (however, theunfolding of events over a span of years is rarely cleanly reducibleto the single variable). A clean, simple example of debt reductionwithout any meaningful intrusion of other balance-sheet/operatingissues, would be Church & Dwight. However, in this case, its startingpoint was leveraged only on a balance-sheet basis, not on an incomestatement/interest coverage basis. Therefore, it was not obviouslyundervalued at the start, and its share price appreciation over timewas more a function of its business expansion than its balance-sheetimprovement (Table 6.7).

As shown in Tables 6.5 and 6.6, investing in companies that areentering a deleveraging phase can provide very rewarding returns.An additional benefit from investing in deleveraging firms is thatreturns tend to be less correlated to exogenous events such as theeconomic cycle or the competitive environment, since the equityvalue expansion is largely a function of the debt reduction processitself. Furthermore, these companies have typically established theircompetitive positions already, and do not need to incur the costs (anduncertainties) required to gain market share or develop a new prod-uct. Clearly, the objective should be to select companies with stablebusinesses, good management and for which leverage has not beenthe result of deteriorating fundamentals, but the most effective strat-egy to finance the business, and enhance returns on equity. As with

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Table 6.7 Church and Dwight (CHD) deleveraging process

Total Book Debt/ Interest Operating Interest Interest Book value/debt value equity Sales∗ expense∗ income∗ savings∗∗ coverage share

(US$ mn) (US$ mn) (%) (US$ mn) (US$ mn) (US$ mn) (%) ratio (US$)

Sep 2011 254 2,086 12 2,704 −10 457 142 45.8 29.10Dec 2010 340 1,871 18 2,589 −28 445 24 16.0 26.34Dec 2009 816 1,602 51 2,521 −36 413 16 11.6 22.76Dec 2008 856 1,332 64 2,422 −47 340 34 7.2 19.62Dec 2007 856 1,080 79 2,221 −59 305 −9 5.2 16.41Dec 2006 933 864 108 1,946 −54 252 4.7 13.31

∗Sales, operating income and interest expense for 2011 based on nine-month results, annualised. ∗∗As a percentage of change in operatingincome.

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any other publicly traded security, investing in leveraged equitiesrequires a considerable amount of analysis and scrutiny, includingconsideration of both quantitative and qualitative aspects. Indeed,investing in deleveraging companies is similar to the business ofa leveraged-buy-out (LBO) firm, which will typically acquire anundervalued company with reasonably stable cashflows (borrowingagainst the acquired company’s balance sheet and future cashflows)and then spend several years in debt-reduction mode, before sellingthe company to the public, or a strategic investor, once again.

“Busted” convertible securities

Traditionally, convertible securities (ie, bonds or preferred stock)have been employed as equity alternatives, for reasons describedbelow. This periodically creates a pricing opportunity that permits aconvertible to be used in a different and, we believe, more effectivefashion.

Companies issue convertibles securities as a way to reduce theirborrowing costs. As an illustration, consider an A-rated corporationthat can issue a bond at a 5% interest rate, versus a lower creditrated company, say BBB, which would have to pay 7% on a bond ofsimilar maturity.10 The BBB-rated company might opt to sell a bondwith an equity conversion feature as an inducement to a different setof buyers. Specifically, it might issue a convertible bond at a lower(5%) interest rate, yet for which the buyer also receives an embed-ded call option on the company stock. Usually, this type of issuanceoccurs when the company’s shares have experienced some positiveappreciation, since this is the time when its convertible security ismore likely to be perceived as being attractive from the perspec-tive of optionality, due to the fact that a call option is about theupside. Typically, the call option embedded in the convertible bondhas a conversion price (‘strike’ in traditional option terminology)higher than the current stock price (20–30% being a common rangeof the premium to market, depending on the maturity of the secu-rity and market conditions). Several structures might be issued, withthe option exercisable only at bond maturity (similar to a Europeanoption) or at a discrete set of future dates. A variation on the sametheme occurs when a company issues convertible preferred stock.11

In summary, convertibles are hybrid fixed-income/equity securi-ties that permit the investor to potentially benefit from appreciation

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of the stock while retaining the interest income stream, final matu-rity (unless a perpetual preferred, ie, a preferred stock with no finalmaturity) and superior capital position and legal rights of tradi-tional debt. For these reasons, convertibles are conventionally usedas a conservative equity substitute.12

Yet, in practice, when a convertible security is sold, two premiumsare paid: a premium to the common share price13 and the share priceitself, which is likely to have already appreciated to a fair degree.Moreover, in comparison with other bonds, it provides a below-market yield as a trade-off for its optionality. Accordingly, whateverthe future return prospects might be, we cannot say that, on a proba-bilistic basis, the risk–reward trade-off favours the buyer. Moreover,in comparison with other bonds, it provides a below-market yield asa trade-off for its optionality.Accordingly, whatever the future returnprospects might be, we cannot say that, on a probabilistic basis, therisk–reward trade-off favours the buyer. If for no other reason thanmean reversion behaviour, much less the normal vagaries of the mar-ket, there is a reasonable (perhaps more than reasonable) chance thatthe underlying shares may decline sharply at some point.

If the shares do decline sharply, the bond, which was originallypriced relative to the share price, will fall as well. So long as cred-itworthiness is not at issue, the bond should decline only to a pricethat provides the same 7% yield at which the company would havehad to issue a conventional bond. It is now a “busted” convertibleand it still retains the embedded equity option, although this willhave fallen very far out-of-the-money. It now has more intriguingcharacteristics.

Let us observe an example of such a cycle from start to finish. Con-sider XYZ Corporation (XYZ), a well-regarded growth14 companywith a BBB credit rating, which is considering obtaining financing inthe market for a term of 10 years. Given its credit rating, XYZ couldissue a traditional bond (at par), paying an interest rate of 7% perannum. Fortunately, the XYZ shares have recently appreciated fromUS$20 to US$30. Let us say that US$20 was an appropriate valua-tion at the time, based on generally accepted metrics, and that US$25was appropriate enough as a forward value, but that US$30 couldbe deemed excessive.

• XYZ Corp capitalises on this opportunity by issuing a con-vertible note. The note is priced with a 5% coupon, is due

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in 10 years and is convertible into common shares once theyappreciate by 25% (from the current price of US$30 to a con-version price of US$37.50). Dividing the US$1,000 face value ofeach bond by the US$37.50 conversion price, the note holder isentitled to receive 26.67 shares of stock, upon conversion, foreach US$1,000 face value of bonds held.15

• Suppose that, during year 1, the stock falls sharply to US$15,or by 50%.

• The price of the convertible security at year 1 is still the sum ofthe discounted value of the conventional bond cashflows plusthe equity options, but given the sharp decrease in share price,the convertible is “busted” and falls to a yield-to-maturityequal to the conventional bond,16 ie, 7%, which equates to aprice of 86.97. While a US$1,000 notional amount of the con-vertible bond is now priced at US$868, the underlying shares,having fallen by so much more, are priced at only US$400 perbond (26.67 shares × US$15). The conversion premium17 hasexpanded from 25% to 117%.

• At this point, from the perspective of the original buyer, thesenotes are no longer suitable. They served one purpose in hav-ing outperformed the underlying stock in the decline but, ata 117% conversion premium, they no longer contain muchoptionality or equity sensitivity. The shares would have tonearly double in value for the convertible equity sensitivityto be restored to levels similar to those at inception.

However, at this same point the “busted” convertible does haveintriguing characteristics from the perspective of inflation mitiga-tion, depending upon the characteristics of the issuing company andits equity. Used in this way, “busted” convertibles function more asbond substitutes than equity substitutes. In the favourable case, theassessment might be as follows.

• The “busted” convertible note now has the full bond yield thatthe company would have to offer for a conventional bond (7%in this example).

• The “busted” convertible also provides a “free” (or nearlyfree) warrant. Although, given the 117% conversion premium,there is little near-term possibility of meaningful equity-based

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appreciation, most fixed-income investors do not require thesignificant levels of appreciation sought by equity or mostconvertible investors. The “busted” convertible still has nineyears of optionality remaining. If viewed from a fixed-incomeinvestor’s perspective, the extended time frame has great util-ity, whereas for a typical equity investor that time frame ismeaninglessly long.

For instance, what if, by the end of year 2, the common shares wereto recover to a price of US$25, the fair value originally expected forthat time frame, but still well below the US$30 that was consideredexcessive at the time the bonds were priced? If the shares were to thenappreciate, on average, by 8% per annum, their price at the time thebonds mature at the end of year 10 would be US$46.27 = 25×(1.08)8.At that price, the equity value of the bond would be US$1,234 =26.67 shares×US$46.27. This amount would represent appreciationof 23.4% above the US$1,000 maturity value of the bond, for an addi-tional 2.4% per annum above the 7% yield to maturity, and a roughly9.4% annualised return.

We can contrast the prospective return profile of a “busted” con-vertible with that for a common stock. A common stock with no div-idend must rely, all things being equal, on 10% annualised earningsgrowth in order to provide a double-digit rate of return. To achievethis return, there must be no share dilution, such as from the exer-cise of employee options, and it must be accomplished in the face ofcompetition for market share, possible pricing competition, chang-ing economic conditions and other challenges. There must be nocompression in the P/E multiple (as a lower P/E multiple generallyimplies a lower price). This superior rate of return is matched by fewcompanies. If the S&P 500 Index is a suitable measure, the earningsgrowth rate for the companies comprising the index over the 30-yearperiod ending in 2010 was less than 6%.

All that is required for the “busted” convertible of the exampleabove to produce at least a 7% annualised return is the solvency ofthe issuer: nothing else. In order to achieve a total rate of return of10%, from the position of fair value (US$25 at year 2 in our example),the share price would need to appreciate by 8.75% per year:

• US$25 per share, compounded at 8.75% for eight years =US$48.91;18

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• US$48.91 × 26.67 = US$1,304 equity conversion value atyear 10, ie, a 30.4% additional principal return;

• 30.4% earned over the nine years that the bond is held isequivalent to 3.0% per annum of appreciation above face value.

• Total return = conventional bond return (7%) + equity-drivenreturn (3%) = 10%

Thus, an equity-like (double-digit) return can be achieved withthe income, credit and legal claims benefits that otherwise redoundto a bondholder.

There is a subset of convertible securities that can offer inflationprotection even when trading close to par. This is the case for long-maturity convertibles issued by companies that are inflation benefi-ciaries. An example of such a security is the perpetual19 convertiblepreferred share issued in June 2011 by Bunge Limited. Bunge, likeADM, is also one of the world’s major processors of agricultural com-modities, such as grains and oil seeds. This preferred was priced justabove its notional value, at 100.35, and has an annual dividend of4.875%, which is a bond-level yield, versus the common stock yieldof 1.5%. The conversion premium on the issue date was 33%. Sinceby definition there is no maturity date for a perpetual security, thereis a great deal of time for even a modest earnings growth rate tocumulate sufficiently to ultimately realise the optionality inherentin the security. If, to distort the manner in which conversion pre-miums operate in order to make a point, Bunge were to improveits earnings by merely 6% per year over the course of five years,the conversion premium would, in a sense, be fully amortised, andany further growth would inure entirely to the preferred holder. Inthe case of Bunge, a positive variable would be an environment ofinflating food prices, in which case the earnings growth rate couldexpand at a yet greater rate.

CONCLUSIONSIn this chapter we discussed the many factors affecting equity pricesand several investment strategies that can help to protect the realvalue of assets from the effects of inflation.

The complexities of inflation and how certain equity investmentsmight mitigate its effects are not always as obvious as they may seem.In fact, while equity prices are generally thought to incorporate an

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inflationary component, the process of exploiting this relationshipcan often prove counterintuitive.

To conclude the chapter, we reiterate a point that was made duringthe discussion of the impact of expectations on market prices. Inparticular, return forecasts must be compared with the expectationsembedded in the market price of securities. For example, if inflationis widely anticipated and if gold royalty companies become a focusof investors’ attention, then their share prices might not provide anattractive risk–return profile after all. By the same logic, the best timeto acquire inflation protection is often when inflation is not widelyanticipated, or when a given sector or instrument is not in favour,which is to say that its fundamental merits are not fully reflectedin its market price. Accordingly, there is no single security, securitytype or industry sector that can be relied upon at will. It is criticalthat investors have a valuation methodology (or, even better, a rangeof methodologies) to be able to assess with relative confidence thevalue of any potential investment in the context of its expected futurereturns in several circumstances.

1 Carmike Cinemas, Inc (ticker CKEC), one of the largest cinema operators in the US is usedhere, as it has the longest history of public ownership (according to company 10-K filings). Infact, Carmike Cinemas has not thrived, though for other reasons related to secular challengesto this particular business model.

2 Data for Newmont and Franco-Nevada from 1983 and later is sourced from Bloomberg LP,which is a generally accepted data aggregator source. Data before 1983 was obtained fromthe company. Gold prices are sourced from Bloomberg LP.

3 Being low-profit-margin intermediaries, interim changes between input costs and outputprices can have a large impact upon year-to-year profitability for grain processors like ADM.To provide figures more representative of normalised earnings, the three-year average P/E isused here: 10.4 times for the three fiscal years June 1970 to June 1972; 10.0 times for the threefiscal years June 1980 to June 1982.

4 The market capitalisation rate is the rate used to discount future cashflows in the net-present-value formula for the share price, or also the market expected yield on the equity investment.

5 Use of the current prevailing commodity price is typical in these financing contracts.

6 Often, the royalty contract will contain a schedule such that at the initial gold price, sayUS$1,000, the royalty rate might be 2%; at a higher gold price, US$1,100, the rate will behigher, say 2.5%, and so forth. It is designed in part to limit costs to the miner in the earlyproduction phase, and to generate additional returns for the royalty company in a morefavourable environment for the miner.

7 Generally, Franco-Nevada neither hedges nor employs debt leverage.

8 http://www.wilshire.com/.

9 The CPI is published by the US Bureau of Labor Statistics.

10 These are the credit ratings issued by Nationally Recognized Statistical Rating Organizations(NRSROs) such as Moody’s, S&P, Fitch, etc.

11 This is preferred stock with an embedded option of conversion into common shares. In prac-tice, convertible preferred stock can be seen as a long-maturity convertible bond, but with

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higher credit risk, given its junior position in the capital structure relative to debt, ie, preferredstock with an embedded option of conversion into common shares.

12 Depending on market conditions (interest rates, credit spreads and stock prices in particular),a convertible security might, over time, behave more like a bond or more like a stock, andthus offer distinct properties and attract interest from different sets of investors at differenttimes.

13 As mentioned before, the conversion price is typically higher than the current share price.

14 A growth stock is from a company that is expected to grow its earnings and/or revenue fasterthan its industry sector or the overall market.

15 The convertible bond can be written as a conventional bond (paying a coupon of c = 5% andpriced at a yield of y = 7%) plus 26.67 equity calls.

16 Assuming a flat and unchanged credit curve for the issuer in question, ie, XYZ Corporation.In reality, a plunge in stock price would typically imply wider credit spreads.

17 The conversion premium is given by (convertible price/conversion value) − 1, where theconversion value is the value that could be realised by converting into shares immediately.In our example, the convertible price is US$868, and the conversion value is 26.67 shares ×US$15 price per share = US$400. Thus, the conversion premium is (868/400)−1 = 117%. Thehigher the conversion premium, the lower the equity sensitivity of the convertible.

18 Average equity appreciation over the nine-year period (from year 1, when the “busted”convertible is bought to maturity at year 10) is 14% per annum.

19 This means that, contrary to a convertible bond, there is no maturity date when notional willbe returned.

REFERENCES

Modigliani, F., and M. H. Miller, 1958, “The Cost of Capital, Corporation Finance and theTheory of Investment”, American Economic Review 48(3), pp. 261–97.

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7

Inflation-Linked Markets

Gang Hu; Stefania PerrucciCredit Suisse; New Sky Capital

Since 1981, when the UK government issued the first inflation-linkedbond (linker),1 the linker market has established itself as a distinctasset class within the global fixed income universe. With a marketnotional close to US$2.5 trillion outstanding (Table 7.1), includingboth developed and emerging countries, this asset class has attracteda variety of market participants, ranging from asset managers, retailinvestors and pension funds to central banks. In addition to thisglobal bond market, liability-matching programmes in the Euro-pean Union (EU) and the UK and corporate issuance in the UShave planted the seeds for the development of a growing inflationderivatives market, which has quickly gained global acceptance andliquidity.

In this chapter, we focus on inflation-linked bonds and linear infla-tion derivatives. The first two sections provide a brief recap of thedifferent characteristics of linkers, and give a specific example intro-ducing some key concepts and illustrating trading conventions forUS Treasury Inflation Protected Securities (US TIPS). Next, we dis-cuss the macroeconomic variables affecting real rates, the investmentallocation process and both fundamental and technical factors whichtypically drive investment opportunities in the inflation-linked bondmarket. Finally, inflation derivatives and inflation-linked bondsissued by municipalities and corporates are introduced, and theirrole as important tools in the investor’s arsenal is explained. A briefsummary section concludes the chapter.

INFLATION-LINKED BONDSInflation-linked bonds are designed to compensate investors for theloss in purchasing power caused by changes in overall price lev-els (Bénaben 2005). To this end, coupon and principal payments are

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linked to an inflation index. Both developed and emerging marketgovernments and non-government entities have issued inflation-linked bonds, although the level of activity and liquidity varies foreach local market. Issuers of linkers include the US, the UK, severalEurozone countries (eg, France, Germany, Greece and Italy),2 severalLatin American countries (eg, Mexico, Brazil, Argentina, Colombiaand Chile), severalAsian countries (eg, Japan, South Korea and Thai-land), Canada, Sweden, Denmark, Iceland and Australia, as well asseveral countries in Eastern Europe (eg, Poland), the Middle East(eg, Turkey) and Africa (eg, South Africa).

The reasons for either issuing or investing in inflation-linkedbonds are several. Issuers might be able to lower their cost of debtby exploiting the positive inflation risk premium3 between nominaland inflation-linked bonds. Furthermore, by issuing inflation-linkedbonds, a government might also help to establish market credibilityfor its monetary policy, and thus indirectly lower the cost of its nomi-nal debt as well. In addition, owing to the inflation protection offeredto investors, a government might be able to extend the maturity andcashflow profile of its liabilities; for example, countries like Mexicoand South Africa were able to issue long-term inflation-linked debtwell before they could issue nominal debt at comparable maturities.Indeed, for many emerging market economies traditionally plaguedby high levels of inflation, linkers have been an effective way todecrease hard currency (dollar) funding and increase investors’participation in domestic, local-currency-denominated debt.

Asset–liability management is also a key consideration for bothissuers and investors in the space. Issuers will have an incentive touse inflation-linked debt if their revenue is implicitly or explicitlylinked to price levels. Clearly, this is the case for governments, forwhom taxes are the principal revenue source. In addition, since infla-tion tends to be positively correlated with the real economy, inflation-linked liabilities will also have a stabilising effect on the governmentfiscal budget, as debt service levels and tax receipts will tend tomove in the same direction. Several corporations, particularly in theinfrastructure and energy sectors, also have revenues linked to pricelevels and often issue inflation-linked debt. Finally, asset–liabilitymanagement also drives considerable interest from investors whoseliabilities are linked to inflation, particularly insurance companiesand pension funds.

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It is worth noting that many governments globally have recentlystepped up linker issuance efforts. This reflects not only the increasedfunding needs following the financial crisis of 2008–11, but alsosurging demand from investors, given the uncertainty surroundinginflation in this environment.

As mentioned before, inflation-linked bonds provide coupon andnotional payments, which are linked to an inflation index, with atime lag that goes from a few weeks to a few months dependingon issue and country of issuance. Some, but not all, also have anembedded notional floor struck at par, eg, US TIPS. A few, for exam-ple, Australian government linkers, also have coupon floors. Origi-nal maturities range from 1 to 45 years. Each inflation market has itsown specific characteristics, as detailed in Table 7.1. We next intro-duce some key concepts and definitions, using the largest and mostliquid market for linkers, ie, US TIPS, as an illustration. With thenecessary modifications, analogous concepts and mechanisms areapplicable to other global linkers.

US TREASURY INFLATION PROTECTED SECURITIES

In a US Treasury Inflation Protected Security, the bond notional isindexed to the non-seasonally adjusted Consumer Price Index (CPI)for all Urban Consumers, published monthly by the US Bureau ofLabor Statistics (BLS).4 The US Treasury Inflation Protected Secu-rity pays a fixed rate coupon semi-annually on a notional, which isindexed to the CPI. At maturity, as well as the last coupon, the fullyindexed notional is paid, and the latter is floored at par. This meansthat the notional redemption at maturity cannot be less than 100%of notional at issuance, even if the cumulative inflation rate over thelife of the security is negative (this is why it is called deflation floor).Historically, the reason behind this feature has not been investors’concern about deflation risk (which came to the forefront only duringthe global financial crisis of 2008–11), but the preferred accountingtreatment of assets with principal guarantee, which usually are notrequired to be marked-to-market, thus avoiding the related incomevolatility (Bénaben and Goldenberg 2008).

Since coupon and notional payments are indexed to inflation, aninflation-linked bond provides a fixed real rate of return (if held tomaturity, and with index-lag considerations aside). In other words,

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TSTable 7.1 Major government inflation-linked market characteristics

Market MaturityNo. of Lag Coupon Deflation size range

Market bonds Index (months) frequency floor (US$ bn) (yr)

US 31 US CPI NSA 2–3 Semi-annual Par 643 1–30UK 16 RPI 8 or 2–3 Semi-annual None 392 1–45

France 12 French CPI ex-tobacco 2–3 Annual Par 222 1–30Euro HICP ex-tobacco

Brazil 13 IPCA Index Up to four weeks Semi-annual None 210 1–40Italy 9 Euro HICP ex-tobacco 2–3 Semi-annual Par 143 1–30

CPI, Consumer Price Index; NSA, non-seasonally adjusted; RPI, Retail Price Index; HICP, Harmonized Index of Consumer Prices;IPCA, Índice Nacional de Preços ao Consumidor Amplo.Source: data from Bloomberg, Credit Suisse, New Sky Capital. Data is as of June 2011.

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a linker is a real rate product whose market price does not dependon inflation,5 although its nominal return of course does.

We next discuss the trading and settlement mechanisms for USTIPS. As a concrete example, consider the US TIPS issued in April2011, with a 0.125% fixed coupon (semi-annual compounding) andmaturity of April 15, 2016. On Wednesday, October 12, 2011, itsquoted (clean) price was Q = 103 − 4+.6 Settlement convention isT + 1, meaning that the trade will settle on Thursday, October 13(this will be set to t = 0 in the formulas below), when the full (dirty)price P will be exchanged for the bond. For a US Treasury InflationProtected Security, the full price P is given by

P(0) = (Q(0)+AI(0)) IR(0), where IR(0) = CPI0

CPIbase

where Q is the quoted price, AI denotes the interest accrued fromthe last coupon payment date to the settlement date and IR denotesthe index ratio.

Accrued interest is calculated from the last coupon payment (theissue date in our example) to the settlement date, using an actual/actual day-count convention. In our example, there are 151 daysbetween April 15 and October 13, and the next coupon date is Octo-ber 17 (since October 15 is a Saturday). The IR is defined as the ratioof the daily reference index value at settlement, ie, CPI0, and at bondissuance (the base index CPIbase). The daily reference index value atany given date is the result of an interpolation between the indexvalue with a three-month lag (CPI3mo-lag) and the index value witha two-month lag (CPI2mo-lag). Details of the calculations are shownin Table 7.2, where the following equations are used

AI = 0. 1252

× 151155

= 0. 060887 (7.1)

CPId = CPI3mo-lag+d − 1

days in month(CPI2mo-lag−CPI3mo-lag) (7.2)

Putting it all together, the full invoice price to be paid on settlementday is

105. 742333 = (103. 140625+ 0. 060887)× 1. 02462

At this stage, it is helpful to introduce two key concepts and definethe real yield at time 0 for maturity T, ie, r = r(0, T), and the marketexpectation for inflation, or inflation break-even, ie, BE = BE(0, T).

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Table 7.2 US CPI: all urban consumers, non-seasonally adjusted

Year Jan Feb Mar Apr

2011 220.223 221.309 223.467 224.906

Year May Jun Jul Aug

2011 225.964 225.722 225.922 226.545

Days Daily3-month 2-month in Reference

Date lag lag d − 1 month Index

Issuance 15 Apr 220.223 221.309 14 30 220.72980Settlement 13 Oct 225.922 226.545 12 31 226.16316

Index ratio 1.02462

Daily Reference Indexes and Index Ratio are rounded to five decimalplaces.Source: data from BLS, New Sky Capital, Credit Suisse.

According to the Fisher equation (Fisher 1930),7 their link to nominalyield n = n(0, T) is as follows

1+ n = (1+ r)(1+ BE)

Using this equation, we can write the net present value formula forthe price at time t of the inflation-linked bond P(t), with fixed couponC and a notional redemption floor struck at par

P(0) = (Q(0)+AI(0)) IR(0)

=T∑

k=1

C IR(0)(1+ BE)k

(1+ n)k + 100 IR(0)(1+ BE)T

(1+ n)T + Floor(0)

Note that we have written the index ratio in the future (ie, the infla-tion accretion on the linker notional) as the product of a knowninflation factor at t = 0, ie, the index ratio IR(0), and the future mar-ket expectation of inflation, ie, the break-even, over the remaininglife of the bond, eg

IR(k) = IR(0)(1+ BE)k

The deflation floor is struck at par, and its payout at maturity givenby

Floor(T) = 100 max[1− IR(0)(1+ BE)T, 0]

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Since the market expectation for inflation, ie, the inflation break-even(BE), simplifies on the numerator and denominator of the presentvalue equation, dividing by the known index ratio IR(0), we areleft with a formula that links the quoted price of the linker (Q) plusaccrued interest (AI) directly to real rates

Q+AI =T∑

k=1

C(1+ BE)k

(1+ n)k + 100(1+ BE)T

(1+ n)T + Floor′(t)

=T∑

k=1

C(1+ r)k +

100(1+ r)T + Floor′(t)

where the deflation floor has payout at maturity given by

Floor′(T) = 100 max[IR(0)−1 − (1+ BE)T, 0] (7.3)

Neglecting the value of the floor for simplicity,8 the break-even canbe interpreted as the inflation rate that equalises the nominal yieldof the inflation-linked bond with the yield on the nominal bond.In reality, the bond break-even is not just a pure measure of marketinflation expectations (which are more directly priced in the inflationswap market covered later in the chapter), as it also contains a liquid-ity component, which can be material in newly established inflationmarkets or during liquidity dislocations such as in autumn 2008.In any case, this measure has become an important relative valuemetric between the nominal and inflation-linked bond markets.

Going back to the linker cashflow formula, note that, since thelinker’s coupon is generally smaller than the coupon on the nom-inal bond of comparable maturity and there is typically a positiveinflation accretion at maturity, the cashflows of the inflation bondtend to be back-loaded relative to the nominal bond and, as a corol-lary, the linker exhibits higher rate duration than the nominal bondof equal maturity (and thus higher credit risk as well). Regardingduration, Equation 7.3 shows that inflation-linked bonds are sensi-tive to changes in real rates, while nominal bonds react to changesin nominal rates (with real and nominal rates typically positivelycorrelated). Specifically, the duration of a linker, ie, the percentagechange in the full price of the linker for a 1% move in real rates, canbe written as (neglecting the floor)

D = − 1P∂P∂r= − 1

Q+AI∂(Q+AI)

∂r

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Thus, the linker’s duration does not depend on the index ratio, asthe latter simplifies on both numerator and denominator. However,the dollar change in the linker’s price for a basis point move in realrates (also called DV01) does depend on inflation accretion

DV01 = PD = −∂P∂r= − IR

∂(Q+AI)∂r

This formula shows how the DV01 of a linker is the balance of twoeffects that occur over time: a decrease as we move closer to matu-rity (similar to what happens for nominal bonds) and possibly anincrease in the index ratio (ie, positive inflation accretion over time).

We can also define (real) rate convexity for linkers in a way thatmirrors nominal convexity for conventional bonds. Here, as before,the index ratio simplifies in both numerator and denominator

C = 1P∂2P∂r2 = −

1Q+AI

∂2(Q+AI)∂r2

Finally, a few points on the carry (ie, coupon income minus financ-ing costs) provided by linkers are worthy of mention. Initially, carryis a function of the fixed coupon (typically lower than the couponon the nominal bond of similar maturity) and inflation accretion (ie,the index ratio), which may partially offset the lower (relative tonominal bonds) fixed coupon. Returning to the linker cashflow for-mula, since the latter is indexed to the non-seasonally adjusted CPI,carry on linkers will not only move with the price index but alsomirror its seasonality fluctuations. Therefore, a (short-term) forecastof inflation, including seasonal patterns,9 is necessary in order tocalculate carry and is often an important driver of relative value andbreak-evens, especially for short maturity linkers.

In the following sections, we discuss how macroeconomic vari-ables, such as real GDP, influence real rates and thus the price ofinflation-linked bonds, and we introduce the different approachesused by market participants to analyse value in the sector. Theseinclude both non-leveraged and leveraged investors. Typically,while non-leveraged investors have a long-term horizon and aremainly driven by the absolute level of real rates, leveraged investors,who often act as liquidity providers, employ a complementary setof value metrics and can have an important influence on the marketpricing in the short term. Realistically, most asset managers do endup playing both roles when managing a linker portfolio, as they will

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Figure 7.1 Ten-year US TIPS real yield

2.0

1.5

1.0

0

–1.0

0.5

–0.5

6 Ja

n 20

10

6 M

ar 2

010

6 M

ay 2

010

6 Ju

l 201

0

6 S

ep 2

010

6 N

ov 2

010

6 F

eb 2

010

6 A

pr 2

010

6 Ju

n 20

10

6 A

ug 2

010

6 O

ct 2

010

6 D

ec 2

010

6 Ja

n 20

11

6 M

ar 2

011

6 M

ay 2

011

6 Ju

l 201

1

6 S

ep 2

011

6 F

eb 2

011

6 A

pr 2

011

6 Ju

n 20

11

6 A

ug 2

011

6 O

ct 2

011

Sources: Credit Suisse, New Sky Capital.

typically combine long-term positions with more tactical purchases.In either case, understanding both the long-term views and short-term tactical themes at play in the market is a crucial step for anysuccessful investment strategy.

Real rates: consumption, insurance benefit and economicgrowth

When it comes to the inflation-linked bond market, the primaryfocus of both domestic and international (non-leveraged) investorsis the level of real yields. In other words, the incentive to invest relieson the premise that sacrificing consumption today will provide theinvestor with the ability to consume more, in real terms, in the future.Therefore, it is natural to compare real rates, as a market-determinedmeasure of investment growth, with other benchmarks of economicgrowth.

The consumption argument provides a lower bound to real rates,as it suggests that investors should not be willing to invest ininflation-linked instruments when real rates in the market are neg-ative, as this implies willingness to postpone consumption today inexchange for less consumption tomorrow. This has generally been

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the case historically, although, at times (for example, in the wakeof the massive fiscal and monetary response to the 2008–11 finan-cial crisis) real rates have traded negative for extensive periods.When this happens, it is a sign that investors are driven not by thepromise of greater consumption in the future but by the insurance/hedging benefit of investing in real rate products, albeit locking intoa (slightly) negative real rate in the process (see Figure 7.1 for anexample).

Real rates in the market influence not only the behaviour ofinvestors but also of borrowers, and in turn affect real economicactivity. For example, if real borrowing rates greatly exceed real pro-duction rates, a company, rather than investing in production, mightdecide against financial leverage, which will force market real bor-rowing rates down. This is true even if the company takes on nominaldebt, as long as inflation affects the asset and liability side of its bal-ance sheet to the same degree. Therefore, it is natural to compare theeffective real rates at which financing can be obtained by corporateentities or the government10 with the rate of change in real GDP.

In general, different borrowers incur a different real cost of debt.In particular, with the exception of the spike in sovereign credit riskoccuring at the time of writing,11 developed markets’ governmentshave been able to achieve better credit ratings and lower borrow-ing costs (on both a nominal basis and a real basis) than domesticprivate enterprises, whose output is generally a greater driver thangovernment’s to overall GDP. However, credit spread considerationsaside,12 real rates should all be sensitive to real GDP growth, as therelation between the two is a key input in decision making for alleconomic agents involved (these include the government, privatecorporations and individuals).

On these grounds, we can actually derive a long-term equilib-rium value for real rates, based on macroeconomic arguments. Inparticular, although real GDP growth will fluctuate along the busi-ness cycle, in the long term it should revert to its equilibrium value,which is the potential GDP growth that is unique to each country.13

Although the latter should be interpreted as a dynamic equilibriumlevel, in practice it is relatively stable, changing only gradually overtime. As a consequence, potential GDP growth provides an equi-librium level for real rates, as well as a simple value benchmarkagainst which investment opportunities in inflation-linked bonds

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Figure 7.2 Ten-year US TIPS real yields and real GDP growth

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.5

4.0

0

Q4

1997

Q4

1998

Q4

1999

Q4

2001

Q4

2002

Q4

2004

Q4

2006

Q4

2000

Q4

2003

Q4

2005

Q4

2007

Q4

2008

Q4

2009

Q4

2010

10-year real yield

Real GDP growth

%

Sources: Federal Reserve Bank of St Louis, New Sky Capital.

can be evaluated. In particular, although linker market prices candecrease at times, real economic growth is a constraining factor, ifnot a firm upper bound, for real rates. This of course cannot be saidof nominal bonds.

As a graphical illustration of this relation, Figure 7.2 shows histori-cal real yields for the 10-year US TIPS versus real GDP growth (sim-ilar relationships can also be uncovered in other non-US inflationmarkets).14

ASSET ALLOCATION WITH INVESTMENT-LINKED BONDS

Several studies have been done on asset allocation on portfolios thatinclude inflation-linked bonds among other competing traditionalasset classes. Most of these studies rely on the classic efficient frontierapproach (Markowitz 1952, 1959), where risk-adjusted returns areestimated in nominal space.

The usual notes of caution for these asset allocation approachesapply. First, their results tend to be quite sensitive to inputs, ie, assetclass returns, and volatilities and correlations in particular. The latterare usually estimated from historical data, and might not be repre-sentative of returns distributions going forward. This is especially

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true when considering inflation risk, as the 1980s onwards saw asteady decline of inflation rates and their volatility in developedcountries, which may or may not be what could be experienced in thefuture. In any case, even if historical relations hold going forward,such asset allocation frameworks are intrinsically for the long-terminvestor, as short-term deviations can be material, especially in timesof market stress (as in the 2008–11 financial crisis). In addition, webelieve that, consistently with the consumption argument, it makessense to consider inflation risk explicitly, and thus translate theseapproaches from nominal into real return space.

Specifically, consider the portfolio optimisation problem with nasset classes in real return space (Perrucci 2011). Portfolio weightsand expected real returns are contained in the (n×1) column vectorsW and R, respectively, while Σ is the (n× n) real returns covariancematrix. The vector R and the matrix Σ are inputs (either estimatedfrom historical data or expressing investors’ views going forward);the model output is the vector of asset class weights W, represent-ing the optimal portfolio, ie, the portfolio satisfying the constraintsspecified in the optimisation process. In addition to the usual con-straints required to interpret W as a vector of weights (ie, weightsare non-negative and sum to 1), the investor might want to impose aminimum portfolio real return, rmin, and a maximum portfolio realvolatility, ρmax, ie

WTR = rmin and WTΣW ρmax

(the superscript “T” indicates the transpose). Mathematical machin-ery aside, it is interesting to analyse how an investor might use suchan allocation process in practice. As an example, consider a retailinvestor who is engineering a financial plan to ensure a safe andcomfortable retirement. To this end, they will initially need to esti-mate and commit to a sustainable saving and investment schedule,with the objective being to have enough proceeds later in life to sat-isfy their consumption needs. These needs also have to be estimatedand, as mentioned before, a consumption level should be targetedin real rather than nominal terms, given the uncertainty on inflation.Based on these projections, the investor can infer the minimum port-folio real return that is required, ie, rmin. Then, depending on theirrisk and volatility tolerance, they can solve for the optimal portfolio.Of course, there is a possibility that this optimal portfolio might not

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Figure 7.3 Cumulative real return for Barclays US Treasury and USTIPS Indexes

200

180

160

140

120

100

80

Mar

199

7

Mar

199

8

Mar

199

9

Mar

200

0

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1

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2

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0

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1

Mar

201

2

US Treasury

US TIPS

autumn 2008Flight to liquidity

Both indexes equal 100 at the beginning of March 1997.Source: data from New Sky Capital, Barclays.

exist, in which case the investor will need to save more, bear morerisk or adjust their projected retirement lifestyle.

In essence, we propose to focus on liability matching in real terms,ie, funding future retirement consumption, instead of a simple assetallocation framework. The real return constraint provides a baselineinvestment objective, and in effect ensures that the investor is tak-ing the minimum level of risk compatible with funding future con-sumption. Of course, this does not prevent them from being moreaggressive if their risk tolerance allows.

Clearly, in a liability-matching framework in real return space,inflation-linked bonds become the true risk-free asset, as their returnvolatility is limited (see our previous discussion on the linkage withreal economic growth), and their cash proceeds are indexed to infla-tion. This is why they contribute to a better overall portfolio whenadded into the mix with other asset classes. In addition, in contrast toan investment in traditional asset classes such as equities and nomi-nal bonds, their real return profile is intrinsically more stable and isnot dependent on inflation forecasts, and thus their model outputsare less sensitive to biases in historical estimates or regime shifts ininflation going forward.

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Table 7.3 Summary statistics for monthly returns

Monthly Monthlyreal nominal

returns returns︷ ︸︸ ︷ ︷ ︸︸ ︷US US US US

Treasury TIPS Treasury TIPS

Average (%) 0.31 0.36 0.51 0.56

Standard deviation 1.49 1.72 1.36 1.72

Correlation 66 64

Number of observations 175 175

Source: data from New Sky Capital, Barclays.

As an illustration, Figure 7.3 shows the cumulative returns ofBarclays US Treasury and US TIPS Indexes in inflation-adjusted(real) terms. Despite the flight to liquidity in autumn 2008, wherenominal treasuries dramatically outperformed, the inflation-linkedindex cumulative return is 88.9% in real terms, versus 72.9% for thenominal index.15

Using (continuously compounded) monthly return data, we havealso derived some summary statistics (Table 7.3) for both inflation-adjusted and nominal returns.

Finally, the efficient frontiers in real and nominal space are plottedin parts (a) and (b) of Figure 7.4, respectively. Note that the optimalportfolio blend depends on whether the exercise is conducted inreal or nominal space, with 50% of portfolio allocated to TIPS in theformer case and only 30% in the latter.16 These results suggest thatcalculating optimal portfolios using nominal returns (as is routinelydone, contrary to the approach suggested in this chapter) would tendto underestimate the target allocation to inflation-linked securities.

PRICING DISTORTIONS AND OPPORTUNITIES ININFLATION-LINKED BONDSInflation-linked bonds trade in both the primary and secondary mar-kets. The primary market is where inflation-linked securities areissued and sold to investors, most of whom are non-leveraged, witha medium- to long-term investment horizon. The primary marketis a major mechanism through which global capital imbalances are

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Figure 7.4 Efficient frontier and optimal portfolio results

3.7

3.8

3.9

4.0

4.1

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5.8 6.04.4 4.6 4.8 5.0

Ann

ualis

ed r

eal r

etur

n (%

)

Annualised volatility of real returns (%)

Annualised volatility of nominal returns (%)

Ann

ualis

ed n

omin

al r

etur

n (%

)

(a)

(b)

100% TIPS portfolio

100% Treasury portfolio

Optimal blend: 50% Treasury and 50% TIPS portfolio

100% TIPS portfolio

100% Treasury portfolio

Optimal blend: 70% Treasury and 30% TIPS portfolio

Results for (a) real return space; (b) nominal return space.Source: data from New Sky Capital, Barclays.

corrected and capital surpluses from savers and investors are put touse by producers and issuers, respectively.

A secondary market is also active, and this is where investorscan rebalance and adjust their portfolios and issuers can get priceindications for where the market is trading. In the secondary mar-ket for inflation-linked bonds, liquidity is relatively good, albeit

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Figure 7.5 Real yield and inflation break-evens for selected US TIPS

3.0

2.5

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011

TII Q5 Apr 15 real

TII Q5 Apr 15 BE

TII 1.125 Jul 20 real

TII 1.125 Jul 20 BE

(a)

(b)

%

%

(a) Five-year time horizon; (b) ten-year time horizon.Source: data from Credit Suisse, New Sky Capital.

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Figure 7.5 (Continued )

3.0

2.5

2.0

1.5

1.0

1.5

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18 O

ct 2

010

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010

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ov 2

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an 2

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an 2

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eb 2

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eb 2

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ar 2

011

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ar 2

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pr 2

011

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pr 2

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ay 2

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2 M

ay 2

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un 2

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ay 2

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ul 2

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ul 2

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ep 2

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22 A

ug 2

011

3 O

ct 2

011

TII 1.125 Feb 40 real

TII 1.125 Feb 40 BE

(c)

%

(c) Thirty-year time horizon.Source: data from Credit Suisse, New Sky Capital.

not nearly as good as in other larger asset classes, such as nom-inal government bonds. This opens the way for temporary pricedislocations, and thus opportunistic plays, where providing liquid-ity at the right time is greatly rewarded. Because of the very natureof these opportunities, most liquidity providers are sophisticatedleveraged investors, such as banks’ proprietary desks and hedgefund managers, who have their finger on the pulse of technicalflows, and can quickly position accordingly. Although their timehorizon can vary, it is usually short to medium term (typically afew days or weeks), and thus complements other investors, suchas traditional asset managers, who tend to have a more fundamen-tal long-term approach. Furthermore, while several non-leveragedinvestors have a long-only bias (investing in real rates), these liquid-ity providers take positions on both the long and short sides of themarket, thus betting on either real rates or inflation break-evens.17

Because of the diversity in investors’ objectives, time horizons andvaluation approaches, the market might be pricing certain securitiesor market variables efficiently, while at the same time pricing othersinefficiently.

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And this is precisely where opportunities come about (Perrucci2010). Specifically, some common price dislocations in the inflation-linked bond market arise from the following:

(i) market pricing driven by real rates levels versus inflationbreak-evens;

(ii) lack of index sponsorship at the very front end of the curve;

(iii) liquidity driven issue-specific opportunities;

(iv) new issue auctions and month-end index rebalancing; and

(v) risk-adjusted inflation break-even rates.

We shall analyse these one by one in the following.

Market pricing driven by real rates levels versus inflationbreak-evens

As mentioned above, two important factors driving the pricingof long maturity inflation bonds (ie, of the long-end of the realyield curve, 10-year maturity or longer) are demand from long-onlyliability-matching investors and equilibrium growth rates for thereal economy (as measured, for example, by potential GDP growth).In other words, for long tenors (ie, a long time to maturity), the priceof inflation-linked bonds will be most sensitive to the level of realrates, reflecting how most market participants in the long-end of thecurve evaluate investments in the space.

The mix of investors is quite different for short-maturity inflation-linked bonds, ie, for the short end of the real yield curve (five-year maturity or shorter). Over short time horizons, inflation rates(and monetary policy actions) are somewhat more predictable, andmany investors look at relative value between nominal and inflation-linked bonds. In this regard, it is inflation break-evens that matter,and an investor might be willing to buy an inflation-linked bondeven if real rates are very low, if they can pair the trade by sellingthe comparable maturity nominal bond. In other words, if inflationbreak-evens are attractive, it makes sense to buy a rich inflation-linked bond if it is possible to sell an even richer nominal bond atthe same time. These relative value comparisons, rather than theabsolute level of real yields, drive market pricing in the short end ofthe real curve.

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Intermediate maturities along the curve are less clean-cut, withmarket pricing being driven by rate levels at some times and infla-tion break-evens at others. Naturally, the prevailing mix of forces inthe market also varies with time, with different investors providingpricing dislocations and opportunities for each other.

Lack of investment index sponsorship at the very front end ofthe curve

At the very front end of the real yield curve, rates often displaytechnical price distortions. These are mainly due to the fact that mostinflation-linked bond indexes exclude securities with maturities ofone year or less, so that there are fewer natural holders of thesebonds. As a consequence, the latter tend to trade at a discount tofundamental value, which at very short maturities can be assessedby combining near-term inflation and monetary policy outlooks, orat a discount to other parts of the curve.

Liquidity driven issue-specific opportunities

Although the US TIPS market is large (Table 7.1), it is only a fractionof the total US Government debt, in terms of both size and daily trad-ing volumes. As a result, transaction costs and bid–ask spreads aretypically higher than those on comparable nominal bonds. Indeed,the US TIPS market has displayed a persistent liquidity risk pre-mium, with average bid–ask spreads of the order of 5–10 basis points(bp) around the quoted real yield.

These transaction costs can be material, especially for long dura-tion bonds: for example, a 10bp bid–ask spread on a ten-year US TIPS(assuming an eight-year duration for illustration sake), amounts toabout 26 ticks (1/32 of a point). In addition, even within the linkermarket, certain bonds have better liquidity than others, for example,on-the-run (ie, the security most recently issued) versus off-the-runsecurities (older issues).

Because a large share of the market is owned by managers whopassively invest in the index, and whose investment guidelines limitthe number and type of linkers they can actually trade, these liquid-ity distortions can be magnified for certain specific issues, especiallywhen indexed managers are forced to transact large amounts in rel-atively illiquid bonds. Given the size of the bid–ask spread, there isclearly scope for the active manager (who provides liquidity for the

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right issue and at the right time) to add value to an active portfolioby just achieving superior execution.

Other inefficiencies: market-on-close prices, new issueauctions and index rebalancingThe influence of passive-indexed-investors in the US TIPS marketalso creates other opportunities. To start, as benchmarks use market-on-close prices to calculate returns, many passive investors tend totrade at, or near to, market close to better track their index. Indeed, itis not uncommon to see the market richen near closing time (by half apoint or even more) purely owing to this technical effect, and to thencheapen again the following day. This structural pattern has beenconsistent over time, and offers opportunity for the active investorto buy cheap bonds intra-day and sell them rich near the close of thetrading session.

In addition, new issue auctions and month-end rebalancing aretwo calendar events that typically have a material technical effect onthe market. For example, it is not unusual for US TIPS to cheapen inthe weeks ahead of auction dates (there are eight US TIPS auctionseach year) in anticipation of supply, and then richening again in theweeks following, as many passive investors are obliged to buy newlyissued benchmark-eligible securities. A similar mechanism is at playwhen the benchmark index is rebalanced at the end of each month.Although the specific issues that will be leaving or joining the indexare known in advance, passive investors, wishing to closely matchtheir benchmark price performance, tend to rebalance their portfolioonly close to the end of the month. This offers a structural mechanismto add value for active managers who can anticipate buying/sellingactivity and position accordingly.

Risk-adjusted inflation break-even rateIn most market conditions, inflation-linked bonds have lower pricevolatility than the nominal bonds of similar maturities. This isbecause, despite the fact that linkers have higher interest rate dura-tion, real yields tend to be less volatile than nominal yields.18 Thisimplies that risk-constrained investors can hold a higher notional ofinflation-linked bonds than of notional bonds. Therefore, if we wereto compute the inflation break-even rate between a real bond and asmaller risk-adjusted notional of the equal maturity nominal bond,the result would be a risk-adjusted break-even rate smaller than the

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typical inflation break-even measure, which assumes equal notionalfor both securities. Specifically, if we assume that n is the nominalrate, r is the real rate and BE is the inflation break-even, p < 1 is theratio between the volatility of the linker and the nominal bond andthe linker can be financed at rrepo < n, then19

pn = r + BE−(1− p)rrepo

or

BE = pn+ (1− p)rrepo − r < n− r

To conclude, because different investors have their own uniquedefinition of the inflation break-even rate, it can differ from themost commonly used break-even measure, which is basically thedifference between the nominal and the real rate.

NON-GOVERNMENT INFLATION-LINKED BONDSOver the years, many corporations and local municipalities, witheither revenues linked to inflation or real assets on their bal-ance sheet, have issued inflation-linked debt. Issuers include infra-structure, real estate, toll-road and utilities companies. Asset–li-ability management and attractive financing (ie, low real yields evenonce a credit spread is included) resulting from the strong demandfor such assets by pension funds and insurance companies are twomajor drivers for non-government issuers of inflation-linked bonds.

A corporation can match inflation-linked revenues with fundingby either issuing inflation-linked debt directly or issuing nominaldebt and pay inflation (while receiving a fixed rate) in an infla-tion swap (we shall discuss inflation swaps in the next section).Historically, the latter option has often been the more attractive, asinflation swaps have typically traded rich to cash, given the strongdemand for non-capital-intensive inflation indexation from pensionfunds in particular. However, besides the economics of the trans-action, accounting rules (specific to each country of issuance, espe-cially in regard to the swap) also influence the choice of one fundingalternative over the other (Figure 7.6).

Note, however, that the issuance of inflation-linked debt does notalways result in a net supply of inflation-linked cashflows to the mar-ket. In fact, several non-government entities have issued inflation-linked debt while receiving inflation in a swap at the same time (Fig-ure 7.7). This might seem odd, given the typical richness in inflation

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Figure 7.6 Non-government supply of inflation-linked cashflows

Inflation-linked revenues Inflation-linked bondCorporate

issuer

Inflation-linked revenues Nominal bondCorporate

issuer

(a)

(b)

Pay inflationin a sw

ap

Rec

eive

fixe

d

Inflation swap

(a) Issuing an inflation-linked bond. (b) Issuing a nominal bond and paying inflationin a swap.

Figure 7.7 Inflation-linked issuance with no net supply ofinflation-linked cashflows

Inflation-linked bondCorporate

issuer

Pay fixed

in a swap

Rec

eive

infla

tion

Inflation swap

swaps at which we hinted earlier. However, this type of issuancehas flourished as a result of strong demand for specific inflationstructures from pension funds and retail investors in particular. Inthese swapped inflation-linked notes, coupons are typically linked

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to the year-over-year inflation rate (floored at zero), thus avoidingthe unfavourable tax treatment of sovereign-style linkers, where theprincipal accretion is taxed immediately but payment is receivedonly at maturity. Not surprisingly, the issuance of these inflation-linked structures has been one of the main drivers in the develop-ment and increasing liquidity of the year-over-year swap and optionmarkets.

In addition, although inflation exposure can be obtained in severalways by combining cash bonds and/or derivatives, many investorsare typically restricted by investment guidelines to only a subset ofthese instruments (in particular, some may not be allowed to shortnominal bonds or enter derivative contracts). For the latter, investingin a non-government inflation-linked note might be the only wayto combine inflation indexation with a credit risk premium and/orthe tax benefits of a municipal bond, as replicating indexation witha cash break-even strategy or an inflation swap is not a viable orpractical option.

INFLATION DERIVATIVES WITH LINEAR PAYOUTSOver time, along with the inflation bond market, a global infla-tion derivatives market has also developed. In fact, derivatives witheither linear (ie, futures and swaps) or non-linear (ie, options andmore complex exotic structures) payouts are traded every day, albeitwith different degrees of liquidity. These instruments are less cap-ital intensive than cash bonds, and can be tailored to the needs ofinvestors to a greater degree.

In this section, we shall limit our analysis to linear derivatives, andswaps in particular, given that volume and liquidity of exchange-traded inflation futures are both quite limited. Inflation swaps playan important role in many inflation markets, especially in the Euro-zone and the UK, and to a lesser degree in the US. Several structures(zero-coupon swap, year-over-year swap, linker asset swap, multi-plicative swap, additive swap, total rate of return swap, etc) with asimilar underlying theme are traded, ie, the exchange of inflation-linked cashflows for fixed rate or variable (based on the LondonInterbank Offered Rate (Libor)) payments.

Natural payers of inflation-linked cashflows include corporationswith inflation-linked revenues (this case is illustrated schemati-cally in Figure 7.6(b)) and asset-swap buyers (a case that we will

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Figure 7.8 Zero-coupon inflation swap

Inflation

Fixed rate K %

Inflationreceiver

Inflationpayer

At maturity the inflation payer pays notional× (index(T)/index(base)− 1) and theindex receiver pays notional× ((1+ K%)T − 1).

Figure 7.9 Additive year-over-year inflation swap

R % + inflation

Libor (quarterly)

Inflationreceiver

Inflationpayer

Each year Y the inflation player pays notional× (R%+max[index(Y)/index(Y −1)− 1, 0]). The inflation receiver pays quarterly notional × Libor × day count.

Figure 7.10 Multiplicative inflation swap

Inflation linked

Libor (quarterly)

Inflationreceiver

Inflationpayer

The inflation payer pays semi-annually a fixed rate R% on an inflation-accretingnotional × day count. At maturity the cumulative inflation accretion (floor mayapply) is also paid. The inflation receiver pays quarterly a notional × Libor × daycount.

discuss in the next section). Receivers of inflation include severalinvestors, such as insurance companies and pension funds wishingto hedge their liabilities, and retail investors. Corporate entities thatissue swapped inflation-linked debt (a case shown in Figure 7.7) arealso on the receiver side of inflation. It is fair to say that demand

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for off-balance-sheet inflation exposure (ie, for receiving inflation-linked cashflows in a swap) has often, albeit not always, outstrippedsupply, resulting in a premium offered to inflation payers relative tothe cash market (we hinted as to this effect when comparing parts(a) and (b) of Figure 7.6).

The simplest and most liquid inflation swap is the zero-couponswap, with only one cashflow exchanged at maturity. Specifically, atmaturity T, the inflation payer will pay the realised inflation overthe life of the contract, in exchange for a previously agreed fixed rateK%. This is shown schematically in Figure 7.8.

In each market, the price index underlying the swap is typicallythe same as the corresponding bond market (eg, CPI (all urban con-sumers, non-seasonally adjusted) for the US), while rules for thecalculation of the relevant daily price index, in particular the lengthof the lag and whether or not interpolation is used, can vary quite alot.20 As for settlement, the inflation swap market typically followsnominal swap market conventions (eg, t+ 2 in the US and EU, t+ inthe UK), and thus usually differs from the bond market.

On each trading day, zero-coupon inflation swap quotes forannual tenors (typically up to 10 years, although sparser quotesoften extend to longer maturities) are readily available (for exam-ple, on Bloomberg and other brokers’ screens). From these inflationswap quotes, it is straightforward to derive a discrete (annual inter-vals) curve of forward index price levels and implied inflation rates.To construct a continuous (in this context, monthly) curve,21 twoadditional tools are required:

• a method for interpolation (linear, cubic spline, etc) betweenthe annual tenors; and

• monthly adjustments for seasonality.

The inflation swap curve thus derived provides the base from whichall other more complex swaps can be priced.

Another common swap is the additive, or year-over-year, infla-tion swap. In this structure, one party pays a fixed coupon plusinflation (typically floored at zero) annually in exchange for fixed orvariable (Libor) rate payments. As mentioned in the previous sec-tion, this structure (Figure 7.7) has developed to match similarlyadditive corporate inflation-linked notes issuance (common in theEuropean retail market in particular), where there is no accretion on

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notional, but inflation is carried by the coupon, thus allowing for amore favourable tax treatment. An example of year-over-year swapis shown in Figure 7.9.

The multiplicative (also known as “accreting” or “bond-style”)swap is meant to exactly mirror the inflation cashflows of linkerswith accreting notional (eg, government linkers like US TIPS). Inthis structure, one party pays a fixed coupon (semi-annually) on anotional that is linked to inflation, in exchange for fixed or variable(Libor) rate payments. If there is a deflation floor in the inflation-linked bond (as in the US market), the inflation accretion correspond-ing to the notional payment at maturity is typically also floored atzero. Multiplicative swaps are those used in inflation asset-swaptransactions discussed in the next section. An example is shown inFigure 7.10.

ASSET SWAPS AND INFLATION ASSET SWAPSThe asset swap (ASW) a is transaction where the ASW buyer goeslong an underlying bond, and swaps the bond cashflows for Liborplus a spread (the ASW spread)22. Any bond can be used in an ASWtransaction (nominal, inflation-linked, government or corporatecredit bond, etc). A generic example is shown in Figure 7.11.

Through this transaction, the ASW buyer has effectively trans-formed the underlying bond into a synthetic Libor floater (plus aspread),23 while the ASW seller has secured off-balance-sheet term-financing of the underlying asset at a cost of Libor plus the ASWspread. The ASW buyer bears the default risk from both the underly-ing bond and swap counterparty, and the market risk from changesin the spread between the curve used to discount the bond cash-flows (driven by interest rate, credit or liquidity factors) and theswap curve (Table 7.4). An ASW is, at the core, a financing transac-tion, where the buyer retains the credit24 and liquidity component ofthe underlying asset (columns (c) and (d) in Table 7.4), while trans-ferring interest rate risk (column (a) plus column (b))25 (and inflationrisk for linkers; see column (e) in Table 7.5) to the ASW seller.

Among the several flavours of ASW traded, the most common arethe proceeds ASW (ASWproceeds) and the par–par ASW (ASWpar–par).In a proceeds ASW, the swap notional is set equal to the dirty priceof the underlying bond. This is a natural choice, given that the dirtyprice of the asset is the amount to be financed through the swap

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Figure 7.11 Generic bond asset swap

Bond cashflowsBond cashflows

Libor + ASW spread

ASWseller

ASWbuyer

Bond

The ASW buyer buys the bond and pays bond cashflows and receives Libor plusASW spread in the swap. The ASW seller receives the bond cashflows and paysLibor plus ASW spread in the swap.

Table 7.4 The effect of interest rate and spread changes

Interest rate Spread︷ ︸︸ ︷ ︷ ︸︸ ︷Tsy yield Swap yield Liquidity Credit

Market value of up up up upbond and swap (a) (b) (c) (d)

ASW buyerBond Down N/A Down DownPay bond cashflows N/A Up N/A N/AReceive Libor + AWS N/A ∗ N/A N/A

ASW sellerPay Libor + AWS N/A ∗∗ N/A N/AReceive bond cashflows N/A Down N/A N/A

Par–par ASW Up Down Up UpProceeds ASW Up Down Up UpZero volatility spread Up Down Up Up

∗Slightly down because of the small duration from the ASW fixed spread.∗∗Slightly up because of the small duration from the ASW fixed spread.The market movements shown are essentially partial derivatives.The fourvariables are the nominal Treasury yield corresponding to the bond matu-rity, the swap yield for the same maturity, the bond liquidity spread and thebond credit spread. For example, in column (a) the Treasury yield goesup, while the other three variables are fixed (unchanged swap yield meansthat the swap spread narrows). In column (b), the swap yield goes up, butthe Treasury yield, the bond liquidity spread and the bond credit spreadare unchanged.

transaction. However, ASWs are at times executed and quoted on apar–par basis, meaning that the swap notional is set equal to the bondnotional rather than its dirty price. This means that for premium(discount) bonds the ASW seller is effectively financing a smaller

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Figure 7.12 US TIPS asset swap

US TIPS cashflows

US TIPS cashflowsLibor + ASW spread

ASWseller

ASWbuyer

USTIPS

(greater) amount than the price of the bond, so will have to paythe premium to (or receive the discount from) the ASW buyer upfront. In either case, the ASW spread can be determined by settingthe net present value of the swap cashflows equal to zero, but thespecific formulas, and the resulting ASW spreads, differ dependingon whether the swap is quoted on a proceeds or par–par format.

As an example, suppose that the bond has a full (dirty) price P,pays annual coupons equal to Cj and has redemption amount B atmaturity T; ζi is the swap curve discounting factor for maturity ti

(ie, the present value of a US dollar paid at time ti); li is the Liborpaid semi-annually at time ti (and set at time ti−1/2); δi is the daycount to be applied to floating-rate payments at time ti. Then, for aproceeds ASW, where the swap notional is equal to the bond dirtyprice P, the ASW spread calculated as

P100

2T∑k=1

ζi/2δi/2(li/2 +ASWproceeds)

︸ ︷︷ ︸Libor cashflows

+ (P − B)ζT︸ ︷︷ ︸notional exchange

−T∑

j=1

ζjCj

︸ ︷︷ ︸bond coupons

= 0

In comparison, for a par–par ASW, where the swap notional is equalto par and there is an additional upfront cashflow exchange, theASW spread calculated as

(P− 100)︸ ︷︷ ︸upfront exchange

+2T∑

k=1

ζi/2δi/2(li/2 +ASWpar–par)

+ (100− B)ζT −T∑

j=1

ζjCj = 0

By using the fact that a Libor floater is worth par, ie

2T∑k=1

ζi/2δi/2li/2 + 100ζT = 100

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we can derive the following

ASWproceeds =∑T

j=1 ζjCj + BζT − P1

100 P∑2T

k=1 ζi/2δi/2

ASWpar–par =P

100ASWproceeds

from which we can see that the net present value of the ASWproceeds

spread payments compensates for the difference arising from dis-counting the bond cashflows using the swap curve versus the rel-evant bond curve. Also, note that the par–par and proceeds ASWspreads are the same only for bonds trading at par. Therefore, it isnot straightforward to compare bonds using ASW spreads, and thezero volatility spread (ZV), which is the continuously compoundedspread on top of swap rates needed to recover the price of the bond,is often used instead

P = BζT exp(−ZV tT)+T∑

j=1

ζjCj exp(−ZV tj) = 0

When the asset underlying the swap is an inflation-linked bond (Fig-ure 7.12 for an example depicting US TIPS as the underlying assetbond), the analysis is complicated by the fact that we need to projectnominal inflation-linked payments into the future.

To this end, inflation index values implied by zero-coupon swapsare used to project notional accretion on the inflation-linked bonds,ie, the index factor ratios IR(J), from trade date to maturity. Onecan then use the formulas derived above simply by explicitly intro-ducing index factors and the inflation floor at maturity. Specifically(assuming the day count factor for the annual coupon payment is 1for simplicity of notation)

CJ = C IR(J), B = 100 max[IR(T), 1]

It is interesting to reproduce a table similar to Table 7.4 but with theinclusion of all market factors relevant in an inflation asset swap.In particular, the underlying asset’s (ie, the inflation-linked bond’s)market price depends on the real yield (and possibly also a creditspread), which is approximately equal to the nominal Treasury yieldminus the cash inflation break-even (Fisher’s equation). However,as mentioned before, the government-linker inflation break-even

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Table 7.5 The effect of interest rate, spread and inflation break-evenchanges

Interest rate︷ ︸︸ ︷ Spread InflationTsy Swap ︷ ︸︸ ︷ swapyield yield Liquidity Credit BE

Market value of up up up up upbond and swap (a) (b) (c) (d) (e)

ASW buyerInflation-linker Down N/A Down Down Up

Pay linker N/A Up N/A N/A Downcashflows

Receive Libor + AWS N/A ∗ N/A N/A N/A

ASW sellerPay Libor + AWS N/A ∗∗ N/A N/A N/A

Receive linker N/A Down N/A N/A Upcashflows

Par–par ASW Up Down Up Up Nochange

Proceeds ASW Up Down Up Up Nochange

Zero volatility spread Up Down Up Up Down

∗Slightly down because of the small duration from the ASW fixed spread.∗∗Slightly up because of the small duration from the ASW fixed spread.The sensitivities shown are essentially partial derivatives, where one vari-able is moved and the remaining four are held fixed.For example, in column(a) the Treasury nominal yield goes up, but the inflation break-even doesnot move, and so the other spreads and thus the linker price go down (inother words, the real yield moves in lockstep with the nominal yield, thusdriving down the linker price). In column (e), the inflation break-even goesup, but the nominal Treasury yield is held fixed, implying that the real yieldgoes down, thus increasing the price of the linker. The ASW spread doesnot change with a change in inflation break-even, as the swap fixed-legchange in market value is picked up either by the upfront payment (in apar–par swap) or by a change in swap notional (for a proceeds swap).

typically also contains a liquidity component, and market infla-tion expectations are better measured by zero-coupon (ZC) swapinflation break-evens. Convexity considerations aside (the cash infla-tion break-even on a coupon bond will be different from a ZC swapbreak-even even in the absence of a bond liquidity premium), we

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can write

real yield → r ∼ n− BEcash

∼ n− BEswap + liquidity spread

Therefore, in Table 7.5, our market risk factors are:

(a) the nominal Treasury yield n;

(b) the swap yield;

(c) a bond liquidity spread;

(d) a bond credit spread; and

(e) the zero-coupon swap inflation break-even BEswap.

Note that the ASW spread is a liquidity and credit spread. In particu-lar, it does not depend on the inflation break-even, or on interest rates(assuming that both nominal Treasury yields and swap yields movein lockstep, the ASW spreads do not change, ie, (a)+ (b) cancel out).In comparison, the ZV also depends on the inflation break-even.

The fact that linker ASW levels depend not only on the credit butalso on the liquidity spread has become a major driver of linker ASWtrades. Essentially, demand is generally strong because these swapsprovide inflation-linked payments with the extra accounting ben-efit of off-balance-sheet treatment. As a consequence, linker ASWsoften trade more cheaply than their nominal counterparties withthe same credit risk. This has attracted into the sector many hold-to-maturity buyers, who have become inflation-swap payers to takeadvantage of the supply–demand imbalance. It is very common forinsurance companies to buy linkerASWs rather than nominalASWs,to lock-in (receive) a higher fixed or floating rate against their ownliabilities without exposing the firm to any additional credit riskexposure.

CONCLUSIONS

The inflation-linked cash and derivatives markets have developedglobally, providing an attractive set of investment opportunities toa variety of market participants, including asset managers, retailinvestors, pension funds and central banks. In this chapter, wecovered inflation-linked bonds and linear inflation derivatives.

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Inflation-linked bonds are designed to compensate investors forthe loss in purchasing power caused by changes in overall price lev-els. To this end, coupon and principal payments are linked to aninflation index. Both developed and emerging market governmentand non-government entities have issued inflation-linked bonds,although the level of activity and liquidity varies for each localmarket. We discussed how macroeconomic variables, such as realGDP, influence real rates and thus the price of inflation-linkedbonds, and also introduced the different approaches used by marketparticipants to analyse value in the sector.

Over time, along with the inflation bond market, a global infla-tion derivatives market has also developed. Derivatives with eitherlinear or non-linear payouts are traded every day, albeit with differ-ent degrees of liquidity. These instruments are less capital intensivethan cash bonds and can be tailored to the needs of investors to agreater degree. We discussed the most common swap structures andconcluded with an in-depth analysis of inflation asset swaps and theeffect of market factors moves on valuations and quoted spreads.

1 Obviously, we are referring to the modern inflation-linked market. Historically, the indexationof government debt has deeper roots that can be traced back to bills linked to the price ofsilver issued by the Massachusetts Bay Colony in 1742.

2 Note that EU countries have at times issued linkers indexed to either their domestic inflationindex or the Euro Harmonized Index of Consumer Prices (HICP).

3 There has been mixed empirical evidence on the inflation risk premium, as often the liq-uidity premium between nominal and inflation-linked bonds acts in the opposite direction,especially in newly established markets. However, it is plausible that a positive inflation riskpremium exists more often than not in liquid markets, especially for long tenors, where theinsurance benefit is more important.

4 The CPI released in month n is released about two weeks into the following month.

5 However, real rates themselves are correlated to inflation.

6 The quoted price is expressed as an integer (103) plus ticks (4, one tick being 1/32) and half atick (+ = 1/64). Therefore, “103− 4+” translates into 103+ (4/32)+ (0.5/32) = 103.140625.

7 Fisher’s equation neglects the risk premium, which is a function of the correlation betweenreal rates and inflation.

8 This is often, but not always (contrast with what happened in 2008–9) a reasonable approx-imation for long-maturity linkers or for when the floor is far out-of-the-money (old versusnew issue linkers). Alternatively, option-adjusted break-even measures can be developed byaccounting for the value of the deflation floor explicitly.

9 However, the market has become increasingly efficient when it comes to pricing seasonality.

10 As most corporates do not issue inflation bonds, this will be a nominal rate adjusted by exante expected inflation, or ex post realised inflation rate.

11 The Greek debt crisis started in 2009 and is ongoing at the time of writing; this affected otherdeveloped market countries in Europe and elsewhere (eg, US, Japan, Spain, Ireland, Portugal,Italy, UK) with unsustainably high levels of debt.

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12 Note that governments have traditionally been considered more creditworthy than domesticcompanies, at least on debt denominated in local currency, because of the ability to “printmoney”, thus inflating debt away and devaluing the currency. This may no longer be the casefor the Eurozone countries, which have forgone this option by adopting a common currency.

13 Potential GDP growth is not directly observable, but estimates can be derived by empiricalstudy of equilibrium relations as well as macroeconomic considerations.

14 To analyse the link between real rates and economic growth, New Sky Capital uses a pro-prietary blend of realised and potential GDP (as published by the US Federal Reserve; seehttp://research.stlouisfed.org).

15 Note that the Barclays US Treasury Index duration is smaller (about five years on average)than the Barclays US TIPS Index duration (about eight years on average). It is also plausiblethat some of the outperformance of US TIPS over nominal Treasuries might be due to aprogressive narrowing of the liquidity/novelty premium on inflation-linked bonds.

16 Here and in the figures, by “optimal portfolio” we mean the portfolio with highest expectedreturn per unit risk.

17 This being said, many long-only money managers also look at inflation-linked bonds as asubstitute to nominal government securities in their benchmarks. Thus, these investors alsoexpress an implicit view on break-evens.

18 This is a consequence of the positive correlation between real rates, nominal rates and infla-tion. Typically, in a bond rally (sell-off), both real rates and market inflation expectations willdecrease (increase); thus, nominal rates will generally be more volatile than real rates (excep-tions occur, especially at the front end of the real curve, which is more sensitive to inflationsurprises).

19 Differences in haircuts and repo rates between nominal bonds and linkers (usually morevexing for the latter) are second-order effects for the purpose of this calculation.

20 For the US swap market the lag and interpolation formula are the same as those used for USTIPS, but for the UK and Eurozone swap market there is a lag but no daily interpolation inthe swap reference price index.

21 Special care and additional instruments such as inflation futures are typically used to constructthe short end of the curve (with tenor less than one year), but a discussion is beyond the scopeof this section. Note that inflation price index seasonality translates into greater amplitudeof seasonality for inflation swap rates in short versus long tenors (as the same price indexseasonality is damped in long-term swap rates).

22 This spread can be positive or negative (depending on the relative credit and liquidity risksof the underlying bond and the swap market).

23 A synthetic floater is one obtained by combining several underlying transactions, whosecashflows effectively combine.

24 In addition, both ASW parties assume counterparty credit risk.

25 What is meant here is that if both Treasury yield and swap yield move in lockstep, the marketvalue change in the bond and the fixed leg of swap offset. Technically, there is a residualinterest rate risk resulting from different discounting curve on the asset (bond) and swap side(ie, different durations even if all discounting curves involved move in parallel).

REFERENCES

Bénaben, B., 2005, Inflation-Linked Products (London: Risk Books).

Bénaben, B., and S. Goldenberg, 2008, Inflation Risks and Products (London: Risk Books).

Fisher, I., 1930, The Theory of Interest: As Determined by Impatience to Spend Income andOpportunity to Invest It (Philadelphia, PA: Porcupine Press, Reprint, 1977).

Markowitz, H., 1952, “Portfolio Selection”, The Journal of Finance 7(1), pp. 77–91.

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Markowitz, H., 1959, Portfolio Selection: Efficient Diversification of Investments (New York:John Wiley & Sons).

Perrucci, S., 2010, “Inflation-Sensitive Assets: Portfolio Benefits and Opportunities”,Report, URL: http://www.newskycapital.com.

Perrucci, S., 2011 “Efficient Frontier and Optimal Portfolios in Real vs. Nominal Space”,Report, URL: http://www.newskycapital.com.

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8

Understanding and Trading InflationSwaps and Options

Brice Bénaben; Hervé Cros; Franck TriolaireNew Sky Capital; BNP Paribas; Morgan Stanley

Inflation is certainly one of the most watched, analysed and, to someextent, feared economic phenomena. One of the reasons is its wide-spread impact on every individual, company and country, albeitdifferent economic players have different sensitivities to inflation.

Specifically, some economic agents, such as pension funds andinsurance companies, are concerned by the possibility of an unex-pected rise in inflation, which would require higher cashflows toservice their benefits payable, the latter often fixed in real terms. Incontrast, other economic agents, such as utility and infrastructurefinancing companies, and to some extent central and local govern-ments, have revenues correlated to inflation, and therefore are moreconcerned by unexpected disinflation or deflation, which negativelyimpact on the nominal amount of cashflow receivables.

The recognition of inflation as an important macroeconomic factorand the efforts to mitigate and manage this risk have clearly influ-enced both policymakers and financial markets. In terms of policy,one major development has been the adoption of inflation-targetingmonetary policies, which have become standard in most countries.These policies have helped to stabilise inflation and to anchor infla-tion expectations. Another important development has to do withfinancial markets, where there has been an impressive growth intraded instruments designed to transfer and manage inflation risk.

In terms of inflation markets, the initial step was the issuance ofinflation-linked bonds. The UK and several Latin American coun-tries were among the first to issue such products in the 1960s, 1970s

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and 1980s, and they did so in a period of high realised inflation. Afurther milestone in the development of the inflation market wasreached in the late 1990s, when the US and France started theirinflation bonds programmes.

The next step in the evolution of the inflation market, as morecomplex flows developed and more sophisticated investors becameinvolved, was the birth of inflation derivatives (swaps and optionsin particular), which are the focus of this chapter.

In the following, we shall provide some historical perspective asa way to aid our understanding of the origin of the inflation market,and why it evolved the way it did. In addition, we shall explain thedetailed mechanics of the most common inflation derivatives, swapsand options. Indeed, such products have several technical subtletiesof which a trader or a portfolio manager must be aware. Finally, weshall show how to build some of the practical tools that are necessarywhen trading inflation products in the real world.

INFLATION SWAPS: A HISTORICAL PERSPECTIVEPension funds: hedging liabilities’ inflation riskPension funds have been early adopters and eager buyers ofinflation-linked bonds. Indeed, this demand was one of the key rea-sons for governments to issue inflation-linked bonds to begin with.For example, in 1980, the Wilson Report recommended that the UKGovernment issue index-linked gilts to meet pension funds’ demand(Wilson Committee 1980). The Economic Progress Report publishedby the UK Treasury1 in May 1981 stated the following.

There is no doubt that [the introduction of indexed gilts] will intime have significant effects on the pension industry.… It is far toosoon to predict how the generality of funds will adapt to the avail-ability of such an asset… but over time the private sector pensionsindustry will gain [an] additional element of flexibility in tailoringbenefits it can offer. Some companies have already begun to offerindex-linked retirement annuities for self-employed.

Nostradamus would not have been any better at foreseeing thefuture. Those predictions came true, not only in the UK but also inother countries with large pension schemes (such as Canada, Brazil,the Netherlands, Denmark, South Africa and Australia). Further-more, the consequent tailoring of pension benefits contributed tothe birth of the inflation derivatives market.

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Figure 8.1 Inflation risk in defined benefit pension funds’ liabilities

50

25

0

Pen

sion

fund

ca

shflo

ws

(€ th

ousa

nds)

Pen

sion

fund

cash

flow

s(€

mill

ions

)

100

75

50

25

0

One member

All scheme members

Inflows Outflows

Member retires Member dies

Years

1.

2.

Inflation

Years

During the accumulation period (inflows) the pension contributions are implicitlylinked to wage inflation. During the payment period (outflows), pension annuitiesmay be explicitly linked to consumer price inflation. 1. In the UK the annuities arelinked to the RPI. In the Netherlands the annuities can be linked to the CPI. 2.Thefirst annuity is generally proportional to the final contribution.

At this point, we shall review the reasons why pension funds areexposed to the risk of unexpected high inflation in the future. Simplyput, a pension fund cashflows stream can be split into two periods,as shown in Figure 8.1:

1. during the accumulation (cash inflows into the pension fund)period, pension scheme members contribute funds via regularinstalments during their active working life;

2. when members reach retirement age, the distribution (cashoutflows from the pension funds) period begins, and the retireereceives a pension annuity until their death.

The inflation sensitivity of these cashflows is a function of actuarialprojections and accounting valuations. The latter are in turn influ-enced by pension regulations, which differ from country to countryand evolve over time. But the crucial point is to understand howprice levels affect the initial amount of benefits payable and theirgrowth over time.

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In most “defined benefits”2 pension schemes, the initial annuityis often based on the latest salary before retirement; as a result, thehigher the wage inflation during the contribution period, the higherthe pension liabilities. Another source of inflation sensitivity comesfrom the contractually specified formula for the growth in the annu-ity amount over time. In some countries, such as the UK and theNetherlands, pension annuities increase contractually at the infla-tion rate. As a result of these factors, an increase in expected infla-tion rate increases the expected amount of initial annuity payable,as well as its yearly growth.

This risk is further compounded by several other factors. First,pension liabilities have long maturities, as they are based on lifeexpectancy after retirement, so that they concentrate around the10–20 year term, but can be as long as 60 years or more. Thismeans that there is a high sensitivity to future inflation assump-tions, given that, for calculating benefits payable, projected inflationis cumulated each year from inception to the actual distribution date.This is an important issue, as there is great uncertainty around thepath of future inflation, and forecast errors are significantly high,particularly after a three-year horizon.

Second, because of the relevance inflation risk has for these insti-tutions, it should come as no surprise that the development of infla-tion products has been closely intertwined with the growth in hedg-ing needs and sophistication of pension funds. Indeed, the birth ofthe inflation market initiated a virtuous-cycle type of developmentfor both inflation products and the pension industry. We shall nowreview some important steps in this evolution, culminating with thebirth of inflation derivatives.

1. The issuance of the first inflation-linked bonds created a trade-able forward inflation rate. This helped actuaries in setting theinflation assumptions used to project the pension funds’ ben-efits payable. Previously, actuarial inflation assumptions werenot really consistently set, and each pension fund would gener-ally use different assumptions. Some popular choices includedmonetary policy inflation target levels, or long-term inflationassumptions as embedded in the Taylor rule (Taylor 1993).With the issuance of inflation-linked bonds, a break-even infla-tion (BEI) rate could for the first time be derived from the

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market price of traded securities (inflation-linked and nominalbonds).

2. Market liquidity of inflation-linked bonds improved, andadditional bonds were issued with different initial maturities,thus helping to build a more complete (less sparse) BEI curve.As a result, pension funds and regulators could quantify moreprecisely the present value of future liabilities and their sensi-tivity to inflation, which initiated the discussions to encouragepension funds to account for inflation risk explicitly.

3. Gradually, pension funds started to measure the sensitivity ofthe value of their future liabilities to changes in BEI rates, and tomanage this risk. As a result, pension funds began allocatingsome of their assets into inflation-linked bonds, as a way ofproviding a rough hedge to the inflation sensitivity arisingfrom their liabilities. However, these early hedges were farfrom perfect, as the inflation bonds cashflows (concentrated ina few benchmark maturities) were a poor match to the moredispersed pension liability cashflows.

4. New pension regulations played an important role in shapingthe inflation-hedging strategies of pension funds. For exam-ple, in the UK, the Pension Act of 1995 enforced the indexationof pension payments to inflation, subject to a yearly cap of5% (Davis 2000). This spurred pension funds to look for moreaccurate hedges for their liabilities and, in turn, led invest-ment banks and asset managers to structure tailor-made infla-tion hedges. This ultimately resulted in the birth of inflationswaps, where pension funds would typically elect to receiveinflation-linked cashflows in exchange for paying a fixed rate.Such derivatives contracts had several advantages. First, theytransferred most of the inflation risk from the pension fund tothe swap counterpart. Second, they did not require the pensionfunds to make any initial capital investments, unlike inflation-linked bonds. Such swaps became an (almost) capital-freeoverlay to many pensions’ liabilities.

5. Over time, the use of inflation derivatives to hedge pensionfunds’ liabilities became widespread and a new industry, spe-cialising in such hedging technology, emerged. For example,in the UK, most inflation swaps are executed by specialised

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asset managers, which acted on behalf of their pension fundclients.

6. Other countries, such as the Netherlands, implemented similarregulations, which helped the development of both their localinflation-linked bond and swap markets.

Since 2000, the virtuous cycle of demand and supply of inflation-linked cashflows has resulted in increased inflation-hedging activity,limited only by the risk capacity of investment banks, the topic ofthe next subsection.

Investment banks: managing inflation risk

The rapid growth in inflation-hedging activities since the early 2000stransferred a large amount of inflation risk onto the banks’ tradingbooks. As banks were limited in the size of risk they could take,they hedged their inflation exposure with inflation-linked bonds.The main idea was to extract the inflation cashflows from the infla-tion bonds and to “recycle” them to pension funds via swaps. Thatleft the banks’ trading books more or less immune to moves in for-ward inflation rates. Indeed, such moves would change the inflation-linked bond prices, but this change would mirror and therefore offsetthe change in the value of the swap.

However, such hedging techniques created other risks. An impor-tant one was the discrepancy of funding costs between the nominaland the inflation bonds. This problem was exacerbated by the grad-ual accumulation of long-dated inflation swaps. This led banks tolook for other ways to hedge inflation risk more accurately. Part ofthe solution was found within the financing of infrastructure or realestate assets. Infrastructure and real estate assets have long-termstreams of revenues linked to inflation. These cashflows have theopposite inflation risk to that faced by pension funds, and an increasein forward inflation increases the present value of these assets, as itincreases the pension funds’ liabilities. As a result, some of the banksproviding financing for infrastructure assets were able to structure“back-to-back” swaps (Figure 8.2), where they would receive infla-tion cashflows from the infrastructure client, and pay these inflationcashflows to the pension fund client on the other side of the swap.Such transactions were clearly more cost effective, as they did notinvolve the purchase of inflation-linked bonds (“linkers”).

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Figure 8.2 “Recycling” inflation from a project finance deal into apension fund via swaps

InflationInflationProjectfinance(revenueslinked to inflation)

Banks Pensionfunds

Swap break-eveninflation

Swap break-eveninflation

However, such “back-to-back” transactions could not solve thewhole problem. The size of pension funds’ inflation liabilities, andconsequent hedging demand, was indeed huge and could not bemet by these financing transactions alone. In addition, these projectfinance swaps increased the credit exposure to sectors in which thebanks already had large concentration risk.

As a result, inflation-linked bonds remained the main hedging toolused by banks to hedge inflation swaps with pension funds. This cre-ated structural positions in banks’ trading books, which often causedprice distortions between the bonds and the derivatives markets andalso led to the development of linker asset swaps.

Retail demand and inflation-structured notes

Another important step for the inflation market was the develop-ment of inflation-structured notes, which occurred independentlyof the inflation-hedging activity by pension funds, and did not easethe issue of inflation risk on banks’ trading books (in fact it made iteven worse).

The structure of most inflation-linked bonds is such that infla-tion is cumulated over the life of the bond, and mainly paid in alarge cashflow at maturity. As a result the yearly coupon is gener-ally lower than that for a nominal bond of similar maturity, which isnot an attractive feature for some investors. Another issue is the taxtreatment of the inflation-linked bond. Typically, taxes are due notonly on the yearly coupon but also on the inflation-accrued notionalover the fiscal period, albeit the latter is paid only at maturity.

This lag between the tax and the cashflow payments led banks tostructure inflation-linked structured notes where the accrued infla-tion is paid along with the coupons and the tax is paid at thesame time as the cashflow payments. In this structure, the issuer

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Figure 8.3 Flows of a bank hedging the inflation cashflows of astructured note

2%+ inflation + inflation YoY floor

2%+ inflation + inflation YoY floor

Noteissuers

BankNotebuyer

Floating rate Cash at inception

typically hedges inflation risk by entering an inflation swap with aninvestment bank via another inflation swap (Figure 8.3).

Such hedges transferred the inflation risk into the banks’ trad-ing books. In a similar way as before, banks bought linkers tohedge the risk. However, an important difference in the pensionfunds’ case is that the maturity of the structured notes was usuallyshorter (typically five years), which created additional demand forshort-maturity inflation bonds. This demand was met by govern-ment issuers such as the Italian Treasury, which issued one of thefirst short-dated inflation-linked bonds, contributing to improvedliquidity at the short end of the real curve.

All these developments focused the market on the need to activelymanage and efficiently transfer inflation risk, leading to the birth ofthe interbanking market for inflation swaps.

UNDERSTANDING THE INFLATION SWAP MARKET

Inflation swaps developed on the back of pension funds’ hedg-ing activities. Therefore, it is not surprising that the swaps stan-dard adopted by the interbank market is close to the structureused in hedging pension liabilities. Typically, pension funds’ cash-flows grow with the inflation rate. An inflation swap exchanges theunknown inflation rate into a market-determined fixed rate.

Zero-coupon inflation swaps

A zero-coupon inflation swap (ZCIS) involves the one-off exchangeat maturity of an inflation-linked cashflow versus a fixed amount.The counterparty receiving inflation will be compensated for thecumulative inflation accrued over the term of the swap against thepayment of amount accruing at a fixed rate, agreed upon at incep-tion. This rate is equivalent to the average annual forward inflationrate over the period. Note that the maturity of the swap can be very

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Figure 8.4 ZCIS quotes as of July 26, 2011, for the French and theEMU HICPs (Bloomberg tickers: FRCPXTOB and CPTFEMU)

Figure 8.5 ZCIS cashflows

Bank Counterpart

(1 + 2.285%)10

CPI(10Y – 3M)

CPI(today – 3M)

long, from one year to up to fifty years, which is not surprising aspension funds’ liabilities are long term in nature.

As an example, consider the 10Y EMU (European MonetaryUnion) inflation swap. According to the quote circled in Figure 8.4, abank will agree to receive the 2.285% ask rate in exchange for realisedinflation over the course of the swap, both compounded to and paidat the final maturity date, 10 years from inception. Note that realisedinflation measured by the change in the CPI values with a lag of threemonths (3M). Other conventions exist as shown in Table 8.1. See Fig-ure 8.5 for a representation of the swap cashflows, and Table 8.1 fora summary of different market conventions.

Year-on-year inflation swaps

A common variation to zero-coupon swap is the year-on-year (YoY)inflation swap, mirroring the cashflows of the structured inflation-linked notes introduced before. For example, in a YoY swap, thereceiver of inflation will be paid the index return each year untilmaturity (usually with a lag, as before). Clearly, the pricing of such

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Table 8.1 Different market conventions for inflation swaps

EMU France US Japan UK Australia

CPI Ex-tobacco Ex-tobacco CPI Ex-fresh RPI All RPI AllHICP CPI urban food CPI items items

Unrevised Unrevised Unrevised Unrevised Unrevised UnrevisedNSA NSA NSA NSA NSA NSA

Source Eurostat INSEE BLS MPM ONS ABS

Bloomberg CPTFEMU FRCPXTOB CPURNSA JCPNGENF UKRPI AUCPI<Index> <Index> <Index> <Index> <Index> <Index>

Frequency Monthly Monthly Monthly Monthly Monthly Quarterly

Swap inflation index Straight∗ Daily∗∗ Daily∗∗ Daily∗∗ Straight∗ Straight∗

Lag 3M 2M–3M 2M–3M 2M–3M 2M 1Q

Liquidity High Medium High Low Medium Medium

∗The swap index changes once a month. ∗∗The swap index is calculated daily as a linear interpolation between two consecutive inflation indexes.

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cashflows requires a forward Consumer Price Index (CPI) curve, asthe future YoY inflation rate at time t is defined by

YoY(t) = CPI(t− lag)CPI(t− 1Y− lag)

− 1

Part of the forward CPI curve can be derived directly from the zero-coupon swap rates (ie, for the maturities for which ZCIS are quoted).If we take the example of the previous section, we can calculate the10Y forward CPI with a three-month lag from the quoted price of the10Y ZCIS 2.285% as follows (note that the initial index CPI(today−3M) is a known quantity, which is worth 112.75 in the example)

CPI(10Y− 10M) = CPI(t− 3M)(1+ 2.285%)10

= 112.75(1+ 2. 285%)10

= 141. 33

However, these yearly points are incomplete and need to be ex-tended to monthly or daily points in order to recover the wholepricing curve, a topic covered in the next subsection.

Convexity adjustments in YoY inflation swaps

Prices of YoY swaps are not really observable, but can be derivedfrom ZCIS prices, although appropriate convexity adjustments arerequired. These adjustments come from the fact that the YoY inflationswaps (YYISs) can only be partially hedged with a portfolio of ZCISs,as we shall see later. These mismatches are quantified by using spe-cific stochastic models. Each trader has their own model and cali-bration techniques. As a result, the adjustments, and therefore thepricing of YoY swaps, can differ materially.

Incidentally, at-the-money (ATM) YoY inflation option prices alsodiffer, given the lack of consensus on the pricing of the underlying.Indeed, the strikes of YoY inflation options are expressed in absolutelevels (typically −2%, −1%, 0%, 1%, 2%, 3%, 4%, 5%) and not as aspread relative to the current ATM level, as is the case for mostoptions on nominal yields (for example, ATM +50 basis points).

An intuitive way to understand the convexity adjustment is toanalyse how to hedge a YYISs with ZCISs, which trade in the inter-banking market. As an illustration, we shall consider the 10Y cash-flows of a YYIS, where the inflation leg is based on the yearly inflation

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Figure 8.6 Hedging a YoY swap with two ZC swaps

Portfolio: YoYinflation swap

Hedge with twoZC inflation swaps

Reinvestment rate r9

9Y

10Y

10Y1.94%

I9 / I0

I10 / I9

I10 / I0

2.2%

1.97%

Figure 8.7 Impact of changes in BEI9 and BEI10 (parallel shift) on theglobal P/L for a notional of 100M: positive convexity

2.0

1.5

1.5

1.0

1.0

0.5

0.5

0

0

0

–1.0

–1.0

–100

–200

–300

–1.5

–2.0

–0.5

–0.5

Mill

ions

300

200

100

Long

por

tfolio

, sho

rt h

edge

(th

ousa

nds)

Long portfolio,short hedge

–1.5Change in 9Y and 10Y BEI (parallel shift, %)

Portfolio

Hedge

rate, which will accrue between 9Y and 10Y; we denote this stochas-tic cashflow by YoY9,10. The question is: what is today’s value of thiscashflow or the break even inflation rate (denoted by BEI9Y,10Y)?

1. The bank portfolio to be hedged consists of a short positionin a YoY9,10 swap. In other words, in 10 years’ time, the bankpays I10/I9 − 1 (where I9 and I10 are the stochastic 9Y and 10Yforward inflation indices) and receives BEI9Y,10Y (a level that isdefined today). Clearly, the profit or loss (P/L) of this positionis proportional to the change in I10/I9.

2. The hedge consists of two ZC swaps.

(a) Short 9Y ZCIS: the bank pays I9/I0 and receives today’sBEI9 in nine years.

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Figure 8.8 Impact of a positive correlation between I9 and thereinvestment rate r9: negative convexity

1.51.00.50

0

–1.0

–100

–150

150

–50

50

–200–0.5

200

100

Tho

usan

ds

–1.5Change in 9Y and 10Y BEI (parallel shift, %)

Long portfolio, short hedge

PortfolioHedge

Figure 8.9 Inflation zero-coupon and YoY forward inflation curvescalculated using linear and cubic spline interpolation

0 5 10 15 20 25 30 35 40 45 50

LinearYoY forward cubic splineYoY forward linearCubic spline

3.1

2.9

2.7

2.5

2.3

2.2

1.9

1.7

Maturity (years)

For

war

d in

flatio

n ra

te (

%)

(b) Long 10Y ZCIS: the bank receives I10/I0 and pays today’sBEI10 in ten years, where I0 is today’s known inflationindex.

The P/L is proportional to the change in the expected value of bothI10 and I9, and the one-year reinvestment rate r9 of the 9Ynet cashflowinto 10Y (Figure 8.6).

The two main sources of convexity are the following.

1. Figure 8.7: the hedge P/L is proportional to the change in theexpected value of I9 and I10 , whereas the YoYswap P/Lis not (it

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depends only on the ratio I10/I9). A parallel shift up or down ofboth BEI9 and BEI10 (a frequent move) will increase (decrease)the portfolio P/L (non-linear, black line) more (less) than thehedge (linear, grey dashed line). Therefore the combined posi-tion (YoY swap plus hedge) would make money (positive con-vexity) whatever the direction of the parallel move is; this effectshould lower the BEI9,10 (positive convexity correction); themore volatile the BEI is, the higher the convexity correctionwill be.

2. Figure 8.8: the P/Lof the short ZCIS9, that is (1+BEI9)9−I9/I0 isreinvested into 10Y and is negatively correlated to the reinvest-ment rate such that a positive P/L is reinvested at a lower rate,while a negative P/L is reinvested at a higher rate. This effecttranslates into a higher BEI (negative convexity adjustment).

Generally the first effect is higher than the second effect and thereforethe net convexity is usually positive.

Building the yearly forward inflation curveThe first step in building the forward inflation curve is interpolationin between the maturities quoted in the zero-coupon swap market(see the “market mid” column in Table 8.2) and Table 8.3, wheredifferent interpolation methods might be used, such as a simple lin-ear interpolation or a cubic spline methodology (see the fourth andfifth columns in Table 8.2); the latter are typically preferred as theyproduce smoother forward YoY curves (Figure 8.9). Once the yearlyinflation swap rates it are derived, we can calculate the forwardinflation index levels as seen before using the simplified formula(we assume no lag)

CPI(t) = CPI(0)(1+ it)t

Then we can calculate the YoY implied inflation rates, which willneed to be adjusted by a convexity coefficient, as we shall see in thenext section.

Building the monthly forward inflation curveWhen going from the interpolated yearly curve to a more granularmonthly curve, a few new challenges arise.

First, inflation market prices provide poor information for maturi-ties shorter than three years, as inflation swaps are fairly illiquid for

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Figure 8.10 Comparison between an SA and an NSA forward CPIcurve

110

115

120

125

130

135

140

11 13 15 17 19

NSA forward HICPSA forward HICP

those tenors, and there is no liquid real rate product for short maturi-ties either. However, within the one-year horizon, economists’ fore-casts are fairly accurate and can provide some guidance in buildingthe short end of the inflation curve.

Another issue has to do with seasonality, as most indexes used inthe inflation market are non-seasonally adjusted (NSA). In addition,seasonality information can be derived partly from inflation-linkedbonds, but with limited accuracy. Last, seasonality factors changeover time and there is no accepted market standard as to how theyshould be computed.

In Table 8.3, we have chosen to use the latest European CentralBank seasonality factors (European Central Bank 2000) in the sixthcolumn as the best predictors for future seasonality.

Table 8.3 shows an example of calculations where economists’forecasts (third column) are used as a guide to build the short endof the curve (fifth column) until December 2012. From January 2013onwards, the monthly CPI curve is calculated from the yearly for-ward CPI (4th column) implied by the ZCIS prices. The issue is howwe can build monthly CPI from yearly CPI, which are non-seasonallyadjusted (NSA). As Figure 8.10 shows, the seasonality creates anoscillating shape, which prevents interpolation. The solution is firstto make the data seasonally adjusted (SA), by dividing the fifth col-umn by the sixth column to obtain the seventh column (labelled asSA). Then in the eighth column we can interpolate the data to obtainthe monthly SA CPI. In the ninth column we convert the monthlySA CPI back into NSA CPI.

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Table 8.2 ZCIS quotes, forward index levels and YoY inflation rates

Interpolated curve Fwd HICP YoY fwdMarket mid ︷ ︸︸ ︷ HICP ︷ ︸︸ ︷ ︷ ︸︸ ︷ Fwd HICP

Tenor Maturity ICPI Linear Cubic spline Date Linear Cubic spline Linear Cubic spline Cubic spline

0Y 05/2011 112.74 112.74 112.741Y 06/08/2012 1.750 1.872 1.872 05/2012 114.85 114.85 1.87 1.87 114.852Y 05/08/2013 1.770 1.886 1.886 05/2013 117.03 117.03 1.90 1.90 117.033Y 04/08/2014 1.857 1.941 1.941 05/2014 119.43 119.43 2.05 2.05 119.434Y 04/08/2015 1.913 1.969 1.969 05/2015 121.89 121.89 2.05 2.05 121.895Y 04/08/2016 1.975 2.033 2.033 05/2016 124.68 124.68 2.29 2.29 124.686Y 04/08/2017 2.040 2.102 2.102 05/2017 127.73 127.73 2.45 2.45 127.737Y 06/08/2018 2.070 2.140 2.140 05/2018 130.75 130.75 2.37 2.37 130.758Y 05/08/2019 2.107 2.173 2.173 05/2019 133.90 133.90 2.40 2.40 133.909Y 04/08/2020 2.146 2.183 2.182 05/2020 136.92 136.92 2.26 2.26 136.9210Y 04/08/2021 2.173 2.210 2.210 05/2021 140.29 140.29 2.46 2.46 140.2911Y 04/08/2022 2.260 2.262 05/2022 144.16 144.19 2.76 2.78 144.1912Y 04/08/2023 2.201 2.310 2.310 05/2023 148.28 148.28 2.86 2.84 148.2813Y 05/08/2024 2.314 2.330 05/2024 151.79 152.09 2.37 2.57 152.0914Y 04/08/2025 2.319 2.329 05/2025 155.40 155.62 2.38 2.32 155.6215Y 04/08/2026 2.242 2.323 2.323 05/2026 159.10 159.10 2.38 2.24 159.10

Trading date: August 3, 2011. Settlement date: August 4, 2011.Yearly tenors.

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Table 8.2 (Cont.)

Interpolated curve Fwd HICP YoY fwdMarket ︷ ︸︸ ︷ HICP ︷ ︸︸ ︷ ︷ ︸︸ ︷ Fwd HICP

Tenor Maturity mid Linear Cubic spline Date Linear Cubic spline Linear Cubic spline Cubic spline

16Y 04/08/2027 2.332 2.324 05/2027 163.03 162.83 2.47 2.35 162.8317Y 04/08/2028 2.341 2.333 05/2028 167.09 166.86 2.49 2.47 166.8618Y 06/08/2029 2.351 2.346 05/2029 171.28 171.13 2.51 2.56 171.1319Y 05/08/2030 2.360 2.359 05/2030 175.61 175.57 2.53 2.59 175.5720Y 04/08/2031 2.283 2.369 2.369 05/2031 180.07 180.07 2.54 2.57 180.0721Y 04/08/2032 2.371 2.374 05/2032 184.43 184.53 2.42 2.48 184.5322Y 04/08/2033 2.374 2.376 05/2033 188.90 188.97 2.42 2.41 188.9723Y 04/08/2034 2.376 2.376 05/2034 193.49 193.46 2.43 2.38 193.4624Y 06/08/2035 2.379 2.377 05/2035 198.20 198.11 2.43 2.40 198.1125Y 04/08/2036 2.298 2.381 2.381 05/2036 203.03 203.03 2.44 2.49 203.0326Y 04/08/2037 2.395 2.390 05/2037 208.62 208.36 2.75 2.63 208.3627Y 04/08/2038 2.409 2.404 05/2038 214.41 214.10 2.78 2.75 214.1028Y 04/08/2039 2.424 2.420 05/2039 220.43 220.20 2.81 2.85 220.2029Y 06/08/2040 2.438 2.436 05/2040 226.69 226.59 2.84 2.90 226.5930Y 05/08/2041 2.377 2.452 2.452 05/2041 233.18 233.18 2.86 2.91 233.18

Trading date: August 3, 2011. Settlement date: August 4, 2011.Yearly tenors.

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Table 8.3 Building a granular forward inflation curve

NSA Seasonals SA Fwd SA Fwd NSA NSA SATenor CPI Fwd Fwd CPI 2010 CPI CPI MoM MoM MoMmonth (publ.) Forecasts CPI Forecasts ECB (incomplete) Linear Fwd CPI (%) (%)

May 10 109.71 109.71 1.0044 109.23 109.23 109.71Jun 10 109.70 109.70 1.0044 109.22 109.22 109.70 −0.08 −0.1Jul 10 109.32 109.32 0.9996 109.36 109.36 109.32 1.55 −4.1Aug 10 109.54 109.54 0.9999 109.56 109.56 109.54 2.12 2.4Sep 10 109.77 109.77 0.9998 109.79 109.79 109.77 2.63 2.5Oct 10 110.15 110.15 1.0011 110.02 110.02 110.15 2.57 4.2Nov 10 110.27 110.27 0.9998 110.30 110.30 110.27 3.01 1.3Dec 10 110.93 110.93 1.0005 110.87 110.87 110.93 6.43 7.4Jan 11 110.11 110.11 0.9921 110.99 110.99 110.11 1.28 −8.5Feb 11 110.57 110.57 0.9939 111.25 111.25 110.57 2.86 5.1Mar 11 112.11 112.11 1.0007 112.03 112.03 112.11 8.76 18.1Apr 11 112.75 112.75 1.0040 112.30 112.30 112.75 2.94 7.1May 11 112.74 112.74 112.74 1.0044 112.25 112.25 112.74 −0.59 −0.1Jun 11 112.75 112.75 1.0044 112.26 112.26 112.75 0.14 0.1Jul 11 112.25 112.25 0.9996 112.30 112.30 112.25 0.37 −5.2Aug 11 112.71 112.71 0.9999 112.73 112.73 112.71 4.70 5.0Sep 11 113.24 113.24 0.9998 113.26 113.26 113.24 5.88 5.8Oct 11 113.67 113.67 1.0011 113.54 113.54 113.67 2.98 4.7Nov 11 113.74 113.74 0.9998 113.77 113.77 113.74 2.43 0.7Dec 11 114.19 114.19 1.0005 114.13 114.13 114.19 3.89 4.9

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STable 8.3 (Cont.)

NSA Seasonals SA Fwd SA Fwd NSA NSA SATenor CPI Fwd Fwd CPI 2010 CPI CPI MoM MoM MoMmonth (publ.) Forecasts CPI Forecasts ECB (incomplete) Linear Fwd CPI (%) (%)

Jan 12 113.08 113.08 0.9921 113.98 113.98 113.08 −1.54−11.1Feb 12 113.38 113.38 0.9939 114.08 114.08 113.38 1.00 3.2Mar 12 114.65 114.65 1.0007 114.57 114.57 114.65 5.30 14.3Apr 12 115.05 115.05 1.0040 114.59 114.59 115.05 0.25 4.3May 12 115.09 114.85 115.09 1.0044 114.59 114.59 115.09 −0.07 0.4Jun 12 115.15 115.15 1.0044 114.65 114.65 115.15 0.66 0.6Jul 12 114.49 114.49 0.9996 114.54 114.54 114.49 −1.18 −6.7Aug 12 114.73 114.73 0.9999 114.75 114.75 114.73 2.22 2.5Sep 12 115.16 115.16 0.9998 115.18 115.18 115.16 4.68 4.6Oct 12 115.43 115.43 1.0011 115.30 115.30 115.43 1.20 2.9Nov 12 115.38 115.38 0.9998 115.41 115.41 115.38 1.15 −0.5Dec 12 115.70 115.70 1.0005 115.64 115.64 115.70 2.43 3.4Jan 13 0.9921 115.82 114.90 1.90 −8.0Feb 13 0.9939 116.00 115.29 1.89 4.1Mar 13 1.0007 116.17 116.25 1.71 10.4Apr 13 1.0040 116.35 116.81 1.89 6.0May 13 117.03 117.03 1.0044 116.52 116.52 117.03 1.82 2.3Jun 13 1.0044 116.72 117.23 2.11 2.1Jul 13 0.9996 116.92 116.87 2.04 −3.6Aug 13 0.9999 117.12 117.11 2.10 2.4Sep 13 0.9998 117.33 117.30 2.10 2.0Oct 13 1.0011 117.52 117.66 2.03 3.7Nov 13 0.9998 117.73 117.70 2.09 0.4

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From this curve, the inflation cashflows of most “vanilla” infla-tion products can be calculated and priced. However, more com-plex cashflows, which involve non-linear payouts or are based ona forward starting index, require a full distribution and correlationstructure. Some of this information can be extracted from inflationoptions, the topic of the next section.

INFLATION OPTIONS: A HISTORICAL PERSPECTIVEThis section will focus on options, in particular zero-coupon andYoY inflation caps and floors, which are the most liquid inflationoptions. We shall not cover more exotic instruments such as optionson real yields, inflation swaption or hybrid inflation options, whichwould add too many dimensions to fit within one chapter. Readersinterested in a more complete analysis can refer to Bénaben andTabardel (2008) and Brigo and Mercurio (2006).

Floors in inflation-linked government bondsWhen the US and France issued their first inflation-linked bonds inthe late 1990s, they embedded an inflation floor for the principalpayment at maturity. As some large institutional investors can onlyinvest in bonds that pay a guaranteed principal amount at maturity,but cumulated inflation can in principle be negative, these issuersadded a principal protection in the form of an inflation floor. In otherwords, at maturity T, the investor in the inflation-linked bond issuedat t = 0 receives

max[

I(T)I(0)

, 100%]× notional

where I(t) is the inflation index at the maturity of the linker and I(0)is the inflation index underlying the linker. In practice, these defla-tion floors were given little attention, as their value was perceivedto be negligible, because most countries were experiencing inflationrates within the range targeted by their monetary policies, and adeflation episode would have to persist for a long time to affect theredemption floor of long-maturity linkers.

In fact, both traders and investors regularly ignored these optionswhen valuing the linkers,3 and in the rare cases where they triedto account for them explicitly, the models used were typically cal-ibrated on historical data (when inflation was positive and stable),so the risk was underestimated and not managed correctly.

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Figure 8.11 Issuance of YoY inflation structured notes

5,000

10,000

15,000

20,000

25,000

1988

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

Sum

of U

S d

olla

rs (

mill

ion)

equ

ival

ent

Year of issuance

0

US CPIUK RPISwedish CPISpanish CPINot specifiedItalian CPIIcelandic CPI

Colombian CPIChilean CPI

Eurozone HICP (ex tobacco)Eurozone HICP (inc tobacco)

Brazilian IPCABasket

Source: Bloomberg, New Sky Capital, BNP Paribas.

The complacency from the world of practitioners did not pre-vent the academic world from working on a modelling frameworkfor valuing these options. For example, Robert Jarrow and YildirayYildirim (2003) published on this topic, and provided a mathematicalformulation of how to the price the inflation floor.

The structured inflation notes market and YoY inflation options

Inflation trading desks started to look carefully at such models grad-ually, as the option risks on their books grew, which happenedhand in hand with the development of the inflation-structured notes

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market. As mentioned before, strong retail demand developed (par-ticularly in Italy) for inflation-protected structured notes. To meetthis demand, investment banks helped issuers to structure inflation-linked notes, with a typical maturity of around five years and anannual coupon, comprising a fixed rate (say, 2% for our illustra-tion) plus the realised year-on-year inflation. As a coupon cannot benegative, the coupon paid at t was

max[2%+ YoY(t), 0]

In other words, the annual coupons had an embedded inflation floorat −2%. The issuers of such notes did not carry the inflation risk,which was transferred to the trading books of the investment banksvia a swap. In other words, the investment banks were paying thisfloored inflation to the issuers. In the absence of an inflation optionmarket, these floors were priced based on historical data, whichgenerally covered a period a relatively stable positive inflation. Asa result, the cost of such floors, as well as their risk, was under-estimated. Indeed, many banks kept these short floor positions par-tially unhedged, with only limited reserves set aside to cover theevent of an increase in value (a loss on the short position). Overtime, the inflation-structured notes market grew significantly (Fig-ure 8.11), due in part to the rise in commodity prices and its impacton inflation.

These products became particularly popular with retail investorsin Europe and in the US.As shown in Figure 8.11, the peak of issuancecorresponds to 2007 (a year during which oil prices doubled) and thefirst half of 2008 (when oil prices increased by about 50%). Becauseof this large amount of issuance, banks accumulated large short-option positions, mainly in YoY inflation floors struck at 0%. As therisk grew, banks turned to other banks and brokers to offset theirexposure, which then gave birth to the interbank option market.This is the main reason why the YoY format remains the most com-mon structure in the inflation option market, in contrast to the swapmarket, where the zero-coupon structure (similar to the cash bond)tends to prevail.

The hard awakening of risk management in inflation optionbooksThe inter-broker market had an important consequence: it providedmarket prices for inflation options. As a result, the positions in banks

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Figure 8.12 Change in delta while BEI decreases for 1M YoY floor

–4 –3 –2 –1 0Change in BEI levels (%)

0

–100

–200

–300

–400

–500

–600

–700

Cha

nge

in d

elta

(in

€)

for

a 1M

10Y

YoY

0%

floo

r

books started being marked-to-market, and the banks started hedg-ing their trading book more actively. However, all banks had sim-ilar positions: they were short YoY floors and, consequently, theycould not really cover their exposures in the interbank market. Thatled most banks to partially hedge these options, more precisely to“delta hedge” the options; they sold a quantity of the underlyinginflation swap (by paying inflation and receiving a fixed rate), suchthat the option price was immunised against changes in the price ofthe underlying swap. Like in any option the delta hedge ratio varieswith the proximity to the strike price. Most of the floor levels werearound 0%, therefore the closer the BEI was to 0%, the more inflationswap the banks had to sell to hedge the delta of the option.

As long as the BEI levels were stable at around 2% or 3%, thishedging strategy worked well, with the banks pocketing the carryof these options. Indeed, the issuance of YoY structured notes keptrising until 2008. After the collapse of Lehman Brothers, the liquiditycrisis forced the trading books to sell most of their inflation-linkedbonds, causing BEI levels to collapse to unprecedented levels. Forexample, in the US, the market was pricing deflation over a 10-yearhorizon! The drop in BEI levels was also exacerbated by the hedg-ing of these floors. In fact, as the BEI started decreasing and gotcloser to the 0% strike, inflation option desks had to adjust theirdelta hedge by selling more inflation swaps (Figure 8.12). This putfurther pressure on BEIs, which in turn forced the inflation optionbooks to sell more swaps, and so on. This vicious circle caused huge

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losses in inflation trading desks, and the issuance of YoY structurednote plummeted.

This episode shows how the tail risk in 0% strike inflation floorswas given little attention, and led banks to concentrate one-waypositions and implement the same hedging strategy. When the crisishit, this triggered major losses. The irony of the story is that this crisiscaused an unexpected development in the inflation option market,ie, the development of inflation zero-coupon options, which is thetopic of the next subsection.

The development of zero-coupon inflation options

Previously, we discussed how inflation trading books had a shortstructural position in inflation swaps, where banks paid inflationand received a fixed-rate payment. Due to the lack of inflation payersin the swap market, the banks hedged these positions by buyinginflation-linked bonds and selling nominal bonds.

One of the consequences of the liquidity crisis in September 2008was the sudden quasi-closure of the repo market for inflation-linkedbonds. At the same time, the investment banks had to quicklydeleverage their balance-sheet, and one of the ways to do this was toreduce inventory by selling their inflation bonds while trying to buyinflation swaps to hedge their structural short position. This trig-gered one of the biggest disconnections of BEI pricing between thecash and the derivatives market, with bond BEIs becoming muchcheaper than swap BEIs.

Gradually, some institutional and corporate investors took advan-tage of this price disconnection. They bought linkers in asset swaps,where they paid to the banks the inflation cashflow of the bonds;in other words they supplied the banks with inflation via swaps,and received a floating payment or fixed payments that embeddedthe large premium caused by the price distortions. It is importantto stress that this premium was not due to the rise in credit risk butto a distortion of the inflation market. As a result, inflation bondscheapened in asset swaps (see Chapter 7 for an introduction to assetswaps) much more than the nominal bond (both from the same gov-ernment issuer). Over the course of 2009, investment banks sold avery large amount of asset swaps to various institutional and corpo-rate investors and the distortions were partly corrected by the endof the year (Figure 8.13).

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Figure 8.13 The difference between US bond and swap 10Y BEIs from2006 to 2012

180

160

140

120

100

80

60

40

20

0

Bas

is p

oint

s

Mar2006

Mar2007

Mar2008

Mar2009

Mar2010

Mar2011

Mar2012

Figure 8.14 How selling the asset swap partly hedges the shortpension fund inflation swaps and the short YoY floors

BanksPension

fundsASWbuyer

Inflationbond

issuers

1.

Floatingrate

Fixedrate

Inflation

2.

1. Debt: real cashflows plus inflation plus redemption inflation floor. 2. Swap: realcashflows plus inflation plus inflation floor.

What is the connection between the asset swap market and theoption market? In fact, by selling asset swaps the banks bought somezero-coupon inflation options. Indeed, they received the cashflowsof the linkers via swaps and for most linkers the final cashflows werefloored. This fixed not only the issue of hedging the pension fundswaps but also, partly, the short YoY floor positions (Figure 8.14).

A long ZC inflation floor position partly hedges a short YoY floorposition. Intuitively, the CPI ratio of a ZC inflation swap is the prod-uct of CPI ratios of YoY Inflation swaps. Taking the logarithm of thisproduct, we get

ln(

CPI(T)CPI(0)

)

= ln(

CPI(T)CPI(T − 1)

)+ ln

(CPI(T − 1)CPI(T − 2)

)+ · · · + ln

(CPI(1)CPI(0)

)

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Figure 8.15 YoY caps and floors quotes (euro HICP)

Sources: Bloomberg, Tullett Prebon.

Taking the variance of the equation, we see that the ZC inflationvolatility is connected to the YoY volatilities and their correlation (seeBelgrade et al (2004) for the mathematical treatment of this topic).

UNDERSTANDING THE INFLATION OPTION MARKETUnderstanding the YoY inflation optionThe first and most liquid inflation option trading in the interbank-ing market is the YoY inflation cap (floor). A YoY cap (floor) with amaturity T consists of T caplets (floorets).

In other words, the buyer of a YoY cap with a strike K and amaturity T will receive, each year from t = 1 to T, the max(YoY(t)−K, 0) in exchange for an upfront premium.

Figure 8.15 shows a broker screen for such a cap. For example, the10Y 5% YoY cap will cost an upfront premium equal to 2.58% of theoption notional.

The YoY inflation options are the most liquid option (see Table 8.4)but, as we have seen in the previous section, the liquidity of the ZCinflation options rose significantly after 2008 and therefore they havebecome the second pillar of the inflation option market.

Understanding the zero-coupon inflation optionA more recent inflation option in the interbanking market is theZC inflation cap/floor. This option stems directly from the matu-rity floor, which exist in most inflation bonds. A ZC inflation cap

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Figure 8.16 ZC caps and floors quotes (euro HICP)

Source: European Central Bank (2000).

Table 8.4 Assessment of liquidity in inflation swaps (linear) and options(non-linear)

ZC YoY︷ ︸︸ ︷ ︷ ︸︸ ︷Currency Linear Non-linear Linear Non-linear

Euro Good Medium Low GoodSterling Good Low Low MediumUS dollar Good Low/medium Low Medium

(floor) with maturity T consists a call (put) option on the ZC inflationI(t)/I(0) − 1. In other words, a buyer of a ZC inflation cap with astrike K and a maturity T will receive max[I(T)/I(0)−(1+K)T, 0] atmaturity T, in exchange for an upfront premium. Figure 8.16 showsa broker screen for such a cap. For example, the 10Y 5% ZC cap willcost an upfront premium equal to 0.85% of option notional.

Note that this premium is less than that of the 10Y 5% YoY ZCcap. Indeed, the ZC cap is a cap on the average inflation rate over10 years, whereas the YoY cap incudes a caplet for each year. The ZCcap will not protect the buyer if the inflation rate is above 5% for acouple of years but below 5% on average during the 10-year term;the YoY cap will.

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Figure 8.17 BEI rates for 1Y, 5Y, 10Y and 30Y ZC swaps: (a) EMUHICP and (b) US CPI

0–0.5

0.5

1.01.5

2.0

2.5

3.0

3.5

4.0

–5.5

–3.5

–1.5

0.5

2.5

4.5

(a)

(b)

Nov2003

Nov2004

Nov2005

Nov2006

Nov2007

Nov2008

Nov2009

Nov2010

Nov2011

Mar2004

Mar2005

Mar2006

Mar2007

Mar2008

Mar2009

Mar2010

Mar2011

1Y5Y10Y30Y

1Y5Y10Y30Y

Comparison between historical and implied volatility

The historical analysis of inflation options is based on the underlyinginflation swap prices. So, the initial step is to look at the history ofBEI rates for the EMU HICP and the US CPI swaps. In Figure 8.17we identified three periods:

1. a pre-2008 period of relatively stable curves;

2. a sharp drop and steepening of the curves during the 2008crisis; and

3. a partial normalisation from 2009 onwards.

The next step is to analyse the YoY forward BEI rates and their volatil-ity, which is measured by the standard deviation of their changes.

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Figure 8.18 Realised volatility for forward BEI rates (1Y BEI, the 1Y in2Y BEI and the 1Y in 10Y BEI) for (a) the EMU HICP and (b) US CPIinflation swaps

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

12

10

8

6

4

2

0

Rea

lised

vol

atili

ty (

%)

Rea

lised

vol

atili

ty (

%)

Nov2003

Nov2004

Nov2005

Nov2006

Nov2007

Nov2008

Nov2009

Nov2010

Nov2011

Mar2004

Mar2005

Mar2006

Mar2007

Mar2008

Mar2009

Mar2010

Mar2011

10Y CPI2Y CPI1Y CPI

10Y CPI2Y CPI1Y CPI

(a)

(b)

Looking at Figure 8.18 we can see that the peak of volatility occursin 2008.

Note that the YoY volatility presents some jumps; this is partly dueto the fact that the forward curve is extracted from the zero-couponinflation curve. In spite of the smoothing techniques used to derivethis curve, an important issue is the difference of liquidity betweenthe points of the curve. For example the 10Y zero-coupon swap rateis certainly the most liquid point, but the 11Y rate is not so liquidand its level is also dependent on the interpolation methods. These

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Figure 8.19 Comparison of implied YoY at the money volatility of capletand historical volatility for (a) EMU HICP and (b) US CPI

0 5 10 15 20 25 30

0 5 10 15 20 25 30

2.22.01.81.61.41.21.00.80.60.4

%

3.1

2.6

2.1

1.6

1.0

0.6

%

(a)

(b)

•, realised volatility on YoY CPI swaps; , implied volatility on ATM cap/floor onYoY CPI; , power (implied volatility on ATM cap/floor on YoY CPI).

jumps are particularly frequent in the US curve, which is less liquidthan the EMU HICP curve.

Figure 8.19 compares historical and implied volatilities for caplets.The implied YoY ATM volatility curves in the US and the eurozonehave the downward slopes, which implies mean reversion of BEIrates. This is partly reflected in the realised volatility in the eurozone,but not really reflected in the US curve. The US inflation swap isilliquid except for 10Y swaps and, to some extent, the 2Y and 5Yswaps. The liquidity for maturities higher than 10Y is limited due tothe absence of 30Y Treasury Inflation Protected Securities (TIPS) until2010 (which would be the hedging instrument used to hedge longmaturity inflation swaps). This explains why the realised volatilityappears to increase after the 10Y maturity.

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INFLATION OPTION MODELSIn this section we shall detail the evolution of inflation model infinance. We shall focus more on the concepts than on the mathemat-ical formulation (for the latter, see, for example, Brigo and Mercurio2006).

Macroeconomic models of inflationInflation is, above all, a macroeconomic phenomenon, measured bya price index such as the CPI. It is therefore not surprising thatthe first approaches to modelling inflation were the work of macro-economists. An important contribution was the monetary exchangeequation, suggested by Irving Fisher in 1911

Mtv = PtQt

Where Mt is the money supply during year t, v is money velocity(ie, how many times per year each money unit is spent), Pt is theprice of goods and services sold during year t and Qt is the quantityof goods and services sold during year t. From this equation, Fisherderived the so-called “Fisher equation” (see, for example, Belgradeet al 2006)

(1+ i) = 1+ rn

1+ rr

where rn is the nominal rate, rr is the real rate and i is the infla-tion rate. Rewriting this equation with inflation measured by thechange in CPI over period t and using instantaneous continuouslycompounded nominal and real rates gives

ln(

CPI(t)CPI(0)

)= (rn − rr)t

The Fisher equation is key to the financial modelling of inflation,as it defines the CPI as the translation mechanism from the nominalworld and the real world, suggesting the currency analogy discussedin the next section.

The Jarrow–Yildirim model and the currency analogyJarrow and Yildirim (2003) used a Heath–Jarrow–Morton (HJM)model to price TIPS and related derivatives. At that time, the deriva-tives market was in its infancy, and the interbanking market didnot provide any reliable prices for inflation swaps; only TIPS wereliquid enough and their pricing information sufficiently reliable. So

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Figure 8.20 Currency analogy: non-arbitrage conditions

Deposit interest rate rr

Deposit interest rate rn

100

100 CPI(0)

100er,t

100er,t CPI(t )

= exp(rn – rr)t

Forward FX rateCPI(t )

Spot FX rateCPI(0)

Rea

lec

onom

yN

omin

alec

onom

y

CPI(t )CPI(0)

Non-arbitrage

Fisherequation

100er,t CPI(0)

=

it is not surprising that the first models dealt with the inflation struc-ture characteristics of TIPS. In their paper, Jarrow and Yildirim fit-ted their model to TIPS prices, nominal Treasuries prices and theUS CPI. Next, they tested the model for pricing TIPS via its hedg-ing performance and, finally, they used it to price a ZC inflation calloption.

Their approach is an interesting one, as the methodology is basedon an analogy with a currency model. It is illustrated in Figure 8.20.The CPI acts as an exchange rate between the nominal economyand the real economy. Indeed, the forward CPI(t) is defined by non-arbitrage conditions. Specifically, in the real economy, $100, say, isinvested in a deposit at a real rate rr (dotted arrows) until maturity,when the proceeds are converted to the nominal economy at a pre-fixed forward FX rate of CPI(t). Alternatively, $100 is converted intothe nominal economy at the spot FX rate CPI(0) (solid arrows), pro-ceeds are invested at the nominal rate rn. In a non-arbitrage world,the two investments must have the same return, leading us to definethe forward CPI ratio, which measures the return due to inflation asthe differential return between the nominal and real rates; this isprecisely the Fisher equation.

Jarrow and Yildirim added a stochastic component to both nom-inal and real rates, as well as the currency/inflation index. The

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model assumes that the volatilities and correlations are (T − t)dependent but deterministic and historically calibrated (to accom-modate the mean reversion feature of the BEI/downwards volatil-ity curve shown in Figure 8.19). One of the important advantagesof their model was to set the non-arbitrage conditions and to derivea three-factor HJM-type model. The model can be summarised asfollows.

• Real rates and nominal rates are normally distributed and havea non-zero short-term correlation (ρn,r).

• The CPI acts as an exchange rate between the nominal and thereal economy; it has a lognormal distribution and non-zerocorrelation with both nominal and real rates.

• Under the nominal risk-neutral probability Qn we can derivethe prices of both nominal and real bonds, as well as thedynamics of the inflation index, which can be used to priceinflation options (a “cheat sheet” is provided in the appendix;notation conventions, specific formulas and their derivationscan be found in the appendix at the end of the chapter).

Note that, in this model, the expected instantaneous inflation rateis given by the difference between nominal and real instantaneousrates. The model is fitted to the term structure of nominal and realrates and the historical volatility of the CPI.

An alternative calibration exploiting the currency analogy

One of the difficulties of the previous model is its calibration, whichis based on inflation-linked bond yields (as a proxy for real rates).In reality, traded inflation-linked bond yields typically contain aliquidity premium, which is intrinsic to each bond and makes thecalibration tricky. In addition, most inflation-linked bonds (includ-ing TIPS) have a redemption floor (see discussion of these issuesin Chapter 9). Inflation swaps do not have these complications. Infact, an inflation swap is a simple exchange of cashflows at matu-rity. In addition, inflation swaps are quite liquid and thus widelyused to hedge inflation-structured books. This has led to a change ofrisk variables from the triad of nominal rates, real rates and CPI tothe alternative triad of nominal rates, swap BEIs and CPI. The key

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working assumptions are as follows:

• swap BEI rates and nominal interest rates are normally distrib-uted;

• the CPI acts as an exchange rate between the nominal and thereal economy.

We refer the reader to the appendix at the end of the chapter forthe pricing formulas of both nominal and real bonds, and also therelationships linking the old and new set of variables. Note that Brigoand Mercurio (2006) also introduced a model of both nominal andreal interest rates based on the currency analogy, which is similar tothis one.

Market models of inflationThe inflation derivatives market developed a couple of years afterthe seminal model of Jarrow and Yildirim. However, the originalapproach was adapted to the TIPS, but some issues emerged in usingthis approach for some of these new derivatives instruments, suchas (see, for example, Belgrade et al 2004; Mercurio 2005)

• non-observable parameters: inflation rates are derived fromreal rates, but the latter are not directly observable frominflation-linked bonds, for the reasons mentioned earlier,

• there is no obvious link between ZCISs and YYISs,

• the natural discount curve for the options and swaps is theLibor curve.

As a result, new inflation models were devised that mirrored thetechniques used in Libor market models, and are based on informa-tion from the ZCISs and the YYISs in a consistent way. These modelsfocused on a set of forward inflation indexes for selected maturitiesTi, i = 1, . . . , N, ie, CPI(t, Ti) as a lognormal processes under therisk-neutral probability Q

dCPI(t, Ti)CPI(t, Ti)

= µ(t, Ti)dt+ σ(t, Ti)dWQi , i = 1, . . . , N

Different functional choices for the volatilityσ(t, Ti) can be adopted.In addition, under the risk-neutral measure, the zero-coupon nomi-nal bond also follows a lognormal process given by

dB(t, T)B(t, T)

= r(t)dt+ Γ (t, T)dWQB

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The model allows for a much richer correlation structure among the(N + 1) Brownian motions (WQ

i , i = 1, . . . , N; WQB ), than what is

possible in the Jarrow–Yildirim three-factor model.ZC and YoY payouts can be written in terms of the future price

index levels or, alternatively, in terms of the forward index. For exam-ple, a zero-coupon T-maturity payout, be it a swap or an option, isa function of the ratio

CPI(t, T)CPI(T0)

where the denominator has been fixed at trade inception, while thenumerator is unknown before T, and will be determined by thestochastic evolution of the price index CPI(t). The latter can be writ-ten in terms of the stochastic evolution of the forward price indexCPI(t, T) instead, as the two will coincide at t = T. Pricing instru-ments based on ZC payouts requires taking the risk-neutral expec-tations of the discounted terminal payouts. An opportune choice ofnumeraire, ie, adopting the T-forward measure, further simplifiesthings, as the forward price index CPI(t, T) is, by construction, amartingale under such a measure.

Things are a bit more complicated for YoY instruments, where theterminal payout depends on the ratio of two price index levels, bothunknown at

t < T1 < T2CPI(T2)

CPI(T1);CPI(t, T2)CPI(t, T1)

Now there is no clever numeraire choice that can make this ratio amartingale. In other words, convexity adjustments are unavoidablewhen calculating the risk-neutral expectation of the discounted ter-minal payout. Specifically (neglecting lag effects), these will arisefrom the covariance of the two forward price indexes as well as thecovariance of inflation with the nominal discounting entering theexpectation.

As a result, the discounted payment of the YoY(T, T + 1) =CPI(T+1)/CPI(T)−1 must be adjusted for the covariance betweenthe inflation index at the two different times, as well as the covari-ance between the forward discount bond B(T, T+1) and the forwardinflation index.

Mercurio (2005) adopted an alternative market model where bothreal and nominal Libor forward rates for a set of maturities Ti, i =1, . . . , N (thus, 2N Brownian motions) were modelled as lognormalprocesses, and inflation derived from these.

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Using these models, we can derive explicit formulas for infla-tion options that are simpler and more intuitive to calibrate thanthose derived within currency-analogy-based models. Indeed, theadvantage of such models is to allow a rich dependence structurebetween YoY instruments. This has become important as YoY andZC options evolve separately (different players and different flows),which makes this dependence structure more and more complex. Inaddition, it is usually simpler to carry out historical analysis on YoYdata, as there is a relatively long sample which can be used to developintuition about the volatility structure (Figures 8.17 and 8.18).

CONCLUSIONSThe inflation swaps market developed on the back of the hedgingactivities of pension funds. Although pension funds initially boughtinflation-linked bonds, they readily switched to inflation swaps,which could be more easily tailored to the specificity of their liabili-ties. Naturally, an interbank swap market soon developed, for whichthe standard became the zero-coupon inflation swap, the structureof choice of pension funds.

Another important step for the inflation market was the develop-ment of inflation-structured notes, which paid coupons linked to theyear-on-year inflation, and were popular among retail investors inparticular. These instruments were key in the development of YoYinflation swaps and specifically YoY options, as well as an interbankmarket for these instruments. In fact, the YoY format is the standardformat for inflation options, although the zero-coupon structure alsotrades, with less liquidity. Using the example of inflation swaps, weshowed how it is not straightforward to hedge YoY swaps with ZCswaps, as one has to take into consideration important convexityadjustments.

In terms of options, one of the first models was the Jarrow–Yildirim model, which was calibrated using TIPS prices and his-torical inflation data. This is model was based on the currency anal-ogy, with the inflation index modelled as an exchange rate betweennominal and real bonds. Soon, in part motivated by the YoY optionstandard, new approaches came about, which modelled the forwardinflation index in its forward measure (similarly to Libor-marketmodels) and could be calibrated using inflation and nominal swapsand YoY inflation options.

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Although this chapter has covered the key developments in infla-tion market in Europe and the US, inflation instruments (cash andderivatives) have expanded in other countries as well. Inflation-linked bonds have been issued since the 1960s in some Latin Amer-ican countries. There is an active inflation-linked bond and swapmarket in Australia. Thailand and South Korea have both issuedinflation-linked bonds, and products will keep expanding as theirmarkets evolve and their pension systems reach financial maturity.In any case, we expect the stepping stones to be the same: first, thedevelopment of an inflation-linked bond market as the fundamen-tal building block, followed by inflation derivatives, ie, swaps andpossibly options.

APPENDIX

Jarrow–Yildirim currency-analogy-based model

Using the nominal zero-coupon bond as numeraire and its associ-ated probability QN, the dynamics of the prices of the zero-couponnominal (N) and real (R) bonds are given by the following equations(we use a time-decaying volatility model)

dBN(t, T)BN(t, T)

= rN(t)dt+ ΓN(t, T)dWN,QN

B (t) (8.1)

dBR(t, T)BR(t, T)

= (rR(t)− ρR,CPI(t)ΓR(t, T))dt− ΓR(t, T)dWR,QN

B (t)

(8.2)

Γx(t, T) = σx(t)1− exp(−λx(T − t))

λx(8.3)

The CPI acts as an exchange rate between the nominal and the realeconomy

dCPI(t)CPI(t)

= (rN(t)− rR(t))dt+ σCPI dWCPI,QN

t (8.4)

dWCPI,QN

t dWN,QN

t = ρN,CPI dWCPI,QN

t dWR,QR

t (8.5)

Alternative calibration of currency-analogy-based model

Using the nominal zero-coupon bond as numeraire and its associ-ated probability QN, the dynamics of the prices of the zero-couponnominal (N) bond and the break-even inflation swap (I) are given

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by the following equations

dBN(t, T)BN(t, T)

= rN(t)dt− ΓN(t, T)dWN,QN(t) (8.6)

dBI(t, T)BI(t, T)

= ri(t)dt+ µ(t, T)dt− Γi(t, T)dWI,QN(t) (8.7)

dCPI(t)CPI(t)

= ri(t)dt+ σCPI dWCPI,QN(t) (8.8)

when

Γx(t, T) = σx(t)1− e−λx

λx(8.9)

The change from the old projection into the new projection is basedon the following equations

σi =√σ 2

N + σ 2R − 2ρN,RσNσR (8.10)

dWit =

σN

σidWN

t −σR

σidWR

t (8.11)

1 See ‘Indexed Gilts’ (Economic Progress Report No. 133), http://www.hm-treasury.gov.uk.

2 In a “defined benefits” pension fund, the benefits payable can be a function of several factors,such as earnings history, years worked and age, but do not depend on the fund’s investmentreturns.

3 The Japanese case is an exception, as Japan experienced a long deflation period. Notethat Japanese government inflation-linked bonds do not have an embedded inflation floor,although some banks have structured inflation-linked notes with such a floor.

REFERENCES

Belgrade, N., E. Benhamou and E. Koehler, 2004, “A Market Model for Inflation”, URL:ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/B04050.pdf.

Belgrade, N., E. Benhamou and E. Koehler, 2005, “Modelling Inflation in Finance”,Inflation-linked Products, Chapter 6 (London: Risk Books).

Bénaben, B. (ed), 2005, Inflation-linked Products (London: Risk Books).

Bénaben, B., and H. Cros, 2008, “Global Inflation Derivatives Markets”, in Inflation Risksand Products, Chapter 11 (London: Risk Books).

Bénaben, B., and S. Goldenberg (eds), 2008, Inflation Risk and Products (London: RiskBooks).

Bénaben, B., and N. Tabardel, 2008, “Inflation-Linked Options”, in Inflation Risk andProducts, Chapter 15 (London: Risk Books).

Brigo, D., and F. Mercurio, 2006, Interest Rate Models: Theory and Practice with Smile, Inflationand Credit, Part VI, Second Edition (Springer).

Davis, E. P., 2000, “Regulation of Private Pensions: A Case Study of the UK”, DiscussionPaper PI-0009, The Pensions Institute, URL: http://www.ephilipdavis.com/wp0009.pdf.

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European Central Bank, 2000, “Seasonal Adjustment of Monetary Aggregates and HICPfor the Euro Area, Aggregates and HICP for the Euro Area”, August (Extract).

Jarrow, R., and Y. Yildirim, 2003, “Pricing Treasury Inflation Protected Securities andRelated Derivatives using an HJM model”, Journal of Financial and Quantitative Analysis38(2), pp. 337–358.

Mercurio, F., 2005, “Pricing Inflation-Indexed Derivatives”, Quantitative Finance 5, pp. 289–302.

Mercurio, F., and N. Moreni, 2006, “Inflation with a Smile”, Risk, March, p. 70.

Peng, W., 2006, “Understanding Inflation Convexity”, IXIS Capital Markets, URL: http://inflationinfo.com/CPICvx.pdf.

Taylor, J. B., 1993, Discretion versus Policy Rules in Practice, Carnegie-Rochester ConferenceSeries on Public Policy, Volume 39, pp. 195–214 (Elsevier).

Wilson Committee, 1980, “Report of the Committee to Review the Functioning of FinancialInstitutions (Chairman Sir Harold Wilson)”, Command Paper 7937 (London: HMSO).

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Part II

Research and MacroPerspective

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9

The Role of Models in ModernMonetary Policy

Stefania A. Perrucci and David VavraNew Sky Capital; OGResearch

The objective of most central banks is to maintain price stabilitywhile promoting stable economic growth and employment. To thisend, central banks adopt a systematic approach, ie, a monetary pol-icy regime, which typically differs from country to country. Sincethe early 1990s, inflation targeting (IT) has been part of the mone-tary policy regime of many central banks, contributing credibilityto their efforts, and helping to keep inflation under control in manycountries for the following two decades. In IT regimes, the mainfocus is on the interest rate/monetary policy instrument path that isconsistent with keeping inflation within range, or bringing inflationback to target.

In this chapter, we examine the types of model central banks build,and how they operate them. Usually, central banks maintain a wholesuite of models, referred to as a forecasting and policy analysis sys-tem (FPAS). These models have different capabilities, with statis-tical/empirical models typically employed for short-term analysisand structural/behavioural models used for longer-term horizons.We describe the different components of an FPAS, including the cen-tral core model, the models used to determine initial conditions, theways in which exogenous variables enter the forecasting process andthe judgemental inputs that might be used along the way.

Finally, we discuss how FPASs are used in practice. Simply put,macroeconomic forecasts are never perfect, but, despite their limita-tions, models provide an important tool, assisting central banks inmaking the best policy decisions under unavoidable uncertainty.

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MODELS AND MONETARY POLICY

The legal mandate of most of the central banks at the time of writingis maintaining price stability (which is usually the overriding goal)while avoiding instabilities in real economic activity and employ-ment (which is usually a secondary goal subordinate to price sta-bility, although this is not true in all countries, as we shall seeshortly).

To achieve its goals, every central bank chooses its mode of oper-ation, ie, a monetary policy regime. Traditional monetary policyregimes include various forms of exchange rate management (a peg,a crawling peg or a band) or monetary targeting. Another traditionaloption is a so-called eclectic mix. Under the traditional regimes, cen-tral banks adopt an operational or intermediate variable (the spotexchange rate against a particular currency, or year-on-year growthin a particular monetary aggregate) and set and manage targets forthis operational variable with the aim of maintaining price stabil-ity. Although the links between such intermediate targets and pricestability are neither clear nor necessarily stable and predictable,these operational targets are under more or less direct control ofthe central bank. As a consequence, the central banks under theseregimes devote most of their analytical capacity to designing theiroperations (such as foreign exchange interventions or local moneysupply procedures) to meet the set intermediate targets efficiently.Broader macroeconomic analysis plays a rather secondary role, sim-ply because it is out of the scope of the bank’s core business; whenconducted, the analysis is often dominated by a very short-termoutlook and in-depth sectorial detail.

In the early 1990s, a brand new approach to monetary policyemerged: inflation targeting. Invented and first implemented by theReserve Bank of New Zealand in 1990, it quickly spread into manyother countries, both advanced economies and emerging markets.At the time of writing, the number of IT central banks stands at afew dozen, with a single abandoner so far,1 not including those thatjoined the eurozone as abandoners for obvious reasons.

What is different about IT?2 First, intermediate targets are aban-doned and the central bank’s attention is focused directly on pricestability (and other secondary goals as applicable). Second, IT tendsto involve more active management, especially when a big price

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Figure 9.1 Reserve Bank of New Zealand 90-day interest rate forecast

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shock occurs. Third, IT is more transparent and consistent, as mon-etary policy is committed to targeting a specific price level or rangeof price levels. Typically, the specific target is set in terms of theheadline Consumer Price Index (CPI) or core CPI, or the headlineor core Personal Consumption Expenditure (PCE) prices index. Thetarget itself is most often set not by the central bank alone, but ratherby the government or by agreement by both. The central bank thencommits to using available policy instruments (almost exclusivelythe short-term interest rate, such as the two-week repo) to respondto economic shocks and induce inflation to return to target over amedium run.3

The success of IT hinges on the capacity of the central bank to reactwith the appropriate policy instrument to developments expectedin the future. Today’s actions have to ensure that inflation returns tothe target level at a given horizon, given the most plausible assump-tions. In doing so, small short-term disturbances are often ignored,as the focus is on the medium-to-long-term risk of inflation. Obvi-ously, this requires a good understanding of policy transmission andits lags (which typically range between four and eight quarters, ie,one to two years). Such a task puts enormous pressure on forecast-ing capacity, and on the ability to make decisions under uncertainty.Almost any central bank produces various kinds of economic fore-casts, but many use them only as an indicative macroeconomic out-look and in conjunction with several other inputs. By contrast, in an

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Figure 9.2 Sweden’s Riksbank repo rate forecast with confidencebands (in percent)

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Figure 9.3 Norges Bank policy rate forecast and confidence bands (inpercent)

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IT regime, forecasts become an essential backbone for the decision-making process. Furthermore, there is an intricate complexity aboutthese forecasts. Their main focus is typically not directly on infla-tion but on the trajectory of interest rates. If you look at the inflationforecast charts that IT central banks produce every quarter, you willnote that it is not a very interesting chart: inflation always returns tothe target level sooner or later. The more important chart shows thetrajectory of interest rates that is consistent with this inflation profile,ie, the trajectory consistent with bringing inflation to target under

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Figure 9.4 Czech National Bank three-month Pribor rate forecast andconfidence bands (in percent)

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Figure 9.5 Bank of Israel interest rate forecast and confidence bands(percentage)

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most plausible assumptions. At the time of writing in spring 2012,at least five central banks (the Reserve Bank of New Zealand, Swe-den’s Riksbank, Norges Bank, Czech National Bank and the Bankof Israel) publish their quarterly forecasts together with the futureprojections for their own policy rates (and, with the exception ofthe Bank of Israel, also projections for their exchange rates), whilemost other IT central banks work with such interest rate trajectoriesinternally for policy decisions (Figures 9.1–9.5).

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What do these interest rate trajectories mean? First, for an ITcentral bank’s forecast to make sense, it must have a particular pathfor the monetary policy instrument built into it, and the policy ratepath must obviously be consistent with the rest of the forecast. Sec-ond, the fact that the four central banks publish future short-terminterest rates and exchange rates does not, by any means, implycommitment to these paths. The projections are instead conditionalstatements: given the information on the state of the economy avail-able at the time, this is the most likely course of monetary policy inthe future. And, remarkably, thanks to the clear long-term communi-cation strategies of these banks, aided greatly by their model-basedanalytical frameworks, market analysts, investors and the generalpublic have come to understand very quickly in these countrieswhat message these conditional statements convey. Constructingsuch an interest rate trajectory is not possible without a fairly elabo-rate and model-based forecasting system. This is exactly why centralbanks started developing new types of model, ie, models that tell ussomething about the medium-term forces driving inflation and othermacroeconomic variables, provide key insights and facilitate coher-ent narratives, and allow true policy analysis. Short-term outlooks,detailed information and very accurate statistical properties mightbe still useful, but they are neither a sufficient nor the most essentialinput into policymaking.

Are models all that there is to it? Certainly not, as monetary policyanalysis, economic forecasts and human judgement will always becrucial factors. But models are of great help to the policymaker. Whenbuilt and used properly (and this is a crucial qualification), modelshelp central bank staff to process a large amount of information in aconsistent way and to draw logical conclusions. Most importantly,the use of models increases transparency and encourages communi-cation about policy issues, both inside and outside the central bank.The implications of various risk factors, costs of policy errors andchanges in forecasts from quarter to quarter can quickly be analysedusing a model. This greatly facilitates openness, and thus strength-ens policy credibility. Thus, by facilitating policy debates, model-based forecasting systems help central bankers to be transparent,predictable and accountable: crucial elements of success for an ITcentral bank. Indeed, if people understand what the central bankis doing now and will do next (transparency and predictability),

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why the bank is doing it and how the bank learns from its ownmistakes (accountability), it is much easier to affect and ultimatelyanchor expectations on the inflation target. In turn, if expectationsare anchored, then the actual outcomes will become more favourableand stable.

This new approach to policy making could not be in a starkercontrast with the older paradigm. In the past, monetary policy wasbelieved to be most efficient if it was based on unexpected surprises(in fact, there is still a relatively large amount of academic researchnowadays that finds the so-called “money supply shocks” the propermonetary policy tool to investigate), and assumptions about system-atic behaviour of policy rates had no role in economic projections.There also seems to be a widening gap between the practices ofbanks that have an explicit inflation target and those who do not,most notably the central banks behind the two major currencies: theEuropean Central Bank and the US Federal Reserve System. It is hardto believe that the first ever press conference by the US Fed’s Chair-man occurred only in April 2011, and documents explaining the Fedstaff projections were only released with a six-year lag, until the deci-sion to make forecasts available to the public in January 2012. Untilthen, the US Fed communication strategy had been in sharp contrastwith one of the other central banks, for which making regular publicappearances, publishing full-fledged reports immediately after pol-icymaking meetings and posting models and other analytical toolson websites had been routine practice for a long time. There can beno wonder that markets were very surprised and rather confused tohear Ben Bernanke say in his press release4 that

economic conditions… are likely to warrant exceptionally lowlevels for the federal funds rate for an extended period.

Because it was not properly explained, and such a statement hadnever been heard before, it was, unsurprisingly, considered bymany as an unconditional commitment, and provoked considerablecontroversy.

The ECB appears to be somewhat closer to accepted best practice,having an explicit inflation objective of 2% in the rate of change inthe Harmonized Index of Consumer Prices (HICP), the eurozone’saggregate measure of inflation. However, the ECB resists definingitself as exclusively an inflation targeter (an interesting reading is

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Issing 2008). Instead, the bank relies officially upon a so-called two-pillar strategy, consisting of “economic analysis” and “monetaryanalysis”. This gives its policy a traditional money-targeting flavourto some extent. The ECB staff finds, nevertheless,

the assumptions about short-term interest rates… [to be] of a purelytechnical nature.

(European Central Bank 2011)

FORECASTING AND POLICY ANALYSIS SYSTEMS

Given how useful macroeconomic models have proven to be in mod-ern monetary policymaking, we now turn to the question of whatmodels central banks build, and how exactly they operate them. Firstof all, even though the whole point of building models is to improvethe ability to combine all the pieces of available information in a con-sistent manner, common and best practice is actually not to have oneuniversal model of everything, ie, covering every possible aspect ofthe economy. This is mainly because models (and macroeconomicmodels in particular) are not meant to capture the whole universeof economic phenomena at once, but should help in gaining specificinsights and provide better understanding of the economy. Not onlydo overly complex and detailed models get rather impractical froman operational point of view, but their ability to tell understand-able stories quickly diminishes as complexity increases. In addition,when a model’s level of detail becomes overwhelming, both cen-tral bank staff and end users (ie, policymakers) have the tendencyto fine-tune various trivialities,5 while not attending sufficiently tobroad-picture issues that are of first-order importance.

Typically, central banks maintain a whole suite of models andother tools, each with a clearly defined role, and design processesto combine the strengths of the individual models, to make effectiveuse of all information available at a given time and to make sure thatthe final product is not a simply mechanical model forecast. Such acollection of models and processes is referred to as a forecastingand policy analysis system. Most of the models within the suite arebuilt to complement one another, including providing alternativeor competing views on the same matter. We shall now describe thedifferent models typically found in an FPAS, and explain the mostcommon steps during the forecasting process.

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Figure 9.6 Different forecasting horizon and modelsR

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The structure of many of the model-based systems existing in centralbanks is based on the observation that different methods are suitablefor different things. This is perhaps most evident when we lookat the forecasting horizons applicable to different types of model.Figure 9.6 illustrates the point, showing how statistical models tendto have better prediction power for short horizons, while structuralmodels tend to outperform over medium forecasting horizons.6

In the short term (more below on how this is defined in prac-tice), macroeconomic forecasting is best done by describing idiosyn-cratic developments, exploring empirical correlations and accumu-lating detailed expert knowledge of individual sectors and indus-tries. Short-term (also known as near-term) projections for outputor inflation based on the proximate causes of their movements moreoften than not outperform those relying on macroeconomic funda-mentals by a great margin. On top of that, monetary policy has littleeffect within such a short span of time, perhaps with the only excep-tion of the nominal exchange rate, so that central banks’ policy isusually not an input to short-term forecasts.

In the medium term, though, monetary policy actions, people’sexpectations and behavioural mechanisms7 become the dominat-ing forces in economic projections. Attempts to exploit observedreduced-form relationships (ie, statistical relationships betweenendogenous and exogenous variables) without references to soundeconomic theories can easily hide some critical trade-offs, and hencedrive the policymakers into dangerous waters. Real-world examplesinclude the neglect of inflation expectations in the 1970s, and the

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Figure 9.7 Major components in an FPAS model

Externalprojections

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role of loose monetary policies in changing risk perception duringthe Great Moderation in the 1990s.

Finally, long-term real (as opposed to nominal) trends are viewedas largely immune to the way monetary policies are conducted(although, for instance, broad consensus exists on the real benefits oflow and stable inflation), while monetary aspects (such as inflation)are, on the contrary, under full command of the central bank, at leastin theory.

The specific definition of what constitutes a short-term versusa medium- or long-term forecasting horizon depends on the struc-tural characteristics of each economy. Typically, a short-term forecastmight span a few months or quarters ahead, a medium-term forecastcovers a horizon up to four or five years and a long-term forecastextends to any term beyond that. Note also that the definition ofa short-, medium- or long-term horizon varies considerably acrossdifferent fields of economics.

Major components of an FPAS model

An FPAS is organised around a core projection model. The model isused as a platform to integrate three types of inputs coming fromoutside that model: initial conditions, exogenous projections andjudgemental adjustments (Figure 9.7).

The core projection model is the backbone of the FPAS andthe whole forecast production process. It is a structural or semi-structural business-cycle model describing the main medium-termpropagation mechanisms (or transmission channels). The core pro-jection model instills discipline into the forecasting process, whileproviding a consistent, unified language for both central bank staff

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and policymakers. Given that the model is used to guide the policy-making process itself, this would seem to imply that monetary policyand expectations are exogenous to it. Yet, a considerable number ofcentral banks, including some in advanced economies, still struggleto understand how crucial an assumption this is for good conductof their policies. These issues will be discussed in greater detail inthe next section.

Models for the so-called “now-casts” deliver estimates for the cur-rent month or current quarter of those variables that are not yetavailable due to a publication lag. Techniques used in now-castingare basically the same as in near-term forecasting, which producesa very short-term outlook for the main variables, say a quarter ortwo quarters ahead. These numbers are then commonly treated ashard data when entered into the core projection model (effectivelyextending the actual time-series observations). Most of the centralbanks combine two basic approaches to constructing now-casts andnear-term forecasts (NTFs): expert knowledge-based projections andreduced-form multivariate time-series models. In both, the estimatesand forecasts are built “bottom-up” using an extensive numberof detailed macroeconomic indicators (most of which do not evenappear in the core projection models).8 The multivariate reduced-form models include various sorts of estimated vector autoregres-sions (VARs) adjusted to deal with the problem of potential over-fitting, such as Bayesian vector autoregressions (BVARs) or factor-augmented vector autoregressions (FAVARs); see the appendix onpage 201 for a brief explanation of these two techniques.

Trend-cycle analysis9 is needed because the core projection mod-els are frequently built around economic concepts (such as equilib-rium values) that are not directly observable: two examples are theoutput gap (or, equivalently, potential output) and the natural rateof interest. Trend-cycle analysis is therefore necessary for setting upthe initial conditions for the model. Broadly speaking, there are threeoptions available.

1. Univariate filters, which produce more or less mechanicalresults with the option of judgemental adjustments. Theseinclude the popular Leser (1961) filter, also known as theHodrick and Prescott (1997) filter in economics.

2. Various multivariate filters relating the trends and cycles in thevariable(s) in question to other indicators that are expected to

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co-move with them; consider, for example, using the data oncapacity utilisation to inform the estimates of the output gap,see, for example, Benes et al (2009) for an example of such filter.

3. So-called model-consistent estimation of the unobservablequantities, where the core projection model itself is used tocalculate the decomposition of output, real rates or other vari-ables into their trends and cycles (gaps). However appealingit may be, this technique requires a relatively high level ofsophistication; not all core projection models are suitable for,or even capable of, this job.

Related to trend-cycle analysis are trend projections. As the coreprojection models usually have a very stylised block (or simply nosuch block) describing the long-term evolution of actual trends (eg,potential output, labour productivity, productive capacity), the real-ism in the trend projections is achieved by supplying judgemen-tally adjusted assumptions. These assumptions are the result of abroader discussion among the bank staff, aided sometimes by sim-ple growth models (as opposed to business-cycle models used as thecore projection tools).

External or other exogenous projections are simply trajectories forthose variables that the model takes as given. For instance, in modelsof small, open economies like the five aforementioned IT countries(New Zealand, Sweden, Norway, Czech Republic and Israel), it isforeign output, foreign inflation, foreign interest rates or the termsof trade that need to be predicted. Furthermore, the exogenous pro-jections may also include various fiscal outlooks, the price of oil orother commodities, paths for administered prices in countries withgovernment regulation of some sectors and so on.

Finally, there is an important category of satellite models. Thesemodels are meant to flesh out the sectors that are (too) simplified inthe core projection model, or absent from it, but might occasionallyprove important for the overall macroeconomic developments. Typ-ical candidates are fiscal considerations/assumptions, the bankingsector and labour markets. Furthermore, satellite models may alsooffer alternative views on the workings of monetary policy trans-mission, or examine the implications of various non-linearities thatwould be operationally difficult to incorporate directly into one ofthe forecast production models.10

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All these diverse and conceptually different inputs need to becombined in a single baseline projection, plus a small number ofalternative scenarios. The core model and its software infrastructuremust therefore be flexible enough to allow simulations with vari-ous types of conditioning information and judgemental adjustmentsincorporated in them.11

The forecast production process

In most countries, the forecast production process has a quarterlycycle.Although the policymakers usually meet more frequently, typ-ically every six or eight weeks (with the meetings disguised undera variety of names, such as bank board meeting, monetary pol-icy committee, Federal Open Market Committee (FOMC) meeting),there would not be a sufficient amount of new information to runa fully fledged forecast with a higher frequency. The limiting factoris perhaps the availability of national accounts data, ie, GDP andits components, which are the main indicators of the country’s realeconomic activity.

A typical forecast production exercise takes roughly four to sixweeks and several rounds of meetings to complete, depending onthe factors discussed below. It is generally scheduled so as to complywith two requirements: it be a timely, up-to-date input into one of thepolicymaking meetings; the key data releases, which are inflationand GDP, occur somewhere in the middle of the production. Thestandard practice of the leading central banks is that the forecastpackage submitted by staff to the policymakers contains (at least):

• a baseline projection together with a clear and consistent nar-rative;

• policy recommendations consistent with, and incorporated in,the baseline projection;

• alternative scenarios, including alternative policy paths;

• an assessment of uncertainty (prediction intervals);

• an explanation of what factors caused a change in the baselinecompared with the previous one.

How much attention do policymakers pay to such a forecasting pack-age in their decision-making? And how much of this package ismade public? The trend at the time of writing has been towards

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making clear who in fact owns the forecast (in other words, whetherit expresses staff views or policymakers’ views) and its weight inthe decision-making. Obviously, the ownership of the forecast alsoinfluences the forecasting process itself. If it is to be a policymakers’forecast, the production will almost surely take longer, as the cen-tral bank staff needs to meet with the policymakers more frequently,and eventually fine-tune the results to their liking. Indeed, at somecentral banks, there are two distinct forecasting rounds: the first pro-duces projections based on staff views, while the second incorporatespolicymakers’ assumptions and judgement. When it comes to theissue of forecast ownership and the weight that forecasting has onpolicy, different central banks take different approaches, which areclear for some and more ambiguous for others. A few examples arelisted below.

• The Bank of Canada’s Monetary Policy Report, July 2011,states: “This is a report of the Governing Council of the Bankof Canada.”

• The Bank of England’s Inflation Report, August 2011, states:“The Inflation Report is produced quarterly by Bank staffunder the guidance of the members of the Monetary PolicyCommittee. It serves two purposes. First, its preparation pro-vides a comprehensive and forward-looking framework fordiscussion among MPC members as an aid to our decision-making. Second, its publication allows us to share our think-ing and explain the reasons for our decisions to those whomthey affect. Although not every member will agree with everyassumption…”.

• The Riksbank’s Monetary Policy Report, July 2011, states: “Thereport describes the deliberations made by the Riksbank whendeciding what would be an appropriate monetary policy.…The Executive Board decided to adopt the Monetary PolicyReport at its meeting on 4 July 2011.”

• The Czech National Bank’s Inflation Report, 2011 Q3, states:“The forecast for the Czech economy is drawn up by the CNB’sMonetary and Statistics Department.… The forecast is the key,but not the only, input to the Bank Board’s decision-making.”

• The Reserve Bank of New Zealand’s Monetary Policy State-ment is directly signed off by the Governor.

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• The ECB Staff Macroeconomic Projections for the Euro Areastates: “The ECB staff macroeconomic projections complementthe Euro system staff macroeconomic projections that are pro-duced jointly by experts from the ECB and from the euro areanational central banks on a biannual basis” (European CentralBank 2011). It is not clear from the document what role it playsin the ECB’s policy decision-making.

• The US Federal Reserve System used only to publish a one-page summary of the views of board members and regionalbank presidents on four macroeconomic variables (GDP, un-employment, inflation and core inflation). The release of moredetailed projections, including what the Fed funds rate shouldlook like in the future, without further shocks to the economy,started only in January 2012.12

CORE PROJECTION MODELS

As we stated in the previous section, a core projection model is thefocal point of the forecast production process because it combines allinputs into a coherent scenario; it imposes discipline to both inter-nal and external communication of central banks and allows therunning of alternative scenarios with consistent policy implications.Understandably, its design, development and implementation areusually a lengthy and intellectually challenging undertaking, whichtypically adheres to the following principles.

• Parsimony: core projection models are kept rather simple, asthey need to be understandable and useful in providing keyinsights to its operators. Core models also need to gain accep-tance and some sort of intellectual ownership across the entireinstitution, including non-modellers and senior management.This would be impossible to achieve with a high degree ofcomplexity and mathematical abstraction.

• Top-down approach: monetary policy is primarily about thebroad picture, not about fine-tuning. The first step in designingcore projection models is the identification of a set of key policyproperties, while any further disaggregation and finer sectorialdetail are subordinate to those properties. Some of the commonpolicy properties embedded in models are the following.

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– Long-term neutrality. Real outcomes (as opposed to mon-etary, or nominal, variables) remain unaffected by mone-tary policies in the long run (unless the policies are verybad) and, vice versa, the central bank can set and achieveany inflation target (or other nominal, or monetary, target)without distorting real outcomes. In practice, of course,the neutrality is a convenient assumption only within arange of relatively low and stable inflation rates.

– Medium-term real effects of monetary policy. Unlike inthe long run, the central bank’s actions do impact on realoutcomes in the medium run, thanks to various typesof frictions and rigidities (such as price and wage stick-iness). These rigidities wear off after a sufficiently longtime, allowing neutrality to reign again.

– The stabilising role of monetary policy throughout thebusiness cycle. The systematic reaction of the central bankto macroeconomic shocks must be sufficient to prevent aninflation (or deflation) spiral. For example, an inflationspiral occurs whenever high inflation, not fought againstby the central bank, feeds into expectations, thus reducingreal rates and raising demand. Excess demand adds morepressure still on inflation, and the economy is caught in avicious circle.

– Forward-looking expectations. Although it would beunrealistic to assume fully forward-looking expectationsin practical applications, the rational element in expecta-tions must not be neglected. Otherwise, the model-basedadvice could easily make the policymakers believe theycould exploit permanent trade-offs where there are none;in other words, the model would imply the central bankcould fool all of the people all of the time.

• Robustness to policy errors: the predictive power of core pro-jection models is often defined by their ability to get the tim-ing of the turning points in a business cycle right. This provesmore important than any other statistical test. Accurate turn-ing points are one of the preconditions for avoiding system-atic policy mistakes: such as type “A” policy errors (being too“ahead” of the curve, ie, reacting to false signals) or type “B”

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policy errors (being “behind” the curve, ie, not reacting to truesignals).

Different types of core projection modelsWe can identify four broad varieties of core projection models:

1. large-scale econometric models;

2. weak-form dynamic stochastic general equilibrium (DSGE)models;

3. semi-structural flow (or “gap”) models; and

4. semi-structural stock-flow models.

Large-scale econometric models are considered to be outdated inthe context of monetary policy models (which is not to say they areuseless, but that they are not the right model for monetary policy).They are usually designed “bottom-up”, with great emphasis on dis-aggregation; they also most often lack an explicit role for monetarypolicy or expectations, with the notable exception of the US FederalReserve staff’s model.13 Because they are estimated without propermonetary policy, they tend to incorrectly interpret various monetarystabilities or instabilities observed in the data.

The other three types of model are generally much more com-patible with modern monetary policymaking. There exists, though,a certain trade-off between operational simplicity and theoreticalcoherence across those three varieties. We now briefly explain someof their defining features.

DSGE models start by making explicit and detailed assumptionsabout what types of economic agent act in the model economy (suchas households, producers, retailers, banks, the central bank and gov-ernment), what their objectives are (to maximise utility or profits)and the environment in which they interact (eg, competitive markets,monopolistic markets). Then, they derive the optimality conditionsfor the behaviour of each, aggregate these over the entire economyand impose general equilibrium conditions (ie, that demand equalssupply in each market at the prevailing price). However appeal-ing the concept of a DSGE is, it is in practice impossible to buildDSGEs that perform well in all the desired empirical dimensionswhile keeping all the underlying assumptions about the agents’objectives strictly consistent with microeconomic and behaviouraltheories. Therefore, various shortcuts, simplifications and ad hoc

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additions are introduced when setting up the optimisation problemssolved by the model’s agents. This is why virtually all practical pol-icy DSGEs are of a weak-form variety (as opposed to strong-formDSGEs, which do adhere to rigorous microeconomic foundations: adistinction proposed by Faust (2009)).

The first central bank to announce the official use of a DSGEmodel in its forecast production was the Bank of England in 2004(BEQM). Several other banks have followed since: Bank of Canada(ToTEM), Reserve Bank of New Zealand (KITT), Bank of Finland(Aino), Norges Bank (NEMO), Riksbank (RAMSES), Czech NationalBank (G3) and others.14 These models are (without exception) pub-licly available from the websites of the respective central banks.Note also that there are many more central banks using DSGEs forresearch or occasional analysis, but not specifically relying on themfrom official forecast production.

The semi-structural models apply higher levels of ad hoc adjust-ments still. Their equations do somehow loosely map into weak-form micro-foundations, but to achieve realistic dynamics andexplain the observed data characteristics it is the final equationsthat are modified rather than the underlying optimisation prob-lem. An example of a stylised semi-structural model is given in theappendix on page 202. Semi-structural models include both so-calledflow models and stock-flow models. Flow models either ignore ortreat stock variables (eg, productive capital, foreign or public debt,and balance sheets) as exogenous, and only deal with flow vari-ables (such as output, imports and expenditures). Stock-flow mod-els, on the other hand, keep track of stock-flow consistencies, such ashow investment expenditures increase productive capacity in a cer-tain industry, or how current account deficits result in foreign debtdeterioration. Stock-flow models not only have greater operationalcomplexity but are also more difficult to implement because of prac-tical limitations in the empirical data needed to measure stock-flowrelationships.15

Policy reaction function

As mentioned before, if the baseline projection is to depict the mostlikely scenario, the way the central bank systematically respondsto risks to inflation or output must be an endogenous part of themodel; a formal description of the systematic behaviour of a central

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bank is also known as a policy reaction function or a policy rule. Thecase for incorporating an endogenous policy rule in central bankprojections is stronger still if we consider that the policy rule is (atleast conceptually) rooted in markets’ expectations, in one way oranother. No one certainly believes that the central bankers will sit ontheir hands when inflation is getting a push. Therefore, a forecast orpolicy advice based on the assumption of the policy rates being con-stant no matter what has next to no value. Perhaps even worse thana constant policy rate assumption, some banks, including the Bankof England, make the policy rate follow the path implied by marketexpectations (constructed, for instance, from a yield curve or the for-ward rate market). In that way, the bank effectively gives up on itsrole as a market expectations leader and becomes a follower, expos-ing itself to the potentially fatal risk of falling consistently behindthe curve.

The experience of several central banks, on the other hand, is that,if communicated properly, the policy rule assumptions made in theprojections will be quickly understood and learned by the markets.The benefit of this is clear on both sides: the movements in the yieldcurve are likely to become more predictable (a desirable feature fromthe policy point of view), making the central bank’s job easier toaccomplish.

What form do endogenous policy rules take in projections mod-els? With a very few exceptions, central bankers prefer to use simplerules, such as that proposed by Taylor (1993), or rather its forward-looking variation as detailed in the appendix on page 202. Simplerules try to describe the central bank’s policy reaction function usinga limited number of key variables. A Taylor-type rule usually seesthe interest rate react to deviations in inflation, or model-consistentinflation forecast, from the target, and to some measure of real eco-nomic activity, such as the output gap. Furthermore, the rules areconstructed so as to avoid rapid swings in the policy rate settingsin response to new, potentially noisy and uncertain information (so-called policy smoothing); this is why we typically see autoregres-sive terms in the equations describing the policy reaction functionof central banks. These simple rules have two great advantages:

1. they are very easy to communicate within the central bank andto the public;

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2. they are relatively robust across different models, deliveringgood performance (see, for example, Taylor 1998).

In comparison, at least one central bank, Norges Bank, adopts adifferent approach by applying an optimal rule, based on minimisingan explicit loss function, to model its policy reaction function (seeNorges Bank (2011) for details).

HOW MODELS ARE USEDMacroeconomic forecasts are never perfect, and in practice projec-tions are wrong most often than not. Any policymaker is aware of thelimitations in models given their reliance on a multitude of assump-tions and the inherent nature of the forecasting process. This said, theforecasting exercise should help a central banker in making the bestdecisions under unavoidable uncertainty. This implies that forecast-ing accuracy is not as important as the ability to consistently differ-entiate between alternative future developments. Furthermore, theforecasting system helps to collect the right information, organiseit properly and, most importantly, analyse the nature of economicshocks in order to assist policymakers in their functions. For instance,Figure 9.8 shows how a model-based analysis of inflation data is ableto dissect its underlying causes. With this information, policymak-ers may choose to ignore a rise in inflation if driven by a temporarysupply side shock, even if inflation exceeds the target. Clearly, if therise in inflation were due to a demand shock or a dis-anchoring ofinflation expectation, the policy response might be quite different.

In addition, a model-based FPAS is able to identify the optimalpolicy response in any specific simulated scenario. For instance, ifthe above supply shock proved to be a permanent one, the correctpolicy response can be inferred within the model. Clearly, the modelitself does not necessarily provide much insight on whether a specificfuture scenario is more likely than any other, as this is a judgementcall left to the policymaker. However, a model-based analysis canoffer a comparative view of the different outcomes, including theoptimal responses in each circumstance, as well as the implications ofmaking the wrong economic assumptions. Thus, even if some degreeof uncertainty cannot be avoided, the overall process is helpful tothe policymaker in choosing the appropriate strategy.

As an example, Figure 9.9 shows the change in an interest rate fore-cast due to different effects, specifically a change in model (labelled

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Figure 9.8 Inflation contributions from different underlying drivers

30

25

20

15

10

5

0

–5

–10

–20

–15

2005

Q1

2005

Q2

2005

Q3

2005

Q4

2006

Q1

2006

Q2

2006

Q3

2006

Q4

2007

Q1

2007

Q2

2007

Q3

2007

Q4

2008

Q1

2008

Q2

2008

Q3

2008

Q4

2009

Q1

2009

Q2

2009

Q3

2009

Q4

2010

Q1

2011

Q1

2010

Q2

2010

Q3

2010

Q4

Supply shockImported inflationInflation expectationsDemand and othersInitial conditions

Source: OGResearch.

“model change” in Figure 9.9), new data/assumptions (labelled“combined effect of new data”) and a change in forecasting hori-zon (labelled “data coverage change”). We can see that the modelchange is the main driver for the downward forecast revision in themedium term, while new data and assumptions pull the forecastdown in the short term.

As another example, Figure 9.10 shows the effect that a rise inworld food prices would have on the baseline inflation forecast andreal GDP. This type of analysis helps in determining the sensitivitiesinherent in policymaking, and also in more effective communicationamong bank staff and with the general public.

To conclude, an FPAS provides a disciplined approach and guidespolicymakers in setting policy in a way that is consistent with thedeclared objectives, thus positively affecting its credibility.

CONCLUSIONS

In this chapter, we discussed the forecasting processes used bypolicymakers and argued that, despite their intrinsic limitations,models are a useful tool in guiding the decision-making process ofcentral banks. Specifically, although a model-based analysis cannot

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Figure 9.9 Drivers of change in interest rate forecast

0.5

0

–0.5

–0.10

–0.20

–0.15

–0.25

2012

Q1

2012

Q2

2012

Q3

2012

Q4

2013

Q1

2013

Q2

2013

Q3

2013

Q4

2014

Q1

2014

Q2

2014

Q3

2014

Q4

2015

Q1

2015

Q2

2015

Q3

2015

Q4

2016

Q1

2016

Q2

2016

Q3

2016

Q4

Model change Data coverage change Combined effect of new data

Source: OGResearch.

eliminate the inherent uncertainties in the forecasting process, it canoffer a comparative view of the different outcomes, including theoptimal responses in each circumstance, as well as the implicationsof making the wrong economic assumptions.

After the 2008–9 financial crisis, some people highlighted the fail-ures of policymakers, and their models, in not being able to fore-see the impending disastrous events, and thus mitigate their effect.However, if failure it was, it was not models the that were to blame,but imperfect foresight and judgement on behalf of the users of thosemodels, ie, policymakers themselves. In fact, a model will never becapable of predicting a crisis, although it might provide clues aboutthe possible triggers. It is up to the users to feed in the relevant sce-narios, including possible adverse shocks and other inputs, and letthe model reveal the implications. There are clearly lessons to belearnt from the financial crisis, in particular regarding the importantfeedback effects between the overall economy and the financial sec-tor. Indeed, adding a model component to address macro-financiallinkages, even if simple and stylised (see, for example, Carabien-cov et al 2008), might be helpful, as it provides one more point atwhich a crisis can possibly originate. However, at the core, it will

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Figure 9.10 Change in (a) baseline inflation and (b) real GDP forecastdue to a food price shock

0

2

4

6

8

10

12

14

2007 2008 2009 2010 2011 2012 2013 2014 2015

YoY

infla

tion

(%)

Rea

l YoY

GD

P g

row

th (

%)

20

15

10

5

0

–5

–10

–15

–20

–252 4 6 8 10121416182022242628303234

Baseline

Scenario

Baseline

Scenario

(a)

(b)

Source: OGResearch.

always be up to the analyst’s judgement to create the relevant sce-narios and, in conjunction with all the available quantitative andqualitative information, determine the best policy action path goingforward.

APPENDIX: MULTIVARIATE MODELS FOR NEAR-TERMFORECASTINGIn this appendix, we outline the methodology of Bayesian vectorautoregressions and factor-augmented vector autoregressions. Bothof these methodologies were developed specifically to deal withempirical short-term dynamic relationships between a (potentiallyvery) large number of variables. Empirical models with a very large

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number of variables are always prone to over-fitting: put simply,there are not sufficient degrees of freedom to get reliable and robustestimates of the model parameters.

The BVARs are vector autoregressions in their simplest form, ie

xt = A1xt−1 + · · · +Akxt−k + εt

where xt is an N × 1 vector of observations at time t (with thesize of the vector potentially very large), A1, . . . , Ak are parame-ter matrices to be estimated and εt is a vector of forecast errors.To achieve an acceptable level of identification, we first constructso-called priors for the parameter matrices; most often these aresimplistic assumptions about the individual variables. For exam-ple, if our prior is that all variables are random walks, we chooseA1 = 1, A2 = · · · = Ak = 0, and assign a certain weight to ourpriors. The final estimates, A1, . . . , Ak can then be thought of as aweighted average of the priors and the unrestricted estimates wewould obtain by estimating the system using classical methods.

FAVARs, on the other hand, deal with the identification problemin a different way. We estimate a small number of so-called commonfactors, ft, that drive most of the dynamics in the observed series, andthen estimate a classical vector autoregression (VAR) on the factorsonly

xt = C ft +ωt (9.1)

ft = A1 ft−1 + · · · +Ak ft−k + εt (9.2)

Equation 9.1 links the endogenous variables to a K × 1 vector offactors, where the number of factors, K, is considerably smaller thanthe number of the original variables, N. Furthermore,ωt is a vectorof the so-called idiosyncratic prediction errors, while εt is a vectorof factor prediction errors.

There are numerous applications of the two methodologies in cen-tral bank forecasting; two examples are Banbura et al (2008) andBernanke et al (2005).

APPENDIX: AN EXAMPLE OF A STYLISEDSEMI-STRUCTURAL FLOW MODEL FOR AN OPEN ECONOMYThe model describes an open economy and consists of aggregatedemand and aggregate supply equations, a simple monetary policyrule, relationships with the rest of the world (foreign output, foreign

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inflation and foreign interest rates) and also stylised factors affectingthe cost of borrowing.

Glossary

• Real gaps (percentage deviations in real variables from theirlong-run trends):

yt output gap;rt real interest gap;zt real exchange gap;y∗t foreign demand gap;qt real price of capital gap;ρt external finance premium;ut foreign exchange risk spread.

• Nominal variables:

it nominal policy rate;pt log of domestic price level;πt domestic quarter-on-quarter inflation (annualised);π4

t domestic year-on-year inflation;πm

t import inflation;i∗t foreign nominal interest rate;p∗t log of foreign price level;π∗t foreign quarter-on-quarter inflation (annualised).

• Structural shocks:

εyt aggregate demand shock;επ1

t type-1 (persistent) cost-push shock;επ2

t type-2 (temporary) cost-push shock;εs

t foreign exchange shock;εi

t monetary policy surprise;εq

t financial market shock;ερt external premium shock.

• The superscript ‘e’ denotes expectations in general; the oper-ator Et[·] denotes the model-consistent (rational) expecta-tions; the superscript ‘a’ denotes adaptive expectations. Theexpectations formation is explained in Equations 9.10 and 9.11.

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• Identities between log price levels and inflation rates are notlisted here.

• Real trends and the foreign exchange risk spread are exoge-nous processes, not listed here.

EquationsAggregate demand

Demand for domestic output is affected by real monetary conditions(ie, the real interest rate, including the external finance premium, andthe real exchange rate) and by external demand

yt = α1yt−1 + (1−α1)yet−1 −α2(rt + ρt)+α3zt +α4y∗t + ε

yt (9.3)

Phillips curve (aggregate supply)

Domestic inflation is driven by cycles in excess demand (the outputgap), two exchange rate channels (a direct exchange rate channel,through the prices of directly consumed imports, and an indirectexchange rate channel, through the prices of imported intermediateinputs) and the expectations channel. Note that the Phillips curvedisplays long-run neutrality, as it is easy to show that this equationis consistent with any rate of inflation if the real gaps are closed (ie,the real variables are on their trend paths)

πt = β1πt−1 + β2πet+1 −

1− β1 − β2

1− θ (πmt−1)+ β2yt + β4ztεπt (9.4)

Furthermore, we introduce two types of cost-push shocks to domes-tic prices: one has more persistent effects (type 1), the other is moretemporary (type 2)

επt = επ1t + (επ2

t −ψεπ2t−1) (9.5)

Uncovered interest parity

The following equation describes the reaction of the nominal ex-change rate to the interest rate differential (adjusted for a countryrisk spread), and to future expectations

st = set+1 − 1

4(it − i∗t − ut)+ εst (9.6)

Monetary policy (Taylor) rule

The central bank responds to deviations in inflation from the tar-get (year-on-year inflation k quarters ahead) and to excess demand;the policy rule has an autoregressive term to avoid large and rapidswings in the policy rate settings (policy smoothing).

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Financial market conditions (real price of capital and external priceof capital)

Conceptually, we link the external finance premium to the real priceof capital: the higher the price of capital, the lower the cost of bor-rowing for consumers and investors (given a certain policy rate).The price of capital is, in turn, determined by a simplified asset priceequation: as a discounted sum of future marginal products of capitalapproximated by the cycle in output

qt = −rt + δyet+1 + (1− δ)qe

t+1 + εqt (9.7)

ρt = −ξqt + ερt (9.8)

We give the following definitions for import inflation, the realexchange rate gap and the real interest rate gap

πmt = ∆st +π∗tzt = −st + p∗t − pt − z

rt = it −πet+1 − rt

⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭

(9.9)

Here the bar denotes long-term equilibrium values.We now discuss inflation expectations (other expectations can be

thought of in the same way).Expectations can be mixed in the model: partly forward-looking,

ie, model-consistent (based on the correct one-step-ahead predic-tions made by the model itself), and partly backward-looking oradaptive:

πet+1 = wEt[πt+1]+ (1−w)πa

t+1 (9.10)

πat+1 = πa

t +ϕ(πt −πat ) (9.11)

The authors thank Jaromir Benes for helpful comments anddiscussions.

1 Iceland: although at the time of writing in 2012 the inflation target is still technically in force,the central bank is concentrating mostly on keeping the exchange rate stable.

2 Meyer (2001) has a nice discussion of central bank mandates and objectives from the per-spective of IT.

3 Although the financial crisis revived the use of other instruments, such as FX interventions orquantity based operations, these were employed either to support the transmission of interestrate policy or to satisfy different objectives outside the IT framework, such as pro-exportingindustrial policy.

4 Released by the Federal Open Market Committee on April 28, 2010.

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5 Such as an inflation forecast for a particular rather irrelevant sector, calculated and discussedup to three decimal places.

6 In simple terms, reduced-form models explain a set of dependent variables in terms of a setof independent variables (for example, in a regression framework). Structural models dealwith equilibrium relationships between supply and demand, which are likely to dominate inthe medium to long term.

7 For example, switching expenditures between cheaper and costlier goods, or deciding oninvestment in productive capacity based on the cost of bank lending.

8 For instance, while the core projection model may work with the headline CPI and the five tra-ditional demand components of GDP only (consumption, investment, government, exports,imports), the now-casts and NTFs make use of a detailed sector-by-sector breakdown of theCPI into sub-indexes, and both demand a production view of GDP flows.

9 Models for trend-cycle analysis are called filters because they aim at filtering out high-frequency fluctuations while identifying lower frequency relationships.

10 Non-linearities that may matter for monetary policy include an asymmetric, convex Phillipscurve (prices fall less in recessions than they rise in booms) and endogenous credibility (expec-tations are more difficult to anchor if the central bank has a poor track record in keepinginflation low and stable).

11 Economic modelling software packages that offer a high degree of flexibility in incorporatingconditioning information and judgemental adjustments in simulations include the IRIS Tool-box (http://www.iris-toolbox.com), Troll (http://www.intex.com/troll) and Sirius (http://www.ogresearch.com/products).

12 See http://www.federalreserve.gov.

13 The FRB/US model; see http://www.federalreserve.gov.

14 BEQM stands for Bank of England Quarterly Model. ToTEM stands for Terms of Trade Eco-nomic Model. KITT stands for Kiwi Inflation Targeting Technology. NEMO stands for Nor-wegian Economy Model. RAMSES stands for Riksbank Aggregate Macro-model for Studiesof the Economy of Sweden.

15 For instance, data on physical capital is not readily available or reliable even in many advancedcountries; the relationship between the country’s net investment position and the reportedcurrent accounts tends to be fuzzy because of occasionally unclear definitions or hard-to-trackvaluation effects.

REFERENCES

Banbura, M., D. Giannone and L. Reichlin, 2008, “Large Bayesian VARs”, ECB WorkingPaper 966.

Benes, J., K. Clinton, R. Garcia-Saltos, M. Johnson, D. Laxton, P. Manchev and T.Matheson, 2009, “Estimating Potential Output with a Multivariate Filter”, IMF WorkingPaper 10/285.

Bernanke, B., J. Boivin and P. Eliasz, 2005, “Measuring Monetary Policy: A Factor-Augmented Vector Autoregression (FAVAR) Approach”, Quarterly Journal of Economics120(1), pp. 387–422.

Bernanke, B., M. Gertler and S. Gilchrist, 1999, “The Financial Accelerator in a Quanti-tative Business Cycle Framework”, in J. B. Taylor and M. Woodford (eds), The Handbook ofMacroeconomics, Volume 1C (Elsevier).

Carabiencov, I., I. Ermolaev, C. Freedman, M. Juillard, O. Kamenik, D. Korshunov andD. Laxton, 2008, “A Small Quarterly Projection Model of the US Economy”, IMF WorkingPaper 08/278.

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THE ROLE OF MODELS IN MODERN MONETARY POLICY

Chari, V. V., 2010, “Testimony before the Committee on Science and Technology, Subcom-mittee on Investigations and Oversight”, US House of Representatives, June.

Chen, H., K. Clinton, M. Johnson, O. Kamenik and D. Laxton, 2009, “ConstructingForecast Confidence Bands during the Financial Crisis”, IMF Working Paper 09/214.

European Central Bank, 2011, “ECB Staff Macroeconomic Projections for the Euro Area”,September, URL: http://ecb.europa.eu/pub.

Faust, J., 2009, “The New Macro Models: Washing Our Hands and Watching for Icebergs”,Sveriges Riksbank Economic Review, 2009(1).

Hodrick, R., and E. C. Prescott, 1997, “Postwar US Business Cycles: An EmpiricalInvestigation”, Journal of Money, Credit, and Banking 29, pp. 1–16.

Issing, O., 2008, “In Search of Monetary Stability: The Evolution of Monetary Policy”,Contribution to Seventh BIS Annual Conference, June.

Leser, C. E. V., 1961, “A Simple Method of Trend Construction”, Journal of the RoyalStatistical Society, Series B 23, pp. 91–107.

Meyer, L. H., 2001, “Inflation Targets and Inflation Targeting”, Speech at the Universityof California at San Diego Economics Roundtable, July.

Norges Bank, 2011, “Criteria for an Appropriate Interest Rate Path”, Monetary PolicyReport 2/2011.

Solow, R., 2010, “Building a Science of Economics for the Real World”, Testimony beforeUS Congress Committee on Science and Technology, July.

Taylor, J. B., 1993, Discretion versus Policy Rules in Practice, Carnegie-Rochester ConferenceSeries on Public Policy, Volume 39, pp. 195–214 (Elsevier).

Taylor, J. B., 1998, “The Robustness and Efficiency of Monetary Policy Rules as Guidelinesfor Interest Rate Setting by the European Central Bank”, Seminar Paper 649, Institute forInternational Economic Studies, Stockholm University.

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10

Term Structure of Interest Rates andExpected Inflation

Olesya V. Grishchenko; Jing-Zhi HuangFederal Reserve Board; Penn State University

In this chapter we report some developments in the modelling ofthe term structure of interest rates and expected inflation. We firstreview nominal term structure models and then we discuss modelsof real term structures and expected inflation, and illustrate howinflation expectations and risk premiums can be derived. Finally, wediscuss the implications of this research for investors and monetarypolicymakers.

TERM STRUCTURE MODELLING: BASIC CONCEPTS

One of the most important aims in financial economics is to under-stand how expected bond returns move over time. For this purpose,a successful modelling of both short- and long-term bond yields (ie,the term structure) is called for. The literature on the term struc-ture of nominal interest rates is vast, and the topic has developedinto a separate field of financial economics since the 1990s. For thesake of brevity, we shall highlight only the key concepts and a fewof the many influential papers that have shaped the evolution ofthe term structure modelling over time. Some of the mathematicalderivations are provided in the appendixes.

From the short rate to the yield curve

A crucial idea underlining most of the term structure models is theconcept of no arbitrage, ie, the assumption that there are no ways tomake a riskless profit, or, in other words, there are no self-financing

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strategies that start with zero value, have zero probability of lossand have a positive probability of a positive profit at a later point intime. Under the assumption that a market does not allow arbitrageopportunities, default-free zero-coupon bond prices can be obtainedusing the risk-neutral valuation approach and expressed as an expec-tation under the risk-neutral probability measure Q. If the marketis complete, ie, any derivative can be hedged using a self-financingportfolio of market securities, then the above probability measure Q

not only exists but it is unique. These assumptions, together, result inthe well-defined, unique bond prices (see the appendix on page 235).Namely, let Pt,τ denote the price at time t of the zero-coupon bondmaturing at time t + τ and let yt,τ be the corresponding yield. Wehave

Pt,τ = exp[−yt,ττ] = EQt

[exp

(−∫ t+τ

trs ds

)]

The result above is quite elegant, and offers a potentially useful linkbetween the short rate r (which is influenced by monetary policy)and the rest of the yield curve. However, the problem is that ourobservations of the short rate r belong to the real world under the(data-generating) probability measure (or physical measure) P. Inother words, by collecting data on the short rate (using for examplethe one-month interest rate as a proxy) we might gain insight onits dynamics under P and yet, to calculate bond prices, we have totake expectations under Q. We need a way to relate expectationsunder different (yet equivalent) measures to be able to bridge thegap between the two worlds.

In between two worlds: the price of riskAs mentioned earlier, we need to have a model that captures theempirical properties of the data under the physical measure P. Theno-arbitrage assumption, which ensures the existence of Q alsoensures the existence of a transformation between Q and the realdata-generating measure P (two equivalent probability measures).1

SpecificallyξtE

Qt [· · · ] = EP

t [ξT · · · ]where ξt is the stochastic process, representing the change in prob-ability density between the two measures. Specific functional formsare assumed for ξt, both to ensure that, being a probability den-sity transformation, it is positively defined, and in order to preserve

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Figure 10.1 The market price of risk

Risk-neutralmeasure

Data-generatingmeasure

Price ofriskEQ[…]tλs

EP t

ξτ

ξt

…[ ]

mathematically tractability (for instance, we want to make sure thatwe are dealing with Brownian motions, albeit with different drifts,under both measures). Astandard functional assumption for the dis-crete one-period change in measure is the exponential one, whichhas the effect of only changing the drift terms (see Equation 10.4in the appendix), leaving volatilities untouched and preserving theanalytical tractability of Brownian motions. If the market price ofrisk λt is zero, the two probability measures coincide. As we will seelater, the market price of risk is generally defined to be a functionof the N-dimensional state vector (subject to constraints to allowfor closed-formed solutions of affine models). Figure 10.1 illustratesschematically the relationship between Q and P measures.

Both probability measures work

Bond prices can be calculated under either measure, after adjustingfor the appropriate change in probability density. Specifically

Pt,τ = EQt

[exp

(−∫ t+τ

trs ds

)]

= EPt

[ξT

ξtexp

(−∫ t+τ

trs ds

)]

Both expressions lead to the same prices for zero-coupon bonds.More explicit formulas are derived in the appendix on page 236, andan example of the actual calculation is worked out in the appendix onpage 238. The relation between the price of risk and bonds’ term pre-miums are analysed in the appendix on page 238. A useful recursiverelation for bond prices in discrete time is presented in the appendixon page 238.

Clearly, the choice for the dynamics of the short rate is driven bythe desire for both mathematical tractability and consistency withthe empirical behaviour of yields in the real world. In this regard,

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the most salient empirical features of the US term structure are that

• the nominal yield curve is on average upward-sloping,

• the standard deviation of yields decreases with bond maturity,

• yields are highly autocorrelated,

• term premiums change over time,

• yields are not normally distributed.

Agood term structure model should reproduce all or most of thesecharacteristics, with the Gaussian autoregressive framework beingquite common, as it leads to closed-form solutions.

Note that the term structure models described in this chaptertry to econometrically identify model parameters under the phys-ical measure, together with the market price of risk, in a way thatis consistent with yield data. However, given that these parame-ters are estimated using data on yield curves over a time window,the term structure models do not exactly reproduce all zero-couponbond prices.2 The econometric emphasis is driven by the desire tounderstand the underlying drivers of the yield curve, and provideguidance for bond investors and policymakers alike. Assuming youtrust the model, discrepancies between actual bond prices and modelprices might indicate trading opportunities, and you might even tryto use the model to forecast the yield curve out-of-sample.

This is different from the approach that a bond derivatives traderwould take. The latter would not greatly care about the econometric(real world) identification of the factors driving the yield curve, butwould insist on a no-arbitrage model that can exactly reproduce theentire (initial) yield curve at the time of valuation, so that deriva-tives (for example, bond options) are priced consistently with theirunderlying (whether the latter is fairly priced or not). See Ho andLee (1986) and Heath et al (1992) for a rigorous treatment of thisapproach.

The expectation hypothesis and no-arbitrage modelsBefore the no-arbitrage term structure models, the most commonassumption on bond yields was that they represented the expec-tation of short-term rates (under the data-generating probabilitymeasure P). Specifically

yt,τ =1τ

EPt

[∫ t+τ

trs ds

]

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Clearly, this does not hold in general except when interest rates arecertain, as

• there is in general a non-zero price of risk, λs ≠ 0, and

• even if the price of risk were zero, so that investors are risk-neutral (not a plausible assumption), Jensen inequality terms(which can be substantial, especially for long-maturity yieldsand in high-volatility regimes) are present

EPt

[exp

(−∫ t+τ

trs ds

)]

def=−EP

t

[∫ t+τ

trs ds

]+ Jensen’s terms

Single-factor models of the short rate

Vasicek (1977) and Cox et al (1985) were the pioneers of the term-structure literature. In their models, bond yields are driven by onestochastic variable, namely, the short rate. Assuming no arbitrage,the short rate also determines zero-coupon bond prices, and thusthe whole term structure. In these one-factor models, yields of allmaturities are perfectly correlated (albeit not necessarily movingone-to-one).

In Vasicek (1977), the short rate has a normal distribution andfollows the one-dimensional stochastic process

drt = (θ −αrt)dt+ σ dBQt

where BQt is a standard Brownian motion under the risk-neutral

probability measure Q. The short rate in the Cox–Ingersoll–Ross(CIR) model has a non-central χ2 distribution and follows theprocess

drt = (θ −α · rt)dt+ σ · √rt dBQt

Both models have closed-form solutions for zero-coupon bondprices and yields. Note that since there is only one source of uncer-tainty here, we can hedge any bond with another bond of differentmaturity (using the appropriate hedge ratio). In other words, wecan build a risk-free portfolio using only two zero-coupon bonds ofdifferent maturities.

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Figure 10.2 Multi-factor term structure models

Stochasticstate variables

Instantaneousshort rate

Xt = (X1,t ,…,XN,t) rt = R(Xt

,t)

Multi-factor models of the short rate

Given that the assumption of perfect correlations among bond yieldsis clearly violated in practice, researchers have developed multi-factor models where the starting point is the specification of thedynamics of a vector of stochastic state variables (which, as thename implies, characterise the state of a dynamic system). LetXt = (X1,t, . . . , XN,t) denote the time-t value of an N-dimensionalvector Xt. One commonly used specification under the risk-neutralmeasure Q is as follows

dXt = µQ(Xt, t)dt+ ΣQ(Xt, t)dBQt

where BQt is an N-dimensional Brownian motion vector under Q

(ie, a Markov diffusion). Specific choices of the N-dimensional vec-tor µQ(Xt, t) and the N × N matrix ΣQ(Xt, t) will determine thebehaviour of the short rate, and consequently the price of the zero-coupon bonds, Pt,τ , and the yield yt,τ . Furthermore, the instantan-eous short rate rt is assumed to be a function of the vector of statevariables and time, ie, rt = R(Xt, t), as shown in Figure 10.2. Notethat in an N-factor model we can build a risk-free portfolio usingN + 1 zero-coupon bonds of different maturities.

Examples of multi-factor models include the class of affine termstructure models (see page 215), which include the multi-factorVasicek and CIR models as special cases.

As mentioned before, the Q-dynamics of state variables can betranslated into their counterpart under the P-measure by applyingthe exponential change of measure reviewed in the appendix onpage 236. Namely, the following transformation

dBPt + λt dt = dBQ

t

where λt is an N-dimensional vector of the market prices of risk foreach state variable in the system leading to the specification of X

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under P

dXt = µQ(Xt, t)dt+ ΣQ(Xt, t)dBQt

= µ(Xt, t)dt+ Σ(Xt, t)dBPt

Here BP is a P-Brownian motion and the drift and diffusion termsare given by

µ(Xt, t) = µQ(Xt, t)+ ΣQ(Xt, t)λt

Σ(Xt, t) = ΣQ(Xt, t)

Therefore, the change of measure affects only the drift vector,although under P the dynamics of the state vector is not necessar-ily affine anymore. Specifically, an affine diffusion under the risk-neutral measure Q will be affine under the data-generation measureP only if the vector ΣQ(Xt, t) · λt is itself affine.

How many factors are necessary?

Clearly, as a first step, the number of state variables, or factors, thatspan the time variation of bond yields needs to be determined. In aninfluential study, Litterman and Scheinkman (1991) show that threelatent factors can explain most of the variation in the term structureof nominal interest rates (ie, about 97% of their variance), and callthese three factors “level”, “slope” and “curvature”, respectively.3

As a result, most of the empirical and theoretical literature since thenhas considered three-factor term structure models of interest rates(ie, N = 3 in Figure 10.2). Note that, even with only three factors,there are a large number of parameters to be estimated. This impliesthat over-fitting might become an issue even for the parsimoniouslyspecified term structure models.

Affine term structure models

Although many choices can be made, one important class of modelsarises when

• the drift µQ(Xt, t),

• the variance matrix Σ(Xt, t)TΣ(Xt, t) and

• the short rate rt

are all assumed to be affine functions of the state variables (the super-script “T” indicates transposition). In such models, bond yields also

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turn out to be affine, and zero-coupon bond prices are exponentiallyaffine. Namely, we have

yt,τ = aτ + bTτXt

Pt,τ = exp[−yt,ττ] = exp(Aτ + BTτXt)

where aτ = −Aτ/τ is a scalar, and bτ = −Bτ/τ is an N×1 vector (asbefore, the superscript “T” indicates transposition). Affine dynamicterm structure models (DTSMs) allow for closed-form solutions ofbond prices as shown by Duffie and Kan (1996). This, in turn, makesit possible to explore the models’ ability to fit the time variationof bond yields and forecast expected bond excess returns (see theappendix on page 239 for details on the n-period expected returns).

Constant volatility affine AR(1) modelA simple affine specification, albeit not the most general one, isobtained by assuming a constant volatility matrix Σ and modellingthe state vector as an autoregressive AR(1) process, with both theshort rate and the price of risk depending linearly on the statevariables. In discrete time, this specification can be written as follows

Xt = µ +φXt−1 + Σ · BPt

rt = δ0 + δTXXt

λt = λ0 + λXXt

In this case, the state vector dynamics is clearly affine under both Q

and P measures. See the appendix on page 240 for explicit solutionsfor yields and bond price in this model.

However, note that for an N-dimensional state vector, the equa-tions above introduce a large number of parameters to be estimated(Table 10.1). This poses a common empirical challenge for all multi-factor term structure models. For example, for the case of N = 3,there are a total of 37 parameters to be determined.

Explicit solutions for yields and bond price for this simple modelare derived in the appendix on page 240.

Stochastic volatility modelsThe volatility matrix driving the evolution of the state vector doesnot need to be constant as in the simple AR(1) model introducedabove, and can, in general, be a function of time and the state vectoritself. However, in affine term structure models, the variance needs

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Table 10.1 Parameters in the affine constant volatility, AR(1) N -factormodel

µ Nφ N2

Σ N2

δ0 1δX Nλ0 NλX N2

Total 3N2 + 3N + 1

to be an affine function, so that the volatility matrix has the followingform (Dai and Singleton 2000)

Σ(Xt, t) = Σ0, s(Xt) = Σ0

√s0 + sT

x Xt

where Σ0 is an N ×N matrix, and s(Xt) is a diagonal N ×N matrix,ie

s(Xt) =

⎛⎜⎜⎜⎜⎜⎜⎜⎝

√s10 + sT

1xXt 0 · · · 0

0. . . 0 0

... 0. . . 0

0 0 0√

sN0 + sTNxXt

⎞⎟⎟⎟⎟⎟⎟⎟⎠

where s10, . . . , sN0 are scalars and sT1x, . . . , sT

Nx are 1×N row vectors.As mentioned earlier, to ensure that the dynamics is affine under

both Q and P measures, and that bond yields are affine, the productΣ(Xt, t) · λt should be affine (see also the appendix on page 240 onthis point). This implies that in stochastic volatility term structuremodels, the market price of risk is not affine. The most commonfunctional assumption for the market price of risk, albeit not themost general one (Dai and Singleton 2000), is

λt = s(Xt)λ0

where λ0 is an N × 1 column vector.Dai and Singleton (2000) classify term structure models by explor-

ing the trade-off between a relative goodness of fit and flexibility ofthe affine dynamic term structure models.4 They conclude that athree-factor model (N = 3), with conditional volatility driven byone factor, provides the best fit to historic movements of short- and

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long-term yields. As a comparison, three-factor models with twostate variables driving conditional volatilities require more restric-tions on correlations among factors in order to obtain well-definedbond prices, a property that Dai and Singleton call “admissibility”.

They also show that three-factor models with all three factorsaffecting conditional volatilities theoretically require that the con-ditional correlations be zero and that the unconditional correla-tions be non-negative. This property is inconsistent with histori-cal data of US interest rates, which points to empirically negativecorrelations. Consequently, three-factor models with all three fac-tors driving conditional volatilities are not used in term structuremodelling.

Duffee (2002) argues that “completely” affine models (ie, mod-els where zero-coupon bond yields under physical and risk-neutralmeasures are affine functions of the state vector) fail in forecast-ing future bond yields. He proposes a generalised version of thesemodels, called “essentially” affine DTSMs. These models retain allthe affine time-series and cross-sectional properties of bond prices,yet they allow for a greater flexibility in fitting time-varying mar-ket prices of risk. The essentially affine models nest the class ofcompletely affine models by specifying the market price of risk as

λt = s(Xt)λ0 + s−(Xt)λ1Xt

where

s−ii (Xt) =⎧⎨⎩

s(Xt)ii = (s0 + sTx Xt)−1/2 if inf(s0 + sT

x Xt) > 0

0 otherwise

and λ1 is an N × N matrix. While this formulation preserves thesame physical dynamics as completely affine models do, there aresome important differences. First, λT

t λt is no longer affine in Xt. Sec-ond, the essentially affine set-up allows for an independent variation(from bond yields) in prices of risk. Third, the sign restriction on theindividual elements of the market price of risk λt no longer exists.These features help to make more accurate yield forecasts, albeit ata cost of fitting interest rate volatility.

Dai and Singleton (2002) also generalise market prices of riskwithin the class of affine DTSMs in order to match key empiricalfindings of Fama and Bliss (1987) and Campbell and Shiller (1991).Dai et al (2010) consider a class of discrete-time, nonlinear dynamic

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term structure models, in which the distribution of the state vectoris affine under Q, while the market price of risk is nonlinear in Xt,leading to a nonlinear dynamics of the bond yields under the phys-ical measure P. Ahn et al (2002) and Leippold and Wu (2002) specifya class of term structure models where the short rate is a quadraticfunction of the underlying state vector.

Latent factors and macroeconomic variables

An important question facing financial economists is identificationof the latent factors and/or macroeconomic variables that can poten-tially explain the behaviour of the yield curve. This has motivateda new and yet fast growing literature on so-called “macro-finance”models that include observable macroeconomic variables into theterm structure models of nominal interest rates5 (see, for example,Kim (2009) and Duffee (forthcoming) for surveys of this literature).

In a pioneer study of macro-finance models, Ang and Piazzesi(2003) propose a five-factor no-arbitrage term structure model of thenominal yield curve, where two macroeconomic variables are iden-tified with real growth and inflation, and the remaining three factorsare latent and orthogonal to the two directly observable macro vari-ables; namely, the macro dynamics do not depend on interest rates,an assumption made for mathematical tractability.6 All five factorsare modelled in a Gaussian autoregressive framework, and the shortrate is assumed to be affine in the state vector and driven by growthand inflation (similarly to the Taylor rule) plus three latent factors.The market price of risk is also assumed to be an affine function ofthe five factors. In this set-up, yields are affine in state variables, termpremiums vary over time and yield data can be used to extract thelatent factors.

Ang and Piazzesi (2003) construct the two macroeconomic fac-tors taken to be the principal components of two baskets of eco-nomic variables, one representing price levels (including consumer,producer and commodities prices) and the other representing themeasures of real output (including employment and industrial pro-duction and two other variables). The coefficients for the inflationand growth factors are estimated in a regression framework underthe data-generating probability measure. Both coefficients are foundto be positive (ie, higher inflation and higher growth increase theshort-term rate), although the growth coefficient is dependent on the

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time window used for estimation. Bond data used to estimate thefive-factor term structure model are monthly nominal zero-couponyields (continuously compounded) over the period 1952–2000. Byusing the variance decomposition, Ang and Piazzesi show that thetwo macro factors are major drivers of yields, especially in the shortend of the yield curve, while the latent factors tend to dominate inthe long end of the curve.

To summarise, in addition to the aforementioned studies, the1990s and early 2000s produced a wealth of research regarding theinformation contained in the term structure of nominal interest rates.The interested reader can refer to a thorough treatment of DTSMsand their estimation by Singleton (2006) and a comprehensive reviewby Piazzesi (2010) for a more complete reference.

THE US TIPS MARKETTo a large extent, interest in the modelling of real interest rates hasbeen fostered by the development of the market for US TreasuryInflation-Protected Securities (TIPS), launched in 1997. Since then,government bond markets, the market for US Treasury nominal debtand the market for inflation-indexed debt have provided an excel-lent laboratory for studying macroeconomic issues such as infer-ring inflation expectations, estimating inflation risk premiums andextracting the probability of deflation. See Campbell et al (2009) for adetailed and comprehensive overview of inflation-indexed marketsin both the US and the UK.

Initially the TIPS market did not attract the attention of manyresearchers, partly due to its liquidity problems, and partly becauseinflation (or disinflation) concerns were not as common in late 1990sas they are at the time of writing. However, in the late 200s thischanged, in part because rising global risks contributed to a “flight-to-quality” from riskier equities markets to safer markets such asthe markets for US Treasury nominal and inflation-indexed debt.For instance, according to Morningstar (2010), total net asset valuesof TIPS funds increased by more than 54% (or about US$19.5 billion)over the one-year period from January 2009 to January 2010.

The most important feature of TIPS is that their principal and, con-sequently, the coupon payments are linked to the value of the Con-sumer Price Index (CPI). As such, these payments are denominatedin real rather than nominal terms, and thus TIPS can be considered

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to be almost free of inflation risk. The qualifier “almost” is relatedto the fact that TIPS prices are linked to the inflation index, but withan interpolated lag of between two and three months.7 The differ-ence between nominal Treasury and TIPS yields of equivalent matu-rities represents a compensation required by investors for bearinginflation risk, and is sometimes referred to as a break-even infla-tion rate. This compensation includes both expected inflation andan inflation risk premium due to inflation uncertainty and, in addi-tion, a potential liquidity premium. See Bekaert and Wang (2010) fora comprehensive survey focusing on the inflation risk premium.

Given that the TIPS market has grown significantly and its liquid-ity has improved, researchers have naturally become interested inmodelling the term structure of real interest rates, ie, the term struc-ture of the TIPS yields that can be interpreted as real interest rates.This issue is of considerable interest to both bond investors and pol-icymakers because the joint dynamics of nominal and real interestrates also determine the dynamics of inflation expectations and infla-tion risk premiums.8 First, more accurate forecasts of real rates canprovide more accurate information about future economy growth.Second, joint modelling of the term structures of nominal and realrates provides a wealth of information about inflation compensationand its two components, the expected inflation and the inflationrisk premium. While the literature on the term structure of nomi-nal yields is quite mature, financial economists started developingmodels on real interest rates only in the early 2000s.

Parts (a) and (b) of Figure 10.3 show the 10-year zero-coupon USnominal yield and the TIPS real yield from 2000 onwards; part (c)shows the break-even inflation rate. Note that the 10-year yieldsare used in the figure because they are believed to reflect long-termexpectations about inflation and economy growth. The time series inFigure 10.3 are based on the fitted yield curve procedure of Svensson(1994), which is an extension of Nelson and Siegel (1987). Gurkaynaket al (2010) describe Svensson’s fitting procedure applied to TIPSdata.

MODELLING BOTH REAL AND NOMINAL TERM STRUCTURESThe goal of developing the real term structure models is some-what different from the one behind nominal term structure models.Here, researchers are interested not only in fitting the yield curve

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Figure 10.3 Ten zero-coupon nominal and TIPS yields and inflationbreak-even rates

8

6

4

2

0

6

4

3

2

0

2

1

2000 2002 2004 2006 2008 2010 2012

2000 2002 2004 2006 2008 2010 2012

2000 2002 2004 2006 2008 2010 2012

(a)

(b)

(c)

%

%

%

(a) Ten-year nominal yields; (b) ten-year TIPS yields; (c) ten-year inflation com-pensation.Source: Grishchenko and Huang (2010).

and forecasting excess bond returns, but also in assessing inflationexpectations and inflation risk premiums.

We can write two separate equations (derived in the appendixon page 245), one for real and one for nominal yields, in order toidentify the different risk premiums affecting one and/or the other.Neglecting Jensen’s terms, we have

YRt,τ =

EPt (IR

t,τ)+T Rt,τ

andYN

t,τ =1τ

EPt (IR

t,τ)+1τ

EPt [It,τ]+T R

t,τ + IRPt,τ

where T Rt,τ denotes the real interest rate risk premium and IRPt,τ is

the inflation risk premium.As mentioned earlier, the break-even inflation rate, BEIt,τ , ie, the

difference between nominal and TIPS yields, represents the amountof inflation compensation that investors in the nominal Treasury

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debt require (ignoring liquidity) and is frequently referenced bypolicymakers and market participants alike. Inflation compensa-tion itself consists of expected inflation EP

t [Iinft,τ ]/τ and an inflation

risk premium IRPt,x (see the appendixes on pages 242–248 for themathematical details)

yNt,τ − yR

t,τ = BEIt,τ = 1τ

EPt [Iinf

t,τ ]+ IRPt,τ

Obviously, the inflation risk premium depends on the correlationbetween the real rates and inflation.9 The equation above showshow movements in nominal rates are the result of changes in realrates and the inflation break-even rate.

As Figure 10.2(c) shows, inflation compensation (the differencebetween nominal and real yield) has been quite variable in the 10-year period 2001–11. An interesting question is the extent to whichthis time variation is due to changes in inflation expectations versusthose in the inflation risk premium.

Note that we need to be careful about defining real yields. Theseare not necessary equal to TIPS yields because of

(i) liquidity problems associated with TIPS, such as before 2004and during the financial crisis in autumn 2008,

(ii) inflation indexation lag in the TIPS and

(iii) the embedded deflation floor.

These issues, and possible solutions, are discussed later.As for nominal models, real term structure models also impose

specific restrictions on the factor dynamics in the risk-neutral world,in order to be consistent with empirical data in the real world.For example, Fama (1990) documents that the one-year expectedinflation rate and the expected real return on one-year bonds movein opposite directions and are related to business-cycle conditions(using the yield spread on a five-year bond over the one-year spotrate as a proxy). Yield spread is countercyclical: it is high (low)around business troughs (peaks). Fama finds that the yield spread ispositively related to changes in inflation and negatively to changesin real returns. In particular, the yield spread forecasts a drop ininflation and increase in real returns after business cycle peaks.Thus, a successful term structure model should generate a negativecorrelation between expected inflation and real rates.

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A BRIEF REVIEW OF THE LITERATURE

The literature on real term structure models starts with the workof Barr and Campbell (1997), who model expected log inflation andreal interest rates as trend-stationary autoregressive AR(1)processes(ie, a time-series approach). Using UK inflation-indexed data, theyfind that changes in real rates and expected inflation are negativelycorrelated at long, but not short, horizons.

Ang et al (2008) use a three-factor (two latent ones and one observ-able) regime-switching model in order to derive both nominal andreal yields, and isolate each of the two components of inflation com-pensation: inflation expectations and inflation risk premium. Theyuse a time-varying but regime-independent market price of risk(latent) factor, a (latent) regime-switching factor and an observableinflation factor. In the empirical analysis, nominal yields (one-year,three-year and five-year maturities) and US CPI data are used forcalibration, while real yields are derived within the model. The three-factor model can generate a negative correlation between real ratesand inflation (both unexpected and expected) at short maturities,albeit the correlation turns positive at long maturities. Furthermore,Ang et al show that real rates are mostly flat across maturities, ie,there is no real rate term premium, and that the positive nominalyield term premium is due to inflation compensation (a flat expectedinflation term plus an upward-sloping risk premium). Results fromvariance decomposition show that only 20% of changes in nominalyields is due to changes in real rates, while the remaining 80% iscaused by changes in inflation compensation. Expected inflation isfound to be the main driver even at short maturities (80% at the one-year horizon; 70% at the five-year horizon), while the inflation riskpremium contributes 0% of variance at one-year maturity and 10%of variance at the five-year maturity. In other words, the positivenominal term premium is mostly due to an upward-sloping infla-tion risk premium, but most of the dynamics of the nominal curveare explained by changes in inflation expectations.

An interesting approach is pursued in Chernov and Mueller(forthcoming), who model the term-structure and inflation expec-tations using a five-factor model, with two macro variables (the USreal GDP and CPI) and three latent factors. The first two latent factorsare easily identified as the factors driving the “level” and “slope” of

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nominal rates. The third latent factor is interpreted as a “level” fac-tor for survey inflation expectations (survey-based inflation expec-tations are formed in the real-world probability). While inflationaffects the nominal curve, this latent “survey factor” does not (it is“hidden”), and it represents information about the expected path ofinflation, which is not captured by inflation itself. In addition to quar-terly GDP and CPI data, both nominal and real (ie, US TIPS) yieldsare used in the calibration, as well as inflation expectations fromthree popular market surveys (the Livingston Survey, the Surveyof Professional Forecasters and the Blue Chip Economic IndicatorsSurvey)10. The “survey factor” and survey inflation data are foundto greatly increase out-of-sample forecasting of future inflation. Thestudy also points out the following two consequences of using USTIPS data (from 2003 onwards):

1. the average level of real yields is higher (implying a loweraverage inflation risk premium);

2. real rates are more volatile (implying a decline in the volatilityof the inflation risk premium).

The above findings might partly be caused by liquidity problemson the TIPS market. For example, higher real yields might includea liquidity premium that would result in the downward bias ofthe average inflation risk premium. Therefore, liquidity should beaccounted for when TIPS yields are modelled. D’Amico et al (2009)were among the first to take into account TIPS liquidity in a model ofboth nominal yields and TIPS yields. They found that, while threeprincipal components explain over 97% of weekly nominal yieldchanges, a fourth factor is needed to explain the changes of bothnominal yields and TIPS yields. The latter factor can be interpretedas a liquidity premium in TIPS yields, while the remaining three arethe usual level, slope and curvature (latent) factors driving both yieldcurves. Thus, they use a four-factor Gaussian term structure, wherenominal and US TIPS yields are modelled jointly in order to estimatethe TIPS liquidity premium, expected inflation and inflation risk pre-mium. D’Amico et al show that ignoring the liquidity component canlead to severely biased estimates of expected inflation and inflationrisk premiums. Specifically, if TIPS yields are identified with realrates, model-implied inflation expectations do not fit the empiricaldownwards trend observed in inflation survey data over time, and

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the estimates of the inflation risk premium are low or even negative.When the liquidity factor is introduced, the D’Amico et al modelis able to reproduce the downwards trend in expected inflation, aswell as positive inflation risk premium. Consequently, a change inTIPS break-even rates cannot simply be interpreted as a change ininflation expectations, as both the inflation and the liquidity riskpremiums play important roles.

Adrian and Wu (2010) used a five-factor model with two inflationfactors, two real factors and a factor that governs the dynamics ofvariances and co-variances of state variables. They found that infla-tion expectations differ significantly from the break-even inflationrate when inflation volatility is high. Chen et al (2010) estimated atwo-factor term structure model with real rates and expected infla-tion as state variables, and found that the expected inflation is flat,while the inflation risk premium is upward sloping (in line with Anget al (2008)).

Haubrich et al (2011) estimated a seven-factor term structuremodel, using nominal Treasury yields, inflation survey forecasts(from the Blue Chip Economic Indicators Survey and the Survey ofProfessional Forecasters), realised inflation rates and zero-couponinflation swaps rates. Their data span the period from January 1982to May 2010 (although the inflation swap data only starts in April2003). Inflation swaps are the most liquid inflation derivative con-tracts and are quoted for maturities ranging from one year to 30 years(see Chapters 7 and 8 herein). They assume that nominal and realyields are driven by three state variables that represent the short-term real interest rate, expected inflation and long-run inflation(what they call “inflation’s central tendency”), in addition to fourvolatility (price of risk) factors, which are a mix of normal and chi-squared innovations, follow Garch processes and determine bondrisk premiums. Haubrich et al found that the short real interest rateis the most volatile component of the yield curve and displays sig-nificant mean reversion. Expected inflation over short horizons wasalso found to be volatile, negatively correlated to the real rate andmean reverting. Long-term inflation expectations declined substan-tially over the 1982–2010 sample period, consistent with the FederalReserve’s credibility in maintaining price stability. The study alsofound evidence of a real interest rate term premiumT R

t,τ , which wassubstantial, averaging 102 basis points (bp) and varying between

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TERM STRUCTURE OF INTEREST RATES AND EXPECTED INFLATION

87 and 121bp for the 10-year zero-coupon bonds over the sampleperiod. The 10-year inflation risk premium has an upward-slopingterm structure, with the average of 42bp and varying between 23and 55bp over the sample period. Incidentally, the real interest ratesrisk premium was also found to be predominant in the eurozonearea (Hördahl and Tristani 2007), although an inflation premiumwas also present.

According to Haubrich et al, one advantage of their approach isthat the inflation expectations and real yields obtained from theirmodel are more accurate, because inflation swap rates are lessaffected by liquidity problems in the TIPS market. However, somemarket participants point out that the inflation swaps market is con-siderably more illiquid than the TIPS market, and inflation-swapimplied break-evens are consistently higher than TIPS-based break-evens by about 20bp.11 Therefore, it may be interesting to see if thedifference between inflation swap rates and TIPS inflation break-even rates tends to be correlated with liquidity measures such asthe bid–ask spread in the TIPS market. Note that, during the marketdislocation in autumn 2008, bid–ask spreads widened considerablyin the TIPS market, but this effect was much more muted in theinflation swap market.

Buraschi and Jiltsov (2005) provide a structural approach to esti-mating inflation expectations. They developed a real business cyclemodel with a monetary channel to study the nature of deviationsfrom the expectations hypothesis and estimated a term structure ofthe inflation risk premium. In their model, the inflation risk premiumwas upward sloping, with the estimates between 20 and 140bp andan average of 70bp at the 10-year maturity over the sample period1961–2000.

An alternative “model-free” approach can be found in Grish-chenko and Huang (2010), which, in the spirit of Evans (1998), isarbitrage-free and also easy to implement. Specifically, this approachtakes the nominal and TIPS yields as given, and does not involveany term structure model. Furthermore, various measures of infla-tion forecasts are used to identify expected inflation, and the inflationrisk premium can be estimated without using a term structure modeleither. Grishchenko and Huang derived real yields by includingtwo explicit adjustments to TIPS yields, a three-month TIPS index-ation lag correction and a liquidity premium. Taking these two into

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INF

LA

TIO

N-S

EN

SIT

IVE

AS

SE

TS

Table 10.2 Real and nominal term structure models

Reference Model specification Data used

Barr and Campbell (1997) Two factors, expected inflation and real rate are UK inflation-indexed bondstrend-stationary AR(1) processes

Campbell and Viceira (2001) Two factors: expected inflation and log real rate N/Aare AR(1) processes

Ang and Piazzesi (2003) Five factors: inflation and economic growth and US Treasury bonds, CPI,three latent factors real activity measures

Buraschi and Jiltsov (2005) Structural monetary real business cycle model US Treasury bonds,CPI, M2

Ang et al (2008) Three factors: inflation rate, two latent factors US Treasury bonds, CPIChernov and Mueller (2008) Three factors: inflation, output, short interest rate US Treasury bonds,

CPI, GDPAdrian and Wu (2010) Five factors: inflation, real rates, US Treasury bonds,

variance–covariance factor TIPS, CPID’Amico et al (2009) Four factors: three latent factors and US Treasury bonds,

one liquidity factor TIPS, CPI, surveysGrishchenko and Huang (2010) Model-free approach US Treasury bonds, TIPS,

CPI, surveysChen et al (2010) Two factors: real rate and expected inflation US Treasury bonds, TIPS, CPIHaubrich et al (2011) Seven factors: real rate, two inflation factors and US Treasury bonds, TIPS,

four volatility factors surveys, inflation swap ratesGrishchenko et al (2011) Two factors: nominal rate and inflation US Treasury bonds, TIPS, CPI

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TERM STRUCTURE OF INTEREST RATES AND EXPECTED INFLATION

account, they found that the inflation risk premium overall does notexceed 10bp. This estimate is much lower than those obtained ear-lier via various structural model estimations. Table 10.2 provides asummary of the models in this literature.

ZERO-COUPON TIPS YIELDS VERSUS REAL YIELDS

Liquidity effect in TIPS

Simple TIPS yields are biased estimates of real yields, as they areknown to contain a sizeable liquidity premium, at least in the earlyyears of the development of the TIPS market. Therefore, we needto make an appropriate correction when working with TIPS yields.Clearly, illiquidity drives TIPS prices down and TIPS yields up. Ifwe abstract for a moment from the issue of the indexation lag, thedifference between TIPS yields yTIPS

t,τ and real yields yRt,τ is attributed

to a liquidity premium Lt,τ

yTIPSt,τ = yR

t,τ + Lt,τ

This implies the following relation among nominal yields yNt,τ ,

TIPS yields, the liquidity premium, inflation expectations and theinflation risk premium

yNt,τ = yTIPS

t,τ − Lt,τ + 1τ

EPt [Iinf

t,τ ]+ IRPt,τ

The above equation shows that the inflation risk premium might beunderstated if the liquidity adjustment Lt,τ is ignored. We can useseveral methods to estimate the liquidity premium. For example,Lt,τ can be calculated as the difference between real yields (derivedwithin a term structure model) and actual TIPS yields. Alternatively,we can use other estimation techniques that are less dependent onmodel specification, such as simply comparing TIPS prices with abenchmark fitted curve, or regressing TIPS break-evens on severalproxies for market liquidity.

As mentioned earlier, D’Amico et al (2009) used a four-factor affineterm structure model to fit both nominal and real term structures.In their model, the instantaneous real rate, the instantaneous nom-inal rate, the price of nominal rates risk and the price of real ratesrisk are affine functions of three latent factors Xt = (X1t, X2t, X3t).In addition, the liquidity premium (and an instantaneous liquidity

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INFLATION-SENSITIVE ASSETS

spread) is explicitly modelled as the sum of a deterministic maturity-independent downwards trend Ld

τ , and an (affine) stochastic com-ponent Ls

t,τ that depends on the three latent factors mentioned above(ie, on the status of the economy) plus a fourth (TIPS-specific) factorXt orthogonal to the others

Lt,τ = Ldτ + Ls

t,τ

Lst,τ = aτ + bT

τXt + cτXt

where bTτ is a 1 × 3 row vector and cτ is a scalar. The TIPS liquid-

ity premium represents the difference between TIPS yields and realyields and has both a deterministic component (which decreases thepremium over time to account for the increased liquidity in the USTIPS market) and a stochastic component (in general, correlated withthe three latent factors driving both real and nominal yield curves).D’Amico et al found that the deterministic liquidity component pre-mium was high in the early 2000s (as high as 120bp in 1999), butcame down significantly to about 10bp in 2004–5. After removingthis deterministic trend, D’Amico et al found that stochastic com-ponent of the liquidity risk premium has been stationary since thenand had varied between−50 and 50bp. The term structure of the liq-uidity premium in their model is, generally, flat. D’Amico et al alsofound that the variation in the 10-year liquidity premium drivesover 20% (but with large standard errors) of the variation in infla-tion break-even rates, while the rest is due to variation in inflationexpectations (55%) and inflation risk premium (about 25%). As foryields, US TIPS yield variance is dominated by changes in real yields(119% at the 10-year horizon, with the rest−19% due to the liquiditypremium), while changes in the 10-year nominal yields are due tochanges in real yields (67%), changes in inflation expectations (23%)and variation in inflation risk premium (10%), in contrast with, forexample, Ang et al (2008).

Pflueger and Viceira (2011) derive a higher estimate, about 70bp,for the liquidity premium in normal years (outside early TIPS years,when the liquidity spread was in excess of 100bp, and the 2008–9financial crisis, when it reached over 200bp). They regress the TIPSinflation break-evens on four proxies for market liquidity, ie, the off-the-run 10-year nominal spread, the GNMAspread to the on-the-runnominal treasury, the difference in trading volumes between TIPSand nominal treasuries, and the difference in 10-year asset-swap

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spreads between TIPS and nominal treasuries

BEIt,τ = a0 + b1X1t + b2X2t + b3X3t + b4X4t + εt

Clearly, variables that indicate worsening (improving) liquidityshould lower (increase) the TIPS break-even rate and enter with anegative (positive) slope coefficient. As the independent variablesare normalised to be zero in conditions of perfect liquidity, the liq-uidity premium is taken as the maturity independent estimate fromthe regression above, specifically

Lt = −(b1X1t + b2X2t + b3X3t + b4X4t)

Grishchenko and Huang (2010) computed a liquidity risk premiumusing a regression approach similar to that in Pflueger and Viceira(2011), but controlling for structural changes in liquidity conditionsthrough the 2000s. They found that, while the former is relativelysmall in magnitude, the TIPS liquidity premium was substantial inthe early 2000s (albeit lower than the levels obtained by D’Amico etal (2009) and Pflueger and Viceira (2011)), thereby driving the wedgebetween TIPS yields and real yields.

To conclude, despite different estimates of the magnitude of theliquidity premium, it is clear that a bias exists, and the liquidity effectshould be taken into account when estimating inflation expectationsand inflation risk premiums.

Indexation lag in TIPS

Fully indexed bonds are different from the TIPS, as the latter includesa three-month indexation lag in the CPI level for computing nomi-nal cashflows throughout the bond’s life and also a deflation protec-tion upon maturity. The indexation lag is an interpolation betweena three-month lag and a two-month lag because the price level is acontinuous process, but we measure inflation monthly. Thus, someresearchers view the indexation lag as a 2.5-month lag, while oth-ers assume that investors observe TIPS prices and yields on the lastbusiness day of the month (for settlement on the first day of the fol-lowing month), so that the interpolation lag in the daily price indexis exactly three months. For simplicity of exposition, we considerthe case with the exact three-month indexation lag correction. Thisdoes not materially affect our exposition. The indexation lag cor-rection between real and TIPS yields is derived in the appendix on

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INFLATION-SENSITIVE ASSETS

pages 243–244 and is given by

yRt,τ−3M = yTIPS

t,τ − lagt,τ

Deflation floor in TIPS

The deflation floor, or deflation protection, in TIPS refers to the factthat the principal payment of the TIPS cannot fall below the statedprincipal value in the contract. Thus, if the cumulative inflation isnegative over the bond’s life, the principal payment is not reviseddownwards. The same is not true for TIPS coupon payments, whichcan be revised upwards or downwards based on the cumulativeinflation applied at the time of the calculation. Typically, the valueof the deflation floor is neglected when computing the model-basedTIPS prices and yields. This introduces a negative bias to real yieldscalculated without including the floor, although it could be arguedthat, at least historically (for example, in autumn 2008), the liquidityeffect, which acts in the opposite direction, has dominated.

Grishchenko et al (2011) use a two-factor affine Gaussian model ofthe nominal short rate (using the three-month Treasury bill rate as aproxy) and inflation (using the non-seasonally adjusted CPI, whichis the same index TIPS are linked to) to derive closed-form solutionsfor the values of both TIPS (including the deflation floor) and nomi-nal bonds. Using the data from January 1997 to May 2010, they foundthat the embedded deflation option was economically and statisti-cally significant. Ten-year estimated deflation floor values vary fromzero to US$0.0615 per US$100 face value, while five-year estimatesare substantially larger, with a maximum of US$1.45 per US$100 facevalue. Thus, shorter-term values of deflation floors implied by TIPSprices are higher than longer-term ones. This result is not surprising,given that the TIPS indexation is linked to a cumulative inflation overthe life of the bond. Therefore, it is more likely that a shorter-termoption will end up in-the-money than a longer-term option will. Thereason is that historically cumulative inflation has been larger overthe longer horizons than over the shorter ones, due to the positiveinflation in most of the periods with a few exceptions. For example,the CPI actually fell during two consecutive months in autumn 2008.Finally, Grishchenko et al showed that the time variation in the valueof deflation floor option is useful for predicting future inflation, evenwhen more traditional variables are included.

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IDENTIFICATION ISSUES: INFLATION EXPECTATION VERSUSRISK PREMIUMAs mentioned above, identification issues arise because inflationcompensation includes both the expected inflation, It,τ , and theinflation risk premium, IRPt,τ , as follows

yNt,τ − yR

t,τ =1τ

EPt [Iinf

t,τ ]+ IRPt,τ

Within the affine framework, Iinft,τ is also an affine function of state

variables. In such a set-up, once the model parameters are estimated,expected inflation is calculated within the model, while the inflationrisk premium is computed as the difference between inflation com-pensation, yN

t,τ − yRt,τ , and expected inflation, EP

t [Iinft,τ ]. Although this

approach is perfectly consistent when working with the affine DTSMmodels, its implementation requires assumptions about the num-ber of factors, their identification (observable versus latent), and theunderlying factor dynamics (eg, Gaussian versus square root versusregime-switching models).

IMPLICATIONS FOR INVESTORS AND POLICYMAKERSBenefitting from an increasing set of empirical data thanks to therapid growth in the US TIPS and other inflation-linked markets, theresearch on real term structure models has important implicationsfor both bond market investors and policymakers alike. Bond marketparticipants are interested in the forecasting aspect of these modelsfor trading purposes, while monetary policymakers use these mod-els to understand the links between the short and long ends of thecurve, and to gauge inflation expectations.

In addition, term structure models are valuable tools for the USTreasury to determine the best funding options, such as choices ondebt maturity and the issuance of nominal versus inflation-linkedbonds. TIPS can potentially provide significant savings in fundingcosts for the US Treasury because it can issue inflation-indexed debtat lower inflation-adjusted yields than otherwise comparable nomi-nal Treasury debt (although initially the TIPS programme was asso-ciated with significant liquidity-related costs to the Treasury; seeRoush 2008). The reason is that the inflation risk premium does nothave to be paid to “real” bond investors, as opposed to investorsin the nominal US Treasury debt market. Dudley et al (2009) esti-mated the 10-year inflation risk premium to be around 40bp, and

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INFLATION-SENSITIVE ASSETS

concluded that the Treasury could have saved as much as US$22 toUS$32 billion if the TIPS market had been as liquid as the market foroff-the-run nominal Treasury debt.

TIPS are also an important market pricing mechanism, a barom-eter of the market inflation expectations and real rates, and thusare quite useful to policymakers. Given that overall price stabilityis one of the objectives of the Federal Reserve, TIPS can be used tohelp gauge whether long-term inflation expectations remain wellanchored, especially in the face of (short-term) inflation shocks. Fur-thermore, TIPS provide incentives for responsible fiscal policy. Therecognition by the general public and the market that the govern-ment will have to make higher nominal payments on TIPS if infla-tion rises contributes to fiscal credibility and well-behaved inflationexpectations. As an added benefit, the Treasury Department can bet-ter match revenues and expenditures, because TIPS are linked toinflation (as are tax receipts).

Finally, TIPS may give “the Treasury access to a broader investorbase, which may reduce the overall funding costs” (Bitsberger 2003).Indeed, it seems that TIPS have been successful in providing diver-sification benefits to investors. Several studies, including Campbelland Viceira (2001), Campbell et al (2003, 2009), Kothari and Shanken(2004), Roll (2004), Dudley et al (2009), Barnes et al (2010), Bekaertand Wang (2010) and Huang and Zhong (2011) have supported thisclaim. Campbell et al (2009) and Huang and Zhong (2011) providefurther evidence on the negative correlations between TIPS andstock returns. For instance, Campbell et al show that TIPS and theCenter for Research in Security Prices (CRSP) Stock Value-WeightedIndex are predominantly negatively correlated over the period 1999–2009. Huang and Zhong document that the dynamic conditional cor-relation as defined in Engle (2002) between TIPS and the S&P 500index was mostly negative during the period 1999–2010, and that theunconditional correlation between the two asset classes was −0.18over the same period.

Studies of real term structure models also play an important rolein the development of the inflation-linked derivatives market. Forinstance, consider the fast growing inflation swaps market. Thesecontracts are used by dealers to hedge their cash TIPS position, andby other market participants to receive or pay inflation over a specificterm. Inflation swaps can also be used as an alternative measure of

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inflation expectations (Haubrich et al 2011). In addition, investorscan implement an arbitrage strategy using inflation swaps, as shownin Fleckenstein et al (2010). For other inflation-indexed derivatives,such as swaptions, caps and floors, see, for example, Ho et al (2011).

CONCLUSIONS

We have reviewed only a few of the most standard nominal and realterm structure models within the affine framework, and discussedrecent empirical evidence regarding the performance of these mod-els. Identification issues and liquidity problems in the TIPS mar-ket (clearly evident during the financial crisis of 2008–9) were alsodiscussed. In addition, we have summarised the estimates of infla-tion expectations and inflation risk premium that real term structuremodels have produced.

Although, as discussed in detail, different papers take distinctapproaches to the study of this topic and, in particular, to the iden-tification of the several components of real and nominal yields, thekey conclusion is that, in the US, both inflation expectations andinflation risk premiums have been diminishing and well behaved,in line with the Federal Reserve dual mandate to foster maximumemployment and in the context of price stability.

APPENDIXES BY STEFANIA A. PERRUCCI12

Bond prices are expectations under the risk-neutral measure

In the absence of arbitrage, bond prices Pt,τ discounted by the appro-priate numeraire Nt are martingales under the risk-neutral measureQ. That is

N−1t Pt,τ = E

Qt [N−1

t+τPt+τ ,0] = EQt [N−1

t+τ · 1] (10.1)

Choosing the money market (the cash bond) as the numeraire

Nt = exp(∫ t

0rs ds

)(10.2)

the dynamics of the short rate rs determines the whole term structure,ie, the entire zero-coupon yield curve yt,τ

Pt,τ = exp[−yt,ττ] = EQt

[exp

(−∫ t+τ

trs ds

)](10.3)

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The market price of risk

Astandard functional assumption for the discrete one-period changein measure is the exponential form

ξt+1

ξt= exp( 1

2λTt λt − λT

t BPt+1) (10.4)

where λt is an N-dimensional vector, also called the price of risk,and BP

t+1 is a standard (zero drift) N-dimensional Brownian motionunder the physical measure P. In continuous time, this correspondsto the following differential equation

dξt = −ξtλTt dBP

t (10.5)

which has the solution

ξt+τξt

= exp(−1

2

∫ t+τ

tλT

s λs ds−∫ t+τ

tλT

s dBPs

)(10.6)

If BPt is a standard (zero drift) Brownian motion under P, then it can

be shown that

BPt +

∫ t

0λs ds = BQ

t (10.7)

dBPt + λt dt = dBQ

t (10.8)

or, in discrete time

BPt + λt−1 = BQ

t (10.9)

is a standard Brownian motion under the risk-neutral measure Q. Inother words, BP

t has zero drift under P, but it acquires instantaneousdrift −λt under Q.

Zero-coupon bond prices under both measures

Bond prices can be calculated under either the risk-neutral measureor the physical measure, after adjusting for the appropriate changein probability density. Under the former

Pt,τ = EQt

[exp

(−∫ t+τ

trs ds

)](10.10)

Under the physical measure

Pt,τ = EPt

[ξt+τξt

exp(−∫ t+τ

trs ds

)]= EP

t

[Mt+τ

Mt

](10.11)

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where the nominal pricing kernel Mt is defined as

Mt = ξt exp(−∫ t

0rs ds

)(10.12)

Using the exponential form for the change in probability measureintroduced in the previous appendix, the pricing kernel satisfies thestochastic differential equation

dMt

Mt= −rt dt− λT

t dBPt (10.13)

The price of a zero-coupon bond is then given by

Pt,τ = EPt

[exp

(−1

2

∫ t+τ

tλT

s λs ds−∫ t+τ

tλT

s dBPs

)

× exp(−∫ t+τ

trs ds

)]

def= EPt

[exp

(−1

2

∫ t+τ

tλT

s λs ds−∫ t+τ

tλT

s dBPs

)]

× EPt

[exp

(−∫ t+τ

trs ds

)]

+ covPt

[exp

(−1

2

∫ t+τ

tλT

s λs ds−∫ t+τ

tλT

s dBPs

),

exp(−∫ t+τ

trs ds

)](10.14)

where the last equality follows from the very definition of covari-ance. We define

Λt,τdef= exp

(−1

2

∫ t+τ

tλT

s λs ds−∫ t+τ

tλT

s dBPs

)(10.15)

Then we can rewrite the price of a zero-coupon bond as follows

Pt,τ = EPt [Λt,τ]EP

t

[exp

(−∫ t+τ

trs ds

)]

+ covPt

[Λ(t,τ), exp

(−∫ t+τ

trs ds

)](10.16)

This equation can be used to calculate bond prices given the spec-ification of the short rate and the price of risk under the physicalmeasure P.

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INFLATION-SENSITIVE ASSETS

Calculations of zero-coupon bond pricesAs an example of the equivalency of using either probability mea-sure, we now consider a zero-coupon bond. Working again in dis-crete time for simplicity, the time-t price of a one-period bond isgiven by (under the risk-neutral measure Q)

Pt,1 = EQt [exp(−rt)] = exp(−rt) (10.17)

The same result can be obtained working under the physical measureP as follows

Pt,1 = EPt

[ξt+1

ξtexp(−rt)

]

= exp(−rt − 12λ

Tt λt)EP

t [exp(−λTt BP

t+1)]

= exp(−rt − 12λ

Tt λt) exp(+ 1

2λTt λt)

= exp(−rt) (10.18)

The term premiumThe bond term premium Tt,τ is the compensation required to bearthe interest rate risk. It can be defined as the difference between thenominal yield and the yield we would obtain if the price of risk werezero

Tt,τ = yt,τ − yt,τ(λs = 0)

= yt,τ + 1τ

ln(

EPt

[exp

(−∫ t+τ

trs ds

)])(10.19)

Tt,τ = − 1τ

ln(EPt [Λt,τ])

− 1τ

ln[

1+ covPt [Λt,τ , exp(−

∫ t+τt rs ds)]

EPt [Λt,τ]EP

t [exp(−∫ t+τ

t rs ds)]

](10.20)

Clearly, the bond term premium depends on the functional form ofthe price of risk λs, and it is zero if the price of risk is zero. Note thatif bonds yields are affine, then the term premium will also be affine.

Bond prices in discrete timeGiven a bond with time to maturity τ at time t, ie, Pt,τ will have timeto maturity τ − 1 at t+ 1, we obtain the following recursive relation

Pt,τ = EQt [exp(−rt)Pt+1,τ−1]

= EPt

[ξt+1

ξtexp(−rt)Pt+1,τ−1

](10.21)

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In discrete time, the nominal pricing kernel is defined as

mNt+1 =

ξt+1

ξtexp(−rt) (10.22)

and the nominal zero-coupon bond price is given by

Pt,τ = EPt

[ τ∏i=1

mNt+i

](10.23)

Bond expected n-period return

Consider the zero-coupon bond price Pt,τ at time t. The continuouslycompounded return of such a bond over n periods (n τ) is givenby

1n

ln[

Pt+n,τ−n

Pt,τ

]= 1

nln Pt+n,τ−n − 1

nln Pt,τ (10.24)

Its expectation value at time t is given by

ρnt,τ =

1n

EPt ln

[Pt+n,τ−n

Pt,τ

]= 1

nEP

t ln[Pt+n,τ−n]+ τn yt,τ (10.25)

We typically compare the expected return over the n-period holdingwindow with the (expected) return of the n-maturity zero-coupon.The n-period excess return for the zero-coupon bond is then definedas follows

ρnt,τ − yt,n = 1

nEP

t ln[Pt+n,τ−n]+ τn yt,τ − yt,n (10.26)

Consider the simple autoregressive affine model with constantvolatility. In this model, the price of zero-coupon bonds is expo-nentially affine and given by

Pt,τ = exp[−yt,ττ]

= exp(Aτ + BTτXt) (10.27)

Pt+n,τ−n = exp[−yt+n,τ−n(τ − n)]

= exp(Aτ−n + BTτ−nXt+n) (10.28)

Furthermore, since the drift of the state vector is affine, ie

Xt = µ +φXt−1 + Brownian motion (10.29)

the expectation of Xt+n conditional to time t

EPt [Xt+n] = αn + βnXt (10.30)

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INFLATION-SENSITIVE ASSETS

is also affine, where

αn = µ(1−φn)1−φ and βn = φn (10.31)

As a consequence, the expected n-period excess return is affine inthe state variables

ρnt,τ − yt,n =

Aτ−n − Aτ +An + BTτ−nαn

n+ (B

Tτ−nβn − BT

τ + BTn )Xt

n(10.32)

For example, if we take the holding period to be n = 1, the aboveexpression becomes

ρ1t,τ − yt,1 = (Aτ−1 −Aτ +A1 + BT

τ−1µ)+ (BTτ−1φ− BT

τ + BT1 )Xt

= BTτ−1Σλ0 − 1

2 BTτ−1ΣΣ

TBτ−1 + BTτ−1ΣλXXt (10.33)

This shows that a deterministic price of risk (λX = 0) cannotreproduce stochastic expected excess returns.

Constant volatility AR(1) affine model

Within the class of affine models, we consider the simple affineAR(1) diffusion introduced before, with the constant N×N volatil-ity matrixΣ (not dependent on the state variables, although it might,in more general specifications, depend on time)

Xt = µ +φ · Xt−1 + ΣBPt (10.34)

rt = δ0 + δTXXt (10.35)

λt = λ0 + λXXt (10.36)

We will work in discrete time in order to deal with finite differ-ence equations rather than differential equations. Introduced in theappendix on page 238, the following relation

Pt,τ = EPt

[ξt+1

ξtexp(−rt)Pt+1,τ−1

](10.37)

can help us build the whole yield curve at time t, starting fromthe one-period short rate rt. Furthermore, since this rate is assumedto be affine in the state vector, this property clearly extends to thewhole yield curve, thanks to the recursive expression above. In fact,suppose Pt,τ−1 is exponentially affine, ie

Pt,τ−1 = exp(Aτ−1 + BTτ−1Xt) (10.38)

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TERM STRUCTURE OF INTEREST RATES AND EXPECTED INFLATION

Then, recalling the expression for the change in probability densityintroduced in Equation 10.4 we have

Pt,τ = EPt

[ξt+1

ξtexp(−rt)Pt+1,τ−1

]

= exp(−rt − 12λ

Tt λt +Aτ−1)

× EPt [exp(−λT

t BPτ−1 + BT

τ−1Xt+1)]

= exp(−rt − 12λ

Tt λt +Aτ−1)

× EPt [exp(−λT

t BPτ−1 + BT

τ−1Xt+1)]

= exp(−rt − 12λ

Tt λt +Aτ−1 + BT

τ−1µ + BTτ−1φXt)

× EPt [exp[(−λT

t + BTτ−1Σ)BP

t+1]] (10.39)

where the following relation has been used to arrive at the lastequality

Xt+1 = µ +φXt + ΣBPt+1 (10.40)

The expectation of the exponential of the Brownian motion iseasily calculated as

EPt [exp[(−λT

t + BTτ−1Σ)]BP

t+1]

= exp( 12λ

Tt λt + 1

2 BTτ−1ΣΣ

TBτ−1 − BTτ−1Σλt) (10.41)

Note the quadratic terms in the price of risk cancel out, so we areleft with

Pt,τ = exp(−rt +Aτ−1 + BTτ−1µ + BT

τ−1φXt

+ 12 BTτ−1ΣΣTBτ−1 − BT

τ−1Σλt) (10.42)

which is clearly exponentially affine as long as the short rate rt, theprocess variance ΣΣT, its drift µ + φXt and Σλt are exponentiallyaffine. Specifically

Pt,τ = exp(Aτ + BTτ ·Xt) (10.43)

where, after rearranging terms

Aτ = −δ0 +Aτ−1 + BTτ−1(µ − Σλ0)+ 1

2 BTτ−1ΣΣTBτ−1 (10.44)

BTτ = −δT

X + BTτ−1(φ− ΣΛX) (10.45)

with initial conditions A0 = 0 and BT0 = 0.

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INFLATION-SENSITIVE ASSETS

Real bonds, indexed bonds and TIPSThe barter economy and basket-denominated zero-coupon bonds

We can imagine a barter economy where contracts are specified interms of a basket of good and services. In other words, the zero-coupon bond in the barter economy promises one unit of the con-sumption basket at maturity in exchange for a fraction of the bas-ket today. Assuming the barter economy is complete and there areno arbitrage opportunities, after specifying a numeraire, there willbe a unique risk-neutral probability measure QR under which allbasket-denominated tradeable instruments of the barter economyare martingales. For the zero-coupon bonds, paying one unit of theconsumption basket at maturity, we have the expressions

PRt,τ = E

QR

t

[exp

(−∫ t+τ

trR

s ds)]= EP

t

[ξR

t+τξR

texp

(−∫ t+τ

trR

s ds)]

(10.46)

PRt,τ = EP

t

[MR

t+τMR

t

]= [exp(−yR

t,ττ)] (10.47)

dBPt + λR

t dt = dBQR

t (10.48)

The dollar economy and no-arbitrage condition between pricingkernels

In the dollar economy, the basket-denominated bond PRt,τ is not a

tradeable instrument, but its dollar value QtPRt,τ is. Therefore, to

avoid arbitrage, the dollar value of the real bond discounted by thenominal money market numeraire must be a QN martingale

N−1t QtPR

t,τ = EQN

t [N−1t+τQt+τPR

t+τ ,0] = EQN

t [N−1t+τQt+τ] (10.49)

or in the data-generating probability measure

PRt,τ = EP

t

[ξN

t+τξN

texp

(−∫ t+τ

trN

s ds)

Qt+τQt

]

= EPt

[MN

t+τMN

t

Qt+τQt

]

= EPt

[MR

t+τMR

t

](10.50)

Therefore, no arbitrage requires that pricing kernels are such that

MRt = MN

t Qt (10.51)

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Dollar-denominated indexed zero-coupon bonds

Consider the dollar-denominated zero-coupon bond Pindexedt0,t,τ index-

ed to the price index Qt, starting at t0 t, maturing at time T = t+τ.At maturity, its dollar payout is

Pindexedt0,t+τ,0 =

Qt+τQt0

(10.52)

Therefore, in the dollar (nominal) risk-neutral probability measureQN, its price at time t is given by

Pindexedt0,t,τ = E

QN

t

[exp

(−∫ t+τ

trN

s ds)

Qt+τQt

]

= Qt

Qt0

EQN

t

[exp

(−∫ t+τ

trN

s ds)

Qt+τQt

]

= Qt

Qt0

EPt

[ξN

t+τξN

texp

(−∫ t+τ

trN

s ds)

Qt+τQt

]

= Qt

Qt0

EPt

[MN

t+τMN

t

Qt+τQt

](10.53)

That is, using the no-arbitrage condition

Pindexedt0,t,τ = Qt

Qt0

PRt,τ (10.54)

wheredBP

t + λNt dt = dBQN

t (10.55)

Inflation-linked zero-coupon bonds

Note that the indexed zero-coupon bond is different from the zero-coupon TIPS, as the latter includes a three-month indexation lag andalso a deflation floor. The indexation lag is an interpolation betweena three-month lag and a two-month lag, but, for simplicity, we willassume that we observe TIPS prices and yields on the last businessday of the month (for settlement T+1 on the first day of the followingmonth), so that the interpolation lag in the daily price index is exactlythree months. Thus, the TIPS principal payout at maturity is

PTIPSt0,t+τ,0 =

Qt+τ−3M

Qbase+max

[1− Qt+τ−3M

Qbase, 0]

(10.56)

where Qbase is the index base value (see Chapter 7). Typically, thevalue of the deflation floor is neglected when computing zero-coupon TIPS yields. This introduces a negative bias to real yields cal-culated without including the floor, although it could be argued that,

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INFLATION-SENSITIVE ASSETS

at least historically, the liquidity effect, which acts in the oppositedirection, has dominated

PTIPSt0,t,τ = EP

t

[MN

t+τMN

t

Qt+τ−3M

Qbase

]

= Qt

QbaseEP

t

[MN

t+τ−3M

MNt

Qt+τ−3M

Qt

MNt+τ

MNt+τ−3M

](10.57)

PTIPSt0,t,τ =

Qt

Qbase

[PR

t,τ−3MEPt

[MN

t+τMN

t+τ−3M

]

+ covPt

(MN

t+τ−3M

MNt

Qt+τ−3M

Qt,

MNt+τ

MNt+τ−3M

)]

= Qt

QbasePR

t,τ−3MEPt

[MN

t+τMN

t+τ−3M

]

×

⎡⎢⎢⎢⎢⎣1+

covPt

(MN

t+τ−3M

MNt

Qt+τ−3M

Qt,

MNt+τ

MNt+τ−3M

)

PRt,τ−3MEP

t

[MN

t+τMN

t+τ−3M

]

⎤⎥⎥⎥⎥⎦ (10.58)

If we define

lagt,τ = −1τ

ln EPt

[MN

t+τMN

t+τ−3M

]

− 1τ

ln

⎡⎢⎢⎢⎢⎣1+

covPt

(MN

t+τ−3M

MNt

Qt+τ−3M

Qt,

MNt+τ

MNt+τ−3M

)

PRt,τ−3MEP

t

[MN

t+τMN

t+τ−3M

]

⎤⎥⎥⎥⎥⎦

(10.59)

and since (see Chapter 7)

Qbase

QtPTIPS

t0,t,τ = exp[−yTIPSt,x τ] (10.60)

we then have

yTIPSt,τ = yR

t,τ−3M + lagt,τ (10.61)

yRt,τ−3M = yTIPS

t,τ − lagt,τ (10.62)

The index process

Let Qt represent the stochastic evolution of a price index under thereal world probability measure P

Qt+τQt

= exp[(∫ t+τ

tis ds

)+ σT

Q(BPt+τ − BP

t )]

(10.63)

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where σQ is an N × 1 vector. The presence of the Brownian motiontermσT

Q(BPt+τ−BP

t ) in the exponential might (or might not) come as asurprise. In fact, we could model the price index without an explicitBrownian motion term, by simply allowing is to be a function ofthe stochastic state variables. However, the model above is moregeneral and allows for a better fit to the implied volatility surfaceof both nominal rates options and inflation options (not the focus ofthis chapter but still the reason why such a model is predominant).The price index above satisfies the stochastic differential equations13

dQt

Qt= (it + 1

2σTQσQ)dt+ σT

Q dBPt (10.64)

or, alternativelyd ln Qt = it dt+ σT

Q dBPt (10.65)

Note that

lnQt

Qt+τ= −

∫ t+τ

tis ds− σT

Q(BPt+τ − BP

t ) (10.66)

and

− 1τ

EPt

[ln

Qt

Qt+τ

]= 1τ

EPt

∫ t+τ

tis ds (10.67)

The price index might represent, for example, the US ConsumerPrice Index, while is can be interpreted as the instantaneous rate ofinflation.

Real term premium and inflation premiumReal bond yields and real term premium

Similarly to the appendix on page 236 for nominal bond prices,we can derive an analogous relation for basket-denominated zero-coupon bond prices

PRt,τ = EP

t [ΛRt,τ]E

Pt

[exp

(−∫ t+τ

trR

s ds)]

+ covPt

[ΛR

t,τ , exp(−∫ t+τ

trR

s ds)]

= EPt [ΛR

t,τ]EPt

[exp

(−∫ t+τ

trR

s ds)]

×[

1+ covPt [ΛR

t,τ , exp(−∫ t+τ

t rRs ds)]

EPt [ΛR

t,τ]EPt [exp(−

∫ t+τt rR

s ds)]

](10.68)

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INFLATION-SENSITIVE ASSETS

whereΛRt,τ is a function of the price of real risk, similar to that defined

previously. If we introduce a real yield term premium as

T Rt,τ = −

ln(EPt [ΛR

t,τ])

− 1τ

ln[

1+ covPt [ΛR

t,τ , exp(−∫ t+τ

t rRs ds)]

EPt [ΛR

t,τ]EPt [exp(−

∫ t+τt rR

s ds)]

](10.69)

we can derive the real bond yields

yRt,τ = −

EPt

[exp

(−∫ t+τ

trR

s ds)]+T R

t,τ (10.70)

Finally, if we define the integral

IRt,τ =

∫ t+τ

trR

s ds (10.71)

we can write the real yield as a sum of the τ-period expectation ofthe instantaneous real rate, plus a Jensen inequality term, plus thereal term premium

yRt,τ =

EPt (IR

t,τ)+− 1τ

ln EPt [exp(−IR

t,τ)]+1τ

EPt (IR

t,τ)

︸ ︷︷ ︸Jensen’s term

+T Rt,τ

(10.72)If we assume IR

t,τ is normally distributed conditional to informa-tion at time t (ie, an affine model), then we can explicitly calculatethe Jensen term and we have

EPt [exp(−IR

t,τ)] = exp[−EPt (IR

t,τ)+ 12 vart(IR

t,τ)] (10.73)

ln EPt [exp(−IR

t,τ)] = −EPt (IR

t,τ)+ 12 vart(IR

t,τ) (10.74)

Therefore

yRt,τ =

EPt (IR

t,τ)−1

2τvart(IR

t,τ)+T Rt,τ (10.75)

where the first term on the right-hand side represents the τ-periodexpectation of the instantaneous real rate at time t, the second termis the Jensen inequality term and the last term is the real rates termpremium.

Nominal yields and the inflation risk premium

We have already derived nominal yields and term premium in aprevious appendix, but here we express these in terms of real yields,

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TERM STRUCTURE OF INTEREST RATES AND EXPECTED INFLATION

inflation expectations and inflation risk premium

PNt,τ = EP

t

[MN

t+τMN

t

]= EP

t

[MR

t+τQt

MRt Qt+τ

]

= EPt

[MR

t+τMR

t

]EP

t

[Qt

Qt+τ

]+ covP

t

[MR

t+τMR

t,

Qt

Qt+τ

]

= PRt,τEP

t

[Qt

Qt+τ

]+ covP

t

[MR

t+τMR

t,

Qt

Qt+τ

]

= PRt,τEP

t

[Qt

Qt+τ

][1+ covP

t [MRt+τ/MR

t , Qt/Qt+τ]PR

t,τEPt [Qt/Qt+τ]

](10.76)

yNt,τ = yR

t,τ −1τ

EPt

[Qt

Qt+τ

]− 1τ

ln[

1+ covPt [MR

t+τ/MRt , Qt/Qt+τ]

PRt,τEP

t [Qt/Qt+τ]

]

(10.77)

The Jensen term can be identified as follows

ln EPt

[Qt

Qt+τ

]= EP

t

[ln

Qt

Qt+τ

]+ ln EP

t

[Qt

Qt+τ

]− EP

t

[ln

Qt

Qt+τ

]︸ ︷︷ ︸

Jensen’s term

(10.78)The inflation risk premium, IRPt,τ , is given by

IRPt,τ = − 1τ

ln[

1+ covPt [MR

t+τ/MRt , Qt/Qt+τ]

PRt,τEP

t [Qt/Qt+τ]

](10.79)

Note that the inflation risk premium is positive if there is negativecovariance between the price index and the real pricing kernel.

Since

− 1τ

EPt

[ln

Qt

Qt+τ

]= 1τ

EPt

∫ t+τ

tis ds = 1

τEP

t [Iinft,τ ] (10.80)

we have

yNt,τ = yR

t,τ +1τ

EPt

∫ t+τ

tis ds

− 1τ

ln EP

t

[Qt

Qt+τ

]− EP

t

[ln

Qt

Qt+τ

]︸ ︷︷ ︸

Jensen’s term

+ IRPt,τ (10.81)

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INFLATION-SENSITIVE ASSETS

Collecting the two (real rate and price index) Jensen’s termstogether

Jensent,τ = −1τ

EPt [exp(−IR

t,τ)]−1τ

EPt (IR

t,τ)

− 1τ

ln EPt

[Qt

Qt+τ

]+ 1τ

EPt

[(ln

Qt

Qt+τ

)](10.82)

so that

yNt,τ =

EPt (IR

t,τ)+1τ

EPt [Iinf

t,τ ]︸ ︷︷ ︸expectations

+ T Rt,τ︸ ︷︷ ︸

real term premium

+ IRPt,τ︸ ︷︷ ︸inflation premium

+ Jensent,τ (10.83)

Affine models of both real and nominal term structuresThe nominal term-structure pricing kernel

dMNt

MNt= −rN

t dt− λNTt dBP

t (10.84)

BPt + λN

t dt = dBQN

t (10.85)

where QN is the nominal risk-neutral probability measure, underwhich discounted zero-coupon nominal bonds are martingales, and

rNt = δN

0 + δNTX Xt (10.86)

λNt = λN

0 + λNTX Xt (10.87)

The real term-structure pricing kernel

dMRt

MRt= −rR

t dt− λRTt dBP

t (10.88)

BPt + λR

t dt = dBQR

t (10.89)

where QR is the real risk-neutral measure that makes discountedzero-coupon basket-denominated bonds martingales, and

rRt = δR

0 + δRTX Xt (10.90)

λRt = λR

0 + λRTX Xt (10.91)

Under the data-generating measure P, the pricing index satisfies

Qt+τQt

= exp[(∫ t+τ

tis ds

)+ σT

Q(BPt+τ − BP

t )]

(10.92)

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where the instantaneous inflation is also assumed to be an affinefunction of the state variables

it = δi0 + δiT

X Xt (10.93)

In this simple formulation, inflation is driven by the same threefactors that drive the nominal and real yields. However, we mighteasily include additional imperfectly correlated (or uncorrelated)factors into the model.14

Nominal and real term structure parameters

Using the no-arbitrage relation between pricing kernels

MRt = MN

t Qt (10.94)

and, applying Itô’s lemma

dMRt = MN

t dQt +Qt dMNt − λNT

t σQMNt Qt dt (10.95)

we can relate the real and nominal parameters as follows

dMRt

MRt= dQt

Qt+ dMN

t

MNt− λNT

t σQ dt (10.96)

−rRt dt− λRT

t dBPt = (it + 1

2σTQσQ)dt+ σT

Q dBPt − rN

t dt

− λNTt dBP

t − λNTt σQ dt (10.97)

so that

rRt = rN

t − (it + 12σ

TQσQ)+ λNT

t σQ (10.98)

λRt = λN

t − σQ (10.99)

Thus,

δR0 = δN

0 − δi0 − 1

2σTQσQ + λNT

0 σQ (10.100)

δRX = δN

X − δiX + λNT

X σQ (10.101)

λR0 = λN

0 − σQ (10.102)

λRX = λN

X (10.103)

Note that we have been working under the data-generating proba-bility measure, where the price index satisfies

dQt

Qt= (it + 1

2σTQσQ)dt+ σT

Q dBPt (10.104)

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INFLATION-SENSITIVE ASSETS

However, by using the following relations

rNt − rR

t = (it + 12σ

TQσQ)− λNT

t σQ (10.105)

dBPt = dBQN

t − λNt dt = dBQR

t − λRt dt (10.106)

we can derive the price index evolution under the two (nominal andreal) risk-neutral measures

dQt

Qt= (rN

t − rRt )dt+ σT

Q dBQN

t

= (rNt − rR

t + σTQσQ)dt+ σT

Q dBQR

t (10.107)

We thank Stefania Perrucci for very detailed and helpful commentsand suggestions that have helped to improve this chapter signif-icantly. We also thank Min Wei and Refet Gurkaynak for helpfuldiscussions and comments. The views expressed here are solelythose of the authors and do not necessarily reflect the concurrenceby other members of the research staff or the Board of Governorsof the Federal Reserve System.

1 Equivalent probability measures agree on what is possible. In other words, impossible eventswill have zero probability under both measures, and possible events will have different butpositive probabilities for both measures.

2 In particular, only a number of yields equal to the number of latent factors can be exactly fittedat all points in time (for example, three yields can be exactly fitted in a three-latent-variablemodel).

3 Latent factors refer to their lack of further interpretation, although there are cases where amacroeconomic identification might be possible.

4 In other words, the ideal model should be flexible enough to capture the term-structuredynamics, and yet remain mathematically tractable.

5 Note that in many older treatments of this topic, real yields were assumed constant, andtherefore nominal yields changes were simply driven by changes in inflation expectations(the risk premium is obviously zero in this case). This is partly due to the fact that real yieldsare observable (lags and liquidity premium consideration aside) only in countries wherea government inflation-linked market is developed, so the empirical study of real yieldsdynamics has in many cases been limited by the availability of data.

6 In a later paper (Ang et al 2005), the Taylor rule includes only one latent factor contemporane-ously uncorrelated with growth and inflation. The latter assumption is reasonable (as growthand inflation will react with a lag to monetary shocks), and allows for unbiased (albeit notefficient) ordinary least square estimation of the coefficients in the Taylor equation.

7 Grishchenko and Huang (2010) estimate that this effect does not exceed four basis points interms of the real yield. In addition, inflation-linked bonds also have duration risk.

8 Here and later, we refer to real term structure models as models that include the dynam-ics of the instantaneous real rate and the instantaneous inflation, expected inflation or theinstantaneous nominal rate.

9 To be precise, there is both a risk premium (covariance term) and a Jensen’s inequality term(variance term).

10 See http://www.phil.frb.org/ and http://www.aspenpublishers.com.

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TERM STRUCTURE OF INTEREST RATES AND EXPECTED INFLATION

11 Internal estimates by the Federal Reserve Board staff.

12 Stefania would like to thank Lars Tyge Nielsen for helpful comments and review.

13 Other treatments of the topic put the variance term in the price index expression, so that itdisappears in the stochastic differential equation.

14 For an example, see D’Amico et al (2009).

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D’Amico, S., D. H. Kim and M. Wei, 2009, “Tips from TIPS: The Informational Contentof Treasury Inflation-Protected Security Prices”, Working Paper 2010-19, Federal ReserveBoard, Washington, DC.

Dudley, W., J. Roush and M. Steinberg Ezer, 2009, “The Case for TIPS: An Examinationof the Costs and Benefits”, Economic Policy Review 15(1).

Duffee, G., Forthcoming, “The Term Structure and the Macroeconomy”, in G. Constan-tinides, M. Harris and R. Stultz (eds), Handbook of the Economics of Finance (Elsevier).

Duffie, D., and R. Kan, 1996, “AYield-Factor Model of Interest Rates”, Mathematical Finance6, pp. 379–406.

Engle, R., 2002, “Dynamic Conditional Correlation: A Simple Class of Multivariate Gen-eralized Autoregressive Conditional Heteroskedasticity Models”, Journal of Business andEconomic Statistics 20, pp. 339–50.

Evans, M., 1998, “Real Rates, Expected Inflation, and Inflation Risk Premia”, The Journalof Finance 53, pp. 187–218.

Fama, E. F., 1990, “Term-Structure Forecasts of Interest Rates, Inflation and Real Returns”,Journal of Monetary Economics 25, pp. 56–76.

Fama, E. F., and R. R. Bliss, 1987, “The Information in Long-Maturity Forward Rates”, TheAmerican Economic Review 77, pp. 680–92.

Fleckenstein, M., F. A. Longstaff and H. Lustig, 2010, “Why Does the Treasury Issue TIPS?The TIPS-Treasury Bond Puzzle”, Working Paper, UCLA.

Grishchenko, O. V., and J.-Z. Huang, 2010, “Inflation Risk Premium: Evidence from theTIPS Market”, SSRN eLibrary, URL: http://ssrn.com/abstract=1108401.

Grishchenko, O. V., J. M. Vanden and J. Zhang, 2011, “The Informational Content of theEmbedded Deflation Option in TIPS”, SSRN eLibrary, URL: http://ssrn.com/abstract=1695511.

Gurkaynak, R., B. Sack and J. H. Wright, 2010, “The TIPS Yield Curve and InflationCompensation”, American Economic Journal: Macroeconomics 2, pp. 70–92.

Haubrich, J., G. G. Pennacchi and P. Ritchken, 2011, “Estimating Real and Nominal TermStructures Using Treasury Yields, Inflation Forecasts, and Inflation Swap Rates”, SSRNeLibrary, URL: http://ssrn.com/abstract=1361219.

Heath, D., R. Jarrow and A. Morton, 1992, “Bond Pricing and the Term Structure of InterestRates: A New Methodology”, Econometrica 60, pp. 77–105.

Ho, H.-W., H. Huang and Y. Yildirim, 2011, “Affine Model of Inflation-Indexed Derivativesand Inflation Risk Premium”, Working Paper, National Central University of Taiwan andSyracuse University.

Ho, T. S. Y., and S.-B. Lee, 1986, “Term Structure Movements and Pricing Interest RateContingent Claims”, The Journal of Finance 41, pp. 1011–28.

Hördahl, P., and O. Tristani, 2007, “Inflation Risk Premia in the Term Structure of InterestRates”, Working Paper Series, No. 734, European Central Bank.

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Huang, J.-Z., and Z. Zhong, 2011, “Time Variation in Diversification Benefits of Com-modity, REITs, and TIPS”, Journal of Real Estate Finance and Economics, DOI:10.1007/s11146-011-9311-6.

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Leippold, M., and L. Wu, 2002, “Option Pricing under the Quadratic Class”, Journal ofFinancial and Quantitative Analysis 37, pp. 271–95.

Litterman, R., and J. Scheinkman, 1991, “Common Factors Affecting Bond Returns”,Journal of Fixed Income 1, pp. 54–61.

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Nelson, C. R., and A. F. Siegel, 1987, “Parsimonious Modeling of the Yield Curves”, Journalof Business 60, 473–89.

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11

Monetary Policy, Inflation andCommodity Prices

Frank Browne, David CroninCentral Bank of Ireland

The interaction between commodity prices, general inflation andmonetary policy has re-emerged in recent years as a topic of interestamong academic economists, central bankers and financial marketparticipants alike. A sustained, broadly based increase in commod-ity prices started in the mid 2000s, and rising prices have also beenevident in other major asset classes (stocks, bonds, property). Theseprice increases occurred against a monetary policy stance, in themajor advanced industrial countries, that was viewed as broadlyaccommodating in many quarters at that time, and as being appro-priate given that general inflation rates, eg, consumer price index(CPI) inflation rates, were relatively low, and within or close to tar-gets set for, or by, central banks. Moreover, rising commodity priceswere not seen as having any substantial impact on consumer prices.

Most asset prices started to decline in late 2007. Commodity pricesfell rapidly and steeply in the second half of 2008. Ironically, thisoccurred against a background of policy interest rates being reducedto close to zero, and an unconventional monetary policy tool, quanti-tative easing, being introduced by the main central banks. Since then,and against a background of a continuing accommodative monetarypolicy stance, commodity prices have regained upward momentum.

While the pick-up in commodity prices since 2009 has had aneffect on the headline consumer inflation rate, its “core inflation”component, as measured by headline CPI inflation minus its foodand energy components, remains close to acceptable values in themajor developed countries. Commodity price developments, then,

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do not seem to be translating into a broadly based effect on consumerprices, in contrast to the 1970s and early 1980s. This feature of recentdata, and indeed the ability of core inflation to remain anchored atlow values through the 1990s and the 2000s regardless of the shockshitting the economy, has been attributed to the adoption of a mone-tary policy framework, inflation targeting, that has as one of its maingoals stopping one-off price pressures becoming embedded in infla-tion expectations. Of course, another factor behind the diminish-ing pass-through from commodity prices to consumer prices is thesmaller role that raw materials, most notably oil, play in economicactivity in modern developed economies.

It is, nevertheless, now clear that the inflation-targeting frame-work has been found wanting. It did not provide any advance warn-ing of the effect of collapsing bubbles or the massive deflationaryforces unleashed as a consequence. This stemmed, in our view, fromits neglect of the role of asset prices, as well as the vast changesthat have occurred in the financial system since roughly the mid1990s, which have enhanced the substitutability between money andfinancial assets.

This short overview points to the need to examine a number ofspecific issues in seeking to improve our understanding of the nexusbetween commodity prices, CPI inflation and monetary policy. Set-ting an explicit numerical target for inflation, or at least a target oflow and stable inflation, plays a critical role in monetary policy at thetime of writing. This practice of “inflation targeting” anchors priceexpectations, by requiring central banks to set out their inflationtarget and how they intend to achieve it, and holding them account-able for meeting that target. As well as explaining the rationale forand practice of inflation targeting, we also provide an overview ofcriticism of this monetary policy strategy, in particular, versions ofit that ignore developments in financial markets and in money andcredit variables. This strategy meant that central banks, by remainingsteadfast to inflation targeting in the face of imbalances and distor-tions evident in asset markets, contributed to the financial crisis thatwas precipitated in 2007.

The challenges in addressing and rectifying the current difficultiesin financial markets, and the wider economy, are acute for leadingcentral banks, such as the Federal Reserve and the European CentralBank. Policy interest rates are close to zero, thus limiting their scope

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as instruments of monetary policy. As discussed later, one policyinnovation brought in in response to the loss of leverage from con-ventional monetary policy instruments has been quantitative easing.In increasing the amount of liquidity in the economy, and in reducingthe yield on a competing asset class, government bonds, quantitativeeasing may have stoked the surge in commodity prices since 2009.

It may also be that a “super-cycle” is present in commodity mar-kets, with rising prices therein not a temporary phenomenon butpart of a long period of sustained high commodity prices. This isowing to countries such as China and India emerging as industrialsuperpowers, leading to an increased demand for commodities asindustrial inputs, and in building up capacity in those economies.1

At the same time, there appears to be a stronger co-movement inthe prices of different commodities. This suggests that there may becommon factors at play in commodity markets. One such possibil-ity is that the growing treatment of commodities as a separate assetclass, and their being added to asset portfolios as a means of reduc-ing the risk of those portfolios, may have increased co-movement intheir prices.

Another viewpoint, discussed in detail later in this chapter,stresses the capacity of commodity prices in general to respondquickly to changes in monetary policy and, indeed, to overshootequilibrium values, so as to maintain overall prices in the economyin line with the level of the money stock (Frankel 2008; Browne andCronin 2010). High commodity prices then can occur in responseto loose monetary policy conditions, such as have existed since theearly 2000s, and are consistent with a low CPI inflation rate in theshort-to-medium term, with that inflation rate rising subsequently.

INFLATION-TARGETING AND MODERN MONETARYPOLICYMAKINGThe 1970s and early 1980s proved to be difficult times for centralbanks. High inflation rates and low, and even on occasion negative,growth rates (a phenomenon known as “stagflation”) were a featureof the economic environment in many Western countries. Cost-push-related policy measures (direct control of wage and price increases)were pursued in the 1970s to address this malaise, but were unsuc-cessful in bringing inflation down from high rates. Later, however,a form of the quantity theory of money,2 labelled monetarism and

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most closely associated with economist Milton Friedman, came toform the basis for reducing inflation. The so-called Volcker disinfla-tion (named after the former Federal Reserve chairman) in the USsaw the Federal Reserve aggressively raise interest rates in the early1980s, with inflation subsequently declining.

The intervening quarter of a century, up to the late 2000s, saw adecline in inflation rates to low single-digit figures, occurring along-side generally buoyant economic growth. Furthermore, the variabil-ity of inflation, and output growth rates, fell progressively. Whilethere is an acknowledgement that “good luck” in the form of fewerlarge shocks, such as oil price shocks, played its part, it is commonlyaccepted that improvements in macroeconomic policy, in partic-ular, monetary policy, were central to the economic stability andprosperity achieved during this period.

As might be expected, the negative experiences of the 1970s stim-ulated a lot of research in how monetary policy could be improved inpractice. Among the earliest advances in that research was the iden-tification of structural credibility problems in the conduct of mon-etary policy. Specifically, it was found that rules were better thandiscretion in guiding policy. Adherence to rules leaves the publicmore assured as to how the central bank conducts itself and, accord-ingly, guides its own expectations and behaviour that are, in turn,key to the success of monetary policy. In practice, rules-based mon-etary policy was supported by the granting of independent statutesto central banks. This often included specific inflation targets to beachieved. In essence, three “Cs” came to underlie central banking:credibility, consistency and continuity (Stark 2007).

A clear focus on the need to maintain price stability became thecentrepiece of central banks’ activities. Through the late 1980s andinto the 1990s, central banks were increasingly successful at achiev-ing price stability. With inflation reduced to moderate levels, andtheir standing high, central banks faced a new set of challenges inthe 1990s. First, having reduced inflation, over the previous 10 yearsor so, to low levels, central banks now needed to maintain infla-tion rates close to the price stability benchmarks explicit or implicitin their statutes. Secondly, the high standing of central banks meantthat their statements and comments were carefully scrutinised by thepublic. Communication was vital to the success of monetary policy,and openness and transparency were recognised as key elements of

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the communication policy. At the same time, central banks had to becareful and precise in explaining their monetary policy actions andintentions, so that the public would not misinterpret, or be confusedabout, what was being said.

A number of concurrent developments in academic research andpolicy analysis seemed to provide a means of conducting and com-municating monetary policy. Explicit numerical inflation bench-marks were often set for, or by, central banks, and those inflationtargets became the focal point of decision-making. The Taylor Rule(Taylor 1993), named after its proposer, Professor John Taylor, wasinitially used as a descriptive tool, but was promoted in some cir-cles as a means of setting monetary policy. Under this rule, thecentral bank would mechanically set the short-term interest rateas a function of the deviation of the actual inflation rate from itstarget rate and the deviation of output (GNP/GDP) growth fromits long-run potential growth rate. The Taylor Rule became one ofthe three key elements of the so-called “New Keynesian” modelof the economy, which offered, according to its advocates, a par-simonious, but integrated and realistic, description of aggregatedemand and inflation determination. Even where central banksdo not explicitly follow the Taylor Rule, it is accepted as playinga prominent role in how many go about devising their monetarypolicy stance.

There is no need for a money demand function or, indeed, for anymoney variable within the inflation-targeting paradigm. Instead,inflation is seen as originating in the labour market rather thanin money markets. A version of the Phillips curve,3 where the sizeof the output gap indicates inflationary pressures within the econ-omy, plays an important analytical role in the inflation-targetingapproach. These developments in macroeconomic modelling hap-pened to coincide with increased difficulties in assessing and fore-casting the public’s demand for holding money balances. In the USespecially, where the New Keynesian perspective is particularly pop-ular among academics, financial innovation and liberalisation madeit difficult to model the demand for money successfully. The devel-opment of near-money substitutes, such as mutual funds, made ithard to ascertain the public’s demand for money if it shifted its liquidwealth between money and near-money assets. Consequently, theinformation coming from the monetary sphere was not as helpful

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to monetary policy formulation as previously. Accordingly, whatcould be termed “economic analysis”, ie, analysis focusing on thereal economy, became increasingly stressed as the basis for mon-etary policy decision-making. Aggregate demand (and its com-ponents), potential output/aggregate supply, unemployment andinflation expectations are the key variables to be assessed in thissphere.

Inflation targeting appears to have been a success, at least in termsof inflation performance. In a review of emerging market economies,the International Monetary Fund (2005) found that those countriesthat followed an inflation-targeting approach had a better inflationperformance than non-targeting countries, in terms of both averageinflation rates and volatility of those rates. Habermeier et al (2009)found that inflation-targeting countries appear to have done betterthan others in minimising the inflationary impact of the 2007 surgein commodity prices.

This approach has benefited the investment community. Theforward-looking approach taken by central banks to assessing infla-tionary pressures, their willingness to disclose publicly the basisfor their monetary policy decisions, and their determination toensure any price developments do not become embedded in infla-tion expectations, have provided investors with confidence thatswings in inflation rates are not likely to impact on financial out-turns. Furthermore, to the extent that price stability leads to a bet-ter allocation of resources in the economy (one of the main ratio-nales for its pursuit), the waste that is thereby obviated shouldaccrue to investors in the form of an enhanced risk-adjusted rateof return.

The culmination of events in the new millennium, however, hasseen the inflation-targeting approach to monetary policy come underthe spotlight. Most importantly, the question arises as to whetherinflation targeting itself played a role in the shocks and events thathave affected developed economies severely. Advocates of inflationtargeting do not see monetary policy having to react to changesin asset prices, other than to use any information they may pro-vide as to how final goods inflation rates will develop over time.Likewise, as long as central banks remain focused on the long-termpath of the inflation rate, and maintain it close to target values,periodic variations in headline inflation rates owing to commodity

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prices are not of great concern. The credibility afforded to mone-tary policy by inflation targeting can also diminish economies’ vul-nerability to the inflationary impact of commodity price shocks,by ensuring those shocks do not become embedded in expectedinflation.

The narrow focus on the real economy and performance asso-ciated with inflation targeting nevertheless means that importantinformation concerning developments in money and financial mar-ket variables may have been ignored in setting monetary policy.Moreover, inflation targeting operates through one policy variable:the central bank policy interest rate. Whether that interest rate is asufficiently robust instrument in avoiding or addressing major dis-turbances to economic and financial performance is open to ques-tion. Taylor (2009) apportions part of the blame for the financial crisisthat emerged in 2007 to monetary policy having pursued persistentlylow interest rates for an extended period. He suggests that “mon-etary excesses” were the main cause of the boom and subsequentbust that occurred in the mid 2000s (Taylor 2009, p. 2).

While inflation targets were being met in most developed coun-tries during the mid 2000s, monetary policy, mainly through theprovision of cheap credit, was contributing to excessive risk-takingin financial markets, and an over-pricing of financial and real assetssuch as property. Eventually, this led to substantial falls in assetprices, as well as the threat of deflation hanging over Westerneconomies. The inflation-targeting framework could not have fore-seen this, because of its belief in the second-order importance of assetmarkets for monetary policy.

Besides raising potential issues for the maintenance of price sta-bility, an accommodative monetary policy stance, if maintained overa long period, can pose a threat to financial stability. This view thatfinancial imbalances, especially excess money and credit growth,brought about by monetary policy pose a threat to the well-beingof economies was most prominently expressed by Bank for Inter-national Settlements (BIS) economists (see, for example, Borio andLowe 2002; Borio and White 2004) in the years leading up to thefinancial crisis. They argue that the simultaneous development ofimbalances in monetary variables, such as credit, and in asset pricesshould be of concern to central banks. Financial liberalisation andinnovation can generate such imbalances and encourage greater

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procyclicality in financial markets. This can occur against a back-ground of low and stable inflation. Excess demand can show upfirst in asset prices rather than consumer prices, which may explainwhy financial imbalances and rising asset prices occur in a low-inflation environment. The concerns expressed by BIS and othereconomists underline the need for central banks to monitor mone-tary and financial developments, as well as those in the real economy,closely.

MONETARY POLICY IN THE FINANCIAL CRISIS

Inflation targeting, which seemed to do a good job in the not toodistant past, has been found wanting. As others have noted (see, forexample, Canuto 2009), well-behaved inflation and output perfor-mance, which were features of advanced industrial economies lead-ing up to the crash, are no guarantee against a dangerous upwardasset price spiral developing and then collapsing, with enormousimplications for the central bank and its ability to maintain a stablemonetary and financial system.

In the wake of the financial crisis, central banks, faced with either aliquidity trap or the zero lower bound on nominal interest rates, hadto turn to using an alternative policy instrument, quantitative easing.This was utilised because nominal interest rates were already closeto zero, and thus the scope for reducing them further was limited.Quantitative easing involves proactively buying up a large fractionof the stock of government bonds, at whatever price is needed forholders to be willing to engage in exchange. Its purpose is to accom-modate the need for liquidity in financial markets, and the economymore generally.

It goes beyond, however, a normal accommodating monetary pol-icy, which tends to occur at a positive value for the nominal rate ofinterest, when the central bank makes funding available in infinitelyelastic amounts at that rate (subject to good collateral). The difficultywith conventional monetary policy is that the amount of liquidityinjected into the financial system may be deemed to be inadequate,even with full accommodation and at a zero rate of interest, in thetype of distressed state in which financial markets found themselvesin the wake of the financial crisis. This is where the need for quan-titative easing comes in. It involves purchasing what has turned

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out to be an extremely large amount of government securities out-right, as a way of injecting liquidity into the banking system, withthe ultimate objective of kick-starting the economy, and obviatingdeflation.

Quantitative easing was employed by the Bank of Japan duringthe early-to-mid 2000s in its attempts to tackle deflation in theJapanese economy. Assessments of the impact of this policy are thatit had limited effect in raising aggregate demand and prices, but pro-vided some support to the country’s banking sector (Spiegel 2006;Ugai 2007).

The Federal Reserve and other central banks have introducedextremely large amounts of funds into the financial system throughquantitative easing. The sizes of their balance sheets have increasedconsiderably since 2007. This expansion of liquidity was confinedto the banking sector initially. It has since resulted in a correspond-ing improvement in the supply of credit and liquidity to the retailnon-banking sector.

Quantitative easing might also affect behaviour in financial mar-kets in another way. Large purchases of government securities by thecentral bank are likely to drive their prices to levels that reduce, ifnot eliminate altogether, their attractiveness as an investment option.Koo (2011) argues that, with the private sector deleveraging due tobalance-sheet difficulties, fund managers, devoid of both privatesector and public sector borrowers, will turn to commodities as analternative investment option. This effect may have been at play incommodity price behaviour since the introduction of programmesof quantitative easing.

It is important to remember that this is a portfolio-rebalancingeffect and may not have a lasting effect on commodity prices, giventhat other asset markets should be expected to return to normalityat some time in the future. The portfolio-rebalancing effect, how-ever, is distortionary in the short run, as investors are effectivelyconstrained into purchasing commodities. This cannot be beneficialto commodity markets, and to the efficient allocation of investmentresources more generally within the economy.

The acceleration in the growth of the M2 money stock in the latterhalf of 2008 while the US economy was still in recession is likelyto have helped maintain momentum to commodity prices.4 In thenext section, we discuss how a monetary shock has a proportionate

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impact on commodity prices and consumer prices in the long run,while causing an overshooting of equilibrium commodity values inthe nearer term.

THE INFLUENCE OF COMMODITY PRICES ON FINAL GOODSINFLATIONDevelopments in commodity markets routinely and directly affectfinal good prices, as commodities constitute an input into the pro-duction of those goods. The impact of commodity prices, however,is less strongly felt nowadays than, say, in the 1970s, as commodi-ties account for a smaller share of final expenditure. This reflects thechanging structure of the economy over time, away from manufac-turing and towards services. It also reflects improved productiontechniques, requiring less raw material and fewer energy inputs. Asalready mentioned, central banks are also now more skilled in ensur-ing that large commodity price increases do not become embed-ded in the inflationary process. Econometric assessments supportthe diminished influence of commodity prices on overall final goodprices. Blanchard and Galí (2010), for example, found that the pass-through from oil price changes to overall inflation rates had declinedover time in a set of industrialised economies.

The origin of commodity price changes is debated in the eco-nomics literature. One perspective sees developments in commodityprices arising from market-specific, supply–demand shocks. Theremay, for instance, be some new or enhanced source of demand fora commodity, a sudden disruption to supply due to weather affect-ing crop harvests, or political events threatening the availability ofa raw material. The commodity price changes that result are ulti-mately relative price changes, and may often be transitory. Theycan have direct price effects on the CPI, if the commodities area part of the consumer basket, and indirect pass-through effectswhen the commodities affected are part of the production processof consumer goods.

Market shocks can have a rapid and sizeable effect on the prices ofthe particular commodities affected. This follows from the fact thatthey are traded on open markets, which helps make commodityprices relatively flexible. Since final goods prices are less flexible,and adjust slowly to economic developments, commodity pricesmay contain useful information as to how consumer prices will

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behave in the future.5 Many older US studies of the commodityprice-consumer price relationship focused on the predictive powerof commodity prices for CPI inflation.6 The evidence presented inthese studies with regard to the predictive power of commodityprices is mixed.

The price-flexibility attribute of commodity markets may also con-tribute to the view that, since market-specific shocks are short-lived,the resulting pronounced directional changes in commodity priceswill be a temporary, and self-correcting, phenomenon. This view,and the recognition that relative price shifts are a necessary andvalid part of economic activity, may contribute to the aforemen-tioned monetary policy perspective that commodity price shockscan be ignored.

An alternative viewpoint starts from the premise that the levelof prices in the economy is determined in the long run by themoney supply, and that the central bank, through its ability to con-trol the money supply by monetary policy, has an influence on howcommodity prices and final good prices develop over time. Com-modity price increases then may be seen not as originating exclu-sively in market-specific shocks but as arising, in part at least, fromthe monetary policy stance. Insofar as commodity price develop-ments feed through into CPI inflation rates from this source, it hasa monetary basis.

This perspective, focusing on the role of money supply, and mon-etary policy more generally, in driving commodity price changes, re-emerged in the 2000s. Barsky and Kilian (2002), for instance, examinethe Great Stagflation of the 1970s, and produce econometric evidencethat monetary conditions explain the rise in the price of oil and othercommodities at that time. This runs counter to the more orthodoxperspective that supply shocks affected oil prices and caused bothhigh inflation in goods and services and lower output.

Frankel (2008) revisits an overshooting theory of commodityprices that he first put forward some 20 years previously (Frankel1984, 1986). This theory follows from the view that monetary policy-induced changes in interest rates affect real/inflation-adjusted inter-est rates because the CPI is “sticky”, ie, inclined to change onlyslowly. Suppose that monetary policy causes a rise in the nominalinterest rate. This will also lead the real interest rate to increase, sincethe CPI inflation rate is fixed in the short run. The relevance of the

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real interest rate for commodities is that it represents the opportu-nity cost of holding them. A rise in the real interest rate then reducesthe demand for commodities, causing their real prices to fall. In thisway, monetary policy has an impact on commodity prices throughits effect on real interest rates.

In the Frankel model, the amount by which commodity pricesdecline is determined by a no-arbitrage condition. Commodityprices must fall to the extent that their subsequent appreciation tolong-run values compensates their holders fully for the increasedcost of carrying them. Prices, then, “overshoot” equilibrium valuesto meet this market requirement. Subsequently, the CPI inflationrate will itself adjust (slowly) upwards, and the real interest ratewill decline, acting to restore equilibrium to the commodity market.

In his 2008 article, Frankel emphasises the relevance of his over-shooting theory to developments in commodity prices around thattime. He attributes the rise in commodity prices in 2002–4 to declin-ing real interest rates. A number of other studies find a similar rela-tionship between commodity prices and real interest rates. Usingquarterly data covering the years 1990–2007, Akram (2009) findscommodity prices increase significantly in response to reductions inreal interest rates. The econometric results of Anzuini et al (2010)indicate that expansionary US monetary policy shocks increasecommodity prices, albeit to a limited extent.

In Browne and Cronin (2010), we also provide an overshoot-ing theory of commodity prices. Whereas Frankel’s perspectivedraws on the Dornbusch (1976) theory of exchange rate overshoot-ing in framing his model, we use two (essentially Friedman-style)monetarist propositions to develop ours. These are that exogenouschanges in the nominal money stock lead to equivalent percent-age changes in the overall price level (comprising commodity andconsumer good prices), and that exogenous changes in-the-moneystock are neutral in the long run, implying that all individual prices,whether they be of consumer goods or commodities, adjust overtime in the same proportion as the money stock, thus leaving allrelative prices unchanged.

When these two propositions are combined with an acknowledge-ment that commodity prices are more flexible than consumer prices,commodity prices are shown to overshoot their new long-run equi-librium values in response to a change in the exogenous money

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supply, to compensate for the inability of consumer prices to adjustin the short run. In this way, the overall price level moves at thesame rate as the money stock, but, initially, commodity prices movemore than they do in the long run to offset the stickiness of consumerprices.

A THEORY OF OVERSHOOTING

A simple two-period model might help develop some insight, andguide a more formal statistical approach (see also Browne andCronin 2010). We assume there are two exchangeable goods, com-modities and the CPI basket, which together add up to the real out-put Y of the economy. At any time, the overall price level P will bethe weighted average (with weight w, 0 < w < 1) of the commod-ity price index F, which is flexible, and the consumer price index S,whose price is sticky. For example, at time t

Pt = wFt + (1−w)St

The relationship between the money stock, M, and the overall pricelevel is given, at each time t, by the Fisher identity, that is

MtVt = PtYt

We assume both that the velocity of money Vt is constant and equalto 1, and that the volumes of the two goods in our economy, andthus the real output Yt, do not change (this restriction is relaxed inour econometric analysis, where real GDP is one of the statisticalvariables). When the assumptions about the exogeneity of Y andthe constancy of V (equal to 1) are added to the exogeneity of M(controlled by monetary policy), the Fisher identity becomes the so-called quantity theory of money, and the overall price level Pt movesin line with the nominal money stock Mt.

Assume all prices are in equilibrium at time t− 1, and Pt−1 is theoverall price level, as determined by the size of the money stock atthat time, ie, Mt−1

Pt−1 =Mt−1Vt−1

Yt−1

Next, suppose there is a one-off increase in-the-money stock ofµ > 0percentage points (of course, a similar analysis can be done for a

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negative shock)

Mt = (1+ µ)Mt−1

Pt =MtVt

Yt

The overall price level also rises by the same percentage amount,given the proposition that it moves contemporaneously with thesize of the money stock (Vt−1 = Vt = 1; Yt−1 = Yt = Y). Withoutother shocks, the new equilibrium overall price level PNEW EQ willhold indefinitely into the future

Pt = (1+ µ)Pt−1 = PNEW EQ = wFNEW EQ + (1− w)SNEW EQ

Over time, both commodity and consumer price indexes converge totheir equilibrium levels FNEW EQ and SNEW EQ, but it is what happensin the meantime that is of most interest. In particular, we assume thatthe consumer price index is sticky for one period after the moneyshock, that is

St = (1+ σ)St−1 with σ < µ

while commodity prices, which are traded on spot auction markets,are fully flexible, and moveϕ percentage points in order to maintainoverall price equilibrium, ie

Pt = (1+µ)Pt−1 = wFt+(1−w)St = w(1+ϕ)Ft−1+(1−w)(1+σ)St−1

or, rearranging the terms above

1+ϕ1+ µ = 1+ 1−w

wSt−1

Ft−1

[1− 1+ σ

1+ µ]

Thus, it is clear that if µ > 0 and σ < µ, then

ϕ > µ

which means that commodity prices initially overshoot equilibrium,to compensate for the interim stickiness of consumer prices. Next,if we assume that in period t + 1 commodity prices and consumerprices both adjust to their new respective equilibrium levels, ie,

Ft+1 = (1+ µ)Ft−1 = FNEW EQ

St+1 = (1+ µ)St−1 = SNEW EQ

then, from the overall price equation that holds at all times

wFt + (1−w)St = wFt+1 + (1−w)St+1 = wFNEW EQ + (1− w)St+1

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so that

St+1 − St = w1−w

[Ft − FNEW EQ] = −[St − SNEW EQ]

which tells us that the overshooting of commodity prices (or theundershooting in consumer prices) at time t, coupled with our know-ledge of reversion towards equilibrium, should help to forecast thechange in the CPI price index in period t+ 1.

ECONOMETRIC FINDINGS

In Browne and Cronin (2010), we tested this intuitive formal theoryempirically as a basis for shedding light on the nature of bothshort-term dynamics and long-term relationships among four USvariables:

1. the M2 money stock;

2. the Consumer Price Index (CPI);

3. the Commodity Research Bureau Spot Index (CRBSI), whichcomprises 22 basic commodities;

4. real gross domestic product (GDP), which measures output inthe US economy.

These correspond to M, S, F and Y above, respectively. The sampleperiod covered was Q1 1959–Q4 2008. (The data used in the empiricalestimations and the figures are outlined in Table 11.1.)

We initially undertook standard unit root tests on natural logsof the four variables, which indicated that they could be treatedas integrated of order one. This property of the series allowed usto use the Johansen cointegration technique to assess the existenceof a long-run proportional relationship between M2 and each of thetwo price variables and to assess the short-run dynamic relationshipbetween the variables.

Our empirical results provide support for the theory (and aresummarised in Figure 11.1). In summary, we find the following.

(i) Commodity and consumer prices each move in proportionto the money stock in the long run, although convergence israther slow (measured in quarters on the x-axis in Figure 11.1).

(ii) Commodity prices initially overshoot their new equilibriumvalue in response to a money supply shock; the CPI is initially

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Table 11.1 Description and sources of data

CPI for all urban Index: SA US Department of Labor:consumers: 1982–4 Bureau of Laborall items = 100 Statistics

CRBSI Index: NSA Commodity1967 = 100 Research Bureau

M2 US$ billion SA Board of Governors of theFederal Reserve System

Real GDP Billions of SAAR US Department ofchained 2005 Commerce: Bureau ofUS dollars Economic Analysis

CPI, Consumer Price Index; CRBSI, Commodity Research Bureau SpotIndex; SA, seasonally adjusted; NSA, not seasonally adjusted; SAAR,seasonally adjusted annualised rate.

Figure 11.1 Response of variables to an M2 shock

0

0

8 16 24 32 40 48 56 64 72 80 88 96 104 128136144112120–0.01

0.01

0.02

0.03CRBSI GDPCPIM2

Quarters

Source: Browne and Cronin (2010).

slow to adjust, but eventually picks up after commodity priceshave peaked.

(iii) One-quarter lagged values of the deviation of the commod-ity price index from its equilibrium/money-determined valuehave explanatory power for current-quarter CPI inflation.

(iv) The sign of the coefficient for the lagged commodity price gapis positive, as is to be expected from the theory.

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(v) GDP receives a temporary boost from an increase in moneystock, lasting about two or three quarters, but it then revertsto its initial value.

For this chapter, we revisited the relationship between the vari-ables, extending the data set up to Q1 2011, and present the results ina new way. Figure 11.2 contains two series. The first is the year-on-year rate of CPI inflation on a quarterly basis from Q1 1960 to Q1 2011,with the Q1 1960 value reflecting the rate of inflation over the pre-vious four quarters, ie, the percentage change in the CPI betweenQ1 1959 and Q1 1960, and so forth. The second series is a mea-sure of the commodity price gap, where the commodity index is theCRBSI, and the gap is defined as the percentage difference betweenthe actual index value and our estimate of the corresponding equi-librium value, as determined by the money equation at that time. Apositive gap indicates actual commodity prices being above equilib-rium. Given the discussion above, the expectation is that when thegap is positive, the rate of CPI inflation will subsequently increase.

As a general observation, the co-movement between CPI infla-tion rates and the commodity price gap is noticeable. Looking athow the two variables behaved over time, the period up until theearly 1970s was one when the commodity price gap was usually neg-ative and CPI inflation relatively low. A large positive commodityprice gap emerged in 1973–4 and the CPI inflation rate respondedaccordingly, moving into double-digit values. This situation pre-vailed through the rest of the 1970s. The CPI inflation rate declinedsteadily between 1980 and 1983, as the positive commodity pricegap was also eroded. Thereafter, through the 1980s and 1990s, theCPI inflation rate remained at low values and the commodity pricegap moved around the origin.

The 2000s proved a more interesting decade. A large negativecommodity price gap had developed by the end of 2001/early 2002.Over the next six years, however, the gap first closed and then movedinto positive values, reaching a local high value in Q3 2008. CPIinflation increased slowly from a rate just above 1% in Q2 2002 to avalue close to 5% in Q3 2008.

Figure 11.3 helps to illustrate how our overshooting theory canexplain these developments in the early to mid 2000s, as well asthose that have occurred since 2008. It shows year-on-year rates ofchange in US M2, US CPI and the CRBSI from Q1 2001 to Q1 2011 (so,

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Figure 11.2 Year-on-year CPI inflation rates and commodity price gap,Q1 1960–Q1 2011 in percentage points

–40

–20

0

20

40

60

–4–20246810121416

CP

I inf

latio

n ra

tes

(pp)

Com

mod

ity p

rice

gap

(pp)

CPI inflation rates Commodity price gap

Q1

1960

Q3

1965

Q1

1971

Q3

1976

Q1

1982

Q3

1987

Q1

1993

Q3

1998

Q1

2004

Q3

2009

Figure 11.3 Year-on-year rates of change in M2 and price indexes,Q1 2000–Q1 2011, in percentage points

M2 CRBSI CPI403020100

–10–20–30–40

Q1

2001

Q3

2001

Q1

2002

Q3

2002

Q1

2003

Q3

2003

Q1

2004

Q3

2004

Q1

2005

Q3

2005

Q1

2006

Q3

2006

Q1

2007

Q3

2007

Q1

2008

Q3

2008

Q1

2009

Q3

2009

Q1

2010

Q3

2010

Q1

2011

for example, the Q1 2001 observations are the year-on-year changesin the respective variables between the end of Q1 2000 and the endof Q1 2001). A vertical line is added at Q3 2008. Prior to that quarter,the rate of M2 growth can be seen to have been in excess of that ofthe CPI from the early 2000s. The money stock grew by 68% betweenQ1 2000 and Q2 2008, while CPI increased by just 28%. The differencecould not be explained by the greater need for real money balancesfor transactions purposes associated with real GDP growth, whichtotalled 20% over that period. In these circumstances, it is unsurpris-ing to us that the CRBSI rose strongly in value. It more than doubledduring this time-frame, increasing by 115% between Q1 2000 and

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Q2 2008. With the rate of change in the CPI not keeping pace withthat in M2, the monetary impulse affected commodity prices.

The differential between the M2 growth rate and the CPI inflationrate is particularly noticeable between 2001 and 2003, as can be seenin Figure 11.3. The rate of change in the CRBSI did not pick up until2003 and was maintained into 2005. The overshooting theory wouldexplain this by noting that the response of commodity prices to amonetary stimulus is not instantaneous, but rather occurs with alag; however, that lag is relatively short and the response is fasterthan that of consumer prices.

There was some pick-up in the CPI inflation rate in 2004–5, asthe rate of commodity price inflation declined. This would be con-sistent with the eventual catch-up in CPI inflation rates that wouldbe expected in the wake of strong money growth, and in the initialmomentum to commodity prices from that monetary source fallingaway. The period from early 2006 to mid 2008 saw a fresh surge incommodity prices taking place. Money growth was also above theCPI inflation rate at that time. As in 2005, the decline in the rate ofincrease in commodity prices that was occurring just prior to Q3 2008coincided with a steady rise in the CPI inflation rate to a value of 5%in Q2 2008.

The vertical line at Q3 2008 in Figure 11.3 marks the start of asudden collapse in commodity prices in the second half of that year.Year-on-year rates of growth in the CRBSI remained negative untilQ1 2010. Given that the rate of money growth was much greaterthan the rate of the CPI inflation rate in late 2008 and through2009 when commodity prices were, in general, falling, this com-modity price behaviour may appear unusual.7 We suggest that aflight from risky assets, such as commodities, to “safe haven” assets,like money (accommodated by monetary policy), by consumers andinvestors was the predominant force at work in financial markets inlate 2008/early 2009 and goes a long way towards explaining themoney and commodity price growth rates in Figure 11.3 duringthat time. Since the level of uncertainty and investor nervousnessin the economy has receded somewhat since then, it is unsurpris-ing that strong money growth manifests itself in rising commodityprices. A positive commodity price gap is now evident (Figure 11.2).This raises the prospect of CPI inflation rates rising in the yearsahead.

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CONCLUSIONIn this chapter, we described how inflation targeting became a cen-tral plank of modern monetary policy. It contributed to a reduc-tion in inflation rates from the high values that prevailed in the1970s and 1980s, and did so mainly through succeeding in anchor-ing inflation expectations close to low levels. Inflation targeting’sbiggest shortcoming, in our view, is that it has not taken accountof the vast changes that have occurred in the financial system sincethe 1990s. These changes have altered the patterns of substitutionbetween money and financial assets. In our view, these new pat-terns are an important ingredient of the boom–bust cycles of the1990s and 2000s. They have had the effect of enhancing the role ofmoney in the economy, but arguably in a disruptive way: some-thing which was at the heart of the 2007–9 financial crisis, butwhich most advocates of inflation targeting regard as somethingof a sideshow.

Our overshooting model provides some input into understand-ing the potential for money to affect prices, including relative pricesbetween different classes of goods, such as commodities and con-sumer goods. It shows that monetary shocks can cause commodityprices to react quickly to maintain equilibrium in the overall pricelevel. This can arguably prove unsettling for investors, as rising com-modity prices may be interpreted as signalling a higher sustainedlevel of real demand for a commodity or commodity class when,in fact, their prices are only reacting to a generalised, ie, monetary,stimulus to prices in the economy. Monetary policymakers, mistak-enly reading rising commodity prices as caused by market-specificdemand or supply shocks, might thus adopt inappropriate mone-tary policy responses, including no response at all. For both investorsand central banks, money is a variable that needs to be analysed andunderstood, and not neglected.

The views expressed in this chapter are those of the authors and donot necessarily represent the views of the Central Bank of Irelandor the European System of Central Banks. We would like to thankthe editors for their very helpful comments and suggestions.

1 Using an econometric technique called band-pass filtering, Cuddington and Jerrett (2008)provide evidence consistent with there having been three super-cycles in metal prices sincearound the middle of the 19th century, with world metal markets currently being in theearly stages of a fourth super-cycle. They note that the latter is being attributed to Chineseurbanisation and industrialisation.

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2 The quantity theory of money links money supply with the overall price level.

3 Uncovered by the seminal work of A. W. Phillips, the original Phillips curve refers to theinverse relationship between unemployment and money wage rates. Other versions of themodel were later introduced, linking inflation with various measures of broad economicactivity and, later, inflation expectations.

4 M2 is one of the aggregate monetary measures, see http://www.federalreserve.org for adefinition.

5 Within the CPI, there are goods whose prices are more flexible than others. Bils and Klenow(2004) find the fresh-food, energy-related products and durable-goods components of the CPIto change relatively frequently. In the euro area, energy and unprocessed food have the mostflexible prices among consumer goods, while services have the lowest (Álvarez et al 2006).

6 See, for example, Webb (1988), Garner (1989), Marquis and Cunningham (1990), Cody andMills (1991), Pecchenino (1992), Blomberg and Harris (1995) and Furlong and Ingenito (1996).

7 Another factor at play here is that the massive amount of hoarding of liquid balances inducedby the crisis has undermined the assumption of constant velocity, as often happens inrecessions.

REFERENCES

Akram, Q. F., 2009, “Commodity Prices, Interest Rates and the Dollar”, Energy Economics31(6), pp. 838–51.

Álvarez, L., E. Dhyne, M. Hoeberichts, C. Kwapil, H. Le Bihan, P. Lünnemann, F. Martins,R. Sabbatini, H. Stahl, P. Vermeulen and J. Vilmunen, 2006, “Sticky Prices in the EuroArea: A Summary of New Micro Evidence”, Journal of European Economic Association 4,pp. 575–84.

Anzuini, A., M. Lombardi and P. Pagano, 2010, “The Impact of Monetary Policy Shockson Commodity Prices”, Working Paper 1232, European Central Bank.

Barsky, R. B., and L. Kilian, 2002, “Do We Really Know that Oil Caused the Great Stagfla-tion? A Monetary Alternative”, in B. Bernanke and K. Rogoff (eds), NBER MacroeconomicsAnnual 2001, pp. 137–83.

Bils, M., and P. Klenow, 2004, “Some Evidence on the Importance of Sticky Prices”, Journalof Political Economy 112, pp. 947–85.

Blanchard, O., and J. Galí, 2010, “The Macroeconomic Effects of Oil Price Shocks: WhyAre the 2000s So Different from the 1970s?”, in J. Galí and M. Gertler (eds), InternationalDimensions of Monetary Policy, pp. 373–428 (Chicago, IL: University of Chicago Press).

Blomberg, S. B., and E. S. Harris, 1995, “The Commodity–Consumer Price Connection:Fact or Fable”, Economic Policy Review, October, pp. 21–38.

Borio, C., and P. Lowe, 2002, “Asset Prices, Financial and Monetary Stability: Exploringthe Nexus”, BIS Working Paper 114.

Borio, C., and W. White, 2004, “Whither Monetary and Financial Stability? The Impli-cations of Evolving Policy Regimes”, in Monetary Policy and Uncertainty: Adapting to aChanging Economy, pp. 131–211 (Federal Reserve Bank of Kansas City).

Browne, F., and D. Cronin, 2010, “Commodity Prices, Money and Inflation”, Journal ofEconomics and Business 62, pp. 331–45.

Canuto, O., 2009, “The Arrival of Asset Prices in Monetary Policy”, RGE EconoMonitor 20,October, URL: http://www.economonitor.com/blog/2009/10/the-arrival-of-asset-prices-in-monetary-policy/.

Cody, B. J., and L. D. Mills, 1991, “The Role of Commodity Prices in Formulating MonetaryPolicy”, The Review of Economics and Statistics 73(2), pp. 358–65.

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Cuddington, J. T., and D. Jerrett, 2008, “Super Cycles in Real Metals Prices?”, IMF StaffPapers 55(4), pp. 541–65.

Dornbusch, R., 1976, “Expectations and Exchange Rate Dynamics”, Journal of PoliticalEconomy 84, pp. 1161–76.

Frankel, J., 1984, “Commodity Prices and Money: Lessons from International Finance”,American Journal of Agricultural Economics 66(5), pp. 560–66.

Frankel, J., 1986, “Expectations and Commodity Price Dynamics: The OvershootingModel”, American Journal of Agricultural Economics 68(2), pp. 344–8.

Frankel, J., 2008, “The Effect of Monetary Policy on Real Commodity Prices”, in Campbell,J. (ed), Asset Prices and Monetary Policy, pp. 291–27 (University of Chicago Press).

Furlong, F., and R. Ingenito, 1996, “Commodity Prices and Inflation”, Economic Review,Federal Reserve Bank of San Francisco 2, pp. 27–47.

Garner, C. A., 1989, “Commodity Prices: Policy Target or Information Variable?”, Journalof Money, Credit and Banking 21(4), pp. 508–14.

Habermeier, K., I. Ötker-Robe, L. Jacome, A. Giustiniani, K. Ishi, D. Vàvra, T. Kisinbayand F. Vazquez, 2009, “Inflation Pressures and Monetary Policy Options in Emerging andDeveloping Countries: A Cross Regional Perspective”, IMF Working Paper WP/09/1.

International Monetary Fund, 2005, “Does Inflation Targeting Work in Emerging Mar-kets?”, World Economic Outlook, September, pp. 161–86.

Koo, R., 2011, “Commodity Price Increases have Speculative and Structural Roots”, URL:http://www.economist.com/node/21015587.

Marquis, M. H., and S. R. Cunningham, 1990, “Is There a Role for Commodity Pricesin the Design of Monetary Policy? Some Empirical Evidence”, Southern Economic Journal57(2), pp. 394–412.

Pecchenino, R. A., 1992, “Commodity Prices and the CPI: Cointegration, Information andSignal Extraction”, International Journal of Forecasting 7, pp. 493–500.

Spiegel, M. M., 2006, “Did Quantitative Easing by the Bank of Japan ‘Work’ ”, FRBSFEconomic Letter, No. 2006-28, October.

Stark, J., 2007, “Objectives and Challenges of Monetary Policy: A View from the ECB”,Speech to Magyar Nemzeti Bank Conference on Inflation Targeting, Budapest, Hungary,January 19, URL: http://www.ecb.int/press/key/date/2007/html/sp070119.en.html.

Taylor, J. B., 1993, “Discretion versus Policy Rules in Practice”, Carnegie-RochesterConference Series on Public Policy 39, pp. 195–214.

Taylor, J. B., 2009, “The Financial Crisis and the Policy Responses: An Empirical Analysisof What Went Wrong”. NBER Working Paper 14631.

Ugai, H., 2007, “Effects of the Quantitative Easing Policy: ASurvey of EmpiricalAnalyses”,Monetary and Economic Studies, March, pp. 1–48.

Webb, R. H., 1988, “Commodity Prices as Predictors of Aggregate Price Change”, EconomicReview, Federal Reserve Bank of Richmond, November/December, pp. 3–11.

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12

Inflation and Asset Prices

John A. TatomIndiana State University

Changes in the general level of prices and inflation have profoundeffects on asset prices. There are several reasons for these effectsand the influence differs depending on the source of the inflationand whether it is expected or not. To understand these effects, it isimportant to clarify what is meant by inflation, the pure theory ofthe sources of inflation, how inflation affects the prices of goods andservices and how it affects both the equity prices and fixed incomeassets that are used to finance production.

Inflation has had large effects on asset prices in the US, especiallyduring the Great Inflation from 1965 to 1984. There have been lesserbouts of inflation since then, and an acceptable and stable pace ofinflation for more than a few years at a time has been elusive. TheGreat Inflation was followed by the Great Moderation (see Chap-ter 1), a reduced volatility of real GDP growth, which some analystsargue was caused by improvements in monetary policy in pursu-ing lower and more stable inflation (Bernanke 2004). Blanchard andSimon (2001), for example, documented that the variability of quar-terly growth in real output (as measured by its standard deviation)declined by half since the mid-1980s, while the variability of quar-terly inflation declined by about two thirds. Kim and Nelson (1999)and McConnell and Pérez-Quirós (2000) were among the first to notethe reduction in the volatility of output. Kim et al (2004) showed thatthe reduction in the volatility of output is quite broad based, affect-ing many sectors and aspects of the economy. Using more formaleconometric methods, Kim et al also found that structural breaks inthe volatility and persistence of inflation occurred about the sametimes as the changes in output volatility.

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In this chapter we do not explore what constitutes an acceptablerate of inflation. The Federal Open Market Committee of the Fed-eral Reserve System (Fed) has struggled with this question and therelated question of inflation targeting. The policy and investmentcommunities have consensus estimates that the Fed aims for a 2%annual rate of inflation maintained on a year-over-year basis, but ittolerates moves above and below this, especially when the deviationof inflation is perceived by the Fed and the market to be temporary.The European Central Bank targets more explicitly on inflation, aim-ing for a 0–2% inflation rate, closer to the top of the range, again on ayear-over-year basis. The reasons for tolerating a positive target rateof inflation appear to be twofold. First, economists expect there tobe some bias in prices and inflation due to technological change thatresults in measured inflation that actually reflects quality improve-ments. Second, there is reluctance on the part of policymakers toexperience deflation, a falling general level of prices. Given the ran-dom variation of inflation measures, targeting zero inflation couldresult in frequent and sometimes persistent experiences of negativemeasures of inflation.

We do, however, review the theory of inflation, its sources andeffects on asset prices, especially equity, bond and real asset prices.The theory behind these effects is kept to the essentials and isreduced to its simplest details. In the first section, we explore infla-tion, including what it is and what it is not. We develop the importantdistinction between a price level and relative price change, the differ-ence between a sustained pace of price level change and a one-timeor transitory change, and the link between inflation and monetarypolicy, as well as the implications for asset prices. We also discussthe variety of price index and inflation measures and the usefulnessof “core” measures of inflation. The subsequent sections look at therole of money in the economy and the notion of money as a veil,hiding the fundamental real activity in an economy, and establishingthe theoretical benchmark of an economy where money is neutral,which means that inflation has no effect on real economic activityand, in particular, on real asset prices and real returns. This conceptof neutral money is explained in more detail by Fisher (1911). It isrumoured to have originated with Copernicus in the 15th centuryand appears in the work of David Hume in the 18th century (seealso Friedman 1956; Patinkin 1965). The key alternative hypotheses

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of how inflation affects asset prices by altering real interest rates orthe required real rate of return on equity, and/or by affecting realearnings on corporate equity, are examined and evidence is providedsupporting both. Taxation effects, often a neglected topic, are thendiscussed. A final section offers concluding remarks.

WHAT IS INFLATION?Economists and financial analysts recognise several key distinctionswhen discussing inflation. The most important is that the term refersto a sustained rate of depreciation of the purchasing power of a unitof local currency over time. A rise in the price of a kilo of beef from$10 per kilo to $11 per kilo reflects the fact that a unit of money buysless than it did before: after the price rise, $10 buys only 0.91 kilos ofmeat instead of one kilo.

If only the beef price rises, then this is referred to as a relative pricechange: beef has become more expensive relative to everything else,including money. A rise in the relative price of one good or anotheris not inflation if the overall price level (for example, of a relevantbasket of goods and services) is unchanged. However, if all pricesmove in line with beef prices, then the price of a market basket ofgoods and services rises by 10%, or the value of money falls byroughly 10% (9.1%). Measured on a continuously compounded ratebasis (differences in the natural logarithms), prices rise 9.53% andthe value of money relative to goods and services falls by exactlythe same extent (9.53%). If the general level of prices, beef and othergoods and services, rises for some special reason that is not expectedto continue, this is referred to as a rise in the price level, or sometimesas “temporary inflation”, but not inflation.

Inflation is a monetary phenomenonFriedman (1956) famously coined the expression “inflation is alwaysand everywhere a monetary phenomenon.” This captures the factthat the principal cause of inflation is the excess of growth in-the-money stock relative to that of money demand. Like other goodsor services, an increase in the price of money (relative to goods andservices) depends on its relative scarcity, so growth in supply relativeto demand causes decreases in the value of money or inflation.

With fiat money under the control of central banks, the supply ofmoney is determined by actions of the central bank and by changes

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in preferences for currency or deposits. Since the central bank canreadily detect shifts in these preferences and offset their influence onmonetary measures, changes in the stock of money are fully underthe control of the central bank. The demand for money depends onthe cost of holding money and its usefulness in facilitating transac-tions or providing liquidity in asset portfolios. The cost of holding agiven amount of money is the short-term nominal interest rate, typ-ically measured by the most liquid safe domestic security like theUS Treasury bill rate in the US. This captures the alternative returnfrom holding a very liquid and safe asset (a Treasury bill) instead ofcurrency or a bank deposit that can be used for third-party paymentor readily and cheaply converted into such a transaction deposit.Alternatively, the nominal interest rate reflects the real interest rateforgone by holding money and the rate of depreciation expectedon holding money, ie, the expected rate of inflation. The transactiondemand for money depends on income, real GDP and measures suchas the size of wealth relative to income, alternative rates of return onalternative assets and the liquidity of wealth and the degree of uncer-tainty can influence the demand for money. See Friedman (1956)for the classic statement of the demand for money and its link toinflation.

Non-monetary factors

There are other factors that can account for temporary inflation orprice level increases. In particular, as described above, the generallevel of prices can be raised by a decline in money demand. A princi-pal source of such a decline is a negative shock to aggregate supply ofactual and potential output. This can occur because of a reduction inavailable resources or a reduction in total factor productivity. Rascheand Tatom (1977) developed the aggregate supply theory, whichexplains the loss in natural output and price level rise associated witha shock to the relative price of energy. In a broader study of energyand other supply shocks (Rasche and Tatom 1981), they developedthe theory of energy shocks more fully. Examples of energy shocksare plagues, wars, strikes or a decline in resource use because ofshock to the relative price of a key resource such as an energy priceshock. An example of a supply shock is a crop failure or other natu-ral disaster that significantly reduces output, given resource usage.Supply shocks can be permanent or transitory. When permanent,

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they can lead to a permanent rise in the price level, experienced astemporary inflation. The most important empirical example of thisis a rise in the relative price of oil that raises the relative price ofenergy. When transitory, the relative price of the affected good orservice rises temporarily and then returns to its original level afterthe source of the shock is removed. The price level reflects the sametransitory rise and fall in this case. The best empirical example of thisis a crop failure, drought or other natural disaster that temporarilyreduces output in a key sector of the economy. Conceptually, a per-manent continuing shock to supply could be a source of a sustainedrise in the relative price of a resource and therefore inflation, but thisrequires an ongoing reduction in the employment of some resourcethat reflects or causes the reduction in economic growth.

While such non-monetary factors might suggest that Friedmanis wrong in his argument that inflation is always and everywherea monetary phenomenon, this is not the case. In fact, the simplestversion of Friedman’s explanation of inflation is that it occurs whenmore money chases the same goods; but, these non-monetary expla-nations rely on the same quantity of money chasing fewer goods. Inboth cases, inflation occurs because there is a change in the quantityof money relative to potential output.

Measures of inflation

There are several measures of inflation. The broadest measures arethe chain weight GDP deflator, which measures changes in the priceindex for the bundle of final goods and services that make up thenation’s output, or real GDP. Since consumer expenditures makeup the largest share of GDP and are the prices most relevant to con-sumers, analysts often focus on the chain weight personal consump-tion expenditure (PCE) deflator as the benchmark for assessing infla-tion. Many analysts focus on the consumer price index (CPI) as therelevant measure of inflation. This measure has a history of prob-lems. Most importantly, the housing component of the index wasrevised in the 1990s to better measure the price of housing, but theearlier series was not revised in the same way, making the index lessreliable for longer-term studies. Figure 12.1 shows the year-over-year measure of the rate of increase in the PCE deflator, the PCEminus energy and food (a so-called “core” inflation measure) and theCPI. All three measures are broadly similar, though the CPI-based

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Figure 12.1 Personal consumption expenditure, core personalconsumption expenditure and consumer price index

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PCE Core PCE CPI

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measure is slightly higher and more volatile. The Great Inflation in1965–84 stands out, but there are other episodes of relatively highinflation.

Since there are some prices that are very volatile but do not reflectthe underlying trend in the value of money or of the general level ofprices, statisticians and analysts often distinguish a “core” measureof inflation from the overall measure. The measurement of core infla-tion uses price indexes that remove the price movements in non-coreitems: most often the prices of food and energy, but sometimes hous-ing rent or other volatile prices. The reasons for excluding items froman inflation measure are that the volatile changes are not expectedto persist and indeed, at least in the case of food prices, they areexpected to cancel out over time, except for some trend decline inthe relative price of food. In any case, the sustained rate of pricechange, that is inflation, is likely to be obscured by noisy volatilemovements in some price components within the overall index ofthe general level of prices. This may not always be correct, how-ever (especially the presumption that volatile moves up or downin a particular nominal price is likely to be reversed) so care mustbe exercised in the choice of inflation measure. Crone et al (2011)

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provided evidence that overall PCE deflator inflation is a better pre-dictor of its own future rate than is a core measure. Kiley (2008)reached the opposite conclusion about how to estimate the underly-ing trend of inflation. Mankiw et al (2003) provided an earlier surveyon the issues involved in developing inflationary expectations; theysuggest that expectations reflect partial and incomplete updating inresponse to news. In Figure 12.1, temporary surges in inflation in1974–5, 1979–81, 1991, 2000 and 2008–9 reflect sharp increases in therelative price of energy. The end of the Iran–Iraq war in 1986 and theIraq–Kuwait war in 2001 led to declines in the relative price of oiland energy that were reflected in declines in prices and temporarydrops in inflation.

An important issue that is not explored here is how and whetherasset prices should be included in measures of the price level.Alchian and Klein (1973) stressed the importance of including assetsin the market basket of expenditures along with goods and ser-vices. Others have argued for including the prices of the services ofassets, but not the assets themselves, along with other goods and ser-vices. For example, house prices would be excluded, but the owners’equivalent rent or other rental prices of housing would be included.Stock and Watson (2003) examined evidence on the predictive per-formance of asset prices for inflation and real output growth, usingdata from 38 asset price indicators (mainly asset prices) for sevenmember countries of the Organisation for Economic Co-operationand Development (OECD) for the period 1959–99. Their review ofthe literature and empirical evidence points to the same conclusion,ie, that some asset prices predict either inflation or output growth insome countries in some periods. However, no systematic evidence isfound to support the inclusion of asset prices in standard price mea-sures. Bryan et al (2002) found that including asset prices in modelsto forecast inflation does have episodic significance in altering thepattern of inflation forecasts, but that they do not matter much foreconomic significance beyond the quality of forecasts from eitheroverall inflation measures or from core measures of inflation.

Athird critical distinction is that inflation can be expected or unex-pected. A surprise in inflation will have different effects on assetprices and economic performance from a rise in expected inflationthat is in line with ex ante expectations. Most surprises in infla-tion arise from shifts in relative prices, especially food or energy

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prices, and are temporary. More fundamental determinants of infla-tion evolve more predictably, and hence the underlying inflationis also more predictable or expected. The key factor differentiatingexpected and unexpected inflation, in terms of the effects on assetprices, is that capital markets incorporate expected inflation in assetdemand and supply and in pricing of assets, while unexpected infla-tion is not incorporated in the same way. The key effects of unex-pected inflation arise from redistributions of income and wealth. Forexample, an unexpected and temporary rise in inflation will redis-tribute income from creditors, who face an unexpected fall in thepurchasing power of their interest income and principal repayments,that is, a fall in their realised real rate of return, while debtors enjoytheir corresponding unexpected gain. For owners of firms, there areat least two effects of unexpected inflation. The first is the redis-tribution of income from creditors to debtors, as above. Firms thathave external debt will benefit from a rise in unanticipated inflation.Their owners, stockholders, will realise the unexpected decline intheir real interest payments to their creditors as a gain in real profits.The discounted value of the gain will accrue to stockholders as anunanticipated capital gain in the stock price.

Expected inflation usually does not create redistributions ofincome or wealth. Market participants require compensation forexpected changes in the purchasing power of expected future pay-ments in order to acquire assets, and sellers of assets have the where-withal and willingness to provide such compensation, at least in asimple world where institutions or regulations do not prevent suchcompensation. More broadly, it is expected inflation that has moresweeping effects on asset and other prices and that affects portfolioallocation, output and economic growth.

IS MONEY A VEIL? THE MONEY NEUTRALITY HYPOTHESISThe simplest model of inflation and asset prices assumes that thereare no frictions in markets, there are no transaction or adjustmentcosts and that information is freely available. In this model, a risein expected inflation raises nominal prices for unchanged quanti-ties of goods and services along new and higher expected inflationpaths. It simultaneously raises prices of resources and marginal costsby equal percentages, at given quantities of goods and services andresource input flows. Prices move up freely at the specified rates over

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Figure 12.2 Inflation and nominal interest rates

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10Y Treasury yield

Inflation (PCE, YoY)

Source: FRED2, Federal Reserve Bank of St Louis.

time, with no distortion of resource employment or output. Relativeprices of resources, goods and services and assets are unaffected,as are real (ie, inflation-adjusted) rates of return on assets. The useof money is a veil, hiding the relative prices of goods, services andassets, the real rate of interest and real exchange rates for curren-cies. It is these latter prices that matter for economic decisions, andif inflation does not alter them, then it does not affect economic per-formance. In other words, where money is a veil, money is neutral,so that nominal price level changes have no real effects on resourceallocation or incentives to accumulate resources. Inflation has purelynominal effects on asset prices.

Although the money neutrality hypothesis is a long-term rela-tionship that might not hold in the short and intermediate run, itprovides a useful heuristic model to understand money, inflationand asset prices.

NOMINAL INTEREST RATES AND INFLATION

Existing nominal fixed income products are affected, however, whenthe expected rate of inflation increases. This occurs because the rateof depreciation in the purchasing power of future nominal cash-flows has increased. Following the Fisher equation, named after Irv-ing Fisher (1911, Chapter IV; 1907, Chapters V and XIV), the nominal

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interest rate on fixed income securities will rise in line (ie, one to one)with the expected rate of inflation, while real interest rates and sup-ply and demand for credit will remain unchanged. The relationshipbetween nominal rates and inflation is clearly shown in Figure 12.2,where the year-over-year (YoY) PCE inflation is plotted along withthe 10-year Treasury yield.

A rise in expected inflation will cause bond prices to fall, as nom-inal interest rates rise to incorporate the Fisher effect of inflation onnominal interest rates. The fall in bond prices is larger, the longer theduration of the asset, because longer duration cashflows lose morepurchasing power due to a given pace of inflation. The real interestrate on bonds is unaffected if money growth is neutral.

EXCHANGE RATES AND INFLATIONIn this simple model, another key nominal price besides nominalinterest rates is the foreign exchange rate. The benchmark for foreignexchange in the simple world is determined by relative purchasingpower parity, so that the value of a currency will fall over time rel-ative to another currency, in line with the higher domestic expectedrate of inflation compared with expected inflation abroad. The rateof depreciation in a local currency will equal the expected inflationrate in the economy minus the expected inflation rate in the coun-try of origin of the other currency. So long as this holds, the localcurrency prices of domestic and foreign goods or services will riseat the new expected rate of domestic inflation, and the same will betrue abroad.

Even in this simple world, currencies will not adjust fully andimmediately to a change in the expected inflation rate. In fact, cur-rencies typically overshoot in response to factors booting inflationexpectations, falling more than the theory predicts based only onexpected future inflation. This is not unique to exchange rates, asother asset prices also adjust more in the short run than higher infla-tion might suggest. The elasticity of supply of some commodities, forexample, is quite inelastic, so that increases in nominal demand leadto relatively higher relative prices. These relatively large short-runprice adjustments can make commodities an attractive investmentoption in the short run. Balanced against this argument, however,is the short-term nature of these adjustments. Many commoditiesare also very sensitive to the business cycle and relatively more

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Figure 12.3 Inflation (PCE) and real stock prices (inflation-adjustedS&P 500 index)

0

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–2

Infla

tion

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dex

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Source: FRED2, Federal Reserve Bank of St Louis and Standard & Poor’s.

cyclical industrial demand, which also is more adversely affected byany subsequent policy tightening in the face of a rise in inflationaryexpectations.

EQUITY PRICES AND INFLATION

According to the money neutrality hypothesis, the required returnon equities also moves in line (ie, one to one) with the higher expectedinflation rate. According to cashflow valuation models, the price ofa stock is the net present value of future cashflows. If expectations ofinflation rise, but real cashflows and real interest rates do not change,the price of stocks and their real rate of return should be unchangedas well. In this case, equities would be a perfect inflation hedge,providing a constant real rate of return independently of changes ininflation expectations.

In practice, however, there is strong empirical evidence thatchanges in inflation expectations are negatively correlated to thereal (inflation-adjusted) return on stocks. In other words, equities arenot a good inflation hedge. Figure 12.3 provides a perspective on thenegative effect of inflation on real (inflation-adjusted) equity prices.It shows the real (deflated by the PCE deflator) S&P 500 index, andthe PCE-based inflation rate for the period from 1957 Q1 to 2011 Q2.The negative correlation is most apparent during the Great Inflation,

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1965–84, when the real stock was depressed. Other periods of rel-atively higher inflation are also associated with relatively low realstock prices, including the late 1950s and 2007–9. The decline in infla-tion in 1991–8 was notably associated with a sharp rise in the realstock price. The correlation between the two series is−0.44: stronglynegative.

In fact, the negative correlation between inflation and nomi-nal (or real) stock prices has become one of the most commonlyaccepted empirical facts, motivating large numbers of financial andmonetary economics studies. Some of these are briefly mentionedbelow, starting with an exception: one study that disagrees with theempirical finding of the negative relationship between inflation andstock prices. Konchitchki (2011) suggests that inflation raises bothfuture real earnings and real stock prices. He provides evidence thatunrecognised accounting inflation gains raise future cashflows, andyield abnormally high returns on equities, reflecting a failure of themarket to fully account for future gains in nominal cashflow wheninflation initially occurs.

The most widely accepted hypothesis of a negative effect of infla-tion on stock prices is that supply shocks, which reduce output andraise prices, also reduce the marginal productivity of capital, reduc-ing the real earnings of capital and lowering the value of capitalassets and the firm.

Bakshi and Chen (1996) suggested that the negative relation ofinflation and stock prices occurs because of procyclical movementsin real interest rates and in inflation. A cyclical expansion (decline),in their view, will raise the real rate of interest and also raise infla-tion. The higher real interest rate would lower stock prices, givingrise to the negative correlation of stock prices and inflation. How-ever, the empirical support is rather weak, not surprisingly, becauseit depends on controversial empirical assertions of cyclical real inter-est rates and the existence of a Phillips (1958) curve. Fama (1981) andStulz (1986) relied on another channel: a rise in expected inflationreduces wealth and this, in turn, lowers the expected return on equi-ties and lowers stock prices. Fama (1981) also attributed the negativerelationship to supply shocks, again operating via a wealth effect.

Brandt and Wang (2003) provided an alternative explanation ofthe negative relationship of nominal stock prices and unexpectedinflation. They argued that unexpected inflation affects investor risk

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preferences, in particular, raising risk aversion and that, in turn,lowers stock prices.

Hess and Lee (1999) argued that the negative correlation of stockprices and inflation depends on the nature of the shocks creatinginflation. Their theoretical structure also does not allow inflation tohave long-run real effects on output (and, therefore, stock prices).In their view, only adverse supply shocks reduce output and stockprices, with the former causing a temporary surge in inflation. Boththeir model and evidence apply to unanticipated price and tempo-rary inflation changes. Some studies indicate that inflation reduceseconomic growth, which should slow the expected growth rate ofearnings and lower stock prices (see, for example, Barro 1996).

However, Tatom (2002) showed that both energy price (supply)shocks and demand-induced inflation have essentially the same neg-ative effects on stock prices, and that stock prices anticipate theexpected change in inflation from either. In each case, a 1.0 per-centage point rise in inflation raises the Standard & Poor’s (S&P)earnings–price yield by 1.5 percentage points, essentially all cap-tured in a decline in stock prices, since a trailing measure of earningsis used to construct the earnings–price variable. Tatom (2002) alsofound that the temporal causality from an increase in the federalfunds rate goes to increase stock prices first, and then to decreaseinflation. Conversely, a fall in the federal funds rate will lead to a fallin stock prices anticipating a decline in inflation.

As most of these studies, albeit important, do not take into accountnominal taxation effects, the latter are the focus of the next section.

THE EFFECTS OF TAXATION OF NOMINAL AND REAL INCOME

There are theoretical considerations that argue against neutral effectsof inflation on asset prices. Moreover, the evidence is consistent withthese theories. There are two tax-related arguments that indicatethat bond and equity prices are reduced because of an increase inexpected inflation. Income taxation systems tax nominal incomes. Ifthe tax system is not indexed to adjust nominal incomes measuresfor inflation, taxes are levied on inflationary changes in income sothat real incomes are taxed as well. In that event, real asset priceswill be depressed by a rise in expected inflation.

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Tax rate effects on the real rate of interest

The first real effect arises through a rise in the real rate of interest.The Fisher equation indicates that the nominal interest rate equalsthe real interest rate plus the expected rate of inflation. Accordingto the discussion above, a rise in the expected rate of inflation, π ,will raise the nominal interest rate, n, by an equal amount, leavingthe real interest rate, r, unaffected. When nominal interest income istaxed at a percentage rate t > 0, the after-tax nominal interest rate,nafter tax, is

nafter tax = (1− t)n

while the after tax real interest rate rafter tax is

rafter tax = nafter tax −π = (1− t)r − tπ

Therefore, the money neutrality hypothesis will not hold in a world,like ours, where nominal income is taxed. The real rate should beindependent of inflation if money is neutral, but the results hereshow that it is not. In particular, an increase in inflation expectationsshould be offset by a decrease in real rates, or explicitly

dr = t1− t

dπ , dn = dr + dπ = t1− t

For example, for a marginal tax rate of one-third (t = 13 ), each

percentage point of change in expected inflation increases the realinterest rate by 50 basis points (bp), and thus raises the nominalinterest rate by 150bp. With such a rise in the real cost of funds,producers will reduce investment in real assets, perhaps puttingsome downward pressure on the after-tax real return on investment.When the real rate of discount rises, bond prices will fall further thanotherwise, and equity prices will not keep pace with inflation as realequity prices fall.

The empirical evidence is at odds with this result. For example,in Figure 12.2 movements in the inflation rate are not exceeded oreven matched by movements in nominal interest rates. This suggeststhat the real interest rate actually falls when inflation increases, con-trary to the tax argument above. In a traditional IS/LM (investmentand savings/liquidity and money) model, ignoring taxes, there isanother factor that affects the short-run adjustment of the real inter-est rate to a change in expected inflation. A rise in expected inflationrate will reduce the demand for money as investors shift to bonds

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or equities, leading to a reduction in the real interest rate and anexpansion of aggregate demand (of goods and services), real eco-nomic output and prices. The interest rate effect here is temporaryand comparable to a liquidity effect of a monetary expansion. Thereis little evidence for the US that there is a liquidity effect, however.The rise in prices has been referred to as the “Friedman surge” inprices, an overshooting of the price level that will eventually go awayin the long run. The simple evidence in Figure 12.2 is consistent withthis effect dominating the tax effect above.

Tax effects on real earningsThe tax argument above also applies to equity returns. The evidenceof a negative correlation between equity prices and inflation is con-sistent with such a tax effect, though the evidence for real yields onbonds is not.

Indeed, there is a second tax and inflation-related effect on equityprices that reinforces the tax effect just discussed: nominal incometaxation does not adjust depreciation allowances or inventory valua-tion for inflation. Thus, inflation-related increases in inventory valueare treated as income and taxed, even though there has been no gainin real (inflation-adjusted) terms. Similarly, depreciation allowancesdo not adjust for the higher replacement cost of depreciating assets,so that the depreciation cost of capital is understated by an increas-ing amount over time in an inflationary environment. The higherthe inflation rate and the longer-lived an asset, the greater the under-statement of cost and overstatement of taxable income and tax. Thus,real after-tax income from capital assets is depressed when inflationrises.

Feldstein (1981) and Tatom and Turley (1978) are examples ofmodels in which inflation raises the real tax burden (due princi-pally to accounting of inventory valuation and assets depreciation)and lowers real after tax earnings and rates of return to capital. Famaand French (1989) provide an explanation of how monetary policyaffects stock returns by affecting economic performance, but it isnot dependent on tax effects or supply shocks. Nominal income tax-ation, historical cost-based accounting of inventory valuation andasset depreciation imply that inflation affects real earnings and thetax burden.

Inflation raises the replacement cost of inventory and assets, butaccounting values do not reflect this. As a result, when all other costs

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Figure 12.4 Measured versus economic profits

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Source: FRED2, Federal Reserve Bank of St Louis.

and revenue keep pace with inflation, accounting depreciation andinventory costs do not, so costs are understated, and income taxesare overstated. As a result, true economic income is depressed, asare stock prices that are the present discounted value of after-taxeconomic income, even if the real cost of capital used to discountfuture real incomes is unchanged. Interestingly, indirect support forthe hypothesis can be found in Piazzesi and Schneider (2008), whoshowed that the Great Inflation led to a portfolio shift by makinghousing more attractive than equity. This may reflect that depre-ciation rules affect corporate income, but not the market value ofowner-occupied housing.

Evidence for this hypothesis can be found by examining real(inflation-adjusted) after-tax corporate profits (“measured” profitsin the following, as their non-inflation-adjusted version is the baseused to compute income taxes) and real (inflation-adjusted) after-tax profit adjusted for capital consumption and inventory valua-tion adjustments (true “economic” profits in the following). Bothnumbers are reported quarterly by the Bureau of Economic Analy-sis (BEA, US Department of Commerce). Figure 12.4 shows the BEAmeasures of after-tax corporate profits and after-tax corporate prof-its including capital consumption and inventory valuation adjust-ments, both as a percentage of national income. In this figure, eachnominal measure is shown as a percent of national income, but the

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percentages shown are identical to shares of real national income ifthe same price deflator is used. During the period of the Great Infla-tion, measured profits exceeded economic profits by relatively largeamounts. Measured profits were also relatively high compared witheconomic profit in 1947–51, when inflation was also relatively highand depreciation rules were more punitive to longer-term assets.The 1981 Economic Recovery Tax Act was aimed at reducing theexcessive depreciation on capital assets, especially long-term assetssuch as structures, which were most heavily affected by inflation.Note that after 1981 economic profit fell relative to measured profit.

It is interesting to examine the results of regressing the differencebetween inflation-adjusted after-tax economic profits (EP) and com-parable measured profits (MP) after natural logarithms are taken (ie,(ln EPt/Dt − ln MPt/Dt = Yt)) to changes in inflation (∆πt). Again,Y is the logarithm of the ratio of real EP to real MP. The dependentvariable is the percentage excess of economic profit over measuredprofit, measured on a continuous basis. As other factors influencethis ratio, especially the business cycle, the natural logarithm of thecapacity utilisation rate, CUt, is also included to capture such aneffect. A lagged value of both the profit ratio, Yt−1, and capacity util-isation rate variables, CUt−1, are also included. Using quarterly dataover the period from 1972 Q2 to 2011 Q2, the following regressionresults are obtained (the t-statistics in parentheses consistently rejectthe null hypothesis of zero regression coefficients)

Yt = 0.651(2.23)

− 0.018(−7.11)

∆πt − 0.074(−3.20)

∆CUt − 0.149(−2.23)

CUt−1 + 0.97(43.97)

Yt−1

adjusted R2 = 0.93, SE = 0.051, DW = 2.07

The standard error (SE) of the estimate and the Durbin–Watson (DW)statistic are both satisfactory. A one-percentage point rise in inflationreduces economic profits relative to measured profits by 1.8%, as wewould expect. However, a rise in the capacity utilisation rate (ourbusiness-cycle variable) also acts in the same direction, reducingeconomic profit relative to measured profits: a less intuitive result,which will be explained in the following.

The results from this regression support the hypothesis that infla-tion reduces the difference between economic and measured profits,but it does not reveal how inflation affects each individual measureindividually. To this end, consider two separate regressions, one link-ing after-tax economic profits to inflation and the business cycle and

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the other a comparable regression for after-tax measured profits.In both cases, the natural logarithm of inflation-adjusted (using thePCE deflator Dt) profits will be used, with the natural logarithm ofthe capacity utilisation rate CUt included as a proxy for business-cycle effects. After searching for lags in variables (from 1 to 4, andretaining only the statistically significant ones), the regression forreal (inflation-adjusted) after-tax economic profits is (t-statistics inparentheses)

ln(EPt/Dt)EPt−1/Dt−1

= 0.011(2.19)

− 0.007(−2.33)

∆πt−1 + 0.796(2.92)

∆CUt

adjusted R2 = 0.07, SE = 0.062, DW = 1.88

While the adjusted R2 is quite low, the independent variables aresignificant as a group and individually. Lagged inflation changes∆πt−1 have a significant and negative effect on economic profit, witha 1% rise in inflation associated with a 0.7% loss in inflation-adjustedafter-tax economic profit. As expected, cyclical improvements in themanufacturing capacity utilisation rate are associated with highereconomic profit, a result in line with intuition. This supports thehypothesis that inflation lowers inflation-adjusted after-tax profits,which are discounted (using real rates) by the market, and determinestock prices.

For measured profits, the hypothesis is that inflation artificiallyraises the tax burden. The comparable equation for the logarithm ofinflation-adjusted after-tax measured corporate profits is (t-statisticsin parenthesis)

ln(MPt/Dt)MPt−1/Dt−1

= 0.011(2.03)

− 0.022(6.17)

∆πt−1 + 1.382(4.41)

∆CUt

adjusted R2 = 0.31, SE = 0.070, DW = 2.30

A one-percentage rise in inflation increases inflation-adjustedafter-tax measured profit by 2.2%. This also supports the tax effecthypothesis and the popular view that inflation boosts measuredprofits, despite the fact that the true economic effect is negative,as seen in the previous regression. A rise in the capacity utilisationrate is associated with a 1.38% rise in inflation-adjusted after-taxmeasured corporate profit.

Finally, the interaction of inflation and accounting rules can alsobe seen by looking at net (ie, adjusted for depreciation) investment

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Figure 12.5 Long-term (structures) versus short-term (equipment)investments

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in long-term assets (mainly physical structures, more sensitive todepreciation effects) versus short-term investment, such as equip-ment and software. It is evident from Figure 12.5 that investment inlong-term structures has a decisive dip during the Great Inflation ofthe 1970s.

CONCLUSIONSInflation is a monetary phenomenon. A more rapid and sustainedpace of growth in the stock of money is the principal source of ahigher and sustained pace of general price increase or inflation.There are non-monetary sources of temporary inflation, such aslarge relative price changes associated with supply shocks, histor-ically often caused by energy price shocks that can boost inflationtemporarily.

Expected inflation tends to raise nominal interest rates and reducebond prices. If the money-neutrality hypothesis holds, real interestrates and real rates of return should be unaffected by inflation. How-ever, even in this case, supply shocks that reduce productivity andreal income, including the productivity of real capital, reduce realrates of return on equity and bonds. Monetary growth and infla-tion are not neutral, even when expected. For a variety of reasons

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reviewed here, inflation tends to raise investors’ required real rateof return on equity and to lower real capital income for tax-relatedreasons. As a result, there is a strong negative correlation betweeninflation and real and nominal stock prices. The latter effect can becompounded by an expected policy reaction to slow future infla-tion and dampen inflation expectations, but with the potential totemporarily reduce economic activity.

Contrary to popular opinion, equities are not a good hedgeagainst inflation. Some alternative investments may be better, suchas owner-occupied housing, land or other non-corporate invest-ments that are not as affected by tax rules on depreciation andinventory accounting. In this regard, Case and Wachter (see Chap-ter 4) analyse the performance of several asset classes, including realestate, in several inflation scenarios. As for corporate investments,sectors or firms with fewer capital assets, especially long-term assets,should provide better inflation hedges.

Tax effects are most negative for equities of firms that own long-duration assets and for firms that supply such long-lived assets.Temporary inflation associated with supply shocks also has dif-ferential effects across industries, affecting relative prices, outputand employment more heavily in industries that use the affectedresources. Not surprisingly, oil price shocks have larger effects onindustries using energy more intensively, as well as their customersand suppliers. Indexing the tax system to account for inflation tendsto weaken many of the effects highlighted here, especially indexingthe cost basis for depreciation and inventory accounting.

Finally, increasing information on economic policy could providemore stability and accuracy to expectations and alleviate some ofthe redistributive effects that can accompany shifts in the inflationrate. Policy-related considerations, however, are beyond the scopeof this chapter.

REFERENCES

Alchian, A. A., and B. Klein, 1973, “On a Correct Measure of Inflation”, Journal of Money,Credit, and Banking 5(1), pp. 173–91.

Bakshi, G. S., and Z. Chen, 1996, “Inflation, Asset Prices, and the Term Structure of InterestRates in Monetary Economies”, Review of Financial Studies 9, pp. 241–76.

Barro, R. J., 1996, “Inflation and Growth”, Federal Reserve Bank of St Louis Review 48(3),pp. 153–69.

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Bernanke, B. S., 2004, “The Great Moderation”, Speech to Eastern Economics Asso-ciation, February 20, URL: http://www.federalreserve.gov/boarddocs/speeches/2004/20040220/default.htm.

Blanchard, O., and J. Simon, 2001, “The Long and Large Decline in US Output Volatility”,Brookings Papers on Economic Activity 1, pp. 135–64.

Bordo, M. D., and D. C. Wheelock, 2007, “Stock Market Booms and Monetary Policy inthe Twentieth Century”, Federal Reserve Bank of St Louis Review 89(2), pp. 91–122.

Brandt, M. W., and K. Q. Wang, 2003, “Time Varying Risk Aversion and UnexpectedInflation”, Journal of Monetary Economics 50, pp. 1457–98.

Bryan, M. F., S. G. Cecchetti, and R. O’Sullivan, 2002, “Asset Prices in the Measurementof Inflation”, NBER Working Paper 8700.

Crone, T., N. Neil, K. Khettry, L. Mester and J. Novak, 2011, “Core Measures of Inflation asPredictors of Total Inflation”, Federal Reserve Bank of Philadelphia Working Paper 11-24.

Fama, E. F., 1981, “Stock Returns, Real Activity, Inflation, and Money”, American EconomicReview 71, pp. 545–65.

Fama, E. F., and K. R. French, 1989, “Stock Returns, Expected Returns, and Real Activity”,Journal of Financial Economics 45, pp. 1089–1108.

Feldstein, M., 1981, “Inflation and the Stock Market”, American Economic Review, Septem-ber, pp. 839–47.

Fisher, I., 1907, The Rate of Interest (New York: Macmillan).

Fisher, I., 1911, The Purchasing Power of Money (New York: Macmillan).

Friedman, M., 1956, “The Quantity Theory of Money: A Restatement”, in M. Friedman(ed), Studies in the Quantity Theory of Money, pp. 3–21 (University of Chicago Press).

Hess, P. J., and B.-S. Lee, 1999, “Stock Returns and Inflation with Supply and DemandDisturbances”, Review of Financial Studies 12(5), pp. 1203–18.

Kiley, M. T., 2008, “Estimating the Common Trend Rate of Inflation for Consumer Pricesand Consumer Prices excluding Food and Energy Prices”, Board of Governors of theFederal Reserve System Finance and Economic Discussion Series 2008-38, August.

Kim, C.-J., and C. Nelson, 1999, “Has the US Economy Become More Stable? A BayesianApproach Based on a Markov-Switching Model of the Business Cycle”, Review of Economicsand Statistics 81, pp. 608–16.

Kim, C.-J., C. Nelson and J. Piger, 2004, “The Less Volatile US Economy: ABayesian Inves-tigation of Timing, Breadth, and Potential Explanations”, Journal of Business and EconomicStatistics 22(1), pp. 80–93.

Konchitchki, Y., 2011, “Inflation and Nominal Financial Reporting: Implications forPerformance and Stock Prices”, The Accounting Review 86(3), pp. 1045–85.

Mankiw, N. G., R. Reis and J. Wolfers, 2003, “Disagreements about Inflation Expecta-tions”, in NBER Macroeconomics Annual, pp. 209–70 (Boston, MA: MIT Press).

McConnell, M., and G. Pérez-Quirós, 2000, “Output Fluctuations in the United States:What Has Changed since the Early 1980s?”, American Economic Review 90, pp. 1464–76.

Patinkin, D., 1965, Money, Interest and Prices: An Integration of Monetary and Value Theory,Second Edition (New York: Harper and Row).

Phillips, A. W., 1958, “The Relationship between Unemployment and the Rate of Changeof Money Wages in the United Kingdom 1861–1957”, Economica 25(100), pp. 283–99.

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Piazzesi, M., and M. Schneider, 2008, “Inflation and the Price of Real Assets”, StanfordUniversity Working Paper, April.

Rasche, R. H., and J. A. Tatom, 1977, “The Effect of the New Energy Regime on EconomicCapacity, Production, and Prices”, Federal Reserve Bank of St Louis Review, May.

Rasche, R. H., and J. A. Tatom, 1981, “Energy Price Shocks, Aggregate Supply and Mon-etary Policy: The Theory and International Evidence”, in K. Brunner and A. H. Meltzer(eds), Supply Shocks, Incentives and National Wealth, Carnegie-Rochester Conference Serieson Public Policy 14, pp. 9–93.

Rich, R. W., and C. Steindel, 2007, “A Comparison of Measures of Core Inflation”, FederalReserve Bank of New York Economic Policy Review 13(3), pp. 19–38.

Stock, J. H., and M. W. Watson, 2003, “Forecasting Output and Inflation: The Role of AssetPrices”, Journal of Economic Literature 41(3), pp. 788–829.

Stulz, R. M., 1986, “Asset Pricing and Expected Inflation”, The Journal of Finance 41(1),pp. 209–23.

Tatom, J. A., 2002, “Stock Prices, Inflation and Monetary Policy”, Business Economics,October, pp. 7–19.

Tatom, J. A., and J. E. Turley, 1978, “Inflation and Taxes: Disincentives for Capital Forma-tion”, Federal Reserve Bank of St Louis Review, January. Reprinted in Federal Reserve Readingson Inflation, Federal Reserve Bank of New York, February 1979, pp. 167–73.

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13

Inflation and Equity Returns

Jeffrey OxmanUniversity of St Thomas

Inflation is a ubiquitous feature of the modern industrial economy,and therefore we all need to protect our wealth from changes in pricelevels.

Since Irving Fisher (1930) published his “theory of interest”, in-vestors have viewed equities as a sound vehicle for protection frominflation. However, empirical evidence collected since the late 1970s(which will be detailed in this chapter) shows that this may notbe the case: in the short run, stock returns do not adjust for infla-tion. That means that an increase in inflation is not accompanied bya similar increase in stock returns. However, that is not the onlypart of the story. In the long run, there is evidence that returnson stocks will partly compensate for inflation. It is also possible tomake tactical shifts into industries that do better during inflationaryperiods.

In this chapter, we review the theory and evidence behind therelationship between inflation and stock returns. To set the stage,Table 13.1 shows the average (over the period 1995–2010) equityreturns (nominal and real) and inflation rates for 23 of the world’slargest economies. Real equity returns are in general positive,although four countries (Greece, Italy, Japan and New Zealand) hadnegative average real returns over this period.

To get a better sense of the data beyond simple averages, weinclude histograms of nominal and real return data, and inflationdata, for a subset of the countries included in Table 13.1. The nominaland real return histograms are given in Figure 13.1, and the infla-tion histograms are given in Figure 13.2. We chose the US, Germany,Japan, India, Mexico and Brazil as representative of the developed

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Table 13.1 Nominal and real returns (in percent) by country(1995–2010)

Brazil Canada Chile Mexico US

Nominal 17.30 7.25 9.02 17.42 6.30Real 7.84 5.33 5.05 7.22 3.88Inflation 8.77 1.82 3.78 9.51 2.32

Austria Denmark France Germany Greece

Nominal 5.90 9.78 4.40 7.43 3.04Real 4.13 7.68 2.86 5.96 −1.00Inflation 1.70 1.96 1.50 1.38 4.09

Ireland Israel Italy Norway Spain

Nominal 4.72 12.21 −1.37 9.68 7.26Real 2.25 8.36 −3.40 7.53 4.44Inflation 2.41 3.55 2.11 2.00 2.69

Switzerland UK Australia China India

Nominal 5.60 4.09 5.85 13.86 10.91Real 4.72 2.14 3.13 10.99 4.21Inflation 0.84 1.91 2.64 2.58 6.43

Japan Korea New Zealand

Nominal −4.10 4.32 0.75Real −4.03 0.87 −1.56Inflation −0.08 3.42 2.35

Nominal returns data are obtained from Bloomberg for the broadest stockindex with the longest history for each country. Inflation is the ConsumerPrice Index (CPI) as measured by the Organization for Economic Co-operation and Development (OECD). Inflation data were obtained fromthe Federal Reserve Bank of St Louis.

economies (the former three countries) and emerging markets (thelatter three countries). Overlaid on each histogram is a curve fittedto the data using the estimated mean and variance of the country-specific data. We notice immediately that the fitted curves are notGaussian. The US and Germany return charts exhibit negative skew,while Japan has positive skew. Returns in India are close to normallydistributed, but Mexican returns appear to be negatively skewed andBrazilian returns slightly positively skewed.

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Figure 13.1 Nominal and real annual returns

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(a) US, (b) Japan, (c) Germany, (d) India, (e) Mexico, (f) Brazil. Solid line, nom-inal (estimated); dashed line, real (estimated). Grey histogram, nominal; blackhistogram, real.

Inflation in developed countries follows a very different patternfrom that in emerging markets. We have grouped the inflation inthe three developed countries into one histogram in Figure 13.2,but the inflation for the emerging markets economies are displayedindividually. The developed countries have inflation patterns thatare very similar, though their means are different.

The US experienced inflation rates of about 3% per annum onaverage, while those for Germany were about 2% and those for Japanwere only slightly higher than 0%. Occasionally these countries haveexperienced deflation, but it is quite rare, since the central banks ofeach country target positive rates of inflation.

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Figure 13.2 Annual inflation rates

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Inflation in: (a) US, Germany and Japan (solid line, US; dashed line, Germany;dotted line, Japan; light-grey histogram, US; dark-grey histogram, Germany; blackhistogram, Japan); (b) India; (c) Mexico; (d) Brazil.

The emerging markets economies all have much higher meaninflation, and India is the only one of the three with a normal distribu-tion. India’s mean inflation is approximately 6.5%, but has ranged ashigh as 15% and as low as 2.5%. Brazil and Mexico, on the other hand,have extremely fat right tails and distributions that do not follow arecognisable pattern. It is likely that these two countries have fol-lowed different inflation regimes, as high inflation rates were tamedin the 1990s. This is an important point to remember, as some litera-ture (detailed throughout this chapter) points to equities providingbetter protection from inflation in high inflation countries and worseprotection in low-inflation countries.

In the following, we shall discuss some introductory concepts,specifically the Fisher hypothesis (which first laid out the expectedrelationship between stock returns and inflation), the distinctionbetween expected versus unexpected inflation and the “equity–inflation puzzle”, ie, the negative relationship between stock returnsand inflation, which has been documented in many empirical stud-ies. Next, we shall present various equilibrium-based theories that

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aim to explain the negative correlation between stock returns andinflation, and review stock pricing theories that do the same. Finally,evidence of the efficacy of equities as a hedging device, includingthe best hedging methods, will be analysed.

FISHER’S HYPOTHESISIrving Fisher’s hypothesis (Fisher 1930) held that the nominal inter-est rate rN, what might be called the risk-free return, is composedof a real component rR, plus expected inflation iEXP the time horizonunder consideration

rN = rR + iEXP (13.1)

Fisher believed that the real interest rate was independent ofmonetary effects and therefore, in Fisher’s theory, independentof expected inflation. Therefore, the nominal rate should adjustone-for-one with inflation

∂rN

∂iEXP= 1 (13.2)

According to a simple capital asset pricing model,1 the requiredreturn on a stock rstock is equal to the nominal rate plus the productof the stock beta coefficient (β) and the equity risk premium (thelatter being the difference between the required return on the overallequity market rMkt and the nominal rate rN itself)

rstock = rN + β× risk premium = rN + β[rMkt − rN] (13.3)

Therefore, assuming that β × risk premium does depend on ex-pected inflation, stock returns should also increase one-for-one withexpected inflation

∂rstock

∂iEXP= ∂rN

∂iEXP= 1 (13.4)

Furthermore, if we assume thatβ itself is not dependent on expectedinflation, the key empirical issue is the relationship between theequity risk premium and inflation, or equivalently between inflationand the overall market return rMkt.

Although many of the simplifying assumptions above have beenchallenged by the empirical data, Fisher’s hypothesis provides asimple yet powerful starting point in the analysis of the relationshipbetween stock returns and inflation. Specifically, this equation pre-dicts nominal stock returns to be positively correlated with ex ante

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expected inflation. Indeed, it is precisely when returns and inflationfail to behave according to theory that Fisher’s equation provides auniquely useful framework to identify what the reasons behind thatfailure might be. In particular, failures of Fisher’s equation mightstem from a combination of factors, including

• dependence of real rates or real economic activity on inflationand the business cycle,

• variation of β linked to inflation or the business cycle (eg, forcyclical versus non-cyclical companies), and

• variation in the risk premium (eg, in high- versus low-inflationregimes).

EXPECTED VERSUS UNEXPECTED INFLATIONExpected inflation is the percentage price increase that investorsthink will take place over a certain time period in the future, basedon information available in the present. By definition, only expectedinflation can be incorporated into the required return calculation foran asset. However, unexpected inflation, or the difference betweenexpected and actual inflation, has potential consequences for stockreturns.

Among its effects, unexpected inflation constitutes a wealth trans-fer from net creditors to net debtors, increases the real tax burdenof firms with significant fixed assets and inventory and it indicatesthat future inflation may be different from previous expectations. Ifunexpected inflation is positive, then future expected inflation willincrease and cause an increase in required returns.

The transfer of wealth from creditors to debtors results becausecontracts are written in US dollar terms. This transfer will exist forall dollar-denominated contracts that do not adjust for unexpectedinflation, or are renegotiated infrequently. Thus, unexpected infla-tion may also constitute a wealth transfer from the labour force to theshareholders because wages will typically not rise as fast as inflation,so profit margins should improve at least over the short term. Thestock-return effect on any specific firm is a combination of severaleffects and thus unclear a priori.

In addition to the ‘automatic’ effects illustrated above, inflationsurprises might also lead to government intervention to counteracthigh inflation or avoid deflation. Examples include Nixon-era price

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controls, the dramatic increases in interest rates, such as under PaulVolcker’s leadership at the Federal Exchange in the 1980s, or quan-titative easing policies employed by central banks to boost marketliquidity (for example, during and following the 2008–9 global reces-sion). In general, price controls interfere with production and thuslead to stock price losses. Higher interest rates lift the required returnon assets in general, while greater liquidity in the financial systemacts in the opposite direction.

THE EQUITY–INFLATION PUZZLE

The equity–inflation puzzle is, in fact, bad news for stocks. It has longbeen the contention of various investors and financial advisors thatstocks are a good hedge against inflation. Based on Fisher’s hypoth-esis and the nature of stock valuation (eg, discounting of future cash-flows generated by a real asset), this contention has intuitive merit.Unfortunately, the empirical evidence does not confirm the intuition.In fact, stock returns and inflation often move in opposite directions.As we shall find out, though, this is a controversial topic, and thereare still strategies that investors can use to protect their wealth frominflation.

The remainder of this chapter is divided into three sections. Thefirst explains theories of inflation and stock returns from an eco-nomic equilibrium perspective where, at least in the long run, mar-ket prices are set by the balance or equilibrium relationships linkingseveral interacting agents and economic factors. Equilibrium in thiscontext means that the actions taken by households and by busi-nesses are stable in the long run. Thus, any change in the economicvariables will cause these equilibrium relationships to adjust. In gen-eral, these theories explain that the observed negative correlation isa result of spurious correlation because stock returns and inflationreact differently to economic fundamentals like real productivitygrowth.

The second section outlines stock valuation-based theories andreviews the currently popular “inflation illusion” hypothesis. Thishypothesis suggests that the negative correlation between inflationand stock returns is due to investor irrationality. We also discuss analternative hypothesis, ie, that correlation is driven by demand andsupply shocks instead.

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The final section discusses the empirical literature, and exploresthe efficacy of stocks as an inflation hedge, tactical asset allocationand the differences between high- and low-inflation regimes.

Equilibrium-based theories of inflation and asset returnsEquilibrium models of the inflation process tend to be complex anddesigned for the specific purpose the author has in writing the paper.As such, it is not sensible to review every model nor is it possible toprovide general models.

This said, the key empirical findings that equilibrium theories ofinflation and asset returns are attempting to explain are that

1. real stock returns are negatively correlated with both expectedand unexpected inflation, and

2. real stock returns are positively correlated with money growth;in other words, real stock returns tend to increase with thequantity or velocity of money.

This seems in contradiction to the inverse relation between inflationand stock returns, and hints to the fact that shocks to output produc-tion and shocks to the demand for money might have quite differenteffects. Both shocks can cause inflation, but negative supply shocksreduce future stock returns, while positive demand shocks are atleast neutral for stock returns, and may be positive. These empiricalfacts indicate that stock returns are not the inflation hedge they arepopularly thought to be. This is a post-World War II phenomenonthat does not square with Fisher’s hypothesis and the concept ofcommon stock as the present value of future income generated by areal asset.

As for point 1 above, several theories have been advanced toexplain the negative relationship between stock returns and infla-tion. Fama (1981), in one of the earliest attempts to explain the neg-ative correlation, showed that it arises because of an omitted vari-able bias. The basic argument is that both inflation and real stockreturns are related to future real activity: inflation negatively andstock returns positively. Thus, the documented negative relation-ship is actually a spurious correlation due to the omission of realactivity from the model. In other words, when an inflation surpriseoccurs (on the upside), equity values tend to decrease because ofthe market’s anticipation of a slow-down in future real economicoutput.

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Because Fama’s model does not account for all the negative cor-relation between unexpected inflation and stock returns, Geske andRoll (1983) proposed an extension to Fama’s theory. Their argumentfocuses on the effect of stock market returns on government finances.Essentially, government revenues are comprised of personal and cor-porate taxes, which respond to expected economic conditions in thesame direction as the stock market. Thus, stock market returns antici-pate changes in government revenue. Government expenditure, onthe other hand, is largely fixed. Clearly, government deficits arecountercyclical (they tend to decrease when the economy is strong,and increase when the economy is weak). Geske and Roll hypoth-esise that a decrease in the stock market will lead to higher deficitsand, given that under such circumstances the Federal Reserve Sys-tem will have an incentive to monetise the growing debt, this in turnwill lead to growth in-the-money supply and higher inflation. Thus,the measured correlation between stock returns and inflation is neg-ative. This hypothesis is also called the “reverse-causality” link, asit is declining stock prices that cause inflation to rise, and not theother way around.

Regarding point 2 above, Danthine and Donaldson (1986) devel-oped a general equilibrium model and showed that common stocksare not a good hedge against non-monetary inflation, ie, a price levelincrease caused by a negative supply shock (for example, oil prices inthe 1970s); however, common stocks are a good hedge against mon-etary inflation (typically associated with a positive demand shock2)over the long run. This study differentiates between inflation causedby supply shocks and inflation caused by demand shocks (the lat-ter being more equity friendly than the former) and recognises theimportance of the horizon used in the analysis, as different dynamicsmight be at play in the short and the long term.

Marshall (1992) developed and estimated a representative agentmodel where agents hold a mix of money, equities and bonds asassets. The value of money is that it reduces the costs of consumptiontransactions. Agents seek to maximise the present value of expectedconsumption utility. The agents do not have income; rather, they areconstrained by the amount of shares and bonds they hold. Agentscan lend and borrow (issue bonds) at the risk-free real rate of inter-est. Finally, increases in money supply are exogenous (the moneysupply function follows a stochastic process) and new money is

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distributed directly to agents as a lump-sum transfer. The impor-tance of Marshall’s model is that it does not include any irrational-ity or market inefficiencies, which other authors have suggested asexplanations of the negative correlation between real equity returnsand inflation (see the discussion in the next section regarding “infla-tion illusion”). It is clear that the Fisher hypothesis is violated bythe negative correlation between expected inflation and expectedstock returns. Marshall’s contribution shows that this violation ofthe Fisher hypothesis arises because of the importance of moneyfor transactions. Marshall’s model also shows that the hypothesis ofFama (1981) is correct, in that it is fluctuations in the real economythat cause equity returns and inflation to move in opposite direc-tions. Finally, an increase in expected inflation that arises due to anincrease in expected money growth causes agents to hold less moneyand therefore increase balances held in equities or bonds. Marshall’smodel suggests there should be limited or no effects from moneysupply-induced inflation and equity returns.3

While the theoretical work reviewed to this point does not relyon financial intermediaries, the work of Boyd et al (2001) points tothe banking sector as an important agent for transmitting inflation-induced problems to the economy as a whole, including equityprices. In addition to new insights, they have one of the largestdata samples of any papers reviewed: 100 countries from 1960–1995.Inflation affects the real activity through the banking sector becausehigher inflation, even if predictable, exacerbates information asym-metries that already exist in credit markets.As inflation increases, theinformational frictions become more important and result in creditrationing. With fewer loans being made, fewer projects can be startedand thus real output growth declines.

Boyd et al (2001) showed that countries with high inflation (theircut-off is 15% per year) have less developed financial sectors thancountries with low inflation. This leads to some differences in theeffects of inflation on equity returns. In low-to-moderate inflationcountries, inflation rates and stock market liquidity and trading vol-ume are inversely correlated, while inflation is positively correlatedwith equity return volatility. But, above 15% inflation per annum,the correlations between inflation and equity market activity dis-appear. Finally, below 15% inflation they observed no correlationbetween nominal equity returns and inflation, but above 15% they

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found a one-to-one positive correlation between inflation and nom-inal equity returns. Thus, when examining foreign countries forpotential investment, keeping in mind the 15% inflation cut-off islikely to be helpful.

Stock price based theories of inflation and asset returnsIt is helpful to review the Gordon (1962) growth model of stockpricing, which states that the value of a share of equity today is thepresent value of the dividends accruing to the share in perpetuity.Formally

Pt =Dt+1

rstock − g(13.5)

where Pt the current price of one share, Dt+1 the expected dividendnext period, rstock is the required return on the stock and g is theexpected growth rate of the dividend. The Gordon model impliesthat stock prices should not be affected by expected inflation, asthe inflation contribution cancels in the difference rstock − g. How-ever, we know that empirical data does not support this conclusion.The previous section covered various economic reasons for this phe-nomenon. This section explores reasons specifically related to stockpricing models.

There are three possible reasons for stock prices to be affectedby inflation, according to the Gordon model. The first is that theFisher hypothesis for dividend growth rates is incorrect, and realdividend growth is actually a function of expected inflation, amongother things. Second, the Fisher hypothesis for stock returns is incor-rect, and the required real stock return is affected by expected infla-tion. Finally, there is the “inflation illusion” hypothesis, developedby Modigliani and Cohn (1979).

The inflation illusion hypothesis states that investors mistakenlyextrapolate past nominal dividend growth into the future, evenwhen inflation is changing. For example, if inflation is expected toincrease, investors operating under the inflation illusion hypothesiswill increase their estimate of nominal required return rstock but willnot adjust their estimate of nominal growth. This leads to lower stockprices, and a negative correlation between inflation and stock prices.The reverse is also the case: when expected inflation decreases, stocksbecome overvalued.

Sharpe (2002) provided the first set of results in our overview. Hefound that the negative relationship between stock valuation and

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expected inflation is due to two effects. First, an increase in expectedinflation lowers the expected growth of real earnings, which is sim-ilar to the negative correlation between real activity and inflationdiscussed in the previous section. Second, increased expected infla-tion increases the required real returns, probably because higherinflation is associated with a more volatile stock market, therebyincreasing investors’ required return. Both of these constitute viola-tions of the main assumption underlying the Fisher equation, thatis real variables are not affected by inflation. Higher required stockreturn and lower expected dividend growth both combine to reducepresent stock values.

Using the price/earnings (P/E) ratio as his dependent variable,Sharpe documented an initial coefficient on ten-year inflation of−20,which indicates that an increase of 1 percentage point in the expectedten-year inflation rate is associated with a 20% decline in the P/Eratio. The inclusion of estimates of long-term real dividend growthrates and expected real bond yield explain the effect of inflationon the P/E ratio. In his analysis of long-run real expected returns,Sharpe found that the effect of inflation on the expected real equityreturn, ie, rR + β[rMkt − rN] operates through the real bond yield rR.In other words, expected inflation has no effect on the equity returnpremium β[rMkt − rN]. Arguing against Sharpe were Campbell andVuolteenaho (2004): they argued that the components identified bySharpe (2002) do not explain the stock-return–inflation relationshipas well as the inflation illusion hypothesis of Modigliani and Cohn(1979). The Modigliani–Cohn hypothesis states that investors do notincorporate inflation into their nominal dividend projections cor-rectly. Specifically, investors do not adjust the nominal dividendgrowth rate in line with the nominal discount rate, even if inflationshould affect both to the same degree.

Campbell and Vuolteenaho (2004) presented evidence againstSharpe’s findings and in favour of the inflation illusion hypothesis.To analyse the data, Campbell and Vuolteenaho used the dividend/price ratio as the dependent variable, and have as independent vari-ables the excess (over the risk-free rate of return) growth rate individends, a subjective risk premium,4 and a mispricing term thatis essentially the error term from the regression. Qualitatively

Dt+1

Pt

def= rstock − gex ante ∼ β× risk premium+α(gex post − rN)+ ε

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Note that the independent variables on the left represent realised his-torical data (for example, the realised dividend growth rate gex post),while the dividend price ratio on the left embeds (by definition)future expectations of the same quantity, ie, gex ante. The motivationfor the regression is that if the dividend growth rate and subjectiverisk premium explain the dividend/price ratio, then the hypothesisof inflation illusion is rejected. If the error term is significant andpositively related to inflation, then the hypothesis of inflation illu-sion cannot be rejected. The results from the analysis of Campbelland Vuolteenaho (2004) indicate that the realised dividend growthrate gex post and inflation are positively related. Thus, empiricallyspeaking, inflation does not have an adverse impact on the realisedreal growth of dividends. Also, the (subjective) risk premium is notrelated to inflation, so investors do not become more risk aversewhen inflation increases. The mispricing component is strongly pos-itively related to inflation, and this constitutes evidence in favour ofthe inflation illusion hypothesis (ie, that the ex ante projection fornominal dividend growth does not fully account for inflation, sothat rstock − gex ante is a positive relation to inflation). Campbell andVuolteenaho also suggested that, while inflation illusion is presentin the short run, it should diminish over the long run (longer thanone year); therefore, equities tend to be a poor inflation hedge in theshort run, but a better hedge over the long run. This is consistentwith results that we shall review in the next section.

The previous sets of results involve expected inflation. But it mightbe the case that the inflation–equity return correlation is caused byunexpected inflation. Sudden price changes in a commodity or ser-vice might occur because of a sudden and unexpected change inproduction. Negative supply shocks are those that cause supply todecrease and thus the price of the commodity to increase. Positivesupply shocks are the opposite, and are often termed “technologyshocks” because of the close positive correlation between technolog-ical innovation and productive capacity. If the commodity in ques-tion is particularly ubiquitous in the economy, like crude oil, thisprice shock can work its way through the economy generally, thusshowing up as inflation.

Demand shocks are sudden changes in the demand for a certaincommodity or service. Of course, demand shocks have the oppositeeffect to supply shocks. A particularly important type of demand

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shock that affects the whole economy is a sudden increase in thedemand to hold cash, rather than spend it on goods and services.Such a demand shock can show up as a recession or decrease in totalexpenditure (and thus lower GDP, all other things being equal). Ademand shock whereby people want to hold less cash and wantto spend more can show up as price inflation. There is not a greatdeal of evidence regarding the importance of demand shocks for theinflation–equity-return relationship, but supply shocks are anothermatter.

Hess and Lee (1999) explored the explanatory power of supplyand demand shocks in resolving the inflation–stock-return puzzle.Supply shocks are generally real output shocks, which generate anegative inflation–stock-return correlation. Demand shocks, on theother hand, cause a positive correlation between inflation and stockreturns. Hess and Lee provided evidence for the US, UK, Germany5

and Japan. Except for the US prior to World War II, supply shocksdominate the sample, generating the observed negative correlation.

Lee (2010) revisited the inflation illusion hypothesis and foundthat it cannot explain the inflation–equity-returns relationship thatexisted prior to World War II, although it fits the post-war data inthe US and several other countries. Lee proposes a “two-regime”hypothesis that he finds explains the data for the pre- and post-warperiods in his sample of countries. The two-regime hypothesis fol-lows from Hess and Lee (1999). The period before World War II isdominated by demand (ie, monetary) shocks, which created a posi-tive relationship between inflation and equity returns prior to WorldWar II. Conversely, supply shocks created a negative relationshipbetween inflation and equity returns in the post-war sample. Thenegative correlation between inflation and equity returns caused bysupply shocks is a consequence of the negative effect that higherprices (especially energy prices) have on production and real activ-ity. This is reminiscent of Fama (1981) and Danthine and Donaldson(1986).

The inflation illusion hypothesis is also challenged by Wei (2010).Arguing that the vector autoregression (VAR) method used byCampbell and Vuolteenaho (2004) overstates the importance of theresidual term, and thus the solidity of their conclusion, Wei prefersa general equilibrium framework, and is able to show that technol-ogy shocks can yield the same empirical predictions as the inflation

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illusion hypothesis. Wei’s model generates a positive correlationbetween dividend yield and inflation through technology shocks,which operate on the productive sector and thus dividend growth.Therefore, the correlation between inflation and equity returns isspurious. Wei’s model follows similar reasoning to Fama (1981) andMarshall (1992) and thus is not a stock-price based model. It is dis-cussed in this section because it seeks to directly refute the inflationillusion hypothesis.

In the next section, we shall review the empirical evidence onthe efficacy of equities as an inflation hedge, as well as methods ofimproving their performance as an inflation hedge through tacticalasset allocation and other portfolio management techniques.

Inflation and stock returns: empirical evidenceInflation hedge effectiveness

Schwert (1981) examined the effect of unexpected inflation on stockreturns. He found a negative, but small, correlation between unex-pected high inflation and stock returns and showed that the marketreaction was distributed over the days surrounding the announce-ment of the Consumer Price Index (CPI) data, but the daily changeswere too small to offer a profitable trading opportunity.

Solnik (1983) offered evidence based on a short time period (1971–80), but a broad selection of countries (the US, Japan, the UK, Switzer-land, France, West Germany, the Netherlands, Belgium and Canada).Solnik tested for a correlation using real stock returns. Accordingto the Fisher hypothesis, real stock returns should be unrelated toinflation. Solnik found that real and nominal stock returns are neg-atively related to unexpected inflation and suggests this is becauseunexpected inflation leads to changes in expected inflation in thefuture. He also noted a reverse causality: increased stock returnssignal negative revisions in expected inflation.

Kaul (1987) offered empirical evidence in favour of Fama (1981)and Geske and Roll (1983) using evidence from the US, Canada,the UK and West Germany. This empirical data indicates that thepost-war experience of negative correlation between inflation andstock returns was common to industrialised countries. It also con-firms that the negative correlation was due to activity in the mone-tary sector: specifically countercyclical monetary responses used tofinance deficit spending. If central banks were to follow a procyclical

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monetary policy, allowing money supply to rise and fall with grossnational product, then stock returns and inflation would be posi-tively related. Kaul (1987) shows this is the case for the depressionperiod in the US and Canada.

In a follow up paper in 1990, Kaul considered the impact of twodifferent types of monetary policy regimes on the stock-return–inflation correlation. There are two ways that central banks carryout their mandate of price stability and, in the case of the US FederalReserve (the Fed), the additional mandate of full employment. Thecentral bank can target a specific growth rate in the monetary base, orthe central bank can target interest rates, like the discount windowrate or the overnight federal funds rate. The monetary base is thetotal currency held by the public plus vault cash and deposits heldby Federal Reserve banks. The discount window rate is the interestrate charged by the Fed on overnight lending directly from the Fedto its member banks. The federal funds rate is the rate at which bankslend to each other in the overnight lending market.

Kaul (1990) identified periods in which central banks in four coun-tries (the US, Canada, the UK, West Germany) follow the two differ-ent methods discussed above. When monetary policy targets moneygrowth directly, there is no clear link between money supply and eco-nomic activity, and thus there should be no significant correlationbetween inflation and equity returns.

Kaul followed Geske and Roll (1983) in assuming that if cen-tral banks use interest rate targeting as the mechanism of imple-menting policy, then the central banks will follow a countercycli-cal policy. This is because interest rate targeting leads the Fed tomonetise government debt, giving rise to the mechanism identifiedby Geske and Roll (1983) and leading to the negative correlationbetween stock returns and inflation. Kaul’s results confirm that thereason for the apparent shift from no relation or a positive relationbetween inflation and equity returns to a negative relation is due tothe shift in how the central banks implement their mandates. In theUS and Canada, central banks moved from targeting money sup-ply to focusing on interest rates, especially after the oil crisis in the1970s. Moreover, Kaul highlighted that, unlike previous work, it isthe interaction of money demand and money supply that governsthe relationship between inflation and equity returns, not just moneydemand.

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The message of Kaul (1987, 1990) is that in industrialised coun-tries where the central bank uses interest rate management to ful-fill its objective of price stability (and full employment as in theUS), investors should expect a negative relationship between stockreturns and inflation, both expected and unexpected. Therefore,stocks will not be a satisfactory inflation hedge in the short run.

Chang and Pinegar (1987) investigated the effect of security riskon the relationship between stock returns and inflation. They foundthat the riskier the security, as measured by the market beta, themore negative the correlation between inflation (expected and unex-pected) and real stock returns. However, their results are based onthe model developed by Geske and Roll (1983), which posited a mon-etary growth mechanism rather than an interest rate managementmechanism. Thus, it is not clear if Chang and Pinegar’s results areapplicable to the environment of the 2000s.

In the spirit of Danthine and Donaldson (1986), Boudoukh andRichardson (1993) offered the first exploration of the stock-return–inflation relationship over a long horizon. They used stock returnsfrom 1802 to 1990 and a five-year time horizon. Previous studiesused post-World War II data and month/quarter/year horizons.

For the longer time horizon, Boudoukh and Richardson (1993)found that stock returns do compensate for inflation, but not fully.A 1% increase in inflation yields a 0.5% increase in nominal stockreturns over a five-year period. The one-year horizon conforms toprevious studies, where inflation-hedging performance is generallypoor. Thus, over the long run, stocks offer some inflation protection.They confirmed this result for the UK over the period 1820–1988.

Gregoriou and Kontonikas (2010) updated the work of Boudoukhand Richardson (1993) with a shorter (1970–2006) but wider (16OECD countries) sample. Their findings indicate that over the longrun (ie, 10 to 16 years), annual elasticity of stock prices to consumergoods prices is not significantly different from unity. That meansthat, over the long run, stocks will provide a nearly one-to-one hedgeagainst inflation. We have found that these results are the strongestin favour of stocks as an inflation hedge.

Schotman and Schweitzer (2000) derived optimal hedge port-folios for various assumptions regarding inflation persistence andthe long-run relationship between equity returns and inflation. Theirresults indicate that only when inflation is fairly persistent and stock

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returns have a positive relationship with inflation (a beta of 0.7 orhigher) will stocks offer a reasonable inflation hedge, and then onlyover very long time horizons: 15 years or more. Given other findingsabout the correlation between stock returns and inflation, Schotmanand Schweitzer’s findings are not favourable to the use of stocks tohedge against inflation.

In a very interesting paper, Amihud (1996) tested the varioushypotheses that purport to explain the negative correlation betweeninflation and stock returns. It is interesting because Amihud usesIsrael as the test case. Contracts in Israel are specified in real terms;for example, tax brackets and government debt are linked to theCPI; bank yields and other interest rates are also quoted in realterms, which obviates the inflation illusion. Thus, when Amihudfound a negative correlation between inflation and stock returns inIsrael, it could only be because higher inflation leads to decreasedreal activity.

Goto and Valkanov (2002) pursued the monetary shock angle fur-ther by exploring the effects of unanticipated changes in the federalfunds rate. They argued that a surprise increase in federal funds ratecauses the total return on stocks6 in excess of the risk-free rate todecrease, and increases both expected and observed inflation. Theirfindings indicate that monetary shocks can explain between 20% and25% of the covariance between excess returns and inflation. Thus,keeping an eye on the Fed is important for forecasting stock returnsand inflation.

In the early 2000s the focus shifted to the effects of inflation acrossthe business cycle. Inflation news carries different information inbooms and recessions. Adams et al (2004) used intra-day trade7 datato show that a 1% increase in inflation in a weak economy causes adecline much greater than 1% in stock returns; in a strong economythis decline is only about 0.5%.

Knif et al (2008) examined the effects of good and bad inflationnews across the various stages of economic growth, which are cat-egorised as: growing, stable and slowing. They examined cumula-tive abnormal returns (CAR) over a 20-day window centred on theinflation announcement day. During a period of economic growth,investors appear to take a dim view of unexpectedly high inflation,with a CAR of −9.43. So an unexpected inflation of 1% above theexpectation would lead to a decrease in the S&P 500 of 9.43%. This is

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exceptionally high. On the other hand, a negative inflation surprisehas a CAR of −1.95, but it is not statistically significant. The pooledresult is −2.00, and is also not significant. Thus, in a rising econ-omy, negative surprises tend to occur more frequently than positivesurprises, but positive surprises are very damaging to the market.

In a stable period, negative inflation shocks dominate and leadto negative market returns of around −6.5% for a 1% differencebetween expected and actual inflation. Positive inflation shocks arenot statistically significant in stable periods. In a slowing period, noinflation shock was found to be statistically significant, althoughthere was a positive effect of negative shocks on the stock mar-ket. This is in contrast to Adams et al (2004), who highlightedthe importance of the measurement horizon. Ultimately, Knif et al(2008) showed that the state of the economy matters greatly whenconsidering inflation effects on the stock market.

Finally, the effects of the business cycle on inflation were discussedin a working paper by Wei (2009). He confirmed the importanceof these effects, but illustrated two interesting points that can helpwith hedging. He noted that firms with lower book-to-market ratios(which are typically characterised as growth firms) and medium-sized firms have a higher negative correlation with unexpectedinflation; thus, choosing large value firms instead may offer furtherhedging against inflation surprises.

Tactical asset allocation in relation to inflation

Pearce and Roley (1988) examined the role of various firm charac-teristics in determining individual equity response to unexpectedinflation. They found, as do others, that the average response tounexpected inflation is negative. They had a short sample period(1977–1982) and used only 84 firms. Thus, their results may not appli-cable to the entire market. Nevertheless, it is worthwhile exploringpotential avenues for improved performance against inflation. Theirresults indicate that firms with high inventories experience a morenegative response to inflation if they use the first in, first out (FIFO)method, as this understates cost of goods sold and therefore over-states taxable income, resulting in higher taxes. This effect does notappear for firms that use the last in, first out (LIFO) method forinventory valuation. Firms with more debt experience a positivewealth effect if inflation is unexpectedly high. The same is true for

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firms with large pension expenses (if the latter are fixed in nom-inal terms). Depreciation does not appear to have any significanteffect. Thus, to summarise, if we want a better inflation hedge, weshould avoid firms that carry large inventories, and seek to hold netdebtors.

Boudoukh et al (1994) investigated the negative correlation by dis-aggregating the stock market into industries. They found that, in theshort run, non-cyclical industries tend to have a positive correlationwith expected inflation, while cyclical industries have a negativecorrelation. Over the entire sample in their paper (1953–1990), mostindustries have a positive correlation. It appears that those industriesthat are related to consumer goods have a much stronger relationshipto consumer inflation than industries that are related to producers’goods. Thus, if we are looking for an inflation hedge over the longrun, it is best to focus on industries such as tobacco, apparel or foodand beverage.

Ely and Robinson (1997) updated the literature by taking an inter-national view, offering evidence in favour of stocks as a hedgeagainst inflation. Their work indicates that focusing on the US maydeliver anomalous results. In the US, the efficacy of stocks as a hedgeagainst inflation depends on the source of inflation. If inflation occursbecause of a real output shock, then stocks do not offer a good hedge.If it is monetary-induced inflation, then stocks do offer a good hedge.Their work is based on a vector error-correction model (VECM) anduses a 16-quarter horizon; it also covers Canada, Western Europe,Australia, the UK and Japan. Many of the countries display theirown idiosyncratic relationship to inflation; thus, it is valuable forthe reader to investigate the specific country of interest. Some impor-tant observations are in order though. Canada and Italy both havesimilar responses to the US to output shocks. Switzerland does notoffer protection from inflation, as stock prices decrease for both realoutput and monetary shocks. Spain is the only country to offer solidprotection from output-related inflation.

Brière and Signori (2009) make an important contribution to theasset allocation literature, but did not focus exclusively on equities.Working in a real-return maximising portfolio environment, theyfound that equity weight should be increased in a portfolio whenthe targeted real return is greater than zero or the investment horizonis long (typically two years or more).

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Bekaert and Wang (2010) and Ang et al (2011) offered evidenceregarding inflation betas for world equity markets and individualequities, respectively. Inflation betas are estimated using a standardfactor model, where asset returns are modelled as a function of oneor more factors. It appears that inflation betas are not sensitive todifferent factor specifications.

Bekaert and Wang (2010) confirmed much of the previously pub-lished research. Using one-year holding periods, they found thatdeveloped markets have negative but insignificant inflation betas,whereas emerging markets offer a near-perfect inflation hedge. Thisis the case for both expected and unexpected inflation. Asia andAfrica stocks offer the worst expected inflation hedges, while NorthAmerican and EU stocks are the worst hedges against unexpectedinflation. Latin American stocks are a strong hedge against bothexpected and unexpected inflation. Using longer horizons, up tofive years, also leads to similar conclusions.

Ang et al (2011) found that, while the US stock market in generalis not a good inflation hedge, certain individual equities may be.They estimated the inflation beta for all stocks in the S&P 500 for theperiod 1989 to 2010. They then sorted the stocks into quintile port-folios according to their inflation beta. The quintile with the highestinflation beta had an inflation beta of 1.65. The lowest quintile hadan inflation beta of −2.22.

While their in-sample analysis is encouraging, they found thatpast inflation hedges are not a guide to future inflation hedges, anda firm that has a high inflation beta in the past is not guaranteed tohave a high inflation beta in the future. The quintile with the highestinflation beta in-sample has only a 0.45 inflation beta out-of-sample.There is also evidence of reversal, as the quintile with the lowestin-sample inflation beta has an out-of-sample inflation beta of 0.52:the highest recorded out-of-sample inflation beta.

High- and low-inflation differences

Most studies have focused on industrialised countries, where infla-tion tends to be low. Barnes et al (1999) examined a group of 25 coun-tries, including several high inflation countries. Their sample covers1957 to 1996. For most countries, nominal equity returns and infla-tion are negatively correlated. Austria, India, Italy, New Zealandand the UK were found to have positive but low correlations. Equity

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returns in Chile, Israel, Mexico and Peru all have high positive corre-lations with inflation, and these are the four highest inflation coun-tries in the sample. It appears that in high inflation countries thereis sufficient compensation through nominal equity returns to enjoya sound inflation hedge, as nominal equity returns adjust close toone-to-one with inflation.

Barnes et al also explored the effects of spillover inflation fromthe US into other countries. They found that for Germany,8 Lux-embourg, the Netherlands, Peru, Portugal, Switzerland and the UKthere is a significant negative relationship between equity returns inthe country and US inflation. Only in the case of Israel is the spilloverpositive. As Amihud (1996) showed, Israel is a special case due tothe differing institutional treatment of inflation.

Choudhry (2001) examined four countries that experienced highinflation from the 1980s to the end of the 1990s: Argentina, Chile,Mexico and Venezuela. Nominal stock returns were, on average,higher than inflation. The efficacy of stocks as an inflation hedgedepends on the country under investigation. Argentina and Chileoffer the strongest inflation hedge, with Chile having a slightly largercompensation than Argentina. Both are close to a one-to-one rela-tionship between nominal returns and contemporaneous inflation.Mexico also offers some inflation protection, but it is lagged onemonth compared with Argentina and Chile. In Venezuela, however,no inflation protection can be expected.

Choudhry’s results are somewhat puzzling, in that Argentina hasthe highest inflation in the group, and Chile has the lowest. Thismay be because Choudhry does not calculate the source of the infla-tion: real output shocks or monetary policy. As we discussed earlier,knowledge of the root cause of inflation is of utmost importance.

CONCLUSIONAt this point investors may be quite discouraged regarding the in-flation-hedging ability of equities: the bulk of the evidence does notfavour equities in this role. Nevertheless, there are many lessons tobe found in the above discussion.

First, in order to be a good hedge against inflation, equities shouldbe held over the long term. The Fisher relationship is more likely tohold for investment horizons of five years or longer than for short-term investment horizons. Thus, selling after a large inflation shock

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that causes equity prices to decrease is likely to be counterproduc-tive. Abetter response would be to hold on and wait for equity pricesto restore themselves.

Second, equities in high-inflation regimes offer better inflationprotection than equities in low-inflation regimes. Latin America isthe test case for this in most of the literature. Even in the short run,countries like Brazil and Argentina offer an inflation hedge muchcloser to one-to-one than more developed economies such as theUS and the UK. Of course, we are trading off against other risks byinvesting in emerging markets.

Third, there is some evidence that defensive industries, liketobacco and food and beverage, provide better inflation hedges thanmore cyclical industries. This evidence is not strong, however, andout-of-sample testing suggests past inflation betas are not reliableguides to future inflation betas.

Equities may not be a reliable inflation hedge in a low-inflationenvironment. They do, however, offer a positive real return in mostcountries, which is some protection against inflation.

1 The capital asset pricing model (Sharpe 1964; Lintner 1965).

2 In other words, easy monetary conditions (low real interest rates) increase the demand formoney and possibly consumption.

3 See Bakshi and Chen (1996) for an analysis of a broader array of model economies. They findthat conclusions similar to Marshall’s hold for a variety of assumptions about utility functionsand money supply dynamics.

4 See Polk et al (2006) for a discussion of the subjective risk premium.

5 Evidence was provided for West Germany and reunified Germany after 1989.

6 Total return on stocks is measured as the value-weighted portfolio of all stocks included inthe Center for Research in Securities Prices (CRSP) database. This includes all stocks on theNYSE, AMEX and Nasdaq exchanges.

7 Adams et al (2004) use a variety of time horizons, including calendar time (eg, 15-minuteintervals) and transaction time (tick data).

8 Results for West Germany and reunified Germany after 1989.

REFERENCES

Adams, G., G. McQueen and R. Wood, 2004, “The Effects of Inflation News on HighFrequency Stock Returns”, The Journal of Business 77, pp. 547–74.

Amihud, Y., 1996, “Unexpected Inflation and Stock Returns Revisited: Evidence fromIsrael”, Journal of Money, Credit and Banking 28, pp. 22–33.

Ang, A., M. Brière and O Signori, 2011, “Inflation and Individual Equities”, WorkingPaper, URL: http://ssrn.com/abstract=1805525.

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Bakshi, G. S., and Z. Chen, 1996, “Inflation, Asset Prices, and the Term Structure of InterestRates in Monetary Economies”, The Review of Financial Studies 9, pp. 241–75.

Barnes, M., J. H. Boyd and B. D. Smith, 1999, “Inflation and Asset Returns”, EuropeanEconomic Review 43, pp. 737–54.

Bekaert, G., and X. Wang, 2010, “Inflation Risk and the Inflation Risk Premium”, WorkingPaper, URL: http://ssrn.com/abstract=1600312.

Boudoukh, J., and M. Richardson, 1993, “Stock Returns and Inflation: A Long-HorizonPerspective”, The American Economic Review 83, pp. 1346–55.

Boudoukh, J., M. Richardson and R. F. Whitelaw, 1994, “Industry Returns and the FisherEffect”, The Journal of Finance 49, pp. 1595–1615.

Boyd, J. H., R. Levine and B. D. Smith, 2001, “The Impact of Inflation on Financial SectorPerformance”, Journal of Monetary Economics 47, pp. 221–48.

Brière, M., and O. Signori, 2009, “Inflation-Hedging Portfolios in Different Regimes”,Working Paper, URL: http://www.institutlouisbachelier.org/risk10/work/4302987.pdf.

Campbell, J. Y., and R. J. Shiller, 1988, “The Dividend-Price Ratio and Expectations ofFuture Dividends and Discount Factors”, The Review of Financial Studies 1, pp. 195–228.

Campbell, J. Y., and T. Vuolteenaho, 2004, “Inflation Illusion and Stock Prices”, TheAmerican Economic Review 94, pp. 19–23.

Chang, E. C., and J. M. Pinegar, 1987, “Risk and Inflation”, The Journal of Financial andQuantitative Analysis 22, pp. 89–99.

Choudhry, T., 2001, “Inflation and Rates of Return on Stocks: Evidence from High InflationCountries”, Journal of International Financial Markets, Institutions, and Money 11, pp. 75–96.

Danthine, J.-P., and J. B. Donaldson, 1986, “Inflation and Asset Prices in an ExchangeEconomy”, Econometrica 54, pp. 585–605.

Ely, D. P., and K. J. Robinson, 1997, “Are Stocks a Hedge against Inflation? InternationalEvidence Using a Long-Run Approach”, Journal of International Money and Finance 16,pp. 141–67.

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Gordon, M., 1962, The Investment, Financing, and Valuation of the Corporation (Homewood,IL: Irwin).

Goto, S., and R. Valkanov, 2002, “The Fed’s Effect on Excess Returns and Inflation IsBigger than You Think”, Working Paper, URL: http://www.personal.anderson.ucla.edu/rossen.valkanov/page1.htm.

Gregoriou, A., and A. Kontonikas, 2010, “The Long-run Relationship Between StockPrices and Goods Prices: New Evidence from Panel Cointegration”, Journal of InternationalFinancial Markets, Institutions, and Money 20, pp. 166–76.

Hess, P. J., and B.-S. Lee, 1999, “Stock Returns and Inflation with Supply and DemandDisturbances”, The Review of Financial Studies 12, pp. 1203–18.

Kaul, G., 1987, “Stock Returns and Inflation: The Role of the Monetary Sector”, Journal ofFinancial Economics 18, pp. 253–76.

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Kaul, G., 1990, “Monetary Regimes and the Relation between Stock Returns andInflationary Expectations”, The Journal of Financial and Quantitative Analysis 25, pp. 307–21.

Knif, J., J. Kolari and S. Pynnönen, 2008, “Stock Market Reaction to Good and BadInflation News”, The Journal of Financial Research 31, pp. 141–66.

Lee, B.-S., 2010, “Stock Returns and Inflation Revisited: An Evaluation of the InflationIllusion Hypothesis”, Journal of Banking and Finance 34, pp. 1257–73.

Lintner, J., 1965, “The Valuation of Risk Assets and the Selection of Risky Investments inStock Portfolios and Capital Budgets”. Review of Economics and Statistics 47, pp. 13–37.

Marshall, D. A., 1992, “Inflation and Asset Returns in a Monetary Economy”, The Journalof Finance 47, pp. 1315–42.

Modigliani, F., and R. A. Cohn, 1979, “Inflation, Rational Valuation, and the Market”,Financial Analysts Journal 35, pp. 24–44.

Pearce, D. K., and V. V. Roley, 1988, “Firm Characteristics, Unanticipated Inflation, andStock Returns”, The Journal of Finance 43, pp. 965–81.

Polk, C., S. Thompson and T. Vuolteenaho, 2006, “Cross-Sectional Forecasts of the EquityPremium”, Journal of Financial Economics 81, pp. 101–41.

Schotman, P. C., and M. Schweitzer, 2000, “Horizon Sensitivity of the Inflation Hedge ofStocks”, Journal of Empirical Finance 7, pp. 301–15.

Schwert, G. W., 1981, “The Adjustment of Stock Prices to Information about Inflation”,The Journal of Finance 36, pp. 15–29.

Sharpe, S. A., 2002, “Reexamining Stock Valuation and Inflation: The Implications ofAnalysts’ Earnings Forecasts”, The Review of Economics and Statistics 84, pp. 632–48.

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Solnik, B., 1983, “The Relation between Stock Prices and Inflationary Expectations: TheInternational Evidence”, The Journal of Finance 38, pp. 35–48.

Wei, C., 2009, “Does the Stock Market React to Unexpected Inflation Differently across theBusiness Cycle?”, Applied Financial Economics 19, pp. 1947–59.

Wei, C., 2010, “Inflation and Stock Prices: No Illusion”, Journal of Money, Credit, and Banking42, pp. 325–46.

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14

Inflation Hedging through Asset andSector Rotation

Alexander Attié, Shaun RoacheInternational Monetary Fund

Long-term investors face a common problem: how to maintain thepurchasing power of their assets over time and achieve a level of realreturns consistent with their investment objectives. Both dimensionsof this problem are often considered together, but there remainsan active debate regarding the first, namely which types of assetsprovide the most effective hedge against inflation.

The focus on inflation-hedging properties of different asset classessharpens and fades along with the fluctuations in inflation itself, butwhat matters the most are unanticipated increases in the rate of infla-tion. Inflation cycles often begin with an unexpected rise – a “shock”– that then persists. The most intense burst of interest and researchin this area followed the persistent rise in inflation through the 1970sin several developed economies. Following the 2007–9 global finan-cial crisis, and large inflows of liquidity by major central banks tosupport economic activity and shore-up the financial sector, someinvestors fear, at the time of writing, that inflation may at some pointagain rise beyond expectations. This implies that inflation hedgingremains an important component of long-run investment policy. Ofcourse, inflation-linked bonds and derivatives are employed by mar-ket participants to hedge the effects of inflation, but their limited sup-ply and liquidity across various markets still lead many investors torely on the indirect hedging properties of traditional asset classes.

In a previous paper (Attié and Roache 2009), we argued that theinflation-hedging features of traditional core assets such as cash,bonds, equities and commodities vary over time. For a long-only

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investor, this implies that static hedges may not grant adequate pro-tection. At short horizons, commodities, and to some extent cash,provide some protection against the eroding effect of unanticipatedinflation. Over the long run, their efficiency fades away, and nom-inal bonds start to offer better real return features as higher yieldsprovide a greater income cushion. Like many others (see, for exam-ple, Bodie 1976; Jaffe and Mandelker 1976; Fama and Schwert 1977;Solnik 1983), we found that nominal equity returns are negativelycorrelated to inflation.

This chapter extends our earlier work on long-run dynamics andfocuses on two issues. The first is to identify the most effective infla-tion hedges, going beyond broad asset classes, and looking into arange of US domestic and international fixed-income instrumentsand equity sectors. The second is to study asset class hedge perfor-mance after an inflation shock, over different time horizons, in orderto gain insight into possible active asset allocation/sector rotationstrategies.

In the context of a diversified investment portfolio, we use a multi-variate vector error-correction (VEC) model, and calculate impulseresponses, so as to assess how inflation shocks affect asset and port-folio returns over time. We find that long-term investors could ben-efit from sector rotation amongst different categories of bonds andequities. As expected, these properties experience large variationsover time.

WHAT CAN WE LEARN FROM PREVIOUS RESEARCH?The theory surrounding this subject suggests that some traditionalasset classes should provide relatively effective inflation protection.American economist Irving Fisher suggested that the nominal returnon short-term debt should comprise a real interest rate and com-pensation for expected inflation (Fisher 1930). In other words, Trea-sury bills (T-bills), commonly referred to as cash, or the risk-freerate, would provide a perfect hedge when inflation is anticipated.That is, short-term real interest rates would remain unchanged. Thishypothesis was subsequently challenged by Mundell (1963) andTobin (1965), who both argued that nominal interest rates shouldchange by less than one-to-one with changes in expected inflation,1

reducing the effectiveness of cash as a hedge.Attié and Roache (2009)also found that cash is an imperfect hedge against unanticipated

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shocks in headline inflation. In contrast, the inverse relationshipbetween nominal bonds and inflation surprises is not a point ofdebate. The return on bonds that pay nominal coupons and prin-cipal should decline when inflation increases over the maturity ofthe bond (Balduzzi and Green 2001).

Much attention has been focused on “real assets”. During the1970s, inflation rose and most of the major equity markets sufferednegative real returns, triggering a reappraisal of the view that equi-ties, by offering a claim on the dividend stream of real assets, werea good inflation hedge. Real estate and commodities are often con-sidered to be good, albeit imperfect, inflation hedges, with muchempirical work backing this claim (see Attié and Roache 2009 andreferences therein).

Fewer studies have examined the inflation-hedging properties ofasset classes in the context of complex and diversified investmentportfolios. Strongin and Petsch (1997) include a broad range of assetclasses commonly used by institutional investors. They find thatcommodities and cash are the only assets that provide significantprotection against global inflation risk. They also note that interna-tional allocation on a currency-unhedged basis is likely to hedgedomestic inflation risk in an equity dominated diversified portfolio.Brière and Signori (2010) note that inflation-hedging features of tra-ditional assets vary across macroeconomic environments; Bekaertand Wang (2010) show that traditional securities are, after all, poorinflation hedges.

All may not be lost for investors seeking inflation protection, how-ever. Advocates of active management rightly point out that not allstocks are alike, and holdings of individual firms may offer betterhedging properties, this being also true of bonds and commodities.In an investment bank report, Buckland (2008) suggests buying firmsthat are causing the bout in inflation, and to look for companies oper-ating in industries with inelastic demand. Ang et al (2011) find thatlarge caps, growth stocks and the oil, gas and technology sectorsoffer better inflation protection in-sample, but out-of-sample analy-sis reveals unstable inflation betas, thus making it difficult to forecastefficient inflation-hedging strategies.

We embrace the idea that a more selective approach within eachbroad asset class is necessary to improve inflation-hedging results.In this chapter, in addition to cash and commodities, we consider

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three types of nominal bonds, ie, government bonds, mortgage-backed securities and corporate bonds. Furthermore, we analyse10 global equity sectors, as well as international diversificationthrough foreign equities and bonds.

MODEL SPECIFICATIONMany investors set their strategic asset allocation and their invest-ment decisions based on expected risk and return over a rela-tively long time period, often five years or more. To assess assetclass inflation-hedging properties over such horizons, we use a co-integrated vector autoregressive (VAR) approach that allows us toboth identify whether asset class returns and inflation share com-mon trends over the long run, and assess their dynamics over theshort run.2 Specifically, our objective is to estimate how differentasset classes react to an unexpected rise in inflation. An inflationsurprise is defined here as an increase in the US Consumer PriceIndex (CPI) that is not anticipated by the VAR model. Clearly, mar-ket participants, who have access to a larger information set, mayanticipate what might be a surprise for any specific stochastic modelemployed. However, one of the strengths of the VAR approach is thatit encapsulates a lot of information already. It can be written as

Zt = γ +P∑

p=1

Φ′pZt−p + νt (14.1)

Each variable in the vector Zt is assumed to be a function of aconstant intercept (the vector γ), and a specified number P of lags(Zt−1, Zt−2, . . . , Zt−P) of its own value, and those of the other vari-ables. The lag coefficients are collected in the P constant vectorsΦp, while the residuals are denoted by the vector νt (the latter areassumed to be normally distributed with a constant contempora-neous covariance matrix). We conduct the analysis using monthlydata, as can be seen in Table 14.1. As is customary with financialtime series, natural logarithms of the variables are taken. Not sur-prisingly, these time series turn out to be non-stationary and followstochastic trends.3

This type of model has many parameters that need to be esti-mated. Since our returns data set is relatively limited, estimating asingle model with all of the variables included at once leaves littleroom for degrees of freedom and is therefore prone to over-fitting.

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We overcome this “over-parameterisation” problem by estimatinga large number of models with six variables (US inflation, US cash,US bonds, global developed market equities, the (hedge) asset classunder investigation and a global commodity index) instead of onemodel with a large number of variables. We assess the inflation-hedging properties of different asset classes by rotating them in andout of a six-variable model that always includes a core set of fivevariables. In each case, the specific variables included in the esti-mated VAR model(s) will be highlighted as we address and useeach of the models. We will deal with six-dimensional multivariatesystems; thus, Zt, γ, Φp and νt are always 6× 1 column vectors.

The first step is to identify the optimal lag length, which in generalmight be different for each of the specific models used in the chapter.However, using standard selection techniques, such as the Akaikeand Bayesian information criteria (Akaike 1974), we find that P = 7is a reasonable choice for all.

Following Granger’s Representation Theorem, we can rewriteEquation 14.1 in its equivalent VEC form (of order P− 1)

∆Zt = µ+J∑

j=1

αjβ′j Zt−1 +P−1∑p=1

Ψp∆Zt−p + εt (14.2)

In this representation, the first log difference (or approximatemonth-on-month percent change) in the vector of variables Zt isas a function of

(i) the constant vector of intercepts µ representing deterministiclinear trends in the variables,

(ii) J constant coefficientsαj, determining the speed of adjustmentto long-term dynamic equilibrium relationships,

(iii) J cointegrated vectors β′j Zt−1, expressing stochastic equilib-rium relationships and

(iv) P − 1 lags of the changes in the vector of variables.

This VEC form is only valid if there are indeed long-run relation-ships among the variables. We find strong evidence, using standardJohansen cointegration tests on the VEC representation in Equa-tion 14.2, of at least two such relationships for a wide range of spec-ifications. This indicates that among our variables there are at leasttwo common stochastic trends; therefore, J = 2. The results that

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follow are all based on the maximum likelihood estimation of theVEC model described by Equation 14.2. Identifying the long-runeconomic relationships that lead to these results is difficult, partic-ularly as they typically involve a linear combination of many assetclass returns. This precludes the use of an intuitive identificationscheme for the cointegrating vector. However, both the role of thetrend rate of real economic growth and investor risk premiums arelikely to be important common factors behind long-run asset classrelationships.

To assess inflation-hedging properties, we use the estimatedmodel in Equation 14.2 to trace out the response of the total returnindex of each asset class to a 1% shock to the US CPI. In other words,we assume that month-on-month inflation rises by a greater-than-expected 1% in month t, and study the evolution of all the variablesat several time horizons after the shock. This response reflects thedirect effect of the one-off inflation shock on the asset class, but alsoall of the interactions between the other assets in the model. Thedegree of confidence we have in these results is provided by thestandard errors, which were calculated using bootstrap methods,and 500 replications.

As the error terms in Equation 14.2 are generally contempora-neously correlated, we have to find a vector of orthogonal residu-als that can be interpreted as structural shocks. To fully specify thelatter, and identify the shocks to inflation, we impose a standardCholesky triangular identification scheme (ie, we specify an orderin variables, and a hierarchical structure of contemporaneous corre-lations). Specifically, we assume that none of the financial variablesaffect inflation during the same month, which, given the well-knownstickiness of retail prices, is a reasonable assumption, widely usedin macroeconomic models (this is even true for retail petrol prices,which typically lag changes in the price of crude oil). Variables areordered as follows:

1. inflation;

2. cash;

3. bonds;

4. global developed markets equities;

5. the asset class under investigation;

6. commodities.

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In other words, inflation shocks affect all other variables, cash returnshocks affect all variables except inflation, bond return shocks affectall other variables except inflation and cash, and so on.

Although the ordering of variables is somewhat arbitrary, ourempirical results turn out to be insensitive to this ordering, largelyreflecting the low correlation of the reduced-form residuals from theestimated model.4

DATA

In our study, we use monthly data from a variety of domestic andinternational total return series. Total return series, in addition toprice returns, assume interest and dividend earned are reinvestedin subsequent periods. Wherever possible, we selected indexes (asdetailed below) that are widely used by investors as performancebenchmarks.5 The data set spans a time window from January 1970to April 2011 (with a few exceptions highlighted in the paragraphbelow).

For inflation, we use the CPI (all urban consumers) publishedmonthly by the US Bureau of Labor Statistics. For cash, we use the 90-day US Treasury bills total return index provided by Global FinancialData.6 For nominal bonds, we use the Barclays US Aggregate Index.We also analyse a few sub-indexes within investment grade bonds,namely the Barclays US Treasury Index, the Barclays US MortgageBacked Securities (MBS) Index, and US corporate bonds (measuredby the Merrill Lynch Corporate Master Index). The data set fromthese four nominal bond indexes starts from December 1975.

While global equity indexes are widely available for the entireperiod under review, global aggregate bond indexes are availableover a much shorter time span (since about 1990 for the Bar-clays Global Aggregate index). For the purpose of this chapter, andbecause of the breadth of reliable data in the US bond market, weopted to measure the sensitivity to inflation shocks of US-only invest-ment grade bonds. Possible discrepancies in the degree of responsesto those shocks are, in fact, relatively limited: the correlation betweenthe US and global bond indexes since 1990 is high at about 0.9 andthe impulse response results from the model are qualitatively sim-ilar and within 25bp of the response on US bond aggregates forthe same sample periods. This reflects the large share of US bonds

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in these global aggregates and high correlations of mature marketsbond yields.

For emerging market bonds, we use the JP Morgan Emerging Mar-ket Bond Index Plus (EMBI+) and the JP Morgan Emerging LocalMarkets Index Plus (ELMI+), each starting from December 1993. Thedifference between the two indexes is that the first includes only USdollar denominated issues (across the yield curve), while the lat-ter tracks money market instruments (up to three-month maturity)denominated in each country’s local currency. The two indexes alsohave different country weights.

As for equities, our focus is global, given the abundance of reli-able return data stretching back to the 1970s, and the internationalapproach to equity investing by many institutional investors. Inaddition to the aggregate MSCI World Index (starting in January1970),7 we analyse each of the 10 Global Industry Classification Stan-dard (GICS) sectors, as well as growth and value stocks indexes,tracked through DataStream, and MSCI (GSCI sector indexes startin January 1973; growth and value indexes start in December 1974).

For emerging market equities, we use the MSCI Emerging MarketIndex, beginning in December 1987; finally, for commodities, we usethe S&P Goldman Sachs total return index. The performance of thelatter starts from January 1970 and includes spot price returns, aswell as the return from rolling over futures positions and investingcollateral. A summary of the data is provided in Table 14.1, for themaximum sample period available in each case. This table confirmsmany well-known stylised facts about our asset return data, includ-ing that equities are more volatile than bonds (see the “standarddeviation” column in Table 14.1), risk asset returns are in generalnegatively skewed (see the “skew” column in Table 14.1) and assetreturns follow a random walk (as shown by the unit root tests thatindicate the probability of a non-stationary trend is very high for theseries in levels and very low in first differences).

IMPULSE RESPONSE FOR CORE ASSET CLASSESOur first set of results compares the impulse response of our five corevariables (CPI and four core asset classes, ie, US cash, US aggregatebonds, developed market equities and commodities) following a 1%shock to the monthly CPI at t = 0. Three six-dimensional VAR mod-els are estimated, with the rotating variables being first the EMBI+,

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Table 14.1 Variables: summary statistics (%), January 1970–April 2011

Unit root testp-value︷ ︸︸ ︷

log logMean Max. Min. SD Skew level change

US inflation 0.4 1.8 −1.8 1.2 0.0 0.06 0.15US T-bill 0.5 1.3 0.0 0.9 0.4 0.10 0.28

Bond indexes:Barclays US 0.7 10.8 −6.3 5.6 0.5 0.58 0.00

AggregateBarclays US MBS 0.7 14.5 −7.9 6.6 0.9 0.81 0.00Barclays US Treasury 0.7 9.2 −5.1 5.5 0.3 0.43 0.00Merrill Lynch/BoA 0.7 11.3 −7.7 6.9 0.0 0.76 0.00

Corporate MasterJP Morgan EMBI+ 0.8 10.2 −33.9 15.3 −2.8 0.90 0.00JP Morgan ELMI+ 0.7 7.6 −9.1 7.0 −0.7 0.95 0.00

MSCI equity indexes:World 0.8 13.7 −21.0 15.1 −0.8 0.72 0.00World value 1.0 14.4 −20.5 14.9 −0.8 0.45 0.00World growth 0.8 14.0 −21.5 15.9 −0.7 0.61 0.00Energy 1.0 16.6 −23.4 18.3 −0.4 0.93 0.00Materials 0.8 16.9 −31.0 19.5 −0.8 0.89 0.00Industrials 0.8 15.6 −24.7 17.2 −1.0 0.80 0.00Consumer 0.7 17.2 −19.5 17.1 −0.6 0.84 0.00

discretionaryConsumer staples 0.8 16.3 −19.5 14.9 −0.7 0.93 0.00Health care 0.9 19.0 −18.7 14.6 −0.4 0.86 0.00Financials 0.8 20.9 −29.8 19.7 −0.6 0.68 0.00IT 0.7 21.4 −31.2 22.7 −0.6 0.83 0.00Telecoms 0.8 26.8 −17.3 17.5 0.1 0.65 0.00Utilities 0.9 22.5 −14.3 14.5 0.0 0.80 0.00GSCI Commodity 0.8 22.9 −33.1 19.9 −0.4 0.26 0.00

Total Return IndexMSCI Emerging 0.8 32.9 −24.0 20.5 0.5 0.21 0.00

Markets

SD denotes standard deviation. We use the difference of the logs of eachindex multiplied by 100 (eg, for US inflation, the average monthly return,continuously compounded, is 0.4% in our sample). Sample periods differby asset class and sector, depending on data availability.Source: Thomson Datastream and authors’ estimates.8

then the ELMI+ and finally the MSCI Emerging Market Equity Index.The impulse responses of the core variables from these three models

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Table 14.2 Impulse response to a 1% shock to US CPI (%)

6 months 12 months 2 years Long run

Inflation 1.65 1.70 1.94 2.17(0.33) (0.49) (1.81) (1.01)

Cash −0.01 0.15 0.58 1.45(0.20) (0.43) (0.56) (1.11)

Bonds −0.97 −1.13 −0.96 0.03(0.04) (0.28) (0.57) (1.07)

Equities −1.65 −2.38 −2.64 −2.20(0.17) (0.60) (1.85) (3.35)

Commodities 5.59 4.24 3.56 3.65(0.51) (1.03) (2.06) (3.96)

Bootstrapped standard errors are given in parentheses. The data repre-sents cumulative total log change for the CPI, and cumulative total rate ofreturn for the four core asset classes.

are the average from each of the separately estimated models, whichtended to be qualitatively similar.

Table 14.2 shows the results, specifically the cumulative totalchange for the CPI, and the cumulative total rate of return for the fourcore asset classes. For illustration, four time horizons (six months,one year, two years and ten years (labelled as “long run”)) are shownin the table.

US inflation: shocks persistAs expected, US inflation exhibits strong autoregressive properties.In fact, an initial month-on-month shock of 1% to the CPI causesan increase in subsequent months, with an effect felt long in thefuture. After one year, the cumulative increase in CPI is 70% higherthan the initial annualised shock. Over a 10-year horizon, consumerprices have risen a cumulative 2.17%, ie, more than twice the initialshock.

US cash: a far-from-perfect inflation hedgeAs a proxy for US dollar denominated cash, we use three-month USTreasury bills. Given that the short-end of the yield curve is mostdirectly affected by monetary policy actions, cash returns shouldincrease in response to an inflation surprise, if there is an expectationof tighter monetary policy. However, as shown in Table 14.2 andFigure 14.1, the response is gradual, and the hedge is far from perfect.

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One year from the shock, consumer prices have increased by 1.70%(see the “12-month” column in Table 14.2), while cash returns areonly 0.15%. In the long run, the cumulative return from cash reaches1.45% (see the “long run” column in Table 14.2), but still does notcompensate for the loss in purchasing power up to that point (2.17%).

US aggregate bonds: negative real returnsThe inverse relationship between US nominal bonds (measured bythe Barclay USAggregate Bond Index) and US inflation is clear, as thepurchasing power of fixed nominal coupons and notional paymentsnaturally diminishes with rising inflation. Indeed, following an infla-tion shock, bonds underperform in comparison to cash. Among thesecurities in the aggregate index, long-duration bonds are obviouslythe worst performing (due to their long duration). Six months afterthe initial consumer prices shock, cumulative inflation has reached1.65% (see the “6-month” column in Table 14.2), while the US aggre-gate bond index has lost 0.97% (ie, a −2.62% real return). There islimited recovery over time: at year 10, the US Aggregate Bond Indexreaches a flat cumulative nominal return, but its real return remainsdeep in negative territory (−2.14%).

In the next section, we analyse the impulse response functionof other inflation-hedging alternatives; specifically, instead of anaggregate bond index, we consider sector indexes (US treasuries, USmortgage-backed securities and US corporate bonds) and comparetheir performance following an initial consumer prices shock.

Developed markets equities: the worst performing core assetclass hedgeDeveloped market equity returns (both nominal and real) are deepin negative territory for all time horizons considered. In the longrun, nominal returns are −2.20% (long run column in Table 14.2),while inflation-adjusted real returns are −4.37%. These findings arein line with our earlier work (Attié and Roache 2009), and add furtherevidence to other empirical observations, which have questioned thetheoretical underpinnings of equities as an inflation hedge (becauseof their real asset characteristics).

In the next section, we shall extend the impulse response analysisto non-core asset classes, and consider the inflation-hedging perfor-mance of the 10 GSCI equity sectors (Table 14.1), value versus growthequity strategies, and emerging market equities.

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Commodities: the best performing core asset class hedge

Table 14.2 shows that commodities are the best performing asset classfollowing a shock in US consumer prices. In previous work (Attiéand Roache 2009), we found that the inflation-hedging properties ofcommodities diminished over time, but, in this study, commoditieshold on to most of the gains made during the initial stages afterthe inflation shock. Differences in these findings reflect the natureof the commodity index used (ie, the more energy-focused GSCI inthis chapter versus the more balanced Thomson Reuters/JefferiesCRB Index, which grants a larger share to the agricultural sector inour previous work). Another source of difference is the fact that atotal return index is selected in this study (which includes the pricereturn, the return from collateral and the return from rolling futurescontracts forward), as opposed to the simple change in spot pricesused in our previous work.

IMPULSE RESPONSE BEYOND BROAD ASSET CLASSES

Following the analysis of asset classes at the aggregate level, weanalyse the impulse response at a more disaggregated level, ie, the“rotating” variables in our VAR models (a total of 17). Specifically,we shall consider the inflation-hedging performance of

• two US bond sector indexes: mortgage-backed securities, andcorporates (two VAR models),

• ten GICS global sector indexes of developed markets equities(ten VAR models),

• two developed global market equities style indexes (value andgrowth, two VAR models),

• two emerging markets bond indexes, one including US dollardenominated securities only (EMBI+) and the other in moneymarket instruments denominated in local currency (ELMI+)(two VAR models),

• one emerging market equities index (one VAR model).

Illustrative graphs of the impulse response function of some ofthe variables are shown in Figure 14.1.

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Figure 14.1 Percentage response (vertical axis) of asset classes to a1% shock to US CPI

0.5

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Treasuries

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(a) (b)

(c) (d)

(e) (f)

–2

–2

–6

Energy

Utilities

(a) Inflation; (b) US three-month T-bills; (c) US bonds; (d) MSCI World Equity Index;(e) MSCI world equity sector indexes; (f) S&P GSCI.

US bond sector indexesTo examine the impulse responses of different bond investmentssuch as US mortgage-backed securities and US corporate bonds,both of which are likely to be included in the toolset of many insti-tutional investors, we replaced the US aggregate bond index withUS Treasuries as our “core” bond index (in the sense that Treasuriesaffects equities and other bonds, such as mortgage-backed securi-ties, during the same month, but not vice versa). Then, to study theimpulse response function of Mortgage-Backed Securities and Cor-porate Bonds, we estimate two VAR models. In the first, the variablesused are indexes for Treasury bills, Treasury bonds, developed mar-ket equities, US mortgage-backed securities, commodities and theCPI. In the second model, the Barclay US MBS Index is substituted

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Table 14.3 US bonds: impulse response to a 1% shock to US CPI (%)

6 months 12 months 2 years Long run

US Treasuries −0.59 −0.41 −0.23 0.05(0.05) (0.11) (0.22) (0.42)

US MBS −1.13 −1.08 −1.08 −0.72(0.15) (0.36) (0.72) (1.34)

US Corporates −1.80 −1.90 −1.96 −2.26(0.21) (0.41) (0.82) (1.44)

Bootstrapped standard errors are given in parentheses.

with the Merrill Lynch US Corporate Master Index. The results areshown in Table 14.3.

As can be seen in Table 14.3, mortgage-backed securities and cor-porate bonds underperform Treasuries following an inflation shock.The impulse response for Treasury performance is taken from themortgage-backed securities model (the results for Treasuries fromboth models, including the standard errors, were almost identical).

In the case of mortgages, their negative convexity makes mort-gage-backed securities particularly sensitive to rising real yields. Ashomeowners are less likely to prepay, the value of the embeddedoptionality in mortgage-backed securities decreases and lengthensthe residual duration of the bond. In the case of corporate bonds, per-formance is affected in a similar fashion to the case of traded equities:higher real yields weigh on firms’ borrowing costs and future overallprofitability.

Over the long run, once the effect of the shock is fully priced in byinvestors, Treasuries recover with the help of higher coupons (andcurrent yields). However, as seen in Figure 14.1, their real cumulativereturn remains negative, owing to large early losses that are neverfully recouped.

Developed market equities: sector indexes

After analysing the aggregate global equity index in the previoussection, here we look at the inflation-hedging performance of the10 traditional Global Industry Classification Standard (GICS) sectorsdistinguished by MSCI (Table 14.1).

We estimate 10 different six-variable VAR models with US CPI,US cash, US bonds, global equities and commodities as the fixed

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Table 14.4 Global equity sectors: response to a 1% shock to USCPI (%)

6 months 12 months 2 years Long run

Energy 3.14 1.03 0.10 −0.93(0.51) (1.08) (2.16) (3.76)

Materials −2.26 −2.73 −3.24 −4.68(0.67) (1.34) (2.73) (4.89)

Industrials −2.78 −2.62 −2.47 −3.19(0.57) (1.18) (2.37) (4.27)

Consumer −3.40 −4.22 −4.48 −4.89discretionary (0.51) (1.03) (2.11) (3.81)

Consumer −3.70 −3.86 −4.01 −4.22staples (0.36) (0.77) (1.60) (2.88)

Health care −2.42 −2.73 −2.57 −1.13(0.46) (0.93) (1.85) (3.60)

Financials −0.05 −1.44 −1.90 −1.96(0.67) (1.39) (2.83) (5.15)

IT −2.52 −3.70 −3.91 −4.01(0.67) (1.39) (2.83) (5.15)

Telecoms −3.09 −3.09 −3.04 −3.09(0.62) (1.23) (2.47) (4.42)

Utilities −5.25 −4.94 −4.58 −4.12(0.51) (1.03) (2.06) (3.96)

Bootstrapped standard errors are given in parentheses.

variables, and each of the 10 GICS sectors rotating in and out of themodel in turn.

The first key finding is that the poor performance of developedmarkets equities following an inflation shock is broadly spreadacross sectors, and occurs rapidly (Table 14.4). Out of the 10 tradi-tional GICS sectors, 9 register a negative impulse response at everytime period following the shock. This adverse effect on returns fol-lows very quickly after the initial shock. For example, total returnsfor the Industrials sector are −2.78% six months after the initialinflation shock, and remain negative thereafter. A similar profile isevident for most other global equities sectors.

The second key result is that there is noticeable difference inperformance across sectors. Unsurprisingly, following an inflationshock, the energy sector has positive nominal returns in the shortrun, although this effect appears to dissipate over time.

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This partly reflects the important role that oil prices play in infla-tion shocks, and underscores the importance of understanding theunderlying cause of higher inflation. However, the materials sector,which includes mining companies, fails to offer similar short-runinflation protection. This may change, as commodity prices havebecome more positively correlated with oil prices. Perhaps surpris-ingly, financials have tended to perform relatively well in the after-math of inflation shocks (Table 14.4), although high standard errorsindicate that this is not a particularly robust result. In the short run,the worst performer is the utilities sector, which underperforms sig-nificantly in the first year following the shock. Again, this may reflectthe nature of the shock, as utilities use inputs whose prices are closelylinked to those of crude oil, including coal and natural gas. It is alsodue to the frequently regulated nature of pricing which often pre-vents higher input costs from being passed to consumers, thus neg-atively impacting profitability. Furthermore, leverage might play apart, as utilities often have high levels of debt, reflecting the rela-tively more stable nature of their business. Firms in sectors with lessstable revenues and profits cannot achieve comparable leverage inthe market as they are perceived as more risky. Clearly, an increase ininterest rates and debt servicing costs has a negative impact on theiroverall profitability. In the long run, all equities sectors post neg-ative nominal, and inflation-adjusted, returns, with materials andconsumer discretionary being the worst performing indexes.

Developed market equities: growth versus value styles

We next assessed the inflation-hedging features of global equitiesacross different investment styles (Table 14.5). Again, our two six-variable models consisted of five core variables (US inflation, UScash, US bonds, developed market equities, commodities), with onemodel including as our rotating variable a global equity growth styleindex, and the other a global equity value style index.

Albeit with a large standard error, results show that, followingan inflation shock, growth stocks perform worse than value stocks(Table 14.5). One reason for this could be that growth stocks are “longduration”, with a larger portion of the dividend stream occurringfurther in the future. Therefore, they are more sensitive to a risein inflation, and consequent high interest rates, than value stocks,which typically offer a higher current dividend yield.

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Table 14.5 Global equity styles: response to a 1% shock to US CPI (%)

6 months 12 months 2 years Long run

MSCI World growth −2.21 −2.93 −3.24 −3.45(0.51) (1.08) (2.16) (3.81)

MSCI World value −1.80 −2.21 −2.32 −2.47(0.46) (0.98) (1.96) (3.45)

Bootstrapped standard errors in parentheses.

Table 14.6 Global investments: response to a 1% shock to US CPI (%)

6 months 12 months 2 years Long run

EM bonds (EMBI+) −3.50 −3.76 −1.65 −2.11(0.36) (0.77) (1.60) (2.78)

EM bonds (ELMI+) 1.97 1.40 2.90 3.01(0.27) (0.56) (1.14) (1.99)

Emerging market −1.65 −4.01 −2.98 −1.23equities (0.77) (1.60) (3.29) (5.92)

Bootstrapped standard errors are given in parentheses.

Emerging markets: money markets, bonds and equities

From a US dollar-based investor’s perspective, diversifying awayfrom domestic markets could help hedge all, or part, of a US inflationsurprise. In the event of a global inflation shock, however, globaldiversification might be less effective.

We specifically analysed dollar and local currency emerging mar-ket bonds, and emerging market equities. Due to data availability,our model uses data starting in January 1993 for emerging marketbonds and January 1987 for emerging market equities. These resultsare presented separately in Table 14.6 because a direct comparisonwith the earlier results (Tables 14.3–14.5) is made difficult by the dif-ferent sample sizes; in particular, both the nature of inflation shocksand the response of broad financial asset classes may have changedover time.

Although results bear large standard errors, it appears thatregional diversification into local currency emerging market bondscould represent a useful hedge for a US investor confronted with adomestic inflation shock. Six months following the shock, the return

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of local currency emerging market bonds (ELMI+ index) is almost2% (see the “6-month” column in Table 14.6), and positive nominal(and real) returns persist over the long run as well (see the “long run”column in Table 14.6). It is worth noting that differences in the mod-ified duration of bond indexes influence some results (for example,the ELMI+ is a money market index); however, while Treasuries arecharacterised by a higher duration than mortgage-backed securities,they still record a better performance.

INVESTMENT IMPLICATIONS: DYNAMIC ASSET AND SECTORROTATIONFor long-term investors with conviction in their views about thefuture path of inflation, these results have major implications. Thisis particularly true for “non-consensus” views in which investorsmay expect positive inflation surprises, and are willing to repositiontheir portfolio ahead of the shock.

Our results show that it is difficult for a static long-term strate-gic asset allocation to protect a portfolio against unexpected infla-tion using traditional asset classes. However, it might be possible toachieve some degree of inflation protection through tactical assetallocation, and sector rotation within each broad asset class. Forexample, in anticipation of an inflation shock, investors could tiltthe portfolio towards commodities and away from bonds, and thenprogressively start to rebalance after 12–18 months. For bond-onlyinvestors, the key is to overweight Treasuries. This is because aninflation surprise has typically led to higher short-term interest ratesand reduced expectations for economic and profit growth, which hasan adverse effect on credit sectors. Government bonds sector indexesoutperform credit-spread products and mortgage-backed securitiesfollowing inflation shocks. Notwithstanding these differences, all USdollar denominated fixed-income instruments, including US cash atthe short-end of the yield curve, post negative real returns in thelong run.

As for equities, our results suggest that for investors who do nottake tactical portfolio positions, the rationale for holding equitiesshould be based on a very long-term horizon to ensure that the effectsof inflation cycles average out. After all, historical evidence showsthat equities outperform (safer) government bonds over very longperiods of time (Dimson et al 2011). However, equities do not appear

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Figure 14.2 Passive versus dynamically rebalanced diversifiedportfolios

90

95

100

105

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125

130

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Benchmark

Por

tfolio

per

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ance

Number of months

Equally weighted top fiveinflation hedgers

Firstrebalancing

Secondrebalancing

Back toneutral

The vertical axis shows the portfolio index value, which starts at 100.

to offer much protection against unanticipated inflation, a result thatis robust across developed markets sectors and styles, and emergingmarkets as well. To a large extent, this is likely to be due to the effect ofhigher interest rates reducing the present value of future dividends(equities are a long-duration asset), and also depressing expectationsof economic and dividend growth. Investors with the scope to tilttheir portfolios could underweight certain industry sectors, notablyutilities, and overweight those that are the most likely to benefitfrom rising prices, namely the energy sector. Furthermore, from anequity-style perspective, value outperforms growth, and aggregateemerging market equities outperform the developed market index.

Although both developed and emerging market equities andbonds do not provide adequate protection from an inflation shock,international portfolio diversification can still be valuable. In partic-ular, holding short-duration emerging market assets denominatedin local currency, which are less correlated to US price movements,provides a valuable hedge in our data sample.

Historically, our global aggregate commodities index records thebest performance following a US inflation shock. Indeed, commodi-ties, together with the ELMI+, are the only asset classes postingpositive real, ie, inflation-adjusted, return in the long run.

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For illustrative purposes, we backtested the findings of thischapter by constructing a rules-based in-sample portfolio. Perfectinvestor foresight is assumed in each of the five largest US infla-tion shocks estimated by the VAR model in the period since 1970(these shocks occurred in 1977, 1981, 1982, 1993 and 2001), whichmeans that the investor adequately tilts their portfolio just beforethe release of a higher-than-expected CPI reading. Against a bench-mark portfolio allocated to domestic and global bonds (40% weight),developed and emerging markets equities (50%) and commodi-ties (10%), a sample active portfolio is rebalanced such that it isequally invested in the top five best performing inflation-hedgingassets in year 1, and it is then rebalanced again to hold the bestfive inflation hedgers in year 2, before going back to the benchmark(Figure 14.2).

This means that the portfolio would, for example, hold commodi-ties and energy stocks in year 1, then reallocate to utilities and emerg-ing market equities in year 2, as the hedge properties of some of thebest performing assets at the onset of a shock begin to diminish.Although it is obvious that other important factors besides inflationexpectations are driving asset returns, the use of a dynamic assetand sector rotation strategy in periods of elevated inflation pressuresgenerates superior in-sample performance, while keeping volatilitybroadly unchanged. In fact, annualised returns are about 1% higherafter three years, or about 3% higher cumulatively.

Of course, one important aspect not considered here is the natureof the inflation shock. Cost-push inflation (eg, from an oil supplyshock) has different effects from demand-pull inflation, and thegeographical spread of the shock, including whether it is country-specific or global, is important as well. In general, cost-push inflationtends to be more transient, caused by volatile commodity prices, forexample. Demand-pull inflation instead might be the result of morepersistent price changes, such as rising wages and rising demand ingeneral, and thus drive both headline and “core” inflation higher.

Clearly, these considerations have implications for the responseof policymakers. In the cost-push case, central banks with suffi-cient credibility and a well-understood (even if implicit) inflation-targeting regime may absorb the temporary rise in headline inflationwithout resorting to monetary action and rising short-term interestrates. This would suggest that cash underperforms both bonds and

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equities. In this case, commodity investments would tend to do well,given the nature of the shock. In contrast, demand-pull inflation islikely to elicit a more aggressive response by central banks, resultingin higher (short-term) interest rates. Depending on whether or nottheir response is deemed adequate by markets, this might tend tofavour cash over bonds, with equities likely to perform poorly inanticipation of a policy-induced economic slowdown.

CONCLUSIONS

This chapter explored the long-run dynamics of different assets fol-lowing a US inflation shock. We were able to identify the most effec-tive inflation hedges, going beyond broad asset classes, and look-ing into a range of US domestic and international fixed-income andequity sectors.

Our first set of results compared the impulse response of our fivecore variables (CPI and four core asset classes, ie, US cash, US aggre-gate bonds, developed market equities, and commodities) followinga 1% shock to the monthly CPI. As expected, US inflation exhib-ited strong autoregressive properties; commodities were the bestperforming class, while equities underperformed.

Following the analysis of asset classes at the aggregate level, weanalysed the impulse response at a more disaggregated level, detail-ing our results along the way. Hedge performance was analysed atdifferent time horizons, in order to gain insight into possible activeasset allocation/sector rotation strategies.

What are the practical implications of these findings? First, tra-ditional broad asset classes provide an imperfect inflation hedge,at best, and in some important cases, including equities, do verypoorly. But, for long-term “long-only” investors, there is still hope.In particular, for those with confidence in their views about thepath of future inflation, there is scope to enhance inflation protec-tion through tactical asset allocation and sector rotation within eachasset class. Even within equities, there is broad divergence acrosssectors in their inflation-hedging properties. Similar divergence isevident within the bond universe. In summary, investors need tolook beyond broad asset classes and be willing to take sectoral betsto ensure optimal inflation protection.

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1 The Taylor Rule, which is a descriptive model of how the US Federal Reserve have beensetting the funds rate since the early 1990s, empirically contradicts this, as a 1% change ininflation translates into a higher percentage change in the short-term rate.

2 Granger and Newbold (1974) and Johansen (1991) are the seminal papers describing thesestatistical techniques.

3 The hypothesis that the first differences follow a unit root process can be rejected at the 5%level for all variables, except for the Treasury bill total return index, for which rejection ispossible only at the 10% level.

4 See Attié and Roache (2009) for further details on model specifications.

5 Bailey (1992) lists six qualities of a valid benchmark: unambiguous, investable, measurable,appropriate, reflective of current investment opinions and specified in advance.

6 See http://www.globalfinancialdata.com.

7 See http://www.msci.com.

8 See http://online.thomsonreuters.com/datastream/ and http://www.crbtrader.com/.

REFERENCES

Akaike, H., 1974, “A New Look at the Statistical Model Identification”, IEEE Transactionson Automatic Control 19(6), pp. 716–23.

Ang, A., M. Brière and O. Signori, 2011, “Inflation and Individual Equities”, URL: http://ssrn.com/abstract=1805525.

Attié, A., and S. Roache, 2009, “Inflation Hedging for Long-Term Investors”, IMF WorkingPaper WP/09/90.

Bailey, J. V., 1992, “Are Manager Universes Acceptable Performance Benchmarks?”,Journal of Portfolio Management 18(3), pp. 9–13.

Balduzzi, E., and C. Green, 2001, “Economic News and Bond Prices: Evidence from theUS Treasury Market”, Journal of Financial and Quantitative Analysis 36, pp. 523–43.

Bekaert, G., and X. Wang, 2010, “Inflation Risk and the Inflation Risk Premium”, EconomicPolicy, October, pp. 755–806.

Bodie, Z., 1976, “Common Stocks as a Hedge against Inflation”, The Journal of Finance31(2), pp. 459–70.

Brière, M., and O. Signori, 2010, “Inflation-Hedging Portfolios in Different Regimes”,Working Paper 5, Amundi.

Buckland, R., 2008, “The Inflation Threat”, Citi Global Equity Strategist, July 5.

Dimson, E., P. Marsh and M. Staunton, 2011, “Credit Suisse Global Investment ReturnsYearbook”, CSFB Research Institute.

Evans, M. D. D., 1998, “Real Rates, Expected Inflation, and Inflation Risk Premia”, TheJournal of Finance 53(1), pp. 187–218.

Fama, E. F., and G. W. Schwert, 1977, “Asset Returns and Inflation”, Journal of FinancialEconomics 5(2), pp. 115–46.

Fisher, I., 1930, The Theory of Interest (New York: Macmillan).

Gorton, G, and G. K. Rouwenhorst, 2006, “Facts and Fantasies about CommodityFutures”, Financial Analysts Journal 62(2), pp. 47–68.

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Granger, C. W. J., and P. Newbold, 1974, “Spurious Regression in Econometrics”, Journalof Econometrics 2, pp. 111–20.

Jaffe, J. F., and G. Mandelker, 1976, “The ‘Fisher Effect’ for Risky Assets: An EmpiricalInvestigation”, The Journal of Finance 31(2), pp. 447–58.

Johansen, S., 1991, “Estimation and Hypothesis Testing of Cointegration Vectors inGaussian Vector Autoregressive Models”, Econometrica 59, pp. 1551–80.

Mundell, R. A., 1963, “Inflation and Real Interest”, Journal of Political Economy 71(3),pp. 280–3.

Solnik, B., 1983, “The Relation between Stock Prices and Inflationary Expectations: TheInternational Evidence”, The Journal of Finance 38(1), pp. 35–48.

Strongin, S., and M. Petsch, 1997, “Protecting a Portfolio against Inflation Risk”, InvestmentPolicy 1(1), pp. 63–82.

Tobin, J., 1965, “Money and Economic Growth”, Econometrica 33(3), pp. 671–684.

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Part III

Practical Insights fromMarket Participants

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15

Practical Models forInflation Forecasting

Nic JohnsonPIMCO

There are many different schools of thought as to what causes infla-tion, and over the years many explanations have been put for-ward to explain historically observed inflation dynamics. There aremonetarists, who believe that changes in-the-money supply are themost important inflationary dynamic, while Keynesian economistsargue that underlying pressures in the economy play a large role indetermining inflation levels.

In this chapter, we shall not delve into the academic and philo-sophical issues surrounding inflation but instead focus on theforecasting methods used by practitioners, including top-down,bottom-up and time-series-based models. We shall look at the appro-priateness of different frameworks, depending on the type of datainputs available, as well as the frequency and length of forecastdesired. Finally, we shall consider some of the differences involvedwith modelling inflation in the US, and other developed globalmarkets, relative to emerging markets.

FUNDAMENTAL TOP-DOWN MODELS FOR FORECASTINGINFLATIONThe goal of a top-down macro inflation model is to identify eco-nomic variables that are leading indicators of changes in the priceof various goods and services. From these leading indicators, aninvestor will be able to better predict both the direction and themagnitude of changes in the rate of inflation. Top-down models aremostly used for analysing core inflation, since the prices of food and

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Figure 15.1 Unemployment and core inflation

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Unemployment rate (%; lagged 1 yr)

1997–2010

1985–1993

1975–1984

1975–84: y = −1.4774x+0.1883, R2 = 0.6428; 1985–93: y = −0.4866x+0.0742,R2 = 0.5164; 1997–2010: y = −0.3549x+ 0.0396, R2 = 0.4793.Source: data from PIMCO, Bloomberg and BLS.

energy are often driven by exogenous shocks (geopolitical, weatherrelated, etc), which are difficult to forecast within such a model.In the next section, we discuss how food and energy inflation canbe modelled using a bottom-up approach, thereby allowing a top-down core inflation forecast to be extended to a forecast of headlineinflation.

Top-down macroeconomic models typically rely on a relationbetween inflation and the unemployment rate, or the output gap,plus information on money supply and inflation expectations. Thebenefits of using a top-down framework are that the model tends tobe quite tractable and not overly data intensive. In addition, a longforecasting horizon of the order of 1–3 years is typically possible.

A theoretical framework should guide the process of identifyingleading indicators. For example, one such framework might be basedon supply–demand equilibrium. When a good is in short supply,its price must rise in order to encourage incremental productionand reduce demand. Similarly, when a good is plentiful, its priceis likely to fall in order to discourage incremental production andincrease demand. Thus, forecasting inflation within such a frame-work requires the identification of factors that will drive the relativesupply–demand balance for a large variety of goods.

The unemployment rate is one macroeconomic variable that bothaffects and reflects the supply and demand dynamics of manygoods and services. Intuitively, the unemployment rate should be

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positively correlated with the general availability of labour, for eitherservices or the manufacturing of goods. Since labour represents adominant portion of the cost and availability of many goods andservices, the unemployment rate is a good proxy for the availabilityof supply of many goods and services. In addition to the informationprovided about the supply of goods and services, the unemploy-ment rate also has implications for the demand for goods and ser-vices, since high levels of unemployment coincide with lower levelsof consumption. This inverse relationship between the unemploy-ment rate and inflation was first discovered by Irving Fisher (1926),and later formalised by William Phillips (1958), through what hasbecome known as the Phillips curve. The inverse relation betweeninflation and unemployment is shown in Figure 15.1.

The inverse relationship between inflation and unemploymentbecomes much clearer if the historic data is broken down into differ-ent periods of time, as done in Figure 15.1. The primary reason forthis is that the level of inflation expectations changed over the periodfrom 1975 to 2010. Inflation expectations anchor the overall prevail-ing level of inflation in an economy and they form the baseline orreference point around which relationships like that between unem-ployment and inflation operate. For example, we expect to see anincrease in inflation when the unemployment rate declines, but anincrease relative to what level? The expected increase in inflation isrelative to the level of inflation expectations. This is why separatingthe data into periods with similar inflation expectations allows us tobetter isolate the impact of unemployment. In contrast, if the com-plete period is used, the relationship between unemployment andinflation is completely obscured by the decline in inflation expecta-tions. Because of this, controlling for the impact of inflation expec-tations is crucial when developing both top-down and bottom-upinflation models.

It should be noted that unemployment is just one measure of over-all economic activity, and much work has been done on looking atthe relation between inflation and other measures of economic activ-ity. In particular, studies have shown that a Phillips-type curve canbe reproduced using several other macroeconomic variables, includ-ing housing starts, inventory levels and capacity utilisation (Stockand Watson 1999). In particular, the Chicago Fed National Activ-ity Index (CFNAI) is an aggregate of several economic indicators,

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Figure 15.2 Chicago Fed National Activity Index and core inflation(1997–2010)

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CFNAI (12-month MA; lagged 18 months)

Source: data from PIMCO, Bloomberg, Federal Reserve Bank of Chicago andBLS.

selected because of their relation to aggregate economic activity andinflation. Historically, the CFNAI, like the unemployment rate, hashad a strong correlation with future levels of inflation, as shown inFigure 15.2. Incorporating multiple variables into a Phillips curveframework improves the robustness of an inflation model by morefully capturing aggregate economic activity and the output gap, andhence better forecasting inflationary pressures. However, care mustbe taken not to over fit the data. Conducting analysis on the stabilityof relationships across multiple slices of history is one way to avoidsuch a pitfall.

In addition to unemployment and measures of aggregate eco-nomic demand, the money supply is another macroeconomic factorwith a strong theoretical link to inflation. Assuming constant veloc-ity, if the money in circulation increases more than the real value ofgoods available for purchase, then the nominal value of those goodswill rise, resulting in inflation. As the monetarist economist MiltonFriedman stated: “Inflation is always and everywhere a monetaryphenomenon” (Friedman 1963). However, the relationship betweeninflation and money supply is more difficult to observe in the data.One of the reasons for this difficulty is that the velocity of moneyis not constant. Another confounding factor is that, historically, themoney supply has had a long leading relationship to changes inthe rate of inflation. While this should provide for a long-horizon

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Figure 15.3 Money supply and core inflation

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1997–2010

1984–1996

1974–1983

0Year-over-year change M2 (%; lagged 3 years)

1974–83: y = 0.582x + 0.0252, R2 = 0.3403; 1984–96: y = 0.1669x + 0.0288,R2 = 0.4106; 1997–2010: y = −0.009x+ 0.0213, R2 = 0.0013.Source: data from PIMCO, Bloomberg, Federal Reserve Bank and BLS.

forecast, it also means that the relationship between money supplyand inflation can be clouded by a great deal of noise introduced byeither a change in money velocity or other non-monetary factors.Hence, although large changes in money supply should eventuallyhave a visible impact on inflation, smaller changes in-the-moneysupply will often be dwarfed by other factors. Furthermore, the bene-fit of a long lead–lag relationship comes at the expense of diminishedforecasting accuracy. Historically, changes in-the-money supply ledchanges in inflation by an average of three years, but the sensitivityof inflation rates to a change in money supply declined in the latterpart of the 20th century, just as was observed in the case of inflationand unemployment. In fact, between 1997 and 2010 the correlationbetween changes in-the-money supply and changes in inflation haddropped to essentially zero, as shown in Figure 15.3. One reason forthe low correlation between money supply and inflation during thisperiod is that the velocity of money was not constant, eg, periodsof increasing money supply were associated with declines in thevelocity of money. This does not imply that money supply changesno longer matter, but it does suggest that models that forecast infla-tion based on changes in-the-money supply, in isolation from otherfactors, should be taken with a pinch of salt.

The relation between inflation and unemployment, or other mea-sures of economic activity, is relatively stable in the short run but,

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periodically, large regime shifts have occurred, as can be seen inFigures 15.1 and 15.3. Since the 1970s, not only has the overallrate of inflation moved progressively lower, but the sensitivity ofinflation to unemployment has also declined substantially, mak-ing unemployment a less relevant indicator. It is indeed interest-ing to consider the reasons behind these regime shifts, and whathas caused inflation changes since 2000 to show a decreasing sen-sitivity to many macroeconomic variables. The factors at play areof course several. Two important factors are increased central bankcredibility and explicit inflation targeting. In the post-Volcker era,lower inflation expectations have moved the Phillips curve lowerand to the left (Figure 15.1). Another contributing factor to lowerinflation sensitivity might have been a decrease over time in thenon-accelerating inflation rate of unemployment (NAIRU). Another,which is often overlooked, is increased globalisation. No longer is itjust the level of unemployment, or the output gap in the US, thatdrives domestic inflation. The growth in the size of the Chineseand other emerging economies, combined with their correspondinggrowth in global trade, has meant that it is increasingly global unem-ployment and the global output gap that drives both US and globalinflation rates. In addition to reducing the sensitivity of domesticinflation to domestic macroeconomic variables, the lower volatilityof the global output gap has also served to reduce the volatility ofinflation. Because of the decreasing sensitivity of inflation with manydomestic macroeconomic variables, as reflected by the flattening ofthe Phillips curve, it is likely that inflation models will soon startto explicitly incorporate more global-based measures of economicactivity.

Because these top-down macro models have displayed severalregime shifts, in line with the changing fabric of our global economy,any solid inflation forecasting framework should not dogmaticallyrely only on a single methodology. Towards this end, the followingsection discusses bottom-up inflation forecasting methods that cancomplement the top-down approaches outlined above.

FUNDAMENTAL BOTTOM-UP MODELS FOR FORECASTINGINFLATIONThe bottom-up approach to inflation modelling is fundamentallydifferent from the top-down approach. Instead of looking at a few

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macro variables that have an effect on the aggregate level of inflation,the bottom-up approach focuses on modelling each of the variouscomponents that make up the consumer price index (CPI), or otherinflation measures. Table 15.1 shows the various sub-indexes thatmake up the CPI, along with some examples of leading indicatorsfor these various sub-indexes.

For example, consider shelter, which has the largest weight inthe CPI. The rental vacancy rate reflects the overall supply–demandbalance in the rental market. In addition, the change in home pricesand mortgage payments is also relevant, because there is a relation-ship between the costs of owning versus renting a home. Finally, itmay be possible to get direct leading forecasts for rental inflationby obtaining survey data about landlord intentions for future rentchanges.

After identifying different factors which may have a meaning-ful (and hopefully stable) relationship to shelter prices, time-seriesanalysis can be used to quantify the exact nature of that relation-ship. For example, does the vacancy rate lead shelter inflation, oris it a concurrent indicator? Is the relationship between a change inthe vacancy rate and the rate of shelter inflation linear? Is it stableover time? Does it depend on other variables that also affect shelterinflation? This question can be answered using a time-series analysissoftware package, or within a customised spreadsheet model.

Regardless of how the individual components are modelled, it isimportant to avoid over-fitting. In fact, it is easy to fit each com-ponent of CPI very accurately using the abundant financial andeconomic data available. However, the purpose of constructing aninflation model is not to fit the past, but to predict the future. Thisis why it is very important that the inputs are sensible and that rea-sonableness checks are put in place. For example, it is economicallymeaningful that vacancy rates and shelter inflation are negativelycorrelated, ie, higher vacancy rates should result in a downwardmovement in shelter inflation. Consequently, if shelter inflation isregressed against several variables, and its sensitivity to vacancyrates turns out to be positive, this strongly suggests that the modelmight be suffering from over-fitting.

An analogous process of collecting multiple data series, testingdifferent lead–lag relationships and selecting the best explanatoryvariables must be repeated for each of the components of the CPI.

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Table 15.1 CPI: components and weights

Weight Examples ofCategories (%) leading indicators

Shelter 31.96 Vacancy rates; mortgagepayments; home prices; utilityprices

Food and beverages 14.79 Prices of grains, meat, milk andproduce

Medical 6.63 Health insurance premiums;service sector wages

Recreation 6.29 Import prices; the value of thedollar; Chinese inflation

New and used cars 5.57 Import prices; wholesale usedcar prices

Motor fuel 5.08 Petroleum retail and futuresprices

Home furnishing 4.41 Import prices; the value of theUS dollar; Chinese inflation

Household energy 4.00 Wholesale power prices; naturalgas and coal prices

Apparel 3.60 Cotton prices; import prices;Chinese inflation

Communication 3.31 Import prices; the value of theUS dollar; Chinese inflation

Education 3.11 Service sector wages anddemographic trends

Personal care 2.59

Public transport 1.23 Jet fuel prices

Residual misc. items 7.45

Source: PIMCO and BLS. Data correct as of December 31, 2010.

Given the large number of sub-indexes, and the amount of workinvolved with developing models for each one, it is important tounderstand which are the components that should be modelled mostcarefully, as they influence the accuracy of the final forecast to agreater degree. One way to assess this is to look at the weight of eachseries scaled by its respective volatility. In other words, the weightsin Table 15.1 are multiplied by the standard deviation (estimatedin the 1994–2010 time window) of the monthly changes for each ofthe individual sub-indexes. The results are shown in Table 15.2. The

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Table 15.2 CPI: relative volatility of individual sub-indexes

VolatilitySector contribution (%)

Petroleum 0.98Shelter 0.35Household energy 0.27Food 0.17New and used cars 0.13Recreation 0.06Communication 0.06Home furnishing 0.05Public transport 0.05Apparel 0.04Medical 0.04Education 0.02

Core 0.43Headline 1.16

Source: PIMCO and BLS.

overall volatility of headline CPI has been 1.16%, with petroleumcontributing a whopping 0.98%. By contrast, the volatility of thecore components of CPI is 0.43%. The relative volatility contributionof core CPI is much smaller than for motor fuel, despite the factthat the core CPI basket comprises over 75% of the weight in thetotal CPI, compared to just 5% for motor fuel. Consequently, theaccuracy of any headline CPI forecast critically depends on how wellone can forecast the most volatile components, petroleum prices inparticular.

In the following, we shall discuss how to approach the fourlargest volatility weighted contributions to CPI, ie, petroleum, shel-ter, household energy and food. Besides volatility considerations,modelling energy (both motor fuel and household components) andfood is also the crucial final step in moving from a top-down macrocore inflation forecast to a forecast of headline inflation.

Petroleum inflation

It is common for investors, possibly lacking a fundamental viewon the underlying supply–demand dynamics, to forecast petroleumprices in the future1 by using the petroleum futures market since

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this price information is readily available and transparent and rep-resents an actual market price that can be used for hedging. Thespot price of petroleum reflects all of the currently known supply–demand factors, both existing and those expected in the future. Thefuture prices are linked to the spot price through an arbitrage con-dition, ie, through the addition of financing and storage costs anda convenience yield. However, the extent to which the futures priceof petroleum is an accurate or reliable forecast of prices in the futureis questionable, considering that realised and implied volatility aregenerally quite high. For example, the typical annual implied volatil-ity of options on petroleum futures is around 30–40%, which pointsto the intrinsic difficulty in obtaining an accurate forecast at compa-rable time horizons. Nevertheless, without a fundamental model ofsupply and demand, the futures curve remains the common startingpoint for petroleum forecasting in the medium to long term.

Forecasting in the very short term, specifically focusing on thenext petroleum inflation number, is actually easier, the reason beingtwofold:

1. the inflation index is published at a monthly frequency,while information on price behaviour is observed at higherfrequency (for example, daily);

2. there is a one-month lag, as the CPI published in month n is ameasure of inflation in month n− 1.2

High-frequency price information can come from various sources.These include daily petroleum futures prices and daily retail marketsurveys such as the one conducted by the Automobile Associationof America (AAA). Each of these daily data sources can then be aver-aged over month n − 1 to accurately forecast the upcoming rate ofpetroleum inflation. Note, however, that using petroleum futuresprices involves a fair amount of basis risk since the contract repre-sents wholesale petroleum prices with delivery in New York Harbor,while the petroleum inflation in the CPI is an average of retail pricesacross the US. As a result of this basis risk in the petroleum future,the AAA petroleum price survey is the most accurate way to fore-cast petroleum inflation in the very short term, since it representsretail prices from gas stations across the country. Not surprisingly,the AAA petroleum survey displays an impressive 99% correlationwith the monthly petroleum CPI inflation rate.

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Shelter inflation

After petroleum, the next most important sub-index in the CPI, whenit comes to volatility contribution, is shelter. Shelter has two maincomponents: the “rent of primary residence” (about 6% of the CPI)and the “owner’s equivalent rent of primary residence” (OER, about23% of the CPI). There is a substantial amount of misinformationabout OER, but the main point is that, for both the rent and theOER components, the US Bureau of Labor Statistics (BLS) uses actualrather than imputed3 rent data (collected in the CPI Housing Survey)to calculate inflation rates. Hence, for both components, the mainvariable to model is the rate of inflation of the average consumer’srent.

As mentioned before, some of the economic factors that couldbe important to forecasting changes in rental rates are those thatdescribe the supply–demand balance of rentals, and those that com-pare the relative cost of renting versus buying a home. In additionto these macro factors, there is also a microeconomic effect that isimportant for higher frequency models, namely utility price adjust-ments. Since most rental rates include some utility payments, if, forexample, the price of water goes up sharply in one month and wateris included in the rent, then the rent is effectively decreased. Thesame dynamic is true for other utility prices, such as electricity ornatural gas. The BLS attempts to compensate for these effects. There-fore, when utility prices increase, this places downward pressure onshelter inflation, and vice versa when utility prices fall. A bottom-upmodel can capture these effects by feeding the output of a householdenergy and utilities model, discussed in the following section, intoa model for shelter inflation.

Household energy inflation

Household energy consists primarily of retail power prices. Alogicalplace to start is wholesale power prices, as these are available acrossEurope, the US and several other countries. By examining this data, itis possible to establish the relationship between wholesale and retailprices, including the relative sensitivity (beta) and the lead–lag.

If the lead time from wholesale to retail power prices is shorterthan the time horizon sought for the forecast (say, for example,wholesale prices have a three-month lead to retail prices, but atwelve-month forecast of retail prices is desired), then we could look

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Figure 15.4 Food inflation and agricultural and livestock price changes

Yea

r-ov

er-y

ear

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tion

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706050403020100–10–20–30–40

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Food inflation Agricultural and Livestock Index

Source: data from PIMCO, Bloomberg, BLS, Standard & Poor’s.

for leading indicators of wholesale prices. In this regard, given thata large portion of US electricity is produced via coal and natural gas,looking at coal and natural gas prices can be very helpful.

Food inflationA similar logic can be applied to forecasting retail food prices. Infact, the processed foods sub-component of the Producer Price Index(PPI) is essentially a wholesale measure of food prices: it tends tobe highly correlated with retail prices, and changes in wholesaleprices typically lead retail food inflation by an average of one totwo months. Just as in the case of household energy, longer fore-casts can be made using supplementary inputs, such as the pricesof corn, wheat, livestock and milk, or a basket like the Agriculturaland Livestock component of the Goldman Sachs Commodity Index(GSCI). Figure 15.4 shows the year-over-year percentage change inthe GSCI Agricultural and Livestock Index, lagged by eight months,along with year-over-year food inflation.

Forecasts can also be extended beyond this eight-month leadperiod by using the futures curves for the relevant agricultural andmeat commodities, along with fundamental supply and demandinformation, such as farmers’ planting intentions, inventory levels,etc. Additional refinements can be made by creating a custom bas-ket of food prices with greater breadth, and also by selecting a set ofweights designed to mirror those in the food component of the CPI.

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To summarise, both top-down and bottom-up approaches havemerits and weaknesses, and this is why they complement, ratherthan substitute, each other. While both rely on fundamental analy-sis, the top-down approach focuses on medium- to long-term macro-economic equilibrium relationships, and it is therefore vulnerable toregime shifts. In this regard, a bottom-up approach, which typicallyrelies on shorter-term dynamics, can provide a warning signal ofpossible structural breakages.

In addition, while several macro-equilibrium relationships areintrinsically long-term conditions, a bottom-up model can be cus-tomised to cover a variety of shorter term forecasting horizons, thusproviding a bridge between the two approaches. The bottom-upapproach uncovers information about the specific channels that aredriving inflation, be it rising housing prices or a falling US dollar,and this insight can be crucial for implementing the right investmentstrategy.

One drawback of a bottom-up approach is that there are a largenumber of moving parts, and an extensive amount of data and analy-sis is required. With this comes the risk of data over-fitting and underappreciation of future forecasting errors.

TECHNICAL TIME-SERIES MODELS FOR FORECASTINGINFLATIONThe previous modelling approaches involved using fundamentalfactors. However, it is also possible to gain significant insights fromtechnical, or time series, analysis.

For example, many of the sub-indexes that make up the CPI tendto have a strong trending tendency, with preceding month percent-age changes generally being the best guess for next month’s per-centage changes. See Figure 15.5(a) for an illustration of this rela-tionship, using owner’s equivalent rent. In addition, changes in thepercentage change (ie, the second derivative) of owner’s equiva-lent rent tend to be mean reverting, with deviations in the rate ofmonthly percentage change often partially reversed in the follow-ing month. Figure 15.5(b) shows that an acceleration or decelerationin the monthly rate of change in the previous month tends to bepartially reversed in the following month.

In other words, if the rate of OER inflation accelerates in month n,it is likely to decelerate in the following month, n+1, thus exhibiting

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Figure 15.5 The nature of owner’s equivalent rent

0.6

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R2 = 0.3005

y = –0.5456x

R2 = 0.5448

y = 0.9421x(a)

(b)

(a) Trending nature; (b) mean-reverting nature.Source: data from PIMCO, Bloomberg and BLS from 2000 to 2011.

mean reversion characteristics. This is common of most other CPIsub-indexes, with a few exceptions showing the opposite tendency,ie, persistence (one example is apparel, for which high inflation inmonth n is generally followed by high inflation in month n+ 1).

In addition to determining if inflation indexes are trending ormean reverting, time-series analysis should also be used to incorpo-rate the seasonality of inflation. In fact, for some sub-indexes, suchas apparel, the seasonal changes alone can be used to explain mostmonth-to-month percentage changes. Adjusting for these seasonaleffects is important because it can materially improve the accuracy

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Table 15.3 Developed and emerging market food inflation

Food Commodity Commodityweighting pass-through pass-through to

Country in CPI (%) to food CPI (%) headline CPI (%)

US 13.7 6.2 0.8EU countries 14.0 5.9 0.8UK 9.3 15.6 1.5Japan 25.9 6.0 1.6Canada 17.0 6.4 1.1Australia 15.4 2.6 0.4

Average 15.9 7.1 1.0

China 33.0 25.0 8.2Brazil 30.2 14.7 4.4Mexico 22.7 9.0 2.0India 47.1 16.2 7.6Russia 38.0 16.2 6.1Turkey 27.6 10.0 2.8

Average 33.1 15.2 5.2

Source: PIMCO, BLS, Haver and Bloomberg.

of both bottom-up- and top-down-type models. Furthermore, cor-rectly modelling seasonal factors is important because the returnsthat an investor earns from holding US Treasury Inflation-ProtectedSecurities are linked to the non-seasonally adjusted level of inflation.

To conclude, technical analysis is useful in studying the time seriescharacteristics of inflation indexes, including seasonality patterns,and thus it can add to the accuracy of both top-down and bottom-upinflation models, particularly at higher frequencies.

FORECASTING INFLATION IN DEVELOPED VERSUSEMERGING MARKETSAlthough similar methods and principles can be used to forecastinflation in both developed and emerging economies, there are somenoteworthy differences.

Emerging markets (EMs) tend to have a much higher food weight-ing in their consumption baskets, while developed markets (DMs)tend to have higher weightings of services. Table 15.3 shows theweightings of food in the CPI basket for a handful of emerging and

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developed market countries. On average, the weight of food in EMconsumption baskets is 33%, roughly twice as large as that seen indeveloped countries.

Another difference between developed and emerging markets isthat, in EM, input costs represent a larger share of the price of thefinished goods. For example, in the US, a 1 lb box of cereal might costabout US$3. The prices of corn and wheat fluctuate widely from yearto year, but from 1991 to 2011 they ranged from 3 ¢/lb to 20 ¢/lb, justa small fraction of the overall price of the box of cereal. This meansthat the sensitivity of inflation rates to changes in input costs indeveloped countries, like the US, is relatively low.

For example, the sensitivity of US food inflation to the GSCI Agri-cultural and Livestock Index has averaged just 6.2% (ie, a 100%increase in the GSCI Agricultural and Livestock Index would causea 6.2% increase in the CPI food sub-index). Therefore, since foodrepresents roughly 14% of the overall CPI basket, a 100% increasein the GSCI Agricultural and Livestock Index implies a 0.9% (14%times 6.2%) increase in the CPI itself.

In contrast, as shown in Table 15.3, the average sensitivity of foodinflation in EM is roughly twice that in DM countries. Combining thegreater sensitivity to input costs (third column in Table 15.3) with thehigher weighting of food in consumption baskets (second column inTable 15.3) means that a given change in underlying food prices hason average almost five times the impact on EM inflation comparedwith DM inflation (fourth column in Table 15.3).

The previous example highlights the necessity to develop separateinflation models for individual countries, although it is clear thatseveral price inputs and macroeconomic variables will be relevantfor all.

CONCLUSIONS

In this chapter we looked at multiple approaches to modelling infla-tion, including fundamental top-down and bottom-up models, aswell as technical time-series analysis. Clearly, each approach hasbenefits and drawbacks.

Typically, the top-down approach has the longest forecasting hori-zon, but relative to a bottom-up approach it tends to have less accu-racy in the short term. In countries like the US where financial and

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economic data are plentiful, a bottom-up inflation model can com-plement a top-down approach, increase short-term accuracy andgive early warning of structural shifts in the underlying inflationdynamics. In practice, building such a model can prove more chal-lenging for emerging economies, where available data might berelatively sparse.

1 Commodity spot and future prices typically exhibit strong seasonality (because either demandor supply is seasonal). The forward price at time t for delivery at T, F(t, T), inherits theseasonality of the underlying spot price P(t) at time t. Consequently, to extract a forecast offuture price at time T, we need to adjust for seasonality effects.

2 Of course, we have to bear in mind that market prices also adjust to the same high-frequencyinformation, so this inflation forecast is likely to be of limited use in trading “ahead of thecurve”.

3 Part of the confusion arises because the relative weight of OER in the CPI (about 23%) iscalculated from imputed expenditures, derived from asking a sample of homeowners thequestion: “If someone were to rent your home today, how much do you think it would rentfor monthly, unfurnished and without utilities?”.

REFERENCES

Fisher, I., 1926, “A Statistical Relation between Unemployment and Price Charges”, Inter-national Labour Review 13(6), pp. 785–92. (Reprinted as “I Discovered the Phillips Curve:‘A Statistical Relation between Unemployment and Price Changes’ ”, Journal of PoliticalEconomy 81(2), pp. 496–502 (1973).)

Friedman, M., 1963, Inflation: Causes and Consequences (New York: Asia Publishing House).

Phillips, A. W., 1958, “The Relationship between Unemployment and the Rate of Changeof Money Wages in the United Kingdom 1861–1957”, Economica 25(100), pp. 283–99.

Stock, J., and M. Watson, 1999, “Forecasting Inflation”, Journal of Monetary Economics 44(2),pp. 293–335.

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16

Protecting Insurance Portfoliosfrom Inflation

Ken Griffin and Edward Y. YaoConning Asset Management

The unprecedented steps taken by the Federal Reserve Bank of theUS towards monetary expansion since the financial crisis in 2008have made the need to protect invested assets against inflation ofutmost importance. It is necessary to combine insurance companymodelling expertise with insurance asset management experienceto develop an investment solution that will help to protect the valueof a portfolio during periods of accelerating price inflation.

INFLATION HISTORY AND OUTLOOK

Inflation in the US has been stable and low since the 1990s. Since 1980,the annual inflation rate, measured by the change of the ConsumerPrice Index-All Urban Consumers (CPI-U) over a 12-month period,has declined from above 10% to the 2–4% range (Figure 16.1). Duringthe Great Recession starting in 2008, it decreased well below 2% andinto negative territory. However, high inflation is more common ifwe look at global inflation over a longer history. There were periodsof runaway inflation in the late 1970s and early 1980s in the US, butit was still dwarfed by the inflation in some other countries. Brazilwas one notable example, with inflation north of 1,900% in 1989 and2,400% in 1993. In most years from 1980 to 1994, the inflation rate inBrazil was into three digits.

Since the 1980s, the Federal Reserve Bank in the US has changedits monetary policy to stabilise inflation within a range (as centralbanks of many other countries around the globe, including Brazil,

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Figure 16.1 US annual consumer price inflation

1614121086420

–2–4

Infla

tion

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1950 1960 1970 1980 1990 2000 2010

Source: US Bureau of Labor Statistics; Conning Risk & Capital ManagementSolutions Analytics.

Figure 16.2 Inflation expectations track past inflation average

Mean survey ofprofessional forecasters

5Y moving averageUS CPI-U inflation

12M US CPI-Uinflation

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have done). However, it is not clear at the time of writing whethercentral banks will be able to rein in inflation at the right time to theright level.

In fact, inflation expectations from economists, consumers andinvestors alike often reflect not much more than a moving averageof realised inflation rates, so it is doubtful whether they can reallybe forward looking. In Figure 16.2, the mean forecast of long-term

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Figure 16.3 Cumulative inflation: (a) actual versus expected and (b) fiveyear cumulative difference between expected and actual inflation

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inflation rate from the Survey of Professional Forecasters by the USFederal Reserve Bank of Philadelphia follows closely the five-yearmoving average inflation rate.

Furthermore, increases in inflation are very often underestimated.Although the risk of unexpected inflation is pervasive, people donot anticipate inflation until it has manifested itself for an extendedperiod of time, at which point it takes longer for monetary policy tobe adjusted to bring inflation down to the target level. In addition,

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Figure 16.4 Increased monetary base in the US

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inflation tends to be serially correlated, with high inflation typicallyfollowed by high inflation, and therefore its devastating impact iscumulative.

Figure 16.3(a) compares the cumulative actual inflation versusexpected inflation since the late 1950s. The five-year moving averageactual inflation rate is used as inflation expectation. Figure 16.3(b)shows the cumulative difference between expected inflation andactual inflation at the five year horizon from 1957 to 2010. The dif-ference swings between −15% and 30%. The cumulated impact ofinflation can be over- or underestimated for an extended period oftime. Based on the data in Figure 16.3(b), clearly its impact hasmore often been underestimated, even though the magnitude ofunderestimation was smaller.

Since the 2008 financial crisis, in order to support economicgrowth, central banks have generally kept interest rates low andpumped liquidity into their economies. As of October 2011, the USFederal Reserve has had two quantitative easing (QE) programmes,whereby they purchased hundreds of billions of US dollars of secu-rities from the capital markets in order to increase liquidity inthe financial system. Figure 16.4 shows how, as a result, monetarysupply skyrocketed in the US after 2009.1

In our opinion, the probability of high global inflation sometimein the future has greatly increased. The first signs of such trendare already showing up in emerging markets like China, prompt-ing these countries to raise interest rates in an attempt to cool down

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their economies. The extended period of low inflation in the post-Volcker era might be contributing to a false sense of security, whileincreasing the likelihood of underestimating inflation in the future.

A reasonable level of inflation in line with expectations is gen-erally not a big threat for businesses and consumers, as nominalprices including output prices and wages should adjust accordingly.However, the insidious risk is an unexpected change in the rateof inflation, especially in the environment at the time of writing,where there are reasons to believe traditional measures of inflationexpectations might be misleading. Therefore, inflation risk shouldbe carefully analysed, as it can negatively affect both consumers andbusinesses. This issue is particularly acute for property and casualty(P&C) insurers: a topic discussed in the next section.

INFLATION RISK FOR PROPERTY AND CASUALTYCOMPANIESProperty and casualty (P&C) insurers are exposed to a wide varietyof risks that must be managed within a company’s risk tolerance.For example, the risk of catastrophic weather events can be managedthrough property location diversification or reinsurance, while otherrisks are more difficult to protect against.

Among such challenging exposures is the risk of unexpected(higher) inflation, which tends to be an insidious peril that growsover time and affects all key financial metrics of an insurer. On theliability side of the balance sheet, claim payments accelerate beyondexpected levels and additional reserves are required in anticipationof higher claims, often leading to poor underwriting results as lia-bilities exceed incoming cashflow streams. Company expenses alsoescalate beyond expectations.

The magnitude of the impact on a company’s performancedepends on a host of factors. Obviously, first in line is the impact ofinflation on liability payments. But other issues are also important,such as the ability to pass higher costs (due to higher inflation) to thecustomers, the magnitude of the upside run in prices and how longthe inflationary period lasts. Finally, the adverse impact on reserveadequacy is more manifest on liabilities further in the future, as infla-tion surprises have a longer time to cumulate, thus increasing cash-flows payable. Clearly, it is not just liabilities that are exposed to aninflation surprise, as higher interest rates will also affect negatively

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Figure 16.5 Dynamic financial analysis of the insurance enterprise

Evaluation ofeconomy and capital

markets

Financialstatementprojections

Financialanalysis and

reports

Asset analysisUnderwriting

analysis

Source: Conning Risk & Capital Management Solutions.

many assets on the opposite side of the balance sheet, includingbonds and equities, thus contributing to the underperformance.

A SIMULATION APPROACHHow significant is the risk of unexpected inflation to an insurancecompany? We adopted a dynamic financial analysis (DFA) approach(a stochastic simulation of the relevant cashflows), to answer thisquestion and more; although the topic concerns investment strat-egy, the importance of the DFA approach goes beyond the invest-ment strategy itself. The framework that was applied in our analy-sis of inflation protective investment strategies can also be used toimprove other business decisions. In terms of risk management,with this approach, the risks will not be managed in silos but inan integrated system. Our analytical framework is illustrated inFigure 16.5.

A DFA model includes an enterprise model, which simulates thecompany at hand, and an economic scenario generator (ESG), which

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simulates the economic and capital market environment facing thecompany. The output of an ESG is a set of simulated scenarios overtime (or paths) that portray future economic and capital market con-ditions in terms of macroeconomic indicators, such as inflation, GDP,interest rates and returns of various asset classes, such as bonds andequities. These scenarios are used as an input into the enterprisemodel where the company’s assets, liabilities and business opera-tions are evaluated under each of these scenarios. Each evaluationgenerates a set of multi-period financial measures reflecting differ-ent aspects of the company’s financial performance in the future.Pro forma financial statements are constructed across each economicscenario and under various accounting bases. In this way, realis-tic distributions of various financial metrics develop in a consistentmanner.

For the purposes of this chapter, we model a hypothetical insur-ance company, with an asset–liability profile similar to the averageUS P&C company. Economic value is used to measure the value ofthe insurance company and is defined as the market value of cur-rent plus future assets (ie, new business the company might develop)minus the present value of liabilities and taxes. Economic value isnot observable,2 but it avoids the distortions of regulatory account-ing regimes, since it marks all assets to market, accounts for the timevalue of money and thus makes the values of different companieseasier to compare with each other. Clearly, there are a lot of assump-tions that go into this calculation, particularly in projecting futurebusiness and cashflows, and in the assumption of what the relevantdiscounting curves ought to be.

Statistically speaking, economic value is a stochastic process. Itsvolatility will be used in this chapter as a measure of economic risk,in order to capture the possibility that the future economic value ofthe insurance company might be different from ex ante expectations.

ECONOMIC VARIANCE DECOMPOSITION

There are four major risks borne by a P&C company: real underwrit-ing risk, asset risk, liability discount rate risk and inflation risk (ie,liability cashflow risk).

1. Real underwriting risk is the uncertainty of economic valuecaused by unexpected changes in the loss ratio. For example,

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Table 16.1 Asset allocation details

Invested assets Allocation (%)

Fixed income:US Government 11.0Municipals 31.9Corporates 20.6Mortgage-backed securities 5.6Asset-backed securities 4.5Collateralised mortgage obligations 4.1Other 1.9

Common stock 12.1Preferred stock 1.5Other assets 6.9

Total lines 100.0

a sudden increase in claim frequency and/or severity due tosome natural catastrophe can lead to an unexpected increasein the loss ratio and a decrease in underwriting profit.

2. Asset risk is the economic value uncertainty, which is due tounexpected changes in the market value of assets. The averageUS property and casualty industry’s liabilities and investmentprofile was used as input in the model (Tables 16.1 and 16.2).Future business was projected based on our study and outlookon the industry.

3. Liability discount rate risk arises from the uncertainty in therates (US zero-coupon yields in this analysis) used to calculatethe fair value of liabilities.

4. Inflation risk was defined earlier as the risk that (at con-stant loss ratio) insurance benefits, which are a determinantof cashflows payable, increase due to an increase in inflation.

The decomposition of economic value risk over one-year and five-year time horizons is shown in Figure 16.6. A one-year horizon isrelatively short, but it is an interesting case, as it is the horizon oftenused by regulators and rating agencies to evaluate economic capital.The five-year horizon better captures the cumulative impact of eco-nomic events in the model. This longer time frame also correspondsto the typical budgeting horizon of many insurance companies

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Table 16.2 Liability composition details

Allocation of lossLines of business and reserves (%)

Private passenger auto: liability 16.0Private passenger auto: physical damage 0.8Homeowners 3.7Commercial auto: liability 4.5Commercial auto: physical damage 0.1Workers comp. 20.8Commercial multiple peril: liability 4.8Commercial multiple peril: property 1.8Other liability 21.3Products liability 2.9Medical malpractice 5.2Fire 0.8Allied lines 0.9Inland marine 0.6Reinsurance 7.7All other lines 8.2

Total 100.0

Source: Conning Risk & Capital Management Solutions.

Figure 16.6 Decomposition of variance of economic value

43

23

15

48

138

29

21

0

10

20

30

40

50

60

Pro

port

ion

of e

cono

mic

ris

k (%

)

One-year horizon Five-year horizon

Real underwritingInflationDiscount rateAssets

Source: Conning Risk & Capital Management Solutions analytics.

(three-to-five years), and provides a reasonable base for investmentplanning.

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Figure 16.7 Negative impact of higher inflation on insurers’ equity value

2010 2011 2012 2013 2014 2015450

500

550

600

650

750

700

Equ

ity v

alue

(U

S$

billi

ons)

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

Infla

tion

shoc

ks (

%)

Baseline

Inflationary shock equity

Inflation rate shock

Source: based on Conning’s insurance company simulation results.

As shown in Figure 16.6, inflation risk is not that significant (15%)over the one-year period, but its importance increases over time andcan dominate over longer horizons. Indeed, over the five-year hori-zon, inflation risk is the largest contributor (48%) to overall economicrisk.

INFLATION IMPACT ON INSURERS’ EQUITYIn this section, we analyse the effect of an inflation shock on com-bined equity value of the insurance sector. As inflation increases,the other variables (eg, discount rates) will also change, as the evo-lution of all these risk factors in the model is calibrated to historicalexperience (where they are correlated). Liabilities will also typicallyincrease, leading to erosion in equity value. The inflation shock is twostandard deviations from a baseline of about 2% (at year 0 = 2010) to5% (at year 2 = 2012), after which inflation starts to revert towardsits baseline (Figure 16.7 shows the first five years as per our horizon).

Changes to insurers’ equity value are primarily driven by netincome (which turns negative) and (unrealised) investment losses.Figure 16.7 shows how damaging and long lasting an accelerating

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inflation rate can be to the insurance industry. By year 3 (2013), higherinflation leads to a 20% loss in equity value, from the US$619 billionbaseline to about US$498 billion.

PROTECTING AGAINST INFLATION RISKWhat makes an ideal investment strategy to protect an insurancecompany from inflation risk? Insurance companies need invest-ment income to supplement their underwriting income, in partic-ular when markets are soft and price competition is fierce. Goodinvestment strategy helps insurance companies to grow their capitalwithout disproportionately increasing their risk exposure.

Because both assets and liabilities of insurance companies are sen-sitive to inflation, a protective investment strategy provides a way tohedge inflation risk on both. Specifically, an ideal inflation-hedgingstrategy for an insurance company should

1. be well diversified and relatively inexpensive to implement,

2. enhance the economic value of the company on a risk-adjustedbasis (in other words, improve the economic value efficientfrontier),

3. not subject the company to substantially higher capital chargesfrom the regulatory or rating agency perspective,

4. not substantially reduce investment income.

Using inflation-sensitive assets to protect against inflation’s harmfuleffects offers the opportunity for higher investment returns with-out onerous capital demands and investment income reductions.Through advanced modelling techniques, the optimal asset alloca-tion can be customised in line with an insurer’s specific business,tax position and risk and reward preferences.

DIFFERENT ASSETS IN INFLATIONARY PERIODSThe first step in the analysis is to investigate historical returns ofdifferent asset classes, particularly during inflationary periods. Wecollected data from different sources, including the US ConsumerPrice Index (CPI-U) from the US Bureau of Labor Statistics for infla-tion, equity and commodity indexes from Bloomberg, fixed-incomeindexes from Barclays Capital and a convertible bond index fromMerrill Lynch. In researching several decades of US inflation data,

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Figure 16.8 Twelve-month rolling annual US inflation (1948–2010)

0.15

0.13

0.11

0.09

0.07

0.05

0.03

0.01

–0.01

–0.03

–0.05

Tw

elve

-mon

th in

flatio

n (%

)

1950M1

1960M1

1970M1

1980M1

1990M1

2000M1

2010M1

Sources: US Bureau of Labor Statistics; Conning Risk & Capital ManagementSolutions analytics.

we found that periods of increasing inflation occurred frequently,and some lasted for several years (Figure 16.8). We identified 10“inflationary periods” (indicated by the grey areas in Figure 16.8)by measuring inflation by its rolling 12-month average. As seen inFigure 16.8, the US experienced an inflation environment for almosthalf of the time between 1948 to 2010. The 12-month rolling inflationrate during these periods was about 2.4%.

As the rate of inflation increases, the following year’s inflationrate is likely to be higher as well, as consumers and businessesbegin to expect greater price changes due to positive serial corre-lation of inflation. Since unexpected inflation is more damaging toinsurers than high but stable inflation, we focused particularly onincreasing inflationary episodes that act as a proxy for unexpectedinflation increases. During these periods, we found that most assetclasses, particularly fixed-income investments, performed poorly.For instance, from 1948 to 2010, the annual total return of the S&P 500index has a negative (−15.6%) correlation with inflation; similarly,from 1976 to 2010 (the difference in dates depends on the availabil-ity of index data), the annual total return of the Barclays US Aggre-gate Bond Index has a negative (−24.6%) correlation with inflation(calculated on a calendar year basis).

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There were, however, certain asset classes that generated supe-rior performance relative to the overall market. Hard assets sec-tors with exposure to commodities used in industrial production,as well as precious metals, generally outperformed during infla-tionary periods. Energy sectors and energy commodities such aspetroleum-based products were also strongly positively correlatedwith inflation, and were often previously the underlying cause ofhigher inflation. Exposure to these hard asset sectors and commodi-ties can be gained through the futures market, financial vehiclessuch as exchange-traded funds (ETFs) or direct equity investmentsin companies that benefit from commodity price increases. Otherselect sectors, such as real estate, retailing, materials and technologyalso provided solid returns. Convertible bonds in inflation-sensitivesectors are a capital-efficient way for insurers to gain equity-likeexposure while still maintaining a relatively high level of investmentincome.

Other financial vehicles are directly linked to the inflation rateitself. Treasury Inflation Protected Securities (TIPS), are indexed tothe US CPI and accrue additional principal at the rate of inflation,although, in a low inflation environment, TIPS will produce lowerinvestment income than most other fixed-income investments. Infla-tion swaps also can provide inflation protection, as a fixed rate ofinterest is paid in return for the rate of inflation realised over theperiod of the swap. No cash outlay is required, but insurers will needto meet certain regulatory standards (such as filing a Derivative UsePlan, which is a legal requirement in many US states) before execut-ing an agreement, and would be subject to the swap mark-to-marketvolatility.

Floating-rate notes can also provide inflation protection, as theunderlying rate should adjust to a higher level along with inflation.When additional credit or liquidity spreads are present, these mightalso provide yield enhancement and extra income.

INFLATION-HEDGING ASSETS AND EFFICIENT FRONTIER

Based on the historical analysis of long-term dynamics of inflation,economic growth, interest rates and returns of different asset classes,we calibrated the economic and capital market simulation model toprovide realistic scenarios for economic indexes and asset returns.

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Figure 16.9 Risk and return of various asset classes

0

1

2

3

4

5

6

7

8

9

10

11

12

0 5 10 15 20 25 30 35 40

Ave

rage

tota

l ret

urn

(%)

Standard deviation (%)

FRN

MBS

Hedge funds

High yieldConvertibles

US equitiesEAFE

Infl.equities

Commodities

Private equity

Cash

Muni. TIPSCorp.Gov.

Source: Conning Risk & Capital Management Solutions analytics.

Figure 16.9 displays the average and standard deviation of ourmodelled asset class returns (the multiple points for government,corporate and municipal bonds along with TIPS represent multiplematurities).

We selected five inflation-hedging assets, which are US TIPS, infla-tion protective equities, commodities, floating rate notes and con-vertibles. Inflation protective equities include the energy, retailing,materials, technology, hardware & equipment and the real estatesectors. Commodities include the crude oil, industrial metals andprecious metals sectors.

Certain asset classes such as TIPS and floating-rate notes hada low-risk, low-return profile, while others, such as commodities,inflation-sensitive equities and convertible bonds, had higher riskand return expectations. By running our industry model throughreal-world economic scenarios, we tested the value of adding var-ious allocations of our five inflation-sensitive assets to the insur-ance industry’s investment portfolio. We then solved for the optimalasset allocations that maximise the economic value of the industrywhile minimising the economic risk, thus identifying the efficientfrontier.

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Figure 16.10 The efficient investment frontier(s) for economic value(five-year horizon)

A

B

CD

E F

G H I J

800820840860880900920940960

55 65 75 85 95 105 115 125 135 145 155 165 175 185

Ave

rage

eco

nom

ic v

alue

Standard deviation of economic value

Add inflation swapAdd other inflation assetsAdd TIPSBaselinePC industry

A–J denote different efficient portfolios.Source: Conning Risk & Capital Manage-ment Solutions analytics.

Figure 16.11 Insurers’ equity value

450

500

550

600

650

750

700

Sha

reho

lder

's e

quity

(US

$ bi

llion

s)

2010 2011 2012 2013 2014 2015

BaselineInflationary shockShock with inflation assets

Source: Conning Risk & Capital Management Solutions analytics.

Figure 16.10 shows several efficient frontiers for our hypothet-ical company, using the asset and liabilities profile of the aver-age US P&C insurer. Each of the four lines in the chart is a plotof the average and standard deviation of economic value of thecompany at the five-year time horizon for a given set of instru-ments (weights varying depending on the risk–return preferences)allowed in the investment portfolio. The baseline is the efficientfrontier using the set of assets in Table 16.1. Note that the aver-age weights in Table 16.1 do not correspond to an efficient port-folio (PC industry point in Figure 16.10). To this set (Table 16.1) ofinvestable assets, we add first US TIPS, then floating-rate notes,commodities, inflation-hedging equities and convertibles; finally,an inflation swap overlay is included. The isolated point in Fig-ure 16.10 represents the average economic value of the insurer before

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the inclusion of inflation-hedging instruments in its investmentportfolio.

Several interesting insights can be gleaned from this type of analy-sis. First, including inflation protection in the industry’s portfolio cangreatly reduce the overall risk and improve its future combined eco-nomic value. Asset portfolio returns are improved during inflation-ary periods, which help to offset the inflation risk held in the insurers’liabilities. During inflationary periods, when other traditional assetssuch as bonds and equities are performing poorly, inflation-hedgingassets stabilise and protect economic value.

Second, while we see that TIPS provide risk reduction, the benefitsare typically seen at the lower end of the risk–return spectrum, wherethe addition provides a material shift of the efficient frontier up andto the left (see the lower left corner in Figure 16.10). Instead, theaddition of commodities, inflation-sensitive equities and convertiblebonds to the investable set causes a material shift of the efficientfrontier at higher risk–return levels (see the upper right corner inFigure 16.10).

Third, when we include inflation protection, we can modestlyextend the duration of the current bond portfolio, which improvesportfolio yields and investment income. By protecting against infla-tion shocks with assets that have historically appreciated in valuein such episodes, we can afford this extension and the incrementalinterest rate risk.

Finally, overlaying the portfolio with an inflation swap increasesaverage economic value or reduces economic risk across the board.As a direct hedge against inflation with no cash outlay, an infla-tion swap provides an inflation hedge without having to reallocatecapital from other investment assets.

Figure 16.11 shows the evolution of the average insurers’ equityvalue over time (baseline) and the effect of an inflationary shock. Ifinflation-sensitive assets are included in the portfolio, the impacton economic value from the same inflationary shock is greatlymitigated.

TAILORING INFLATION-HEDGING STRATEGIESAlthough we analysed optimal inflation-hedging investment strate-gies for our virtual P&C company with an average asset–liabilityprofile, further analysis is needed to customise the strategy to

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any specific insurance company. The following are some importantconsiderations.

Long-tail liabilities versus short-tail liabilities

Payments for long-tail P&C liabilities are so called because they aredisbursed further into the future. This might be due to delays inclaim reporting, adjusting or settlement or the involvement of lit-igation, and often results in higher claim severity. These liabilitiesusually include claims made under such coverage as workers’ com-pensation, medical malpractice, professional liability and generalcasualty. Long-tail liabilities are more susceptible to inflation risk.The insurance companies that underwrite long-tail insurance thushave more need for inflation protection, and their investment strat-egy should be more heavily weighted towards inflation-hedgingassets.

In our analysis, we are able to vary the liability profile andderive the optimal asset allocations for short- and long-tail linesof business. As intuition suggests, the results show that the opti-mal investment strategy to protect long-tail liabilities from inflationrequires a greater allocation to long-maturity TIPS. Furthermore,long-tail liabilities tilt the optimal portfolio towards more volatile,higher-yielding assets, such as commodities and inflation-sensitiveequities, relative to short-tail liabilities, which tend to tilt the opti-mal investment strategy towards floating-rate notes and convertiblebonds.

Capital adequacy/credit rating

Insurance companies operate under many constraints and are heav-ily regulated. The regulators’ intent is to prevent the insurance com-panies from taking too much risk, and to protect policyholders. First,regulators require the insurer to maintain a specific level of capital,which will be a function of the type of asset in its portfolio, andoften their credit rating. Rating agencies also look at capital to deter-mine the credit rating of the company, which is obviously a crucialmetric in the insurance business. Therefore, an insurer’s (inflation)investment strategy needs to take into consideration both the risk-based capital requirements and the impact they might have on thecompany’s rating.

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Investment incomeSome inflation-sensitive investments, such as commodities andequities, do not pay coupons, or their dividend income is uncer-tain. Others, such as TIPS, have a lower fixed coupon yield thanmost other fixed-income securities (although inflation might off-set this). Therefore, the inflation investment hedging strategy mightdecrease book yield in nominal terms, although it should result inlower volatility from a balance sheet perspective, ie, when liabilitiesare taken into account.

Risk toleranceDifferent companies have different risk tolerances and may not usethe same risk measurement metrics. Different measurements andrisk tolerances will lead to different optimal strategies. For example,a company with a higher risk tolerance is likely to have a largerallocation to commodities and inflation-sensitive equities, while acompany with a lower risk tolerance will gravitate towards TIPSand floaters.

INFLATION RISK FOR LIFE INSURANCE COMPANIESWhile most of the impact of inflation on P&C insurers’ profitabil-ity is tied to the adverse growth in claim payments, life insurancecompanies are exposed in a different manner.

In fact, investment portfolios of life insurance companies are heav-ily weighted towards fixed-income investments such as governmentand corporate bonds, and residential and commercial mortgages.These investments typically pay fixed rates of interest and havematurities much longer than those typically held by P&C companies.As capital markets react to an inflation surprise, interest rates willrise, decreasing the market value of these long-term fixed-incomeinvestments. Depending on the timing of the investment purchases,the unrealised loss position of the life insurer’s portfolio will grow,leading ultimately to realised losses if and when the company needsto sell assets.3

On a statutory accounting basis, realised losses are absorbed firstby the interest maintenance reserve (IMR) and then, once IMR isdepleted, by the company’s capital, which will impair the insurer’sability to underwrite new business. On a Generally AcceptedAccounting Standards (GAAP) basis, losses will flow through to

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the company income statement, and both income and capital willsuffer.4 On an economic basis, the economic value of the companywill depend on the duration management of both sides of the bal-ance sheet. If the duration of the assets is shorter than the durationof the liabilities, the market value of the assets will fall less than themarket value of the liabilities such that the net surplus (assets minusliabilities) position may actually benefit. However, if the reverse istrue and the asset duration is longer than the liabilities, the economicvalue of the company may fall. Prudent asset–liability managementis crucial in measuring and understanding this dynamic.

Beyond duration risk, negative convexity may also negativelyaffect a life company’s surplus position. Life companies typically“sell options” on both sides of the balance sheet. For instance, on theliability side, they give policyholders the right to lapse their policieswhen interest rates rise and receive their policy cash values, whichmay cause the company to sell assets just when market values havebeen impaired. On the investment side, life companies often makeinvestments, such as mortgage-backed securities, that allow for thereturn of funds to the company when interest rates fall, requiringreinvestment in a lower yielding environment. The net effect is thatlife companies typically suffer when there are large swings in interestrates, regardless of the direction of the rate changes. Rapidly risinginterest rates in an increasing inflation environment are no exception.

Like P&C companies, life companies are exposed to higherexpenses during inflationary periods. Unlike P&C companies, whichmay have some ability to re-price renewable policies during times ofincreased inflationary pressure, life policies often require long-termfixed contracts, which are priced using ex ante long-term inflationprojections. When actual inflation turns out to be higher than theseinitial assumptions, life companies have a limited ability to recoupthe higher costs that result.

While inflation risk for life insurers can be significant, a mitigatingfactor is that most life insurance benefits are not directly indexed toinflation, to the contrary of what happens for P&C companies, whomust typically pay the full replacement cost of the insured item.

CONCLUSIONSGiven the monetary and economic environment at the time of writ-ing, inflation risk is more relevant than ever. Simulation results

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clearly show that the latter can indeed be the greatest financial riskfaced by P&C insurers, at least at long horizons (five years or more).

Asset classes that perform well during periods of higher inflationare few, and those that exist have different characteristics and quali-ties. To lead to optimal enterprise performance, a successful strategymust combine the knowledge required to invest in inflation-sensitiveassets, with the management experience and understanding of theinsurance business, and the needs of the specific client at hand.

All rights reserved. “Protecting Insurance Portfolios from Infla-tion” is licensed to Incisive Financial Publishing Ltd by ConningAsset Management (“Conning”) and may not be reproduced ordisseminated in any form without the express permission of Con-ning. This publication is intended only to inform readers aboutgeneral developments of interest and does not constitute invest-ment advice. While every effort has been made to ensure the accu-racy of the information contained herein, Conning does not guar-antee such accuracy and cannot be held liable for any errors in orany reliance upon this information.

Conning does not guarantee that this publication is complete.Opinions expressed herein are subject to change without notice.Past performance is no indication of future results. Conning isa portfolio company of the funds managed by Aquiline CapitalPartners LLC (“Aquiline”), a New York-based private equity firm.

1 However, as a counterargument, it is clear from Figure 16.4 that money velocity plummetedduring the same period.

2 For listed companies, stock price is a measure of economic value, although technical effectscan at times be important.

3 Clearly, what matters at the end is the duration difference between assets and liabilities.

4 Statutory accounting rules apply specifically to insurance companies. GAAP accountingcovers a wider range of public and private companies.

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17

Inflation, Pensions andLiability-Driven Investment Solutions

Markus AakkoPIMCO

Pension plans play a significant role in most developed marketsocieties. As investments, they provide capital to the economy; asfunded pools of savings, they provide security to millions of retirees.Changing demographics have put the solvency of several pensionschemes to the test, as ageing societies mean more retirees and fewerparticipants contributing to the savings pool.

In developed markets, most of these pensions are stated in nom-inal terms, but some are tied to price indexes. If inflation were torise substantially, more pension funds may choose to provide someindexation. Consequently, finding ways of mitigating inflation hasbecome important for most pension managers, as inflation is one ofthe potential risks associated with the solvency of their schemes.

In this chapter, we focus on how inflation can potentially influencethe solvency of pension funds; we review how private pension plansin selected countries differ in their pension commitments, and meth-ods of assessing the required contributions to the plan. We find that,while many countries have private pension systems with exposureto inflation, the discount curves used for valuation are almost alwaysbased on nominal rates: in other words, inflation is usually implicitlyincluded as a forward-looking expectation in liability estimates.

Using the example of a US pension fund, we review the types ofanalytical tools that can be used to measure the inflation sensitivityof a pension plan, and also how traditional risk budgeting processesand risk decomposition techniques can be expanded, using a factormodel that uses unanticipated inflation as one of the factors.

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We conclude by reviewing some of the instruments and strategiesthat can be used to mitigate inflation risk, and discuss their efficacyas inflation hedges and the degree to which they are employed inpractice by pension plans in selected countries.

INFLATION INDEXATION OF PENSION BENEFITS AROUNDTHE WORLDThe typical model of pension financing revolves around pre-fund-ed liabilities, ie, an arrangement where funds (from the pensionsponsor1 and/or plan participants) are set aside and invested inorder to meet future liabilities (pension benefits). In the past, pay-as-you-go models, where current workers’ contributions and/or taxespay benefits payments to current retirees, dominated most countries,as corporations’ and governments’ abilities to meet their obligationswere viewed as infinite, in the light of continuing population andproductivity growth. The rebalancing of economic power betweendeveloped and emerging economies, and the demographic trendsunderlying that rebalancing, are calling into question the credit-worthiness of those future promises. Hence, most countries havemoved towards requiring substantial “down payments” for futurecashflows in the form of pre-funded pension plans.

A primary objective of most pension sponsors and any contribut-ing participant is to minimise required contributions to the pensionfund over the life of the scheme. Contributions at any given pointin time are driven by a combination of asset returns, liability dis-count rate assumptions, actuarial projections and, often, the localregulatory framework.

The pre-funding of these liabilities has, in turn, created the neces-sity of being able to value the future liabilities accurately. Given thatcashflows associated with future liabilities can be estimated with areasonable degree of accuracy, traditional discounting models canbe used to estimate the present value required to fund the futurecommitments. Actuarial projections usually include an assumptionfor inflation, since many schemes are based on average or final payformulas, or include an explicit tie to inflation through cost-of-livingadjustments (COLAs). Required contributions may rise, therefore, ifinflation exceeds the assumed rate.

There is a distinct difference between open plans, with new par-ticipants earning future benefits, and closed or frozen plans, where

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Table 17.1 Private pension plans’ indexation policy

Country Indexation policy

US Only a small percentage (∼3%) provideautomatic adjustments

UK Mandatory up to 5% per year

Netherlands Most plans have conditional indexationbased on fund’s solvency

Canada Not mandatory

benefit payments are largely predetermined. For closed and frozenplans, the expected shape of the liability is substantially more pre-dictable and the plan’s sensitivity to inflation is also more stable asthere are no further benefit accruals.

In the US, most private pension promises do not carry a COLA,and because of this they are nominal obligations that tend to decreasein real terms during inflationary periods. In 1995, only 7% of privateplans had a provision for inflation indexation, and only in 3% of thecases the plan had an automatic escalator (Mitchell 2000, p. 13).

While inflation may not be fully included in the benefit formulas,in cases where pension benefits are calculated as a result of final oraverage wage, inflationary periods in excess of actuarial expecta-tions may also alter the liability in relation to the supporting assetpool. This is the most common way in which US private pensionfunds end up having sensitivity to inflation. The link is, however,weaker than an explicit COLA.

Comparatively, in Europe, practices vary by country. The UK hasan explicit link between pension promises and inflation, even forprivately organised schemes (Davis 2000), and the Netherlands (thesecond largest private market in Europe) typically has indexationbuilt into the benefit formulas, although the latter are often condi-tional to the fund being in sufficient health to support such increases.In many, if not most, countries the public part of the pension system(eg, Social Security in the US) is fully indexed to inflation (Piggottand Sane 2009, pp. 8–9).

The inflation sensitivity of pension plans varies by country, byindustry, by sponsor and by plan. In some cases, benefit paymentslinked to inflation may be provided to one class of participants and

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not others; this may happen, for example, as a result of corporatemergers.

The assumption that nominal pension benefits have no inflationsensitivity is most likely wishful thinking. Pensioners may be ableto tolerate small amounts of inflation (1–2%), but are unlikely to beable to adjust to sudden and prolonged bouts of much higher, say10%, inflation, simply because the fall in purchasing power undersuch a scenario becomes disruptive.As an extreme example, Germanhyperinflation in 1923 was particularly hard for those with savingsor living on fixed income, eg, pensioners.

In the US, it has been observed that pension plans have resortedto voluntary increases in benefits during periods of inflation. Non-formulaic one-time increases in private-sector pension plans wereprevalent in the inflationary period of 1978–81, when about 40% ofretired pension plan participants received increases (Schmitt 1984),and less so during the subsequent disinflationary period, when only6% did (Weinstein 1997). Presumably, no pension plan can providesuch benefits merely out of kindness: these are ultimately arrange-ments where the sponsor must step up to the plate in order tomake good on the pension promises, which ultimately are viewedby participants as a form of deferred compensation.

A BRIEF HISTORY OF INFLATIONARY PERIODS

While the spikes in inflation throughout the 1970s had perplexedinvestors and economists alike, the issue suddenly became ananachronism over the last two decades of the 20th century, wheninflation and volatility were both on a sustained downtrend. In theearly 2000s, however, lack of fiscal discipline in the developed worldeconomies, consumption growth in emerging markets and overalldemographic headwinds raised concerns about what may lie ahead.

During inflationary periods, all monetary obligations, includingwages and pension benefits, are affected by rising price levels. His-torical experience (from developed markets in the 1970s, and manyLatin American markets in the 1980s) shows that, once sufficientlyhigh price-change thresholds have been reached, most economicagents become concerned about inflation. Nazmi (1996, pp. 13–14)identifies indexation as typical of economies with chronically highinflation, which he defines as persistent double-digit inflation not

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Figure 17.1 Annual inflation rate in the US

25

20

15

10

5

0

–5

–15

–10

%

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Source: US Bureau of Labor Statistics.

exceeding 50%. Inflation can also feed further inflation, as index-ation removes the ability of a reduction in real cost of produc-tion, postpones the necessary adjustments and makes the economysusceptible to exogenous shocks (Durevall 1998).

Humankind has known inflation at least since records of pricesbegan. Often driven by local weather, prices of grain would fluctuate,driving the cost of living up and down, as costs associated withtransportation did not allow for substantial trade between areas withfood surpluses and deficits (see, for example, Fischer 1996, pp. 92–3).Another strong influence on price levels came from new discoveriesof precious metals, used as money through the expansion of moneysupply (Pettee 1936).

The “modern” period2 saw the establishment of central banksand monetary policy, and a shift in inflationary tendencies: weatherplays a diminished role due to robust logistical networks around theglobe, and the main drivers of inflation are now supply and demandof key commodities, labour costs and the activities of central banks.

During the 20th century, the key events that shaped public con-sciousness of inflation were the hyperinflationary period in Ger-many (1923), which gave the German Central Bank (the Bundesbank,established in 1957) and its effective successor, the European CentralBank (ECB), a permanently hawkish tone, the deflationary periodduring the Great Depression in the US (1930s) and the inflationarydecade of the 1970s in most Western countries.

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In each period, further damage came from misunderstandingthe root causes of inflation, and the flawed policy and monetarymedicines that were administered. Price controls existed in bothdeflationary (Shlaes 2007, p. 225) and inflationary (Rockoff 1984,pp. 92, 203) periods. In both cases, the result was an imbalance insupply and demand: unemployment in the 1930s and fuel shortagesin the 1970s.

Forecasting inflation also has a chequered history: many investorsexpected the return of deflation after World War II and, against manyprofessional financial projections (Scitovsky 1979), inflation was sub-dued after the 1970s, with the expectation of price stability pervad-ing the following decades, and only modest inflation since. Lookingforward, most investors would agree that it is unlikely for inflationto be negative over sustained periods of time. While, theoretically,inflation and deflation may both occur, central banks generally havea bias, if not an explicit target, towards a stable, low rate of pos-itive inflation. With explicit inflation targeting common in devel-oped countries, it is less likely that inflation will be allowed to growunchecked; most central banks have a specific mandate to maintainprice stability, and the effective tools to tackle inflation when needed.

HOW CHANGES IN LIABILITY AFFECT CONTRIBUTIONS

Fluctuations in the market value of assets and liabilities change thesurplus of pension funds.3 For example, based on the way pensionliabilities are discounted, a fully funded plan invested mainly in cashmight become underfunded if interest rates were to fall. But ratescould rise again in the future, reversing the underfunding. In otherwords, provided that these fluctuations are mean reverting, surplusvolatility should not particularly matter in the long run. The driversof surplus volatility are

• returns on asset pool,

• changes in liability discount rates,

• changes in liability cashflows, through COLAs and/or actuar-ial assumptions.

As mentioned earlier, pre-funding liabilities mitigates the risk ofwhether of not the company will actually meet its pension obli-gations in the future (in other words, the counterparty risk of

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the company). Furthermore, national legislation typically definesthe requirements for pre-funding, and accounting practices4 haveevolved to recognise unfunded parts of the pension fund on cor-porate balance sheets, as a form of implicit debt (Yermo 2007).In essence, these provisions take the pension funds close to fullmark-to-market accounting.

Liability-driven investing, which has gained traction in the US, theUK and many countries in continental Europe, is most commonlydefined as the practice of adjusting the investment policy of the assetpool to match the reference rates used to discount liabilities. The lia-bility discount rate has a sizeable impact on most plans’ surpluses,and therefore significantly affects the variance of future contribu-tions. Consequently, when the returns of the asset pool and changesin liability value are strongly correlated, the expected variance offuture contributions is reduced.

As illustrated by Table 17.2, the impact on actual contributions isa function of country and other considerations. While most coun-tries do not require immediate contributions when plans fall intodeficit, many sponsors may be sensitive to the impact on their bal-ance sheet through applicable accounting rules. This results in agreater focus on short-term movements in the surplus. Therefore,focusing on surplus volatility is the most efficient way of managingthe asset–liability mismatch of pension funds.

There has been a global debate about whether the discounting offuture cashflows should be done using a government curve, a swapcurve or a corporate bond curve. When liabilities are expressed notin nominal but in real terms (in other words, when they are indexedto inflation) the framework for determining fair value becomes evenmore complicated. The appropriate discount rate for credit-risk-freeinflation-adjusted liabilities is the government real rate curve, ie,the curve derived from inflation-indexed government securities.5

Of course, this is satisfactory only if the pension liabilities and thegovernment inflation-linked bonds are tied to the same index (forexample, the consumer price index (CPI) for US inflation). On thispoint, however, note that pension benefits are often closely relatedto wage growth.6

Because of the implementation of this mark-to-market frame-work, the major contributors to most plans’ surplus volatility arethe returns on the asset pool and changes in the liability discount

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INF

LA

TIO

N-S

EN

SIT

IVE

AS

SE

TS

Table 17.2 Private pension plans’ discount curve and other characteristics

Privatepension Discount Discountassets curve curve Deficit National

Country (US$ bn) (accounting) (funding) amortisation insurance

USA 2,121∗ Corporate AA Corporate A–AAAbonds

Usually 7 yr PBGC

UK 1,485∗∗ Corporate AA Trustees selectdiscount rate basis

Usually up to 10 yr PPF

Netherlands 1,079∗∗∗ High-qualitycorporate bond rate(IAS 19)

Euro-swap curve Usually up to 15 yr None

Canada 845 Yield on high-qualityfixed income

Commuted valueassumptions,depending onliabilities

5 yr; in some casesup to 15 yr

None∗

∗Ontario has one for the Province. PBGC, Pension Benefit Guarantee Corporation. PPF, Pension Protection Fund. Accounting curve: the discountrate used to determine the present value of liabilities in the financial statements of the sponsor. Funding curve: the discount rate used to determinethe present value of liabilities for assessing the required annual contribution under local pension regulation. Deficit amortisation: the period definedby local pension regulation as the maximum allowed for calculating the required annual contribution. For example, a seven-year amortisation meansthat any deficit must be funded in installments over seven years or less. National insurance: collective, typically government-sponsored, funds thatact as insurance for participants against insolvency of pension plans.Sources: ∗Halonen (2011), data as of December 31, 2010; ∗∗Pensions Protection Fund (2010); ∗∗∗OECD (2007).

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Table 17.3 Example: US private pension plan

Assets (US$ million) Liabilities (US$ million)

Equities 216 Present value 1,000

Fixed income 540 of liabilities

Alternatives 144

Total assets 900 Total liabilities 1,000

rate. These are also the most easily observable changes in real time,as actuarial calculations are usually done infrequently,7 and inflationindexes are typically released with a lag of several weeks or months.

MEASURING THE INTEREST RATE SENSITIVITY OFLIABILITIES

Most plans measure their sensitivity to changes in discount ratesusing interest rate duration. By calculating duration on both assetsand liabilities, we can use the difference (the duration gap) to esti-mate changes in the surplus based on various market scenarios. Mostplans are underweight in duration, which is to say that their liabili-ties have a substantially higher sensitivity to changes in interest ratesthan their assets do.

As an illustration, consider the example of a hypothetical US pen-sion plan that is 90% funded ($900/$1,000), and has 60% of liabilitieswhose cashflows are linked to CPI.8 The plan has also taken signifi-cant steps towards reduction of surplus volatility through durationoverlay strategies. The characteristics of this pension plan are shownin Table 17.3. The plan employs an interest rate swap overlay for anotional amount of US$540 million (60% of assets) with duration of8.7 years. Due to a recent merger of two corporate plans (one with fullindexation and one entirely nominal), 60% of pension liabilities areindexed to inflation through a COLA. The overall liability durationis 12.7 years. The resulting balance sheet is shown in Table 17.4.

The duration of assets is the sum of the weighted duration of equi-ties and fixed income securities, that is 8.2 years, while liabilities havea weighted duration of 14.1 years, leaving a negative duration gapof −5.9 years. In other words, a rise in interest rates is beneficial, asit decreases the amount by which the pension fund is underfunded.

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Table 17.4 Duration contributions

WeightedWeight Duration duration

(% of assets) (years) (years)

Equities 24 N/AFixed income 60 5 3.0Overlay 60 8.7 5.2Alternatives 16 N/ALiabilities∗ −111 12.7 −14.1

Total −5.9

∗Plan is 90% funded, and thus the liability expressed as a percentage ofassets is 1/0.90 = 111%.

MEASURING THE INFLATION SENSITIVITY OF LIABILITIES

Siegel and Waring (2004) suggested the use of “dual duration” tomeasure the sensitivity of a pension plan’s surplus to changes inboth interest rates and inflation. Their premise is that changes innominal interest rates are driven by changes in real rates or infla-tion expectations, or both. Depending on the nature of liabilities, theduration of each of these components may differ. Siegel and Waringuse the decomposition proposed by Fisher (1930, p. 39), where thenominal interest rate n can be expressed as the sum of the real rater and expected inflation iEXP for the period

n = r + iEXP (17.1)

Using this framework, we can distinguish between the sensitivityto changes in real rates r, and sensitivity to changes in expectedinflation iEXP.9 Using the pension plan in the previous section, thesensitivities of the assets, liabilities and the surplus are shown inTable 17.5.

This example highlights the difference in changes in the surplus,depending on whether the change is in the real curve or the inflationexpectations. Specifically, in this example, rising real rates (eg, higherdiscount rates at constant cashflows) are beneficial to the plan, asthey increase the surplus; conversely, a rise in inflation expectationsembedded in actuarial projections (at constant real rates) has theopposite effect, as part of the liability’s cashflows are indexed toinflation.

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Table 17.5 Real rate duration and inflation duration

Assets Liabilities Surplus

Weight (%) 100 111Real rate duration (years) 8.2 12.7 −5.9Inflation duration (years) 8.2 5.1∗ 2.6

∗That is 40% × 12.7 = 5.1 years, reflecting the liabilities not linked toinflation. We assume that there are no inflation-linked instruments amongthe assets.

The implications of contribution requirements for the plan are fur-ther complicated, as liabilities are marked-to-market using nominaldiscount rates, typically on a monthly basis, while a rise in inflationexpectations would be reflected through actuarial cash projectionson a less frequent basis (typically a few times per year). In additionto delays, actuarial assumptions often include further lags due tosmoothing assumptions.

Using cashflow (inflation) duration also assumes that there is thesame change in inflation expectations for all terms across the yieldcurve (this “parallel shift” assumption is common to all durationmeasures). Finally, meaningful changes in inflation and interest rateswill typically not happen without some attendant changes in the val-uation of other asset classes. As a result of the complex interrelationof equity returns, spreads, interest rates and inflation, the durationmeasure is a useful, but by no means comprehensive, measure ofrisk.

RISK BUDGETING

Sensitivity measures such as duration are useful in evaluatingexpected changes in surplus given changes in a single market vari-able. An alternative, and more comprehensive, measure is volatil-ity or, in the case of pension funds, volatility of the pension sur-plus. To estimate surplus volatility, most plans use a covariancematrix, derived from historical data, forward-looking views or somecombination of the two.

By obtaining an estimate for both surplus volatility and requiredreturn on surplus, we can set up an optimisation problem. Specif-ically, using modern portfolio theory, it is possible to seek optimalallocations of assets in order to minimise surplus volatility, under

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Table 17.6 Modelling assets and liabilities with proxy index

Wt Vol.Asset class Proxy index (%) (%)

Equity S&P 500 24 16Fixed income BarCap US Aggregate 60 4Alternatives DJ/CSFB Hedge Funds Index 16 8Liabilities BarCap US Long Corporate A− and higher −111 9Overlay BarCap 10-year Swap Bellwether 60 8

the constraint of achieving the return required for the plan. Theresulting optimal allocation strategy is usually called a risk bud-get. As inferred by the name, a risk budget is meant to help pensionplan managers allocate a scarce resource, surplus risk, across vari-ous investments. A typical way of analysing the risk budget is riskdecomposition, which is the process of estimating the contributionto surplus variance arising from each investment. If ω denotes therow vector of weights for each asset in the portfolio, and Σ denotesthe covariance matrix, we can calculate the overall variance of thesurplus (Litterman et al 2003) as

σ 2 =ωΣωT

(the superscript “T” indicates transposition). We can then decom-pose the overall variance into each individual asset’s contributions.LettingΣi denote the ith row in the covariance matrix andσ 2 denotethe portfolio variance, the percentage contribution to the overallvariance for asset i is

ωiΣiωT

σ 2 (17.2)

Risk budgeting can be expanded to include liabilities, in whichcase the total volatility estimated through the covariance matrixrepresents surplus volatility.

As a numerical example, we consider the pension plan of the pre-vious sections, and use proxy index benchmarks for both assets andliabilities, as detailed in Table 17.6. Our interest rate assumptions areas follows.

(i) The pension plan’s liabilities are represented by the BarclaysCapital US Long Corporate A− and higher, with a nominalduration of 12.7 years (as before).

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Table 17.7 Correlation matrix

Equity Fixed income Alternatives Liabilities Overlay

1.0 0.1 0.6 0.2 −0.10.1 1.0 0.2 0.9 0.90.6 0.2 1.0 0.2 0.00.2 0.9 0.2 1.0 0.7−0.1 0.9 0.0 0.7 1.0

Table 17.8 Surplus variance decomposition

VarianceWeight (%) decomposition (%)

Equities 24 25Fixed income 60 −11Overlay 60 −13Alternatives 16 4Liabilities −111 95

Total 100

Table 17.9 Variance decomposition

Variance VarianceReturn-seeking contribution Liabilities contributionassets (%) and hedges (%)

Equities∗ 25 Liabilities 95Alternatives 4 Fixed income −11

Overlay −13

Total 29 Total 71

∗Given that the liability proxy consists of corporate bonds, positive cor-relation between equities and corporate bonds reduces the contributionto risk attributable to equities. If a Treasury index had been used to proxyliabilities, equities and alternatives would have contributed a further 48%to total surplus variance.

(ii) The fixed income assets are invested in the Barclays CapitalUS Aggregate Index, which has a duration of five years.10

(iii) The interest rate overlay can be modelled using the BarclaysCapital 10-year Swap Bellwether Index.

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By using the appropriate covariance matrix (Table 17.7), we can cal-culate the total surplus volatility, expressed as a percentage of assetsor in US dollar terms. For our example, we obtain an overall volatilityσ = 6%, or about US$54 million (the assets’ value is US$900 million).

The next step is to decompose the overall portfolio variance intoits individual contributions, based on Equation 17.2 (Table 17.8). Asit is clear from this risk decomposition, the largest influence on thetotal surplus variance comes from the liabilities (Table 17.9). Nega-tive contributions to risk, from the fixed income sector (−11%) andthe interest rate overlay (−13%), are a result of their being hedgingassets, or, in other words, assets highly correlated with the liabilities,thus reducing overall volatility.

It is useful to consider each asset and investment as either a return-seeking asset or a liability-hedging asset. Return-seeking assets(equities and alternatives in our example), which typically do nothedge liabilities, provide an opportunity for additional returns inexchange for higher risk. Conversely, liability-hedging assets (fixedincome and the interest rate overlay in our example) reduce surplusvolatility, but their expected return might be less attractive comparedwith the liability discount rate.

With this type of analysis, risk managers can refine their allo-cation process, reduce unwanted risks and optimally allocate theirrisk budget and capital to asset classes, in line with the goals of thepension fund. For underfunded plans, this may mean increasingallocation to return-seeking assets, at the expense of hedging assets,thus increasing the overall surplus volatility. For fully funded plans,especially the ones that are closed to new entrants, the plan’s objec-tives may be best served by closely matching assets and liabilities,and by minimising surplus volatility.

FROM ASSET-CLASS MODELS TO FACTOR MODELSEach of the asset classes considered in the risk budgeting analysisabove is sensitive to several risk factors, including interest rates,inflation and equity. Some sectors embody one risk factor in partic-ular (eg, US Treasuries have interest rate and inflation risk; commonshares mainly have equity risk), while others present a more com-plex combination of sensitivities (eg, convertible bonds are sensi-tive to interest rates, inflation, volatility, equity prices and corporatespreads).

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Traditional approaches to asset allocation tend to focus on assetclasses, but many of these asset classes are highly correlated becausethey contain similar risks. For example, US and Japanese equities areoften considered to be different asset classes but, in reality, they arehighly correlated, especially after adjusting for currency risk. Conse-quently, optimisation techniques become unstable, as each asset classis a perfect substitute for another, apart from return assumptions. Inother words, small differences in return expectations substantiallychange the outcome of the optimisation.

Factors, on the other hand, can be designed to be nearly orthog-onal, and often have a more stable correlation structure thanasset classes. Taborsky and Page (2010) illustrate this through asimulation where asset-class cross-correlation is compared withcross-correlation of factors during “turbulent” and “quiet” marketregimes. Correlations of asset classes were higher during “turbu-lent” market regimes, whereas factor correlations tended to exhibitlower correlation under both regimes separately, and also for thecomplete data sample.

Factor-based analysis can also diagnose the source of surplusvolatility more precisely. In many cases, the equity risk premiumplays a larger role in pension plan surplus volatility than wouldbe anticipated from looking at market values of each asset classalone. Expanding on the pension plan example presented earlier,the following three factors are chosen for the risk decomposition.

1. An equity risk factor: the total return of the S&P 500 index willbe used a proxy.

2. A (swap-like) duration risk factor, representing sensitivity tonominal interest rates: the total return volatility per unit dura-tion of the Barclays Capital 10-year Swap Bellwether Index willbe used as a proxy.

3. Acorporate risk factor: the excess return of the Barclays CapitalCorporate Index over comparable maturity Treasuries will beused as a proxy.

Using these factors, we can disaggregate each of the asset classesinto factor exposures. Inflation risk is not explicitly considered at thisstage, but it will be discussed in detail in the next section. The resultsfrom regressing asset-class returns versus risk factors are shown

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Table 17.10 Risk factor loadings by asset class

Equities∗︷ ︸︸ ︷Coefficients t -stat.

Intercept 0.0 N/ADuration risk∗∗ 0.0 N/ACorporate risk 0.0 N/AEquity risk (S&P 500) 1.0 N/A

R2 N/A

Fixed income︷ ︸︸ ︷Coefficients t -stat.

Intercept 0.0 10.6Duration risk∗∗ 3.8 56.5Corporate risk 0.3 16.8Equity risk (S&P 500) N/A N/A

R2 0.9

Alternatives︷ ︸︸ ︷Coefficients t -stat.

Intercept 0.0 4.0Duration risk∗∗ 0.9 1.9Corporate risk 0.5 4.0Equity risk (S&P 500) 0.2 6.8

R2 0.4

Liabilities︷ ︸︸ ︷Coefficients t -stat.

Intercept 0.0 −0.6Duration risk∗∗ 7.9 33.3Corporate risk 1.1 21.0Equity risk (S&P 500) N/A N/A

R2 0.9

∗Since both the equity asset class and the equity risk factor are defined bythe S&P 500, the factor loading is 1.0.∗∗Duration risk is expressed as unitof volatility per year of duration. Hence, the coefficient value approximatesthe duration of the asset.

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Table 17.11 Risk factor loadings for the pension fund’s surplus

Risk factor loadingsAssets and ︷ ︸︸ ︷liabilities Weight (%) Equity Duration Corporate

Equities 24 1.0 0.0 0.0Fixed income 60 0.0 3.8 0.3Overlay 60 0.0 8.7 0.0Alternatives 16 0.2 0.9 0.5Liabilities −111 0.0 7.9 1.1Surplus −11 0.3 −1.2 −1.0

Table 17.12 Risk factor correlation matrix

Equity Duration Corporate

1.0 −0.1 0.5−0.1 1.0 −0.3

0.5 −0.3 1.0

in Table 17.10. Note that the intercepts are, in most cases, statisti-cally indistinguishable from zero. The swap overlay is not shown inTable 17.10, since, by virtue of our choice of factors, it will have anon-zero loading to duration risk only, as displayed in Table 17.11.Based on the risk factor loadings and the weights of assets and liabil-ities, we can assess the factor exposures of the pension fund surplus(Table 17.11).

After deriving the covariance matrix for the three factors (Table17.12), we calculate the overall volatility of the surplus,11 as well asthe variance decomposition and risk contribution from each factor(Table 17.13). The variance decomposition by factor offers a unifiedapproach to examining the underlying risks within each asset classas well as in the overall portfolio or pension fund surplus.

Most notably, the corporate spread risk factor now plays a promi-nent role, highlighting the mismatch between the asset side (wherethe Barclays Capital Aggregate Index used as a proxy contains lim-ited corporate exposure) and the liability side, where the large factorloading arises from the corporate curve used for discounting. As aresult, the surplus benefits from a widening in credit spreads. Thisis also the reason why the duration loading of the surplus at −1.2 is

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Table 17.13 Variance decomposition by risk factor and factor-modelsurplus volatility

VarianceRisk factor Loading decomposition (%)

Equity 0.3 47Duration −1.2 3Corporate −1.0 50

Total 100

Factor-model surplus volatility 4

less in absolute value than that found when analysing risk by assetclass, as the negative duration is now split between the (swap-like)duration factor and the corporate risk factor.

Further insight comes from comparing the correlation structuresof asset classes versus risk factors. While equities and liabilitieswere previously positively correlated (Table 17.7), risk factor analy-sis breaks this (as seen in Table 17.12) into a negative correlationbetween equity risk and interest rate duration (ie, falling equityprices often coincide with rising swap prices) and a positive correla-tion between equity returns and corporate bonds’ excess returns (ie,equities drop when corporate bond prices fall in relation to treasurybonds).

Risk factor analysis can provide considerable insight on the riskand return drivers of any portfolio. As usual, the selection of factorsand the empirical data (or implicit views) used for estimation willhave an important effect on the covariance matrix and model outputsand thus need to be scrutinised in detail.

MODELLING INFLATION IN A FACTOR FRAMEWORK

The factor framework is useful for modelling risk factors that influ-ence the performance of several asset classes. Inflation is an exam-ple of such a factor. Factor or asset-class volatility models typicallyuse nominal returns and volatilities as inputs. Inflation is thereforerepresented as a static expectation contributing to asset-class returns.

One approach to addressing inflation explicitly is to move fromthe nominal to the real return space, which would include deriving

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Table 17.14 Excess inflation: summary statistics for total sample(1947–2011)

Mean (%) −0.3Standard deviation (%) 1.5t-statistic −2.2Observations 129

Excess inflation is equal to the annualised realised inflation (over asemester) minus the survey’s median from the previous semester. Thet-statistics indicate that the sample mean is statistically different from zero.

an inflation-adjusted covariance matrix. This may pose some com-putational issues, as inflation data is published with a lag and lessfrequently than market prices, which can be observed in real time.Moreover, this may limit the ability to rely on third-party vendors formarket return data series, as these are almost invariably calculatedin nominal terms.

Another way to go about this is to include a new variable: unantici-pated or excess inflation, which would represent inflation in excess ofany actuarial assumptions. According to the Fisher equation (Equa-tion 17.1), most asset classes embed some level of expected infla-tion iEXP in their price; in other words, their market value is derivedby discounting future cashflows using a nominal curve. Since bothactuarial projections (used for cashflow projections) and nominaldiscount curves already include an inflation assumption, the onlyremaining issue for pension plans is the effect of excess inflation overthe relevant (typically long-term) time horizon. In practice, thingsare not so simple, as market prices (ie, discount curves) adjust inreal time, while the actuarial assumptions used to estimate futureliabilities’ cashflows do not.

With the advent of the inflation-linked bond market, we havea market-based measure of expected inflation (for different tenorsacross the term structure), also known as break-even inflation.

For example, the 10-year US Treasury Inflation-Protected Secu-rities (TIPS) break-even, a measure of long-term inflation expecta-tions, has ranged from 0.1% to 2.7% (Figure 17.2). One drawback ofthese market-based measures is the short history of the data series,which, in particular, does not contain any period of high inflation(US TIPS were first issued in 1997). In addition, there is evidenceof a substantial liquidity premium affecting break-even inflation in

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Figure 17.2 Break-even Inflation for the 10-year US TIPS

3.0

2.5

2.0

1.5

1.0

0

0.5

%

Jan

4, 1

999

Jan

4, 2

000

Jan

4, 2

001

Jan

4, 2

010

Jan

4, 2

011

Jan

4, 2

002

Jan

4, 2

003

Jan

4, 2

004

Jan

4, 2

005

Jan

4, 2

006

Jan

4, 2

007

Jan

4, 2

008

Jan

4, 2

009

Source: Bloomberg.

the US, at least for the first few years since first issuance (becauseof this, inflation break-evens are likely to underestimate inflationexpectations in at least part of the period considered).

It is possible to extend these market-based time series back in timefor more meaningful historical comparisons, although the meth-ods used to do this will introduce their own bias. One option is touse information from publicly available inflation surveys (althoughthese surveys typically poll expectations over a short time horizon:six months in the following analysis).

In Tables 17.14 and 17.15, we look at the excess inflation seriesderived as the difference between actual realised inflation rates andinflation expectations. The latter are measured by the median ofthe Livingston Survey (specifically, the median of the semi-annualsurvey is used as an estimate of inflation expectations for the nextsix months).12

It should be noted that the data shows two very different periods:during 1947 to 1974, the surveyed economists persistently under-estimated inflation (on average by 0.5%), whereas between 1975 and2011, economists persistently overestimated inflation (on averageby 0.9%).

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Table 17.15 Excess inflation: subsamples’ summary statistics

Sample︷ ︸︸ ︷1947–1974 1975–2011

Mean (%) 0.5 −0.9

Standard deviation (%) 1.5 1.3

t-statistic 2.3 −6.0

Observations 57 72

Table 17.16 Factor volatilities and correlation matrix

Annualised Excessvolatility (%) Equity Duration Corporate inflation

Equity 16 1 −0.1 0.5 −0.1

Duration 1 −0.1 1 −0.3 −0.4

Corporate 4 0.5 −0.3 1 0.2

Excess inflation 2 −0.1 −0.4 0.2 1

Adding excess inflation to the factor model described earlier,13 wederive the correlation and volatility estimates shown in Table 17.16.

In order to estimate the factor exposures, we need to determinethe relationship between the inflation factor and the pension plan’sassets and liabilities. To this end, we use the concept of inflationduration. In the previous pension plan example, 60% of benefitscashflows were explicitly linked to consumer price changes. In prac-tice, this means that liability valuations will depend on cashflowestimates based on actuarial assumptions of long-term inflation.Whether an inflation surprise today will cause a change in long-term inflation expectations, and thus actuarial assumptions and/or long-term discount rates, will be a function of several factors. Ifthe inflationary surprise turns out to be a one-time event, expecta-tions may stay anchored, and the consequent impact on actuarialassumptions, long-term discount rates and the value of liabilitiesmay be limited. A study by Gürkaynack et al (2006), found that, inthe US, the relationship between an inflation surprise and change inlong-term expectations was mostly relevant when the surprise waslarge.

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Table 17.17 Risk factor loadings and variance decomposition

VarianceLoading decomposition (%)

Equity 0.3 42Duration −0.8 −1Corporate −1.5 46Excess inflation −0.8 13

Total 100

Regressing the excess inflation series against changes in 10-year nominal Treasury yields (as a measure of long-term inflationexpectations),14 we find that a 1% inflation surprise moves the 10-year nominal yield by 10 basis points. In other words, the excessinflation factor loading (as a percentage of assets) is equal to theproduct of

• the regression coefficient (+0.1) linking short-term surveyexpectations of inflation to long-term actuarial assumptionsfor inflation,

• the duration of the share of liabilities whose cashflows arelinked to inflation, ie, 60%× 12.7 = 7.6 years,

• the liabilities’ weight as a percentage of assets, ie, −111%.

In detail

excess inflation factor loading = −111%× 0.1× 60%× 12.7

= −0.8

Our convention for the sign should be interpreted as implying adecrease in the surplus as a result of an increase in inflation.

Next, the total variance of the pension fund can be decomposedinto the four risk factors, one representing excess inflation. Theresults are shown in Table 17.17 (cf. Table 17.13).

Inflation may indeed become an issue for pension funds. Fromthe standpoint of risk budgeting, inflation may not rank as high asother risks in the plan; most pension plans have large exposure toequity risk. However, inflation risk, and relevant hedging strategies,should be explicitly analysed, especially if a material percentage ofliabilities, but few or no assets, are indexed to inflation (similarly toour example).

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Finally, variance-based models, such as the one described here,may underestimate the impact of tail events, especially if the latterare not represented in the historical data set. Indeed, mitigating therisk of such events should be a critical consideration, often moreimportant than trying to hedge against small and less consequentialchanges in inflation.

INVESTMENT STRATEGIES

Unlike liability-matching strategies employing nominal interestrates, where instruments are widely available, finding matchingassets for unanticipated inflation is not straightforward. Many assetsprovide compensation for anticipated inflation (eg, nominal bonds),but few have explicit hedging properties against unanticipated(excess) inflation. With the exception of instruments that are con-tractually linked to inflation, most other assets include a substantialamount of basis risk. In the following, we shall consider the dif-ferent asset classes that are most commonly thought of as havinginflation-hedging characteristics. These include

• government-issued inflation-linked bonds,

• inflation derivatives,

• public and private real estate, as well as other real assets,

• commodities,

• equities.

One of the challenges for the inflation market has always beenthat few natural sellers of inflation-hedging instruments exist, whiledemand for inflation assets is definitely growing. In Mercer Con-sulting (2011), 80% of pension plans in Europe view inflation as amajor concern. The predominant investment vehicles for these plansare inflation-linked bonds (18% of respondents), followed by otherinvestments, such as commodities and real estate (12%). Europeanplans on average hold 3–9% in real estate, depending on the sizeof the plan. In comparison, the average plan has only 1.8% in com-modities, with only 7.5% of European funds investing in this assetclass.

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Table 17.18 Government-issued inflation-linked bonds in selectedcountries

Outstanding notional Issuance in 2010Country (US$ bn) (US$ bn)

France 213 28Italy 146 21Germany 62 15Greece 21 0US 568 92UK 260 50Japan 55 0Sweden 28 1Canada 30 2

Total 1,384 209

Entries have been rounded.Source: BNP Paribas.

Government issued inflation-linked bondsInflation-linked bonds are issued by many developed countries (seeTable 17.18 for a snapshot of major markets), as well as severalemerging market countries. At the time of writing, the outstandingstock of developed market issuance is approximately US$1.4 trillion.Compared with the size of total government bond markets in thesecountries, inflation-linked bonds represent only 6% of total notional.In essence, while Treasury inflation-linked bonds are ideal hedginginstruments, the existing stock is likely to be too small to satisfydemand, especially if concerns about inflation become widespread.

In addition, inflation-linked bonds have, from time to time, carriednegative real yields, which may be the result of scarcity of issuance.Using instruments with negative real yields to hedge liabilities maybe too expensive, since there is no certainty that inflation will riseto levels where it would endanger the solvency of a pension plan.Another challenge for pension funds is that inflation sensitivity ofinflation-linked bonds is typically related to overall consumer prices,whereas pension liabilities tend to have specific sensitivity to wageinflation.

Use of inflation-linked bonds in pension funds is widespread;however, each country has differing levels of adoption. In the US,the largest holders have traditionally been mutual funds, rather than

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pension funds; state and other public pension funds have been thelargest pension investors, given their direct indexation of liabilities.In continental Europe, one of the potentially largest markets is theDutch pension market, given that their existing inflation-linked lia-bilities remain largely unhedged. In the UK, where inflation-linkedbonds are well established, approximately one-third of the existingstock is held by pension funds, and another third is held by insur-ance companies (Barclays Capital 2010). Trends in pension buyoutsin the early 2000s have also increased demand, as buyers of liabilitiesseek to hedge their exposures.

Inflation derivativesInflation derivatives can offer more tailored protection against infla-tion. The market has grown rapidly, especially in Europe, and hasmatured over time. The inflation derivatives market can be dividedinto three basic instruments:

1. inflation futures;

2. inflation swaps;

3. inflation options (such as caps and floors).

Futures markets in inflation have struggled around the globe. Inthe US, the most recent attempt was the CPI-linked futures contractlaunched in 2004, which subsequently ceased to trade given the lackof demand.15 The European Harmonised Index of Consumer Prices(HICP) futures are traded at both the Chicago Mercantile Exchange(CME) and the Eurex, but volumes have been virtually non-existentbetween 2009 and the time of writing.

The swap and option markets, on the other hand, have flourished.In the US, there has been demand for inflation total-return swaps,and option volumes have been rising substantially (Figure 17.3).Because of their customisable nature, inflation derivatives probablyhold the greatest promise for the pension industry.

Option strategies could also turn out to be the most efficient wayto hedge against tail risks in inflation. Traditional tail-risk hedg-ing strategies such as out-of-the-money equity puts, collars andput-spread collars can now be implemented using inflation optionsinstead. It should be noted that some of these strategies can getvery complex and, given the relatively recent introduction of infla-tion derivatives, for most institutional investors they may require areliance on outside expertise.

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Figure 17.3 Number of inflation options traded in the US

8

7

6

5

4

3

2

1

0

Infla

tion

optio

ns (

thou

sand

s)

2008 2009 2010

460

1,365

7,225

Source: BNP Paribas.

Arising inflation environment is likely to boost the appeal of thesestrategies, albeit the inherent complexities hinder their widespreadadoption. These growing pains are similar to those experienced inthe credit default derivatives market, which began in obscurity buthas subsequently become an integral, if at times controversial, partof the derivatives market.

Public and private real estate and other real assetsPublic and private real estate are often considered “real assets”, andtherefore expected to perform well during periods of unanticipatedinflation. Most real estate investments by pension funds take theform of either listed real estate (eg, Real Estate Investment Trusts(REITs)), or private real estate funds. Given that REITs trade on stockexchanges and resemble listed equities, they tend to have a relativelyhigh correlation with equity investments. For example, in the periodfrom March 1981 to March 2011, US REITs had a correlation of 55%with the S&P 500 index, and a correlation as high as 74% with theRussell 2000 value (NAREIT 2011).

Fama and Schwert (1977) found that private real estate is the onlyasset that provides protection against unanticipated inflation. Theexperience in 2008 in both the residential and commercial real estatemarkets demonstrated, however, that this asset class is susceptible toperiodic over- and under-valuation (Figure 17.4). In addition, privatereal estate investments tend to be illiquid, which creates challenges,particularly for plans that are nearing the end of their life cycle.

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Figure 17.4 US residential home prices versus consumer prices

Case–Schiller CPI-U

5

–5

0

10

–10

–15

–25

–20

15

25

20

%

Jan

1988

Jan

1989

Jan

1990

Jan

1991

Jan

1992

Jan

1993

Jan

1994

Jan

1995

Jan

1996

Jan

1997

Jan

1998

Jan

1999

Jan

2000

Jan

2001

Jan

2002

Jan

2003

Jan

2004

Jan

2005

Jan

2006

Jan

2007

Jan

2008

Jan

2009

Jan

2010

Source: S&P Case–Shiller Indexes, Bureau of Labor Statistics.

Rebalancing the portfolio, for example, may be nearly impossible ifprivate real estate assets make up a large part of a pension fund’sassets.

While most countries do not have specific limits on investmentsin real estate for pension funds (OECD Secretariat 2009), their alloca-tions have tended to be relatively small. In the Netherlands, overallallocation to real estate is less than 1.3% for the pension sector (DeNederlandsche Bank 2010); comparable figures are 6% in the UK(Kutsch and Lizieri 2005) and 1.2% in the US16. In some countries,investments in real estate are part of most pension funds; for exam-ple, real estate makes up between 5% and 10% of total assets inSwitzerland, Portugal, Finland, Canada and Australia (OECD 2011).

CommoditiesCommodities are considered to be one of the natural hedges againstinflation. Commodity markets are large and liquid, with annual trad-ing volume of the 24 commodities in the S&P Goldman Sachs Com-modity Index (GSCI) totalling over US$56 trillion (Standard & Poor’s2011). While physical commodities are cumbersome to trade, storeand transport, financial contracts linked to commodity prices arewidely available in the form of futures, swaps, options, exchange-traded funds and structured notes. Since most market participants

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do not typically hold physical commodities, investment returnsare different from changes in spot prices. Specifically, Greer (2000)divides the return of the commodities futures into the followingcomponents:

• the real rate of return;

• expected inflation;

• unexpected inflation;

• producers’ insurance premium;

• rebalancing yield.

As can be seen from this decomposition, excess or unanticipatedinflation can be considered part of the commodity contract return.Commodities should therefore function as an effective hedge againstinflation surprises. Greer found that, using asset-class data from 1970to 1999, correlation of commodities to changes in inflation was ashigh as 57%, whereas both stocks and bonds exhibited a similar levelof negative correlation (−53% and −51%, respectively). Commod-ity prices are also one of the typical causes of cost-push inflation,and therefore should be an effective hedge for tail risks like the oilembargo in the 1970s.

The challenge for pension plans arises from the fact that, in addi-tion to inflation, commodity prices are also influenced by many otherfactors. Long-run S&P GSCI monthly data from 1970 to 2011 suggeststhat annualised commodity returns (measured by changes in spotrates) were 4.8% on average, compared with a sample average annu-alised inflation rate of 4.4%. However, using an even longer data set,commodity returns were in fact sharply negative over the 20th cen-tury, declining up to 50% against consumer prices during the sameperiod (Reserve Bank of Australia 2007). The underperformance incommodity prices was driven by many factors, including improve-ment in extraction techniques, discoveries of new sources of energycommodities and enhancements in agricultural productivity. How-ever, some believe that, with the rapid growth of the world’s popu-lation, in particular in the emerging markets countries, commoditiesare entering a period of secular rise. For example, Grantham (2011)identifies 24 commodities that are at least two standard deviationsaway from their previous declining trend.

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Data suggests that commodity investments by pension funds arequite small. While some prominent investors have entered the mar-ket, most pension plans do not have allocations to commodities. Inthe US in 2007, the California Public Employees’ Retirement System(CalPERS) had 3% of its US$207 billion of assets in commodities;Hermes, in the UK, and Algemeen Burgerlijk Pensioenfonds (ABP),in the Netherlands, had similar allocations (Doyle et al 2007). A sur-vey of managers by Towers Watson (2010) suggests that the top 100alternatives managers combined only managed US$20 billion forpension fund clients. Given that global pension assets amount toabout US$26 trillion at the time of writing, this indicates that mostpension funds do not have meaningful exposure to commodities asan asset class.

Equities

Equities are held as an investment by most pension plans. Glob-ally, in 2011, 47% of total pensions assets were in equity investments(Towers Watson 2011). The objective for equity investments is typ-ically to provide higher returns, at the cost of increased surplusvolatility. Historically, the equity risk premium, or return above therisk-free rate, has been on average (geometric mean measured overTreasury bills) 5.8% (Dimson et al 2002, p. 165).

In addition to the attractive returns, allocation to equities has alsotraditionally been considered a (partial) hedge against inflation. Ris-ing prices should, in theory, filter into rising revenues for corpora-tions and therefore provide a natural hedge against inflation. In prac-tice, however, companies are often unable to pass rising raw materialprices on to consumers directly, resulting in erosion of profit margins(Bulthaupt 2004). An example of this dynamic can be found in therelationship between equity prices and inflation during the 1970s,when high inflation was concurrent with poor equity performance(Figure 17.5).

Since the 1970s, significant empirical evidence has accumulatedagainst the efficacy of stocks as inflation hedges. Bodie (1976), forexample, concludes that if stocks have inflation-hedging proper-ties, they actually appear to contradict what is commonly thought;therefore, to use them as a hedge would require going short.

Lastly, equities are likely to have poor hedging properties againstinflation tail risks. A large, unexpected increase in inflation will not

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Figure 17.5 US stock performance and consumer prices in the 1970s

0

50

40

30

20

10

S&P 500 CPI-U

Dec

1, 1

969

Dec

1, 1

970

Dec

1, 1

971

Dec

1, 1

972

Dec

1, 1

973

Dec

1, 1

974

Dec

1, 1

975

Dec

1, 1

976

Dec

1, 1

977

Dec

1, 1

978

Dec

1, 1

979

Jun

1, 1

970

Jun

1, 1

971

Jun

1, 1

972

Jun

1, 1

973

Jun

1, 1

974

Jun

1, 1

975

Jun

1, 1

976

Jun

1, 1

977

Jun

1, 1

978

Jun

1, 1

979

Source: Bloomberg.

only put pressure on earnings but also create uncertainties, and thusincrease the equity risk premium, setting the stage for poor equityperformance.

However, it should be noted that, while equities as an assetclass are not an effective inflation hedge, there may be specificequity sectors with better inflation-hedging properties. Examplescould include commodity producers, such as gold mines, or essen-tial utilities, such as sewer and electricity generators. Investorscould conceivably create baskets of equity securities in multipleinflation-sensitive industries, in order to reduce business cycleeffects.

CONCLUSIONS

Whether inflation is a material risk for a pension plan is largely deter-mined by its specific circumstances. The hedging of nominal liabili-ties, which has been a substantial trend in the industry since the mid2000s, has relied on the easily identifiable duration gap betweenassets and liabilities. Analysing inflation sensitivity of the plans inthe same way is much more difficult, given the complexities asso-ciated with both actuarial assumptions and the estimation of theinflation sensitivity of the underlying investments.

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Considering hedges for inflation risk makes sense, but, given theintrinsic uncertainty associated with estimating the sensitivity toinflation, a partial hedge might be a more practical trade-off. Fur-thermore, the hedge instruments directly linked to inflation, suchas inflation-linked bonds or derivatives, can often be costly, as thereare few natural sellers of inflation protection. For others, basis riskcan be substantial. The latter, however, can be mitigated by diversi-fication, ie, by employing several of the inflation-hedging strategiesat once as a way of reducing the idiosyncratic risk arising from eachasset class.

Lastly, pension plans should be concerned about inflation tail risk.While the implications of moderate inflation are not dire to eitherthe plan sponsors or the pension beneficiaries, substantial and pro-tracted inflation, similar to that experienced in the 1970s, could havea large negative influence on pension funds’ solvency ratios and theirability to meet their obligations.

1 The plan sponsor is the entity establishing the pension programme. It might be a State or localgovernment entity, or a private corporation.

2 Effectively the 20th century, although some central banks did come into existence earlier thanthis.

3 Surplus is equal to the market value of assets minus the market value of liabilities.

4 For example, the US Generally Accepted Accounting Principles (GAAP) and the InternationalAccounting Standards (IAS).

5 See, for example, the discussion on UK public pension discount practices in Ralfe (2011).

6 For a detailed study on relationship of wage growth and price inflation, see, for example,Hess and Schweitzer (2000).

7 Annually in the US and once every three years in the UK.

8 While the pension plan data used here for illustration is based on an actual plan, we havemade many simplifying assumptions. In the actual case, asset classes are represented with ahigher degree of granularity and the relationship between the plan’s liability and inflation issubstantially more complex. We have used proxy benchmarks to represent both assets andliabilities in the illustrative calculations. The size of the pension fund liability is changed toUS$1 billion for illustrative purposes.

9 Of course, we might pick a different pair of variables (nominal rates and inflation, or nominalrates and real rates). For example, in the section discussing the modelling of inflation in a factorframework (page 406), we shall work with nominal rate duration (swap rates discounting)and inflation.

10 Duration estimates for the indexes are based on information from Barclays Capital as ofMarch 31, 2011.

11 This volatility turns out to equal 4% of the asset value per annum, or about US$36 millionper year. It should be noted that, given the more granular approach, the liability risk appearsslightly smaller than that using the asset-class-based approach. This is an illustration of howdifferent covariance matrices may lead to shifts in relative contributions, and overall risk, indifferent models.

12 See http://www.philadelphiafed.org/ for details on this inflation survey.

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13 Data used to estimate factor correlation and volatility for the equity, duration and corporatespread factors represents a shorter period than that used for excess inflation. We have usedmonthly data from January 1994 to the end of December 2010 for the overall factor model,and augmented it with excess inflation using semi-annual data from January 1972 to the endof December 2010.

14 We could have used the 10-year US TIPS inflation break-even instead. We elected to use thenominal Treasury yield in order to avoid the issues with limited data and technical liquiditydistortions in the US TIPS market.

15 Previous attempts to establish the inflation futures include, for example, the CPI futureslaunched in 1985 by New York’s Coffee, Sugar and Cocoa Exchange.

16 See OECD Global Pension Statistics data at http://www.oecd.org/daf/pensions/gps.

REFERENCES

Barclays Capital, 2010, “Global Inflation-Linked Products: A User’s Guide”, BarclaysCapital Inflation-Linked Research, March.

Bodie, Z., 1976, “Common Stocks as a Hedge against Inflation”, The Journal of Finance 31(2)pp. 459–70.

Bulthaupt, F., 2004, “Inflation and Equity Prices”, Economy & Markets, Dresdner Bank,Report 07-08/2004.

Davis, E. P., 2000, “Regulation of Private Pensions: A Case Study of the UK”, DiscussionPaper PI-0009, The Pensions Institute, July, p. 20, URL: http://www.ephilipdavis.com/wp0009.pdf.

De Nederlandsche Bank, 2010, “Macro-Economische Statistiek Pensioenfondsen, Q4/2010”, URL: http://www.statistics.dnb.nl/popup.cgi?/usr/statistics/excel/t8.1nk.xls.

Dimson, E., P. Marsh and M. Staunton, 2002, Triumph of the Optimists: 101 Years of GlobalInvestment Returns (Princeton University Press).

Doyle, E., J. Hill and I. Jack, 2007, “Growth in Commodity Investment: Risks and Chal-lenges for Commodity Market Participants”, FSA Markets Infrastructure Department,March.

Durevall, D., 1998, “Inertial Inflation, Indexation and Price Stickiness: Evidence fromBrazil”, Working Papers in Economics, No. 8, School of Economics and Commercial Law,Goteborg University.

Fama, E., and W. Schwert, 1977, “Asset Returns and Inflation”, Journal of FinancialEconomics 5, pp. 115–46.

Fischer, D., 1996, The Great Wave (Oxford University Press).

Fisher, I., 1930, The Theory of Interest: As Determined by Impatience to Spend Income andOpportunity to Invest It (Philadelphia, PA: Porcupine Press, Reprint, 1977).

Grantham, J., 2011, “Time to Wake Up: Days of Abundant Resources and Falling PricesAre Over Forever”, GMO Quarterly Letter, April.

Greer, R., 2000, “The Nature of Commodity Index Returns”, The Journal of AlternativeInvestments, Summer, pp. 45–53.

Gürkaynack, R., A. Levin and E. Swanson, 2006, “Does Inflation Targeting Anchor Long-Run Inflation Expectation? Evidence from Long-Run Bond Yields in the US, UK, andSweden”, Federal Reserve Bank of San Francisco Working Paper 2006-09.

Halonen, D., 2010, “Fed: US Corporate Plan Assets Up 3.8% in Q4”, Pensions andInvestments, March 11.

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Hess, G. D., and M. E. Schweitzer, 2000, “Does Wage Inflation Cause Price Inflation?”,Federal Reserve Board of Cleveland, Policy Discussion Paper 1, April.

Kutsch, N., and C. Lizieri, 2005, “The UK Pension Industry: A Research Report for thePension Real Estate Association”, University of Reading Business School, December.

Litterman, B., and The Quantitative Resources Group, 2003, Modern Investment Manage-ment: An Equilibrium Approach (Hoboken, NJ: John Wiley & Sons).

Mercer Consulting, 2011, “Asset Allocation Survey: European Institutional Market PlaceOverview 2011”, Report, May.

Mitchell, O., 2000, “New Trends in Pension Benefit and Retirement Provisions”, PensionResearch Council Working Paper (PRC WP 2000-1).

NAREIT, 2011, “REITWatch: A Monthly Statistical Report on the Real Estate InvestmentTrust Industry”, National Association of Real Estate Investment Trusts, April.

Nazmi, N., 1996, Economic Policy and Stabilization in Latin America (New York: M. E. Sharpe).

OECD, 2007, “Global Pension Statistics 2007”, URL: http://www.oecd.org.

OECD, 2011, “Pensions at a Glance 2011: Retirement-Income Systems in OECD 180 andG20 Countries”, Report.

OECD Secretariat, 2009, “Survey of Investment Regulation of Pension Funds”, URL:http://www.oecd.org/dataoecd/30/34/2401405.pdf.

Pensions Protection Fund, 2010, “The Purple Book 2010”, The Pensions Regulator andPensions Protection Fund.

Pettee, E. W., 1936, “Long-Term Commodity Price Forecasting 1850 to 1930”, The Journalof Business of the University of Chicago 9(2), p. 97.

Piggott, J., and R. Sane, 2009, “Indexing Pensions”, Report, The World Bank.

Ralfe, J., 2011, “The Correct Pension Discount Rate”, Financial Times, March 13.

Reserve Bank of Australia, 2007, “The Recent Rise in Commodity Prices: A Long-RunPerspective”, Reserve Bank of Australia Bulletin, April.

Rockoff, H., 1984, Drastic Measures: History of Wage and Price Controls in the United States(Cambridge University Press).

Schmitt, D. G., 1984, “Postretirement Increases under Private Pension Plans”, Bureau ofLabor Statistics 107(9), p. 3.

Scitovsky, T., 1979, “Home Truths about Inflation”, in Essays in Post-Keynesian Inflation,pp. 28–30 (Cambride, MA: Ballinger).

Shlaes, A., 2007, The Forgotten Man: A New History of the Great Depression (New York:HarperCollins).

Siegel, L., and M. Waring, 2004, “TIPS, the Dual Duration, and the Pension Plan”, FinancialAnalysts Journal 60(5), pp. 52–64.

Standard & Poor’s, 2011, Commodities 101: Understanding Commodities and S&P GSCI, S&PIndexes Practice Essentials Series, Standard & Poor’s Research.

Taborsky, M., and S. Page, 2010, “The Myth of Diversification: Risk Factors vs AssetClasses”, PIMCO Viewpoints, September.

Towers Watson, 2010, “Global Alternatives Survey”, Towers Watson and the FinancialTimes, June.

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Towers Watson, 2011, “Global PensionAsset Study 2011”, Towers Watson and the FinancialTimes, February.

Weinstein, H., 1997, “Post-Retirement Pension Increases”, in Compensation and WorkingConditions, Bureau of Labor Statistics, Fall, p. 49.

Yermo, J., 2007, “Reforming the Valuation and Funding of Pension Promises: Are Occupa-tional Pension Plans Safer?”, OECD Working Papers on Insurance and Private Pensions,No. 13.

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18

Ultra-High-Net-Worth Investors andthe Real Asset Value Chain

Ian BarnardCapital Generation Partners

Ultra-high-net-worth (UHNW) investors and their families are adiverse group of investors, more variegated than the investmentinstitutions that aggregate the investable assets of the majority ofcitizens. But, at the same time, they have investment objectives andpractices that overlap with those of investment institutions. Theytoo seek to protect their portfolios from inflation. Indeed, they maypay more attention to the risk of inflation, which is reflected inwidespread ownership of real assets, including particularly, but notexclusively, real estate.

UHNW investors face a perceived inflation sensitivity that isarguably more acute than that which confronts many investmentinstitutions. To start with, their time horizon is inter-generational,thus longer than is typical for inflation-sensitive institutions suchas, for example, pension funds. Moreover, they believe that theirexpected and realised inflation is higher than that of the averageconsumer; their liabilities go up in price at a higher rate than thatmeasured by consumer inflation, as we shall show in the following.And, what is more, the perceived cost of protecting against infla-tion is higher because they have an absolute real-return investmentobjective, which means that meeting inflation is simply not enough.

UHNW investors take many steps to deal with this problem, buta common theme is the extensive use of investments in real assets,rather than inflation-linked financial instruments, in their portfolios.Moreover, there are a couple of strategies often employed in order tomeet both the inflation and the real absolute return objective. One is

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the willingness to invest at an early stage in the real-asset value chain.The other is the use of financial leverage. It is UHNW investors, andtheir real-asset strategies, that we explore in this chapter.

THE ULTRA-HIGH NET-WORTH INVESTOR

What defines the UHNW investor is the scale of their investableassets. There is little agreement on where this category begins, buta useful figure is a sum in excess of US$500 million. It is not thecase, though, that UHNW investors are homogeneous. There aredifferences. For example, when it comes to return expectations,some remain in the “get rich” frame of mind that generated theirwealth. Others have moved to a “stay rich” mindset. Moreover, thereis often a generational divide. First-generation wealth is, perforce,likely to be concentrated in fewer hands, and meeting the liabil-ities of fewer beneficiaries. “Personality” effects are evident, too,particularly if the first generation remains in control of the capital.Older wealth will likely have a more dispersed group of beneficia-ries, which may, but not always, have developed more structure,in part to diminish or manage the influence of personality. All thiscontrasts with the investment institutions, whose numerous bene-ficiaries are actuarially transformed into a relatively homogeneousprofile of liabilities.

THE INFLATION THREAT

Where UHNW investors converge again is in their concern aboutactual inflation, which is commonly held to be higher than consumerinflation. And inflation, much more than deflation, is the historicenemy of private wealth. Many historic fortunes have dissipatedbecause the beneficiaries underestimated inflation. They took divi-dends, which they believed were paid from real returns, but, becausethey underestimated inflation, the dividends were paid from nomi-nal return only and ate into the real value of their capital. Moreover,there are few allies in voicing the reality of inflation for the wealthy.Public authorities try to minimise it, in order to control it. Investmentprofessionals can increase their perceived real-return outcomes byminimising the inflation they deduct from nominal returns. But thefact is that the liabilities of the UHNW investor differ from those ofthe general consumer.

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By contrast, deflation is less of a threat to UHNW investors. Theyare, at root, a rentier class with, by definition, extensive financialassets. They therefore have extensive deflation protection inherentin their portfolios. While some wealthy families were harmed bydeflationary periods, such as the Great Depression, it is inflationthat remains the principal concern of this group.

LEGACY AND TIME HORIZON

Investment institutions are engaged in intra-generational wealthmanagement, ie, spreading capital across the lifetime of their bene-ficiaries. A pension or life assurance policy trades consumption nowfor consumption in the future. But with capital so far in excess ofneed, UHNW investors face an inter-generational question of legacy:what will be left behind? In some cases, the legacy will be devotedto the support of children and subsequent generations. In addition,there is often extensive planning of philanthropic projects, in par-ticular the endowment of educational institutions, for the purposesof teaching, new buildings or scholarships. But the key point is thevery long-term nature of this capital, with a horizon spanning severalgenerations.

LIABILITIES

The liabilities of the ultra wealthy fall into two areas: staff, and otherconsumption services and goods. Both are perceived to inflate morerapidly than headline consumer prices. For example, the wealthyconsume large volumes of services delivered by a diverse set ofstaff. These include domestic services, education, entertainment andinvestment managers, to name a few. Pay inflation is reckoned toinflate with nominal GDP, although in some Western countries theaggregate data is not compelling in this respect. But inflation ofthe high-end service sector has certainly been above average infla-tion for the typical basket. One example is financial services, wherespecialist staffs have seen incomes rise dramatically, to the pointwhere professionals in this sector are becoming HNW investorsthemselves.

In addition, education is an important liability for rich families.They have to educate their children and, as mentioned before, theyhave also been great historic supporters of educational philanthropy.

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Figure 18.1 US Higher Education Price Index compared to CPI

300

250

200

150

100

50

01961 1966 1971 1976 1981 1986 1991 1996 2001 2006

US HEPI US CPI

Sources: HEPI, July 1–June 30 data (Research Associates of Washington andCommonfund Institute).CPI data (US Department of Labor) is calculated to July 1–June 30 (annual published CPI is computed over the calendar 12-month period).Based at 100 in 1983.

Figure 18.2 Colliers International Luxury Residential Index comparedto CPI

300

350

250

200

150

100

50

0Mar2000

Sep2001

Mar2003

Sep2004

Mar2006

Sep2007

Mar2009

Sep2010

Colliers International Luxury Residential Price Index peakUS CPI

Sources: Colliers International, Hong Kong; US Department of Labor; indexesbased 100 in March 2000.

Figure 18.1 shows the US Higher Education Price Index comparedto Consumer Price Index (CPI).

The wealthy consume scarce consumption goods, such as homesin fashionable areas, art, fine wine and other collectibles. The infla-tion in these products is high. The explanation is the path depen-dency embedded in luxury products. The newly created wealthy

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Figure 18.3 Liv-ex Fine Wine Index against CPI

300

400

350

250

200

150

100

50

0Jul

2001Oct

2002Jan

2004Apr

2005Jul

2006Oct

2007Jan

2009Apr

2010

Liv-ex Fine Wine 100 Index US CPI

Sources: Liv-ex Limited (production and supply weighted), US Department ofLabor; both indexes based at 100, in January 2004.

Figure 18.4 Art Market Research indexes versus inflation

Jan1985

Apr1988

Jul1991

Oct1994

Jan1998

Jul2004

Oct2007

Jan2011

Apr2001

1,000

1,400

1,200

800

600

400

200

0

Art Market Research Old Masters Index 100

Art Market Research Modern Art Index 100

US CPI

Sources: Art Market Research, US Department of Labor; based at 100 in January1985. Note: art indexes based on median top 25% of prices named in sector.

compete to own products and goods that are perceived to be of thehighest quality, whether because of location, workmanship or his-toric importance. Indeed, a motivator for wealth creation is to beable to consume such things. Figure 18.2 shows the Colliers Inter-national Luxury Residential Index against CPI starting from 2000.Figure 18.3 shows the Liv-ex Fine Wine index against CPI from 2001.Finally, Figure 18.4 compares two art market indexes against infla-tion. The take-away message from all three charts is clear: in recentyears, luxury goods and services have risen faster than the averagebasket price inflation.

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REAL ASSETS

The perceived realities of UHNW inflation are a simple explanationwhy consumer-inflation-linked securities do not provide an infla-tion solution. With the low real yields that characterised the 2008global financial crisis and are still predominant at the time of writ-ing in 2011,1 such an investor is, in practice, bearing negative realreturns. Additionally, wealthy investors have an absolute return tar-get profile, ie, an asymmetrical return target of inflation or more.In comparison, investment institutions have traditionally tended tohave a more symmetrical benchmark approach. Behavioural financehas shown – if, indeed, it was ever in doubt – that investors havea natural bias against loss: they find losses more painful than gainspleasurable. Since UHNW investors are less intermediated than thebeneficiaries of institutions, their preferences carry through moreclearly to the market. Of course, the fact that absolute returns aredesired does not mean that they are readily available, but UHNWinvestors themselves provide the backdrop and the capital for thefinancing and generation of new opportunities for absolute returninvestments.

It is exactly the wish to own inflation-protected assets with reason-ably high returns that sheds light on the historically material alloca-tion to real assets within UHNW portfolios: particularly real estate,but also agriculture and forestry.2 Good-quality hard assets, in theright location, with stable inflation-exposed cashflows (be they corereal estate, infrastructure, power plants or even forestry) are attrac-tive for many investment portfolios. Historically, the 6–9% nominalreturns on these investments have translated into real, unleveragedreturns in the 4–6% range (once adjusted by consumer inflation). Buteven for real assets, returns have decreased over time, partly becauseof increasing institutional investors’ demand. Hence, two strategieshave been employed by UHNW investors in order to retain inflationprotection while generating target returns: developing real assetsfrom an early stage and using leverage.

Part, of course, of the return available from very early-stage invest-ment is a premium for illiquidity, which wealthy investors havehistorically been willing to receive. Their long, inter-generational,time horizon makes them natural buy-and-hold or buy-and-waitinvestors.

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When it comes to determining allocations to real assets, UHNWinvestors have at their disposal all the tools available to investmentinstitutions. As noted above, this is a variegated pool of investors,and different investors have different approaches to portfolio con-struction or asset allocation. In many cases, it is a target percentageof assets. It can be low, but is typically in excess of 20% and, in somecases, over 75% of investable assets.

When it comes to measuring success, practice again varies. Thereare hard measures of real (after inflation) investment performance.But, in other cases, performance is measured by reference to gen-erating a target income without great concern for appraised value.Finally, there is the fact that performance is not measured but, rather,investors are satisfied by the existence of real assets in their portfoliosin the belief that they provide strong protection against unexpectedinflation or events.

THE REAL-ASSET LIFE CYCLE

Before looking more closely at the benefits, and risks, of engagingin development, it is worth summarising the real-asset life cycle,which, conceptually at least, looks similar across different types ofunderlying asset. The start is project development; then there is con-struction or implementation, commissioning and, finally, operation(Figure 18.5). To take them in reverse, the outcome of the develop-ment of a real asset – be it commercial real estate, forestry or a wind-farm – is a hard asset that generates a running yield. There are, ofcourse, some differences among real assets. For example, the prod-uct – be it accommodation for office staff, wheat or electrical power– can be sold on short-term or long-term contracts. In addition, theprice may be spot market or long-term fixed-price offtake. Differ-ent industries have distinct prevailing models. For example, centralLondon core commercial property is long-let, with often upward-only rent reviews; forest products can be sold spot or into forwardmarkets. But the crucial point is that the outcomes are relativelytightly defined: you produce commodities and receive an income,which offers some inflation protection.

We divide the pre-operational phase into commissioning, con-struction and project development, although these all come underthe umbrella of “development”, ie, the business of producing an

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Figure 18.5 The real-asset life cycle and value chain

Projectdevelopment Construction Commissioning Operation

operating real asset. The stage immediately prior to operation is com-missioning: letting a completed, or soon-to-be completed, propertyor switching on a wind farm. Forestry fits less tidily, but commercialthinning (getting the forest ready for harvest) is analogous. Con-struction or planting precedes and typically represents the largestsingle item of cost to create the asset. Construction of real estate,erection of wind turbines, building roads and planting trees are allcapital-intensive activities.

Project development can be hugely value accretive, and commen-surately risky.At the outset, it involves having the idea to create a realasset, ie, producing a winning concept, and then securing the threenecessary ingredients for successful development. The first one is tosecure use of the land.At the outset, a developer might take an optionbut, in the end, before beginning construction, will want to have theabsolute right to use the land in the way they need. Next are plansand permissions: a building, or likewise an energy-producing asset,needs detailed plans from concept design to detailed constructiondrawings. And, in most cases, public authority permissions are alsorequired. The final element of the triumvirate is finance. Figure 18.5gives a conceptual illustration of this value chain.

RISKS AND RETURNS

At the final stages of the value chain, the owner largely bears themarket risk of the asset, with the expectation that there is inflationprotection. Take the example of real estate. If an investor has devel-oped a core office property, they will let it into the market for officespace. There is some idiosyncrasy around building quality and loca-tion, but its impact will be relatively small in relation to the prevail-ing rents in the area. In the case of real assets that produce fungiblecommoditised outputs, such as energy or timber, there is scope fortrading, but the price is very largely market determined.

As you move to the beginning of the value chain, the risk is moreidiosyncratic, and the expected return is generally higher. Taking the

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three basic building blocks, the risks offer different types of returnat each stage. Most isolated from broader macro factors is the designprocess. A clever, beautiful or efficient design is a purely idiosyn-cratic (ie, not correlated to market factors) source of return. This isevident in real estate projects, as well as in decisions about the layoutof a timberland plantation, a wind farm, or solar park.

As for acquiring land, development land is most often priced byresidual value calculations. That is, you determine what the finalproduct, such as an office building, will be worth; you then deductcosts, including financing, and a profit for the developer, usuallyexpressed as a percentage of costs, before arriving at the residualvalue for the land. This leaves the value of land exposed to the cur-rent assessment of discounted future value of the end product. Ofcourse, this exposure to macro risks embeds some inflation sensitiv-ity: if the price of real estate rises, land values will increase to reflectthis. And, as noted above, it exposes the residual value of the landto the availability of finance: low discount rates both reduce financ-ing costs and increase the discounted future value of the completedasset. Consequently, the price of development land can be wildlyvolatile through the cycle.

When it comes to permits, public authority permissions are largelyindependent of market risk. In fact, public authority decisions relateto policy and the wishes of their electorate, be it national, regionalor municipal. These should be largely uncorrelated to broader eco-nomic factors. Indeed, achieving preliminary, and then final, publicauthority permits is highly value accretive, but also risky in a rela-tively binary fashion. A refusal to approve a new shopping centre ishard to mitigate by means other than simply appealing. The extentto which this development stage is dependent on broader macro fac-tors lies in the possibility that, because of hard economic times, forexample, a public authority might restrict a building permit in orderto avoid undermining existing asset values.

Finally, the availability of finance is most closely correlated tobroader macro factors. In times of capital plenty, more projects arefinanceable. In harder times, securing capital might generate morereturn. Experience suggests that the benefits of capital plenty areonly fleetingly captured by developers and that after an interval thesurplus thus created seeps to other parts of the industry, often thelandowners.

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Figure 18.6 Risks and returns along the real asset value chain

6

8

10

25R

etur

n (%

)

Financedand permitted

Constructioncompletion

Operationalstart-up

Development risk

Construction risk

Commissioning risk

Inflation and beta

Liquidity capital deployment

Figure 18.6 illustrates the changing nature of the risks borne atdifferent points in the value chain and a rough indication of un-leveraged expected real returns.

The model of investing at different stages along the value chainencompasses several assets, with real estate being one of the mostcommonly sponsored by private investors. In fact, it is not an acci-dent that a proportion of any country’s rich list will contain fam-ilies who made, and sustained, their fortunes through real estateinvestment. But other real assets, in addition to real estate, have alsoattracted UHNW investors’ interest. One example is the emergingsector of renewable energy, where the inflation protection embed-ded in the core asset, coupled with attractive real rates of return,has secured increasing amounts of capital from a large number ofprivate investors.

LEVERAGEIn order to meet their dual objectives of inflation protection andattractive real returns, private wealthy investors often use lever-age, as borrowers, and they do so with awareness of the differencesbetween leveraging an asset at an early stage (say, pre-construction)and leveraging an operating asset with on-going cashflows. In thecase of early-stage leverage, the expected return is substantiallyenhanced, although this “grow rich” investment strategy comes atthe price of much higher operational and financial risk. When adevelopment project is financed at a later stage, operational riskis diminished along returns, but financial leverage still provides aboost to this “stay rich” strategy.

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Figure 18.7 Leverage along the real asset value chain

6

8

10

25

Ret

urn

(%)

Financedand permitted

Constructioncompletion

Operationalstart-up

Development risk

Construction risk

Commissioning risk

Inflation and beta

Liquidity capital deployment

+5%+2%

+1%

In addition to the point of development at which leverage isemployed, the investment strategies described above might differ bythe extent to which the lender’s security extends beyond the under-lying asset. The more conservative approach is to borrow moneysecured against the asset only. In this way, only the equity in theproject is at risk, should there be a problem along the way. By con-trast, borrowing that extends beyond the asset is more “get rich”.This might be a guarantee from a holding company relying on addi-tional collateral, or directly from the beneficial owner. Or, there mightbe cross-collateralisation with other assets. The “get rich” path is evi-dently taken in order to achieve terms of leverage that are unavail-able on the “stay rich” path. This “get rich” path might be to increasethe levels of leverage, or to secure any leverage at all, particularlyagainst development assets, the future cashflows of which are con-tingent on events outside the control of the sponsor. Figure 18.7 isa stylised illustration of how the application of leverage enhancesreturns along the value chain.

In addition to enhancing returns, UHNW investors sometimesgive an additional rationale for applying leverage to real assets,which is to benefit from inflation. They judge that inflation willreduce the real value of the debt, thus increasing the real value of theremaining equity. The effect will be more pronounced if the projectis financed by long-term fixed-rate debt. Clearly embedded in thisview is the assumption that the cashflows of the underlying assetwill also increase with inflation, so its value will not decrease despitea rise in discount rates.

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In this discussion of leverage, the UHNW investor has beenthe borrower rather than the lender. There is the option for suchinvestors to lend into real-asset structures and this occurs. Of course,as discussed above, lending at an earlier stage of the real-asset devel-opment process has equity-like characteristics. But, in general, expe-rience suggests that such investors opt to be at the lower end of thecapital structure and look to other participants to provide the seniortranches, be they banks or investment institutions.

CONCLUSIONSIn this chapter, we discussed UHNW investors’ peculiar investmentcharacteristics, in particular their long-term horizon, typically span-ning several generations, and their sensitivity to inflation, whichgoes beyond that measured by the average basket of goods and ser-vices. Next, we explored how UHNW investors pursue their dualobjectives of inflation protection and attractive real returns by invest-ing at early stages of asset development projects, and judiciouslyemploying leverage along the way.

1 This is true of developed inflation-linked markets in particular.

2 UHNW investors’ allocations to mining and energy projects are harder to execute, given thatthe size of capital required to develop these assets is typically very large.

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19

Inflation Markets: A PortfolioManager’s Perspective

Stefania A. PerrucciNew Sky Capital

Because general price levels affect asset returns and the econ-omy as a whole, inflation is an important risk that every investorshould carefully analyse, and actively manage, in order to pro-tect real wealth. In fact, the rationale for managing inflation riskand for evaluating investments in real return–risk space does notneed justification, as it is grounded in common sense. Instead, itmight seem surprising that virtually all commonly used invest-ment metrics rely on nominal measures, which do not explicitlycapture the insidious impact of inflation on wealth. This cava-lier attitude can be in part traced back to inflation-linked instru-ments (which are explicitly and formulaically indexed to inflation)being a relatively recent innovation to fixed-income markets,1 com-bined with the intrinsic difficulty in assessing the correct dynamicrelationship between inflation sensitive assets (such as commodi-ties, real estate, equity or infrastructure investments) and inflationitself.

Besides being an important macroeconomic risk, inflation alsooffers attractive opportunities to the active investor. Indeed, mar-ket inflation expectations displayed equity-like volatility during andafter the 2008–9 global crisis. This coincided with a substantial reduc-tion in risk capacity on behalf of market makers, thus creating pricingdistortions and relative value opportunities due to supply–demandshocks and hedging activities, in a market where liquidity can attimes be limited, despite the impressive growth since the tail end ofthe crisis.

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The inflation market provides a risk-transfer mechanism betweeninvestors and hedgers. In the first section, we explain how infla-tion markets work, the different economic agents involved and whatmotivates them, as well as the role of market makers in providing liq-uidity. Next, we discuss the role of analytics, starting with top-downmacroeconomic models. After explaining some of the key charac-teristics of inflation as a time series, we introduce the expectation-augmented Phillips curve and present some structural equilibriumrelationships that can be helpful in modelling price indexes. Mone-tary policy models in the spirit of Taylor’s rule are also discussed,as are the relationship between real rates and growth, and sce-nario analysis. We then cover bottom-up models, most of whichuse market prices as inputs. We discuss how to extract real ratesfrom zero-coupon inflation swaps, the relationship between swapand cash break-even inflation (BEI) rates and asset swap (ASW)spreads, and the interplay of inflation expectations and risk pre-miums in determining inflation compensation. Next, we show howto calculate carry for inflation-linked bonds, and discuss the issueof seasonality. Finally, we briefly introduce the inflation option mar-ket and summarise the key assumptions and results of the seminalJarrow–Yildirim pricing model.

After having geared up with the indispensable theoretical tools, inthe last section we deal with practical examples and considerationsthat should be useful when investing in inflation products. After adiscussion of our holistic approach to the sector, which combinesboth fundamental and technical information, we present two con-crete strategy examples in detail: a directional BEI trade and an arbi-trage trade relying on mispricing between the cash and derivativeBEI rate. A summary section concludes.

INFLATION MARKETSUnderstanding inflation markets requires an appreciation of theentire mechanism through which inflation risk is transferred. Thisanalysis can be quite complex, and several academic papers andbooks have been written on the subject. In this section, we shallfocus on the main ideas, introduce the different agents active on thesupply and/or demand side of the inflation market, describe theirinvestment/hedging needs and behaviour, characterise the size offlows and the role of governments and, finally, address whether the

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Table 19.1 Estimates of inflation supply and potential demand (in USdollars)

Inflation supply/payers Inflation demand/receiversSize of global IL supply ≈2,750 bn Size of IL demand ≈4,300 bn

Sovereign IL Debt(US, Canada,Brazil, France,Mexico, Italy,France, Germany,UK, Australia,Japan…)

≈2,500 bn Pension Funds ILliabilities

≈1,800 bn

Insurancecompanies ILliabilities

≈1,400 bn

Infrastructure ILdebt (UK,Australia,Canada)

≈80 bn Asset managers,hedge funds ILassets

≈700 bn

Sovereign funds,central banks ILassets

≈300 bn

Utility companiesIL debt (Europe,Australia, Brazil)

≈90 bn IL savingsaccounts

≈100 bn

Commercial realestate IL debt(Europe,Australia)

≈40 bn

IL mortgage debt(Iceland, Chile,Mexico, Brazil,Israel)

<30 bn

Sources: Bloomberg, OECD, New Sky Capital.

inflation market is balanced overall, and can thus function as aneffective risk-transfer mechanism.

The different economic agents active in the inflation market canbe categorised according to whether their exposure is such that theybenefit from an unexpected increase in future inflation (so that theyare natural inflation payers), or the opposite is true (so that they

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Figure 19.1 The growth of sovereign inflation-linked debt

2.5

2.0

1.5

1.0

0.5

0

Infla

tion-

linke

d de

bt (

US

$ tr

illio

n)

Dec

197

1D

ec 1

973

Dec

197

5D

ec 1

977

Dec

197

9

Dec

198

7D

ec 1

989

Dec

198

1D

ec 1

983

Dec

198

5

Dec

199

1D

ec 1

993

Dec

199

5D

ec 1

997

Dec

199

9

Dec

200

7D

ec 2

009

Dec

201

1

Dec

200

1D

ec 2

003

Dec

200

5

Developed countriesEmerging countries

Sources: Bloomberg, New Sky Capital.

are natural inflation receivers). Inflation payers include economicagents, such as central and local governments, whose revenue iscorrelated to inflation and, to a lesser degree, corporate issuers, suchas utility and infrastructure companies. Inflation receivers, on theother hand, are economic agents that are negatively impacted by anunexpected increase in inflation, such as pension funds, insurancecompanies and asset managers. Table 19.1 illustrates these points.

Inflation supply

As seen in Table 19.1, sovereign issuance is the major source ofinflation-linked bonds. Figure 19.1 shows the impressive growthof inflation-linked sovereign bond markets in both developed andemerging countries.

In the 1970s and 1980s, the issuers of inflation-linked debt weretypically governments in countries (especially in Latin America)where high-inflation was common. The UK started issuance in 1981,during a period of high inflation, embracing the rationale, first sug-gested by Keynes,2 that inflation-linked bonds would commanda premium from inflation-risk-averse investors. Indeed, fundingat attractive real yields remains one of the key motivations forinflation-linked debt issuance.

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The sovereign inflation-linked debt market has increased dra-matically to a size of almost US$2.5 trillion, with more and morecountries adopting a regular issuance schedule. This occurred overa time when major economies experienced low, stable (or decreas-ing) inflation rates. In other words, it is not the risk of high infla-tion that has spurred interest in inflation-linked debt (and thuspromoted issuance) in the following two decades, but rather thedemand for a low-volatility investment asset, and effective portfoliodiversification.

However, with the increase in inflation volatility since the start ofthe 2008–9 global financial crisis, new demand for inflation-linkedproducts has developed, with more investors taking an interest inthe space and its renewed opportunities. Incidentally, this demandis likely to deepen the shortage of inflation supply (also shown inTable 19.1), and thus provide good funding opportunities to naturalinflation payers, including non-sovereign issuers, particularly in theinfrastructure and utilities sectors.

Historically, the sourcing of inflation from non-sovereign issuershas been limited, with the exception of the UK and, to some extent,Australia (this is in line with pension fund hedging activity, whichis well developed in these two countries). However, as other mar-kets evolve along similar paths, accounting/regulatory obstacles areremoved and asset–liability management programmes encouraged,we can expect non-sovereign issuers (whose financing needs we esti-mate to be about US$1.8 trillion globally) to progressively gain amore prominent place among the global suppliers of inflation-linkedcashflows.

As for sovereign issuers, the context of large funding needs at thetime of writing points to a likely increase in inflation-linked bondmarkets. However, governments will have to balance conventionaland real issuance, in order not to compromise the liquidity of theirnominal debt markets.

Inflation demand

Traditionally, pension funds have been the main driver of demandfor inflation products. This stems from the linkage of their liabili-ties to inflation, which can be either implicit (eg, taking the form ofannuities calculated from last salaries) or explicit (eg, in the form ofinflation-linked annuities, as in the UK). In some countries, such as

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the Netherlands, indexation can be conditional on pension funds’funding ratios. Pension funds’ demand was indeed a key driver ofgovernments issuing inflation-linked bonds. For example, in 1980,the Wilson Report (Wilson Committee 1980) recommended that theUK Government issue index-linked gilts specifically to meet pensionfunds’ demand.

Insurance companies are the second larger driver of inflationdemand. Hedging inflation tail risk is of particular concern for theproperty and casualty segment of the insurance industry. As insur-ance loss reserves calculations hinge on actuarial assumptions onfuture inflation rates, the two decades from the 1980s to the time ofwriting have been quite benign, as this period has seen an orderlydownwards trend in inflation rates in most developed markets, withrealised rates of inflation often lower than ex ante projections. How-ever, we are now at a crossroads, at a time when it is not implausiblefor future inflation rates to surprise on the upside. As a result, infla-tion companies have been more sensitive to the risk of inflation,and more active in devising strategies to hedge it (sometimes in theinflation option market).

Pension funds and insurance companies’ potential demand forinflation-linked instruments is large, and is likely to grow evenlarger, not only in developed countries but also in emerging coun-tries, where demographics are supportive and financial marketsare evolving rapidly. Clearly, each specific market is at a differentstage of sophistication when it comes to the management of infla-tion risk, from simple awareness of such a risk factor, to quantitativemeasurement and monitoring of sensitivities at the balance-sheetlevel (through, for example, scenario analysis or Monte Carlo sim-ulations), to proactive implementation of specific inflation-hedgingstrategies on assets and/or liabilities. Indeed, the latter do have alarge influence on the market, especially in countries such as theUK and in continental Europe, where pension funds and insurancecompanies are very active players in the inflation sector. Interest-ingly enough, in the US, the demand for inflation products frompension funds and insurance companies has been somewhat lim-ited, which is probably a consequence of the successful anchoringof inflation expectations from the 1980s onwards, thanks to effec-tive monetary policy by the Feds. However, there is a growing con-cern that unconditional reliance on the central bank’s capacity to

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Table 19.2 Market impact of inflation hedging by pension funds andinsurance companies

Market impact︷ ︸︸ ︷Currency BEI Real yield ASW discount Option

US dollars Medium Medium Medium MediumEuro High High High MediumSterling High High High High

keep inflation under control might be misguided going forward,and many institutional investors have focused more attention onmore challenging scenarios for the future.

Inflation-hedging strategies can be implemented on both the assetside and the liability side of the balance sheet. We estimate thatabout two-thirds of these strategies involve purchase of inflation-linked instruments as assets, while one-third involve the use ofinflation swap or option overlays on the liability side. Clearly, thereare trade-offs with both implementations. Inflation-linked bonds aretypically more liquid than swaps (higher volume traded; lower bid–ask spread). However, they have been plagued by credit issues inEurope, and they have not performed well in risk-aversion episodes.The use of inflation derivatives on the liability side is a pure inflationplay, but it has clear limitations in terms of market depth and liquid-ity, especially in the context of decreased risk appetite and inventoryfrom market makers offering these products.

The hedging activities of pension funds and insurance compa-nies have several consequences. These are summarised in Table 19.2,where we consider four market variables: swap BEI; real yields; assetswap discount (the difference between linker and nominal ASWspread, which measures the difference between cash and swap BEI);inflation option volatility. First, as these players keep a watchfuleye on the level of inflation break-evens in relation to long-termaverages, they provide a powerful mean-reversion force in the mar-ket when BEIs are historically low. In other words, these hedgingactivities (where present, eg, in the UK and mainland Europe) effec-tively provide a floor for swap BEI rates (not a cap, as these arebuy-and-hold strategies). They can also provide the backdrop fordivergence in swap versus cash BEI rates, as happened in autumn

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2008. Hedging activity on the asset side provides support to long-term real rates, typically resulting in a relatively flat curve. Finally,option overlay strategies generally provide support to out-of-the-money cap or floor inflation volatility, with large buyers at timesproducing clear distortions in the volatility smile.

These technical flow dynamics are very powerful and cannot beignored, as they clearly exert a strong influence on market pricingin sector.

Asset managers, hedge funds and sovereign funds have alsoentered the inflation market, with important investment allocationsin the space. This source of demand is also on the rise, as alpha oppor-tunities arise in the new climate of higher volatility, and the necessityfor managing beta inflation risk (de facto embedded in many port-folio) is increasingly recognised. Most large asset managers are long-only unleveraged investors, typically with a long-term horizon, whoare looking at locking-in attractive real rates. Some of the large assetmanagers and sovereign funds are also benchmark sensitive. Retailinvestors also participate in the space, and might be an importantprice driver in certain situations, eg, when a specific inflation-linkedsecurity is rebalanced out of a benchmark, so that it is typically soldfrom large institutional portfolios.

As Table 19.1 makes clear, the potential demand for inflation prod-ucts is large and at the time of writing cannot be met by the currentstock of inflation-linked bonds, despite their tremendous growth inrecent years. It is likely that, over time, this demand will be a driver ofadditional supply, from sovereign and non-sovereign issuers alike,as well as a main force behind further developments in the inflationderivatives market.

The role of market makers

The role of market makers in mediating inflation flows is veryimportant, and understanding their structural positions and hedg-ing activities is crucial in order to understand price behaviour in thismarket.

Historically, inflation market makers, ie, investment banks, havebeen structurally short BEIs via swaps (mainly sold to pensionfunds in Europe) and short inflation volatility (mainly as a resultof coupon floors embedded in structured notes sold to the retailmarket in Europe). These positions, and the strategies employed by

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banks in hedging them, had enormous consequences on the market,especially during the 2008–9 financial and liquidity crisis.

Pension funds have been, and still are, a major receiver of infla-tion in the market. This demand has been focused on swaps, as theseallow for better customisation than simply buying linkers and canbe used as an overlay with limited balance-sheet usage. Lookingat the size of pension funds’ inflation-linked liabilities (estimatedat about US$1.8 trillion in Table 19.1), it is clear that such demandcannot be met simply by investment banks acting as match makersbetween swap buyers and sellers. Indeed, there are no natural sellersof inflation through swaps, although some attempts have been madeto structure funding transactions for infrastructure and real estateprojects, where inflation can be stripped from revenues and chan-nelled into a back-to-back swap. Consequently, investment bankshave to hedge most of these short swap BEI positions by buying BEIsin the cash market. This is also why the most liquid inflation swap isthe zero-coupon swap, whose cashflow format strongly resemblesthe inflation-accruing notional in sovereign inflation-linked bondsin the US and Europe.3 As with any hedging strategy, recycling infla-tion from the cash market into the swap market has residual basisrisks and additional costs, most notably the financing of cash BEIs(ie, the difference in the repo rate paid to finance the long inflation-linked bond positions, and the reverse repo rate earned on the shortnominal bond positions). These costs and the risk involved can besubstantial, especially for long-tenor transactions, as well as beingsubject to volatility and changes in market liquidity conditions.

As for volatility, until the 2008–9 financial crisis, investment banksaccumulated short inflation option positions through coupon floorsembedded in structured notes sold to the retail market in Europe.These options were delta hedged by selling inflation swaps.

When the financial crisis hit in autumn 2008, economic activityand energy prices plunged, and so did inflation BEIs. The impact ofdeteriorating fundamentals was greatly amplified by liquidity andtechnical effects. As financing sovereign linkers in the repo mar-ket became more and more difficult, they quickly become casual-ties of the rapid balance-sheet deleveraging that ensued. And asBEIs moved lower, delta hedging of short inflation option positions,moving into-the-money, added insult to injury. To put things intoperspective, bond prices collapsed to the point where the five-year

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Table 19.3 Break-even inflation versus Dow Jones Industrial Average(2011) yearly range

Initial Low High Range

US BEI (%) 2.60 = 100 −17 12 29DJIA (%) 11,671 = 100 −4 10 14

US TIPS had positive nominal yield in the hypothetical scenarioof a replay of the Great Depression, which made us comfortablepositioning against this market view (Perrucci 2009).4

The structural (long linkers on repo; short inflation swaps) expo-sure on banks’ trading books also caused swap BEIs to widen rela-tive to cash, as market makers tried to unwind these trades. In turn,as banks’ eagerness to obtain term financing of long inflation BEIsand volatility exposure grew, inflation asset swaps also widenedconsiderably.5 These pricing distortions provided those investorswho were able to spot them the opportunity of a lifetime.

Technical effects are important not only during a systemic crisisbut also in normal circumstances, as inflation markets are gener-ally not as efficient as nominal rates markets. This is due, in part,to a smaller number of players who often pursue similar invest-ment objectives, and whose behaviour, or change in preferences,can have a large and long-lasting impact on market prices andliquidity.6 Furthermore, bond supply is concentrated around auc-tion dates, while liquidity in the secondary market is limited by thefact that many institutional players in the inflation market are “buy-and-hold” investors with a medium-to-long-term horizon. Indeed,in this market, it is not unusual for supply or demand shocks todrive prices away from fundamental value, thus creating attractiveopportunities for the active investor.

The inflation market after the 2008–9 global crisis

Despite the impressive growth in the market in the first decade ofthe 21st century (Figure 19.1), the effects just described remain veryrelevant at the time of writing, and opportunities in the inflationmarket abound.

One important factor driving investment opportunities is thatBEIs were quite volatile during the global crisis and remain so in

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Figure 19.2 Swap 10-year BEI in Europe and the US

3.5

3.0

2.5

2.0

1.5

0.5

1.0US 10Y BEI

EU 10Y BEI

Jul2004

Jul2005

Jul2006

Jul2007

Jul2008

Jul2009

Jul2010

Jul2011

Sources: Bloomberg, New Sky Capital.

its wake. Indeed, looking beyond the extreme gyrations experi-enced in 2008–9, and taking 2011 as an example, BEI swung up,and then down, in synchronised moves, within a range that isquite wide (29%), and more than double that of an equity indexsuch as the Dow Jones Industrial Average (14%) (Table 19.3 andFigure 19.2).

Another consequence of the crisis is increased awareness of infla-tion risk on banks’ trading books, which, combined with new globalfinancial regulations and higher capital requirements, resulted inlimited balance-sheet and risk capacity on behalf of market makers.At the same time, demand for inflation cashflows by large institu-tional investors has, if anything, increased, due to high volatilityin the market and also as a result of new regulations that focus oninflation risk in a more explicit way. For example, Solvency II setscapital requirements for insurance companies at the balance-sheetlevel; thus, the effect of inflation on assets and claims makes capitalrequirement inflation dependent. Because of these factors, the abilityto provide liquidity and intermediation of inflation risk and flowsstructurally has decreased after the crisis, while demand has actu-ally increased. This, in turn, has provided attractive opportunitiesto the active manager.

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INVESTING IN INFLATION PRODUCTS

While most people are familiar with nominal interest rate strategies,we believe real rates and inflation are the new frontier in fixed-income relative-value investing. Indeed, inflation risk should beactively managed, as it can generate substantial alpha, and do sowith limited risk and leverage.

The truth of the matter is that inflation is a relatively untappedmarket, which has not reached full maturity, and where specialistknowledge is still in short supply. Indeed, traditional asset managershave focused most of their attention on index-replicating strate-gies, rather than active alpha, and there is often a lack of skills inapproaching opportunities, which results in relative value tradesbeing missed or implemented with sub-optimal timing. As we havealready pointed out, the secondary market for sovereign inflation-linked bonds is not as liquid as the nominal one, and thus sup-ply tends to be concentrated around auction times. Furthermore,demand can also be spotty but, at the same time, come in size, giventhe herding behaviour of a number of large investors pursuing infla-tion beta strategies and compelled to replicate their benchmarks byeither their internal guidelines or financial regulations (such as is thecase for many insurance companies and pension funds). These fac-tors are at the root of the structural positions held by market makersand their hedging activities, and thus are key to pricing across thecash and derivatives inflation markets. A 360 view of these dynam-ics is essential to capture opportunities in the space, as is a goodgrasp of both visible and less visible inflation flows (for example,swaps and options, or inflation structures in the over-the-countermarket).

Given the multitude of factors affecting the market, we believea holistic investment approach should be adopted in which funda-mental and technical analyses are seen not as antagonistic, but ascomplementary. Furthermore, although both macroeconomic mod-els and market models are useful, focusing uniquely on equilibriumrelationships as a measure of long-term value has often been the rea-son why (self-defined) value investors have failed to achieve attrac-tive risk-adjusted returns, and ultimately protect the very same valuethey were trying to extract from the market in the first place.

In other words, trying to navigate this market with a fundamentalview of inflation only would be as dangerous as a skipper pointing

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their boat towards a lighthouse in the distance, with no regard forthe unmarked rocks and low waters that stand in the way. The light-house is indeed a helpful sight, but we had better stay alert andadjust our route wisely if we want to get to harbour safely, or getthere at all.

As for analytics and their role, our view of the world is shapedby a number of proprietary, internally developed quantitative mod-els, but is ultimately based on experience and judgment. In otherwords, models provide a framework, not a substitute, for think-ing. We recognise that, in spite of its mathematical sophisticationand analytical complexity, market forecasting often has limited pre-dictive power, and is by nature a conditional exercise (on inputs,assumptions, scenarios, etc). In addition, when it comes to inflation,political considerations may trump economical considerations, forexample, in regard to fiscal and monetary policy. Thus, the valuein our analytics comes not from any point forecast, but from thediscipline they instil in our thought process, by establishing the bal-ance of risks, the latter being far more important to investment deci-sions. Furthermore, it is very important to understand how con-sensus views are formed, even when we might believe them to bewrong, as those have a profound impact on the behaviour of marketparticipants such as asset managers, pension funds and insurancecompanies, with these flows often driving relative value opportuni-ties in the sector. Finally, such a common sense approach is importantin setting an internal risk culture where model error is understood asan intrinsic and unavoidable aspect of modelling the complexities infinancial instruments and markets, and focus is shifted onto the realissue, which, in this author’s opinion, is human error and personalaccountability in the sensible use of models as exploratory tools.

When it comes to inflation, we look at both bottom-up and top-down models, different time horizons and both statistical and struc-tural approaches. In the next section, we shall give a brief qualitativeintroduction to these models, as a full technical discussion would bebeyond the scope of this chapter.

MACROECONOMIC MODELSEmpirically, inflation is a non-stationary stochastic process; thisimplies that its mean and volatility change over time. These featuresare clearly evident from visual inspection (Figure 19.3).

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Figure 19.3 Inflation is a non-stationary stochastic process

US

Germany

UK

Japan

Infla

tion

(%)

–5

0

5

10

15

20

30

25

1961 1971 1981 1991 2001 2011

Source: New Sky Capital.

The difference between stationary and non-stationary processesis important in regression analysis, as non-stationarity violatesthe assumptions upon which statistical inference is based. In fact,consider the simple regression

Yt = a+ bXt + εt, εt ∼ IIN[0,σ 2]

where the error terms are independently and identically distributednormal (IIN) variables, with constant mean (equal to zero) and vari-anceσ 2. If Yt and Xt are non-stationary processes, generally a linearcombination of the two, such as

Yt − a− bXt

will also be non-stationary, thus violating the assumption that theerror terms are IIN. As a consequence, spurious results will arisewhen regressing non-stationary processes. As many economic pro-cesses are naturally non-stationary (as they trend, often in non-deterministic ways, and have changing volatilities), methods havebeen developed to transform non-stationary processes into sta-tionary ones. These include de-trending, taking differences andcointegration.

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A stochastic process is said to be integrated of order k, or I(k),if it needs to be differentiated k times to achieve stationarity. Forexample, if Xt is I(1), then the first difference process will bestationary

Xt ∼ I(1) =⇒ ∆Xt = Xt −Xt−1 ∼ I(0)

Methods have been developed to test the order of integration ofstochastic processes. These include unit-root tests, such as the aug-mented Dickey–Fuller and Phillips–Perron statistics (Dickey andFuller 1981; Phillips and Perron 1988). Although stationarity mightbe obtained by differencing a series, any potential relationship atthe level of the variables is lost. This is a problem, as many eco-nomic theories that we might wish to test, such as the Quantity ofMoney Theory mentioned later in this chapter, are formulated asequilibrium relationships among the level of the variables.

Another method that is used in working with non-stationary timeseries is cointegration. Consider two stochastic processes Xt and Yt,both integrated of order d, ie, I(d). If there exists a linear combinationof the two integrated processes of lower order d− p

Yt − βXt ∼ I(d− p)

then the two processes are said to be cointegrated CI(d, p). Clear-ly, the linear combination is unique (up to a normalisation-multi-plicative constant). Note that if there is a cointegrated relationshipbetween two I(1), then we can regress them together without dif-ferencing, as the residuals will be well behaved, and thus ordinarystatistical inference can be used

Yt, Xt ∼ CI(1, 1) =⇒ Yt − βXt ∼ I(0)

An n × 1 vector of I(1) stochastic processes Xt is said to be cointe-grated of rank r if there are r < n linearly independent I(0) combi-nation of the n variables or, in other words, if there exists an r × ncointegrating matrix β, such that βXt is an r× 1 vector of stationarystochastic variables

Xt[n I(1) stochastic processes]

=⇒ βXt[r stationary linearly independent processes]

It is clear that if the matrixβ is a cointegrating matrix, for every non-singular r×r matrix M, then M·βwill also be a cointegrating matrix.

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Finding an economically sensible normalisation for the cointegrat-ing space is part of the analysis (fixing the r2 terms in the matrix M,ie, imposing just-identifying conditions). Often the number of con-ditions imposed on the model to ensure economic interpretability isgreater than r2, resulting in a restricted model with over-identifyingconditions that can be tested and estimated accordingly.

It is customary to model inflation using a vector autoregressivemodel of order p, ie, VAR(p). This is an n-dimensional model inwhich the level of a stochastic vector process Xt depends on p laggedvalues of the same vector

Xt = At +p∑

k=1

Bk ·Xt−k + εt, εt ∼ IIN[0,Ω]

with constant covariance matrixΩ. Note that we can have both a con-stant intercept and possibly linear or higher-order terms in At. Theabove equation can be estimated by the ordinary least-squares (OLS)method and then residuals checked for the multivariate normal-ity assumption. The link with the cointegration approach becomesclear if we consider the Granger Representation Theorem (Engle etal 1987), which states that, for I(1) variables, a VAR(p) model canbe converted to a model combining both levels and differences (acointegrated model), ie, a vector error correction model VEC(q) oforder q = p− 1

dXt = ΠXt−1 +q∑

k=1

Bk dXt−k + εt

Clearly, the first term must contain the stochastic equilibrium rela-tionships among levels, while the second term is stationary by defi-nition of I(1). Methods have been developed to test the existence andnumber of cointegration relationships, among which is the Johansen(1991) method. The latter infers the cointegration rank r by testingthe number of eigenvalues that are statistically different from 0 inthe error-correction matrix Π of the cointegrated VAR model, thenconducts model estimation under the rank constraints. Note that therank test is based on simulated non-standard asymptotic distribu-tions that depend on the form of the VEC model, and the determin-istic terms in particular. Once the rank r has been determined, theJohansen procedure gives the maximum likelihood estimate of theunrestricted cointegrated r × 1 vector βXt (up to a normalisationmatrix M).

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As an aside, note that we typically work with the logarithm ofthe variables under consideration. In fact, the log transformationhas several advantages in that it ensures that the original variablesremain strictly positive, mitigates some common issues with levelvariables (for example, level-dependent volatilities, a form of hetero-scedasticity, thus often resulting in better behaved residuals) and it isthe natural choice, since the proportional equilibrium relationshipswe expect among our variables (eg, the quantity of money equation)will be turned into linear relationships among the log transformedvariables (and captured by the cointegrated vector).

We know that several macroeconomic factors influence inflation,and their impact varies at different time horizons. These factorsinclude the following.

• Economic activity, eg, as measured by the output gap, whichcan be inferred through statistical techniques or a theoreticalbased approach. We use the latter here and also in our real rateand monetary policy models.

• Inflation expectations, which can influence consumer be-haviour and price-setting patterns and thus become a self-ful-filling prophecy.

• Persistency, which is in great part determined by the credibility(or lack thereof) of monetary policy, and makes reversion toequilibrium levels faster (or slower).

• Exogenous shocks, which can have either a temporary effect ora more structural effect on the economy and prices (commod-ity or currency shocks, changes in productivity or competitivelandscape, etc). By definition, exogenous shocks cannot be pre-dicted, but they can be simulated, which we do extensivelythrough scenario analysis.

In our view, a monetarist approach to inflation is complemen-tary rather than competitive to an expectation-augmented Phillipscurve, so we do look at the link between inflation and money growth,although we realise that, empirically, the relationship is weak fortime horizons shorter than two years. In fact, we use a combinationof the money equation, the expectation-augmented Phillips curveand our proprietary version of the Taylor rule to try to establish a

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Figure 19.4 Macroeconomic models of inflation

Moneymultiplier

Velocity

Moneyaggregates

Outputgap

Supply shocks

Inflationexpectations

Output gap

Inflation gap

Moneyequation

Expectationaugmented

Phillipscurve

Taylorrule

Shocks to the money supplywill influence inflationexpectations and the long-term mean reversionlevel of inflation

Used for inflation forecasting and conditional scenarioanalysis

A proxy for US/EU monetary policy and the path of the shortrates, which determines theterm structure of nominal andreal bonds

general landscape that can then be explored in detail through spe-cific scenario analysis (see Figure 19.4 for the key inputs to thesemodels).

While a bottom-up approach is used to gain insight on likelyshort-term inflation behaviour (and it might be applied in practicewhen estimating carry in short-maturity linkers), a top-down struc-tural approach is typically used to establish long-term trends, andin scenario/response analysis.

Monetary policy modelsThe Taylor Rule, introduced in 1993 as a descriptive model of mon-etary policy in the USA, links the US Federal Reserve funds rate tothe real economy and inflation

Fed funds rate = α+ βGAP × output gap+ βDEFL × deflatorGDP

New Sky’s descriptive model of monetary policy, while belongingto the family of Taylor Rule’s models, is in fact a proprietary model,which provides an edge to our investment process. In fact, while theTaylor rule (Figure 19.5) misses the tightening cycle of the mid-1990s,and later the extent of easing of the post-tech-bubble recession, withour proprietary definition of output gap, we are able to achieve a far

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Figure 19.5 NSC’s proprietary Taylor rule model

12

10

8

6

4

2

Jan

1989

Mar

199

0

May

199

1

Jul 1

992

Sep

199

3

Nov

199

4

Jan

1996

Mar

199

7

May

199

8

Jul 1

999

Sep

200

0

Nov

200

1

Jan

2003

Mar

200

4

May

200

5

Jul 2

006

Sep

200

7

Nov

200

8

Jan

2010

Mar

201

1

Fed funds rateTaylor ruleNew Sky

0

Source: New Sky Capital.

superior fit than the traditional approach. Our framework also shedslight on why the Feds have seen the need for quantitative-easingpolicies, as the current slack in capacity would call for a negativeFed funds rate.

Granted we do not have control on how the Feds set short-termrates, we do have a pretty decent grasp of how the process hasworked in the past 20 years or so. Note that, having a good descrip-tive model of monetary policy is quite useful, but reading the mindsof policymakers does not in any way address the adequacy of themonetary policy process itself.

Growth and real rates

As discussed in Chapter 7, when it comes to the inflation-linkedbond market, the primary focus of both domestic and international(non-leveraged) investors is the level of real yields. Therefore, it isnatural to compare real rates, as a market-determined measure ofinvestment growth, with other benchmarks of economic growth,such as the rate of change in real GDP.

At New Sky, we look at the link between real yields and real GDP(the latter being a proprietary blend of realised and potential growthrates), with the understanding that this is an equilibrium structuralrelationship, which cannot be used to gain insight on short-term

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Figure 19.6 Ten-year US TIPS real yields and real GDP growth

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

Ten-year real yield

Real GDP growth

1997

Q4

1998

Q4

1999

Q4

2000

Q4

2001

Q4

2002

Q4

2003

Q4

2004

Q4

2005

Q4

2006

Q4

2007

Q4

2008

Q4

2009

Q4

2010

Q4

1998

Q2

1999

Q2

2000

Q2

2001

Q2

2002

Q2

2003

Q2

2004

Q2

2005

Q2

2006

Q2

2007

Q2

2008

Q2

2009

Q2

2010

Q2

2011

Q2

Sources: Federal Reserve Bank of St Louis, New Sky Capital.

changes in inflation-linked bond prices (which vary daily), but onlyto gain insight on lower frequency cyclical trends. In other words,we should not conclude, as some have, that, because empirical cor-relation between real rates and growth is dubious at best, there is nolinkage between the two. The truth of the matter is that correlation isnot the right metric to measure structural relationships of this kind(Figure 19.6).

Scenario analysis

As stated before, our focus is not on economic forecasting, as webelieve that forecasting is a fuzzy exercise, even with the “perfect”model, given that many factors remain outside the control of theforecaster. Therefore, we do not rely on a central macroeconomicforecast to identify trade opportunities, but rather we analyse themarket (for example, inflation break-evens) in the context of a plausi-ble distribution of future scenarios, supplemented by stress-testing.As an example, in autumn 2008, when the market was pricing nega-tive long-term inflation expectations, our emphasis was not on fore-casting inflation for the following 10 years, but on establishing thatwe could invest in US TIPS and achieve positive yield if a GreatDepression scenario were to materialise again.

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Table 19.4 A few examples of scenario analysis

Scenario Relativedescription Historical Real to target

Cause trigger example growth inflation Policy

Cost push Oil prices US Below Above Looseshock 1970s

Demand Increase China Above Above Loosepull in demand today

Expectations Deflation Japan Below Below Ineffectivespiral 1990s

Money Increase in Brazil Below Above Ineffectivesupply money early

supply 1990s

Beside the lessons learnt from previous historical examples ofinflation/deflation occurrences (Table 19.4), we also supplementour analysis with ad hoc scenarios, which are relevant to currentconditions and underlying risks.

As explained in Chapter 1, an inflation scenario is not just a pathfor inflation, as the underlying causes of inflation (first and secondcolumns in Table 19.3) are equally, if not more, important in deter-mining the effect on asset prices. Some qualitative details on a cost-push shock are given in the appendix on page 473. Scenario analysisis not just a quantitative exercise, but is supplemented and guidedby qualitative reasoning. In the appendix on page 474, for example,we discuss the balance of inflation risk in the US in the long term,and why we believe there is potential for upside surprises but highinflation is by no mean an inescapable outcome.

PRICING MODELS

Macroeconomic models provide insight on the world and plausibletrends in risk factors, but they need to be supplemented with modelsthat analyse how those same risk factors are priced in the market.We shall review some pricing/market models in the following.

Inflation compensation in the swap and cash market

Inflation compensation, ie, inflation break-even rates, can be ob-served both in the inflation bond (cash) market and in the inflation

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Figure 19.7 US 10-year swap versus cash BEI spread

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0Jul

2004Jul

2005Jul

2006Jul

2007Jul

2008Jul

2009Jul

2010Jul

2011

Sources: Bloomberg, New Sky Capital.

swap (derivatives) market. Although, from a fundamental point ofview, these two measures embed the same market expectations, tech-nically they are not exactly the same. This is clear from a graph ofthe spread between swap and cash BEI, which has typically beenpositive (about 30–40 basis points (bp) on the 10-year tenor; seeFigure 19.7).

The positive spread arises from several reasons. To start, thereis a difference in repo rates between inflation and nominal bonds.In other words, it is more expensive to finance sovereign inflation-linked bonds relative to nominal ones, and the cash inflation BEIincludes a liquidity risk premium, in the notation of Chapter 10 (andthe appendix therein)

yTIPSt,τ = yR

t,τ + Lt,τ

yNt,τ − yTIPS

t,τ = BEITIPS = yNt,τ − yR

t,τ − Lt,τ

Because of the liquidity premium (and the deflation floor), zero-coupon real rates are not directly observable from TIPS. However,they can be extracted from zero-coupon inflation swaps using a no-arbitrage relationship, which is model independent. Suppose that, attime t, the zero-coupon inflation swap with maturity T = t+N (thatis, N years from now), is quoted at a rate equal to KN,t. This meansthat at time T the swap buyer will receive an amount equal to theswap notional multiplied by the realised return on the price index,

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Figure 19.8 Zero-coupon inflation swap and cash hedging strategy

InflationZC swap

Pensionfund

Long ZCIL TSY

Short ZCTSY

Realised inflation

Swap BEIKN,t

yt,τ

yt,τN

TIPS

IL TSYrepo

TSYreverse

repo

Hedging strategy

Net financing cost

rIL – rTSY

Marketmaker

in exchange for the amount (1+KN,t)N − 1 agreed upon today. Thisimplies that the floating and fixed legs of the inflation swap haveequal value at inception t

EQt

(IT

Itexp

(−∫ T

trN

s ds))= E

Qt

((1+ KN,t)N exp

(−∫ T

trN

s ds))

The left-hand side is the price at time t of the zero-coupon real bondmaturing at T, while the right-hand side is a constant times the T-maturity nominal zero-coupon bond price at time t

PRt,T = exp[−yR

t,T(T − t)] = (1+ KN,t)NPNt,T

Therefore, at each point in time t, the real term structure yRt,T can

be inferred from the term structure of inflation swaps and nominalzero-coupon bonds.

The effect of the relative difference in liquidity and financing costsbetween nominal and inflation-linked bonds can be illustrated byconsidering how a zero-coupon inflation swap might be hedgedwith a combination of a zero-coupon inflation-linked bond and azero-coupon nominal bond. In Figure 19.8, it can clearly be seenthat the difference in swap and TIPS BEI comes from the differ-ence in repo/reverse repo costs between the inflation-linked andthe nominal treasury

KN,t = BEISWAP = yNt,τ − yTIPS

t,τ + rIL − rTSY = BEITIPS+rIL − rTSY

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INFLATION-SENSITIVE ASSETS

Figure 19.9 Zero-coupon inflation swap and ASW hedging strategy

Pensionfund

Swapctpty

Swapcounterparty

Realised inflation Realised inflation

InflationZC swap

Swap BEIKN,t

yt,τ

yt,τN

TIPS

Marketmaker

Short ILasset swap

Libor + A

SW

TS

YLibor + ASWIL

Long TSY asset swap

The effect of the liquidity premium can be material, especiallyduring market dislocations, and, as we shall see later, it can be thesource of relative value opportunities between the inflation cashand derivatives markets. For example, in autumn 2008, cash BEIstrongly underperformed swap BEI. This was caused by liquiditydeterioration and balance-sheet deleveraging, and not by sovereigncredit issues (as nominal and inflation-linked asset swap spreadsalso diverged, which they would not have done if the underlyingtrigger had been a perceived credit deterioration of the US Treasury).Specifically, during that time, the repo market for inflation-linkedbonds became severely disrupted and, as market makers looked intosourcing long-term financing of inflation cashflows, linkers ASWsalso widened, while nominal treasury ASWs were not affected. Infact, the zero-coupon inflation swap above can also be hedged by acombination of a long nominal Treasury plus a short inflation-linkedASW. Figure 19.9 illustrates this point, and also makes it clear that

BEISWAP = BEITIPS+ASWIL−ASWTSY

Other sources of disparity between cash and swap BEI come fromthe different convexity between zero-coupon swaps and coupon-bearing bonds (eg, for upwards-sloping inflation curves, zero-coupon BEIs are higher than “par” inflation BEI rates), and also fromdifferences in supply and demand between the cash and deriva-tive markets, with BEIs typically higher, as swaps are the preferred

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INFLATION MARKETS: A PORTFOLIO MANAGER’S PERSPECTIVE

inflation-hedging instrument for many end users, such as pensionfunds.

Inflation compensation: expectation and risk premiumInflation compensation, that is, BEI, is the sum of an inflation expec-tation term plus an inflation risk premium (see the appendix in Chap-ter 10 for details). For example, neglecting Jensen’s terms and dif-ferences in compounding, the10-year swap BEI rate can be writtenas

BEISWAPt,10 = yN

t,10 − yRt,10 = 1

10EPt [IInf

t,10]+ IRPt,10

Clearly, changes in BEI are driven by both terms but it is useful totry to separate the two, and analyse them separately, which can bedone in several ways. We might estimate the parameters of a term-structure model and then derive expected inflation within the model.Alternatively, a forecasting model for inflation (for example, a vector-autoregressive model or a Phillips curve model) can be used. Next,we might use publicly available inflation surveys, such as the Sur-vey of Professional Forecasters (SPF), a quarterly survey, providingexpected inflation over one-year and ten-year terms (Figure 19.10).Finally, a term-structure model could be used but fitted to inflationsurvey data, in addition to nominal and real yields. Interestinglyenough, Ang et al (2008) and Chernov and Mueller (forthcoming)find that surveys outperform other methods of inflation forecast-ing, although they have the drawback of being available only at lowfrequency.

If we accept the qualitative features of the survey series shown inFigure 19.10, the conclusion is that, in the US, long-term (10-year)inflation expectations have been relatively stable since the late 1990s,hovering around an annual rate of about 2.5%. This is likely to be theresult of the Feds having established credibility in maintaining lowand stable inflation, so that short-term shocks in the spot rate quicklyrevert to equilibrium, anchoring long-term expectations. This is alsoconsistent with the flat term structure of inflation expectations foundby Ang (2008) and Adrian and Wu (2010). Of course, we are not tak-ing the 2.5% level literally, as it is just one measure of expected infla-tion, but we believe the inflation risk premium to be a key dynam-ical driver over typical trading horizons. In other words, althoughmacroeconomic models of inflation are important to our view ofthe world, such structural relationships are of somewhat limited

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INFLATION-SENSITIVE ASSETS

Figure 19.10 Inflation expectations from the Survey of ProfessionalForecasters

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

01991Q4

1994Q4

1997Q4

2000Q4

2003Q4

2006Q4

2009Q4

1Y 10Y

Sources: Federal Reserve Bank of Philadelphia, New Sky Capital.

usefulness when trading in the inflation market, unless we believelong-term equilibrium levels will change materially (which clearlywould directly affect BEI rates).

As derived in the appendix to Chapter 10, the inflation risk pre-mium depends on the correlation between the real pricing kernel(which includes both real rates and the price of risk) and the priceindex It. Specifically

IRPt,τ = − 1τ

ln

⎡⎢⎢⎢⎢⎣1+

COVPt

[MR

t+τMR

t,

It

I t+τ

]

PRt,τEP

t

[It

It+τ

]⎤⎥⎥⎥⎥⎦

where

MRt+τ

MRt= exp

[−1

2

∫ t+τ

tλT

s λs ds−∫ t+τ

tλT

s dBPs −

∫ t+τ

trR

s ds]

Indeed, if such a correlation is zero, the inflation risk premium is alsozero, and we recover the Fisher equation. In general, the inflationrisk premium is positive if above (below) average inflation occursin states where real wealth is below (above) average, and vice versa.Before the Great Recession of 2008–9, the inflation swap market dis-played a consistently positive inflation risk premium; however, ourestimate of the latter has turned negative on more than one occasionsince then (Figure 19.11).

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INFLATION MARKETS: A PORTFOLIO MANAGER’S PERSPECTIVE

Figure 19.11 An estimate of the 10-year inflation risk premium

0.8

0.6

0.4

0.2

0

–0.2

–0.4

–0.6

–0.8

–1.0

–1.2

–1.4

%

Jul 2

004

Jan

2005

Jul 2

005

Jan

2006

Jul 2

006

Jan

2007

Jul 2

007

Jan

2008

Jul 2

008

Jan

2010

Jul 2

010

Jan

2011

Jul 2

011

Jan

2012

Source: New Sky Capital.

This underlines the fact that the market might price inflation riskquite differently depending on the overall environment and the bal-ance in risk aversion between investors who prefer fixed real returnsand investors who prefer fixed nominal returns. Specifically, if themarket is focused on the risk of high inflation, then nominal securi-ties will be penalised by a positive risk premium. On the contrary,if the market is concerned about deflation, then the nominal bondwill benefit from being the better deflation hedge, and the inflationrisk premium will be negative. This observation also hints at the factthat, although the price of risk is typically modelled as a Gaussianvariable in affine models, higher moments than variance (skewness,ie, asymmetry in inflation risk, in particular) might be important inorder to model the inflation risk premium realistically (Garcia andWerner 2010). In fact, although the variance in inflation expectations,as measured by the SPF (which also publishes spreads in quartilesof the future inflation distribution), has increased since the GreatRecession, it does not help to explain the dynamics of the inflationrisk premium or indeed the changes in sign. Unusual circumstances,such as quantitative easing by the Feds and sovereign credit woes inEurope, are likely to have contributed to the bipolar pricing of infla-tion risk from 2008 onwards, as well as to long periods of negative

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INFLATION-SENSITIVE ASSETS

real rates and an increased correlation between BEI and the equitymarket.

Carry calculationsCarry can be an important value metric especially for short maturitylinkers. To calculate carry, we have to specify a time horizon, a financ-ing rate and, in the case of inflation-linked bonds, non-seasonallyadjusted inflation rate projections over the relevant time window (sothat linkers’ carry inherits the index seasonality as well, which willbe discussed in the next section). A precise carry calculation shouldtake into consideration coupon income received and reinvested overthe period, the passage of time, yield roll-down, financing costs andinflation accrual for the linker. However, given that these calculationtypically apply to short-term horizons and yet uncertainty aboutfuture inflation rates supersedes concerns of mathematical preci-sion, we shall use a simplified formula to guide intuition and writethe bond carry over a horizon of n = 1, 2, 3 months as

CTSY(n) = (yTSY − rTSY)n12

CTIPS(n) = (yTIPS − rTIPS)n12+

n∑k=1

CPIk

12

where CPIk is the non-seasonally adjusted consumer price indexinflation rate in month k. When comparing a nominal treasury withthe TIPS, we are implicitly assuming a similar roll-down on both(that is, a locally flat BEI curve). In addition, we can derive the repo-adjusted BEI rate as

BEIrepo−adj = BEI+rTIPS − rTSY

It can be seen that when the inflation projection matches therepo-adjusted BEI (which occurs over the three-month horizon inTable 19.5), the nominal and inflation-linked bonds have equal carry.Further details are shown in Table 19.5.

SeasonalityIn general, when analysing inflation opportunities over a specifictime horizon, we should try to determine a plausible distributionof total returns over the chosen holding period. In the case ofan inflation-linked bond, total return includes interim cashflowsreceived (a function of fixed coupon and inflation), quoted price

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INFLATION MARKETS: A PORTFOLIO MANAGER’S PERSPECTIVE

Table 19.5 Simplified carry calculation: BEI and repo-adjusted BEI

Coupon Yield BEI Repo Repo-adj. BEI

10yr nominal Tsy (%) 2.000 1.83 0.2010yr TIPS (%) 0.125 −0.35 2.18 0.30 2.28

1-month 2-month 3-month

NSA CPI projections (%) 0.21 0.46 −0.10Cum. annualised (%) 2.5 4.0 2.28

1-month 2-month 3-monthcarry carry carry

1M Nominal Tsy carry (%) 0.14 0.27 0.411M inflation-linked carry (%) 0.16 0.56 0.41

Difference (%) −0.02 −0.29 0.00

Figure 19.12 The effect of seasonality on US CPI rates in 2011

–0.3

–0.2

–0.1

0

0.1

0.2

0.3

0.4

0.5

%

Jan Feb Apr May Jun Jul Aug Sep Oct Nov DecMar

Sources: US Bureau of Labor Statistics, New Sky Capital.

changes (a function of real rates and time) and interim inflationaccrual on notional (a function of realised inflation) as well asfinancing costs.

Short-term inflation projections are particularly important in cal-culating returns for short-maturity linkers, since inflation accrualon notional is usually the key determinant of value in these cases.Clearly, given that, in the US, the inflation index used for notional

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INFLATION-SENSITIVE ASSETS

Table 19.6 Market-based BEI and forecast-based BE yield

Yield BEI Duration

US Tsy (%) 0.30US TIPS (%) −1.50 1.80 2

BEI Next NSA CPI BE yield

Monthly (%) 0.15 0.60 0.23

accrual is not seasonally adjusted, projections need to take into con-sideration all the seasonal fluctuations, which is not always an easything to do. Indeed, while inflation and real rate changes are often(but not always) positively correlated and tend to mitigate the risk oflonger maturity linkers, short-term fluctuations in realised inflationdue to seasonal patterns (or non-core volatile components) are veryimportant to the value assessment of short-term linkers. In addi-tion, seasonal fluctuations cannot be ignored, as their size can, incertain months, overwhelm other fundamental considerations (see,for example, the magnitude of the seasonality effect for March inFigure 19.12). Clearly, non-seasonally adjusted (NSA) price levelsare the only directly observable quantities. The reason to identifyseasonality factors explicitly stems from the desire to forecast NSAseries (which will in general contain trend, cyclical, irregular andseasonal components) by extracting the regular predictable patters(ie, seasonality) first, and then focus on the rest.

Consider a two-year (remaining maturity) linker with BEI equalto 1.8%, which corresponds to an inflation accrual on notional ofabout 1.8%/12 = 0.15% per month. Even assuming the market hasgot the annual inflation rate correct, in any given month inflationwill fluctuate because of seasonality, and potentially other factorsas well. In other words, monthly inflation rates might still com-pound to give an effective annual 1.8% rate but are likely to havea wigglier pattern, mirroring the seasonality factors shown in Fig-ure 19.12 (which sum to zero). Specifically, suppose that there arereasons (seasonality being one of them) to believe that, next month,NSA inflation will come in at a 0.60% rate (this is about equal tothe monthly BEI rate plus the seasonality adjustment for March inFigure 19.12). This implies that the two-year duration linker’s yieldcan widen 45/2 = 22.5bp before it underperforms the corresponding

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INFLATION MARKETS: A PORTFOLIO MANAGER’S PERSPECTIVE

Figure 19.13 Inflation options implied volatility surface

2.5

2.0

1.5

1.0

0.5

0

%

16

1116

2126Maturity

Low

str

ike

Hig

h st

rike

At-

the-

mon

ey

Sources: Bloomberg, New Sky Capital.

maturity nominal (Table 19.6). Clearly if the NSA inflation forecastand BEI coincide, the BE yield is zero.

Besides short-term carry, seasonality also plays a part in the analy-sis of relative value of longer-term inflation-linked bonds payingcoupons in different months.

Inflation option models

Inflation option quotes are regularly available for both caps andfloors (eg, on Bloomberg, see the screen shots in Chapter 8), but themarket has limited depth, and bid–ask spreads are material (as muchas a few percentage points of option premium). As a consequence,market flows can be as important as (if not more than) fundamentalconsiderations when trading in the space.

There is no natural seller of inflation volatility, especially at highstrikes (ie, caps; inflation floors can be stripped from TIPS by ASWs).The dealer community has traditionally provided volatility to endusers (either directly through inflation options or indirectly throughthe inflation structured note market), while (delta-) hedging theiroption book. Understanding this exposure, and its sensitivity tochanges in BEI, is essential, as it is a key driver of prices (the volatil-ity smile often hints at these relationships, in addition to morefundamental considerations such as the pricing of fat-tails, etc).

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INFLATION-SENSITIVE ASSETS

Figure 19.14 Ratio of implied to realised inflation volatility

250

225

200

175

150

125

100

50

75

%

Aug

200

9S

ep 2

009

Oct

200

9N

ov 2

009

Dec

200

9

Feb

201

0Ja

n 20

10

Apr

201

0

Apr

201

1

Mar

201

0

Feb

201

1Ja

n 20

11

Mar

201

1

Jun

2010

May

201

0

Aug

201

0Ju

l 201

0

Oct

201

0S

ep 2

010

Dec

201

0N

ov 2

010

Ten-year YoY 3% cap. Source: New Sky Capital.

Figure 19.13 shows the inflation implied volatility surface in May2011.

The traditional buyers of inflation volatility are hedgers (eg, insur-ance companies), who have often limited sensitivity to price levelsand the difference between implied and realised volatility (shownin Figure 19.14). In fact, given the technicalities, and the many ana-lytical complexities, dynamical replication has not been a practicalavenue for these market participants.

There are several models used in pricing inflation derivatives.Here we shall briefly introduce the first and seminal one, the Jarrow–Yildirim model, where the price index level is the translation mecha-nism between the money economy and the barter economy (see alsothe appendix in Chapter 10, and Chapter 8). Specifically, in parallelwith the money economy, we can consider a barter economy wherecontracts are specified in terms of a basket of good and services(Figure 19.15). In other words, the zero-coupon bond PR

t,T (where Tis the maturity) in the barter economy promises one unit of the con-sumption basket at time T, in exchange for a fraction of the baskettoday (assuming positive real rates, which should be the case unless

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INFLATION MARKETS: A PORTFOLIO MANAGER’S PERSPECTIVE

Figure 19.15 The barter versus the money economy

Barter economy

Money economy

there are storage costs or a greater utility to later, rather than current,consumption).

In the money economy, zero-coupon bonds denominated in bas-kets of goods, such as PR

t,T , are not tradeable instruments but theirUS dollar value is (this is, in fact, our well known inflation-linkedbond, if one puts indexation lags and deflation floor aside). In otherwords, to transition from the barter economy to the money econ-omy, we need to multiply any basket-denominated quantity by theprice index It, which is denominated in US dollars per basket, thusobtaining a dollar-denominated quantity.

Jarrow and Yildirim (2003) introduce three correlated Brownianmotions driving the stochastic dynamics of nominal and real instant-aneous forward rates (so this model belongs to the Heath–Jarrow–Morton class), and the price level index It under the nominal dataprobability P

PR,Nt,T = exp

(−∫ T

tf R,N(t, u)du

)

f R,N(t, T) = f R,N(0, T)+∫ t

0αR,N(s, T)ds+

∫ t

0σR,N(s, T)dBR,N,P

s

or, in differential form

dt f R,N(t, T) = αR,N(t, T)dt+ σR,N(t, T)dBR,N,Pt

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INFLATION-SENSITIVE ASSETS

The price level index is given by

dIt

It= µI

t dt+ σ It dBIP

t

It = I0 exp(∫ t

0µI

s ds− 12σ

I2t +

∫ t

0σ I

s dBIPs

)

dBNt dBR

t = ρNR dt, dBNt dBI

t = ρNI dt, dBIt dBR

t = ρRI dt

The forward rates volatility functions are chosen as in the Vasicek(1977) model, that is

σR,N(t, T) = σR,N0 e−α

R,N(T−t)

The fundamental tradeable instruments in the money economy arethe nominal zero-coupon bonds PN

t,T , the nominal money marketbond (our numeraire of choice)

BNt = exp

(∫ t

0rN

s ds)

the dollar value of real zero-coupon bonds ItPRt,τ and the dollar

value of the barter economy numeraire ItBRt . Therefore, to avoid

arbitrage, there should be a probability measure Q under whichall our tradeable assets, discounted by the nominal numeraire, aremartingales

PNt,T

BNt

,ItPR

t,τ

BNt

,ItBR

t

BNt−→ martingales under Q

Using the link between forward rates and bond prices and thedynamics equations for rates and the inflation index, by using Itô’sformula, we can derive the stochastic differential equations for thethree quantities above. From these, the change in measure that elim-inates drifts, thus taking us to the risk-neutral probability Q, can beinferred.

In the risk-neutral measure Q, nominal and real zero-coupon bondprices as well as the price index have a lognormal distribution

dIt

It= (rN

t − rRt )dt+ σ I

t dBIQt

dPNt,T

PNt,T

= rNt dt− ΣN(t, T)dBNQ

t

dPRt,T

PRt,T

= [rRt − ρRIσ I

t ΣR(t, T)]dt− ΣR(t, T)dBtRQ

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where

ΣR,N(t, T) =∫ T

tσR,N(t, u)du

The model, by assuming lognormal bond prices (ie, normally dis-tributed rates), has the drawback of allowing instantaneous and for-ward rates to go negative from time to time, but, on the plus side, thelognormal assumption provides analytical solutions for both bondprices and inflation caps and floors. For example, the price at timet of the zero-coupon inflation cap, struck at K and with maturity T,can be written as an expectation under the risk neutral measure

Ct = EQt

[max(IT − K, 0) exp

(−∫ T

trN

s ds)]

where

IT = It exp(∫ T

t(rN

S − rRS )ds− 1

2

∫ T

tσ I2

s ds+∫ T

tσ I

s dBIQs

)

thus leading to a Black–Scholes-type closed-form solution, by virtueof the lognormality assumption.

FROM THEORY TO PRACTICE: INFLATION STRATEGIES INACTIONNew Sky’s investment strategies focus on inflation-linked products(both cash and derivatives) in developed and emerging markets,with other inflation-sensitive assets employed opportunistically.The objective is to build a balanced portfolio of directional andnon-directional (arbitrage) inflation strategies, with attractive risk-adjusted returns.

Risk management, comprising both quantitative and qualitativeaspects, is a very active part of our investment process and inte-gral to our culture, as our foremost aim is to preserve and protectcapital. Indeed, our active approach to risk management, which hasresulted in quick responses to unexpected market conditions (suchas in the aftermath of the 2011 tsunami in Japan, clearly not a foresee-able event), has added considerable value to our portfolio, in termsof both higher returns and lower risk. At its root, we believe thatrisk management is about recognising the possibility that we too, asall others, might occasionally be wrong, and asking what happensthen. Taking risk intelligently should minimise the chance of mis-takes, while effective risk management should mitigate their effectif (when) they do occur.

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In addition, besides identifying individual opportunities, theportfolio-construction process takes into account their return–riskcontribution to the portfolio (diversification, carry), as well as otherpractical considerations (for example, convexity, ease of unwindingunder stressed conditions and market flows). Target stop-loss andprofit-taking exit points are also part of our disciplined process, andare quite effective at limiting downside and creating a positivelyconvex distribution of portfolio returns.

As discussed earlier, we believe that the ideal investment ap-proach to the inflation sector combines a fundamental view of whatis embedded in prices with an appreciation of the technical factorsaffecting the market, the two often being correlated. Using suchan approach, it is possible to identify both directional and non-directional inflation strategies and build portfolios with attractiverisk-adjusted expected returns and positive convexity, as well aslow, or even negative, correlation to other traditional asset classes. Acouple of real life examples of these strategies will be discussed next.

Example: directional tradeIn this section, we shall review an example of a directional strategy.A corollary of the discussion about the inflation risk premium in theprevious section is that, when it comes to trading BEI, unconditionaldistributions have lost some of their significance, while the ability todiscern between different regimes, as well as understanding the rolethat monetary policy and global markets might have in triggeringa transition from one regime to another, has become of paramountimportance.

One example of this is a short BEI trade we entered into onAugust 1, 2011. Over the course of July, several economic indicatorsshowed substantial deterioration, with negative momentum inten-sifying over the last week of the month. Durable goods orders cameout at a negative 2.1% (on July 27; the number refers to the month ofJune), while first quarter GDP was revised substantially lower to anannualised rate of 0.4% (from 1.9%).At the same time, consumer sen-timent plunged to its lowest reading in more than two years (on July29)7, and equities strongly sold off. This string of negative domesticeconomic data came in the mist of political gridlock in the discussionof the increase in the US debt ceiling, the threat of an imminent UScredit downgrade and mounting concerns in Europe (and Greece inparticular).

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INFLATION MARKETS: A PORTFOLIO MANAGER’S PERSPECTIVE

Figure 19.16 Short 10-year BEI trade

2.29

2.71

3.0

2.0

2.9

2.8

2.7

2.6

2.5

2.4

2.3

2.2

2.1

Dec

2D

ec 1

6

Nov

3N

ov 1

7

Jun

2Ju

n 16

Jun

30

Dec

30

Jan

13Ja

n 27

Feb

10

Feb

24

Mar

10

Mar

24

Aug

11

Aug

25

Sep

8S

ep 2

2

May

5M

a7 1

9

Apr

7A

pr 2

1

Jul 1

4Ju

l 28

Oct

6O

ct 2

0Sources: Bloomberg, New Sky Capital.

During the same period, the 10-year BEI rate held pretty steady,and our estimate of the inflation risk premium stood solidly in pos-itive territory, actually above the average of the conditional proba-bility distribution. This and the overall macroeconomic picture sug-gested that a short BEI position had substantial upside in the case ofa regime shift (which we judged likely), and much less of a down-side in case no such switch would occur. In reality, in the course ofthe next 10 weeks, not only were BEI rates re-priced substantiallylower, but the inflation risk premium did in fact turn negative (Fig-ure 19.11), as the market transitioned to pricing downside inflationrisk. The announcement of Operation Twist on September 21 alsocontributed to a further step down in BEI rates, as nominal treasuriesrallied considerably after the news.

As it turns out, we entered the short BEI position on August 1 at2.71%, and exited on October 6 at 2.29% (the actual trading patternwas not linear, as technical effects also played a role).

Example: arbitrage trade

As explained earlier, swap BEI rates are typically higher than cashBEI, mostly due to the difference in repo costs and ASW spreadsbetween nominal Treasuries and inflation-linked bonds.

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INFLATION-SENSITIVE ASSETS

Figure 19.17 EU 10-year swap versus cash BEI spread

Jun

2010

Aug

201

0

Dec

201

0

Feb

201

1

Apr

201

1

Oct

201

0

Dec

200

9

Jun

2009

Feb

201

0

Aug

200

9

Apr

201

0

Oct

200

9

Dec

201

1

Jun

2011

Feb

201

2

Aug

201

1

Apr

201

2

Oct

201

1

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

–0.1

Sources: Bloomberg, New Sky Capital.

However, early in 2011, we saw the positive spread between theeuro 10-year swap and cash BEI compress close to zero (and evennegative) for a short period of time. Reasons for this were technicalin nature, as some demand for inflation swaps shifted to the 30-yearmaturity bucket (given the unusually flat BEI curve), while buyersof inflation bonds shifted capital to EU linkers once their real yieldsbroke above 1%. Clearly this provided an attractive opportunity,and a classic mean reversion trade, as the swap–cash BEI spreadwas close to a historical minimum, with significant upside volatility.

At the same time, higher oil prices at the onset of the Arab Spring,and a substantial supply of inflation bonds in the pipeline (positivefor inflation expectations but not for linkers), provided, in our mind,the likely catalysts for the reversion to equilibrium to quickly takeeffect. There were also qualitative reasons why we liked this trade,specifically the fact that it provided no directional macro exposure,and had insurance qualities in a “flight to liquidity/risk aversion”scenario. As it turns out, we entered the position (long EU 10-yearinflation swap, long 10-year nominal Bund, short 10-year GermanBundei) at a spread of 0.08% on March 9, 2011, let mean reversionwork its way to equilibrium and closed the trade on May 26, 2011,at a spread of 0.31% (Figure 19.17).

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CONCLUSIONSThe inflation market provides a risk-transfer mechanism amonginvestors and hedgers. In this chapter, we explain how this mar-ket works, the different agents involved and what motivates them,as well as the role of market makers in providing liquidity.

Inflation is not only an important macroeconomic factor but alsoa risk that should be actively managed. Indeed, BEI rates displayedequity-like volatility during the 2008–9 global crisis and have contin-ued to do. This coincided with a substantial reduction in risk capac-ity on behalf of market makers, thus creating pricing distortions andrelative value opportunities.

In the first part of the chapter, we introduced some of the toolsessential to the analysis of the inflation market, including top-downmacroeconomic models and bottom-up pricing/market models. Wealso described our investment philosophy and objectives, as wellas our holistic approach to the sector, which takes into account bothfundamental and technical considerations. Finally, we presented tworeal-life examples of inflation strategies and the thought process/analysis behind their evaluation.

APPENDIX: OIL PRICES SHOCK SCENARIOThis scenario might be relevant in a situation of renewed geopoliticaltension (we used this during the Arab Spring in 2011). A spike in oilprices, if sustained, will translate in an increase in global headlineinflation. We shall focus on the impact in the US. In building thisscenario, we consider the direct effect on headline inflation (energybeing about 9% of CPI, although other items in the basket will alsobe affected) and also on consumption (higher oil prices as an indirecttax on consumers). We also assume a negative impact on real growthand GDP.

We use a short-term model of inflation (Phillips curve and bottom-up CPI-component analysis; see Figure 19.18), and output gap, afterwhich we let structural mean-reverting processes take hold. The pathof the short-term nominal rate is given by the Taylor rule (otherassumptions can be made). The evolution of inflation (swap) BEIs isgiven by expectation plus a risk premium. Real rates are given by theFisher equation plus risk premium/covariance effect. As for mone-tary response, we expect the Feds to tighten in response, althoughthe rise in rates will be limited by the still negative output gap (see

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Figure 19.18

Spike in oilprices and CPI; growthslows down

Feds raiserates; outputgap remains

negative

Inflation BEs increase;inflation linkers rally;

nominal bonds sell-off;pressure on currency

and equity

the Taylor rule). If their response is inadequate (as it happened inthe 1970s), long-term inflation expectations will increase, affectingboth the level of and the speed to equilibrium, as well as market riskpremiums.

APPENDIX:THE INFLATION/DEFLATION DEBATE IN THE US

In the US, we believe that inflation surprises are possible, and aremost likely to occur on the upside. Clearly, debt levels are high(about US$15.7 trillion as of May 2012, of which about 70% is heldby the public, slightly higher than nominal GDP as of 2012 Q1), andprojected to increase considerably in the future. Furthermore, thefederal deficit is in the high single digits and balancing the budgetfaces strong headwinds, because of insufficient growth of tax rev-enues, unfavourable demographics (the “baby-boomer” generationretiring) and ballooning pension and medical cost liabilities (SocialSecurity, Medicaid, Medicare whose NPV is estimated to be aboutUS$45–50 trillion). The overall fiscal situation is not only complex,but also politically sensitive.

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In addition, the Fed’s and Treasury’s balance sheets have grownconsiderably since the crisis because of aggressive quantitative eas-ing programmes aimed at avoiding the dangers of a deflation spiral.The effect on the money supply has been modest thus far, but allof this can quickly change as the money multiplier/velocity revertto more typical levels. Pressure from external shocks, such as com-modity/food prices (increased political unrest, bad weather in sev-eral parts of the world affecting crops) slightly subsided after 2011,but clearly affected headline figures, and to a lesser degree coremeasures, in the recent past.

At New Sky, we do not believe high inflation is inescapable. Infact, effective reform in the area of non-discretional spending anddefence would mitigate the risk on the fiscal side. In addition, theFeds, as the first line of defence, do have effective tools of monetarypolicy and have used them judiciously, albeit not perfectly, in the past(at least in the post-Volcker era). The Feds and the Treasury can alsomanage a gradual reduction in their balance sheets without unduedisruption to markets, although the process is intrinsically delicateand sensitivities are high. As for external shocks, these might be,at least in part, self-correcting (although a case might be made forsecularly increasing mean-reverting levels).

However, upside risks to inflation are clearly present, as post-crisis budget battles have focused on a few billions of US dollars’worth of discretional spending, thus addressing neither the core northe magnitude of the fiscal problem. It is not clear how the politicsof the process will play out. In addition, even with reduction in Fedsand Treasury’s QE programmes being underway, given their sheersize, exit strategies are delicate, implying a high sensitivity to errorsin policy.

Despite the debt/fiscal situation, and pressure from energy andfood prices clearly evident in headline CPI and PPI over the course of2011, the Feds have traditionally focused on core inflation measures.This is based on the view that external shocks are temporary, andtheir effect on inflation should also be temporary, provided there islong-term anchoring of inflation expectations (the argument is that,once the shock subsides, headline inflation will mean revert to thelong-term target, unless the market loses confidence in the ability/willingness of the Feds to take any appropriate monetary action).Indeed, in the post-Volcker era, empirical evidence points to the

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fact that the focus on core inflation measures has worked well, inthe sense that core inflation has remained within range, irrespectiveof commodity shocks, and with very limited monetary response tothose shocks (this is not true in the pre-Volcker era; see Evans andFisher (2011)).

In our opinion, however, the argument is dangerously backwards-looking, especially when we consider the difference in secular macrotrends at play, in particular the demographics of higher consump-tions in emerging markets and the possibility that the latter mightturn from a deflationary to an inflationary global force. These sec-ular changes may or may not play out (as usual, other effects suchas moderation of growth in emerging markets and/or technologyadvances might counteract these forces). In any case, these effectsare never captured “within the model”, and if they materialise, theywill come as a surprise to many forecasters.

1 Refer to Chapters 7 and 20 for a brief history of inflation indexation in developed and emergingcountries respectively.

2 Keynes advocated the use of inflation-linked bonds in his testimony before the ColwynCommittee on National Debt and Taxation in 1924.

3 Clearly, inflation-linked bonds also pay a semiannual coupon. Coupon cashflows can bereplicated by a portfolio of zero-coupon swaps and treasury strips, for each coupon date(Fleckenstein et al 2010).

4 The five-year BEI breached the −2% level.

5 The five-year US TIPS Par ASW spread widened to 200 basis points over Libor. This was aliquidity effect that did not affect nominal treasury ASW.

6 Examples of sudden shifts in inflation markets include those triggered by new regulations,such as the indexation of tax-exempt saving accounts in France in 2003 (which created strongdemand for inflation-hedging products almost overnight) and the indexation of UK pensionannuities following the Pension Plan Act of 1995. Accounting regulations, especially thosepertaining to retirement benefits and their valuation (such as FRS17 in the UK), can also havea profound effect on inflation players and markets.

7 See http://www.newskycapital.com/images/JUL11.pdf.

REFERENCES

Adrian, T., and H. Wu, 2010, “The Term Structure of Inflation Expectations”, StaffReport 362, Federal Reserve Bank of New York.

Ang, A., G. Bekaert and M. Wei, 2008, “The Term Structure of Real Rates and ExpectedInflation”, The Journal of Finance 63(2), pp. 797–849.

Chernov, M., and P. Mueller, Forthcoming, “The Term Structure of Inflation Expectations”,Journal of Financial Economics.

Dickey, D., and W. Fuller, 1981, “Likelihood Ratio Statistics forAutoregressive Time Serieswith a Unit Root”, Econometrica 49, pp. 1057–72.

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INFLATION MARKETS: A PORTFOLIO MANAGER’S PERSPECTIVE

Engle, R. F., and C. W. J. Granger, 1987, “Co-Integration End Error Correction: Represen-tation, Estimation, and Testing”, Econometrica 55, pp. 251–76.

Evans, C., and J. D. M. Fisher, 2011, “What Are the Implications of Rising CommodityPrices for Inflation and Monetary Policy?”, Chicago Fed Letter, May, p. 286.

Fleckenstein, M., F. A. Longstaff and H. Lustig, 2010, “Why Does the Treasury Issue TIPS?The TIPS-Treasury Bond Puzzle”, Working Paper, UCLA.

Garcia, J., and T. Werner, 2010, “Inflation Risks and Inflation Risk Premia”, Working PaperSeries, No. 1162, European Central Bank.

Jarrow, R., and Y. Yildirim, 2003, “Pricing Treasury Inflation Protected Securities andRelated Derivatives using an HJM model”, Journal of Financial and Quantitative Analysis38(2), pp. 337–358.

Johansen, S., 1991, “Estimation and Hypothesis Testing of Cointegration Vectors inGaussian Vector Autoregressive Models”, Econometrica 59(6), pp. 1551–80.

Phillips, P. C. B., and P. Perron, 1988, “Testing for Unit Roots in Time Series Regression”,Biometrika 75, pp. 335–46.

Perrucci, S., 2009, “Inflation: The Real Opportunity”, URL: https://www.newskycapital.com/.

Taylor, J. B., 1993, Discretion versus Policy Rules in Practice, Carnegie-Rochester ConferenceSeries on Public Policy, Volume 39, pp. 195–214 (Elsevier).

Vasicek, O., 1977, “An Equilibrium Characterization of the Term Structure”, Journal ofFinancial Economics 5, pp. 177–88.

Wilson Committee, 1980, “Report of the Committee to Review the Functioning of FinancialInstitutions (Chairman Sir Harold Wilson)”, Command Paper 7937 (London: HMSO).

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20

Inflation Indexation and Products inEmerging Markets

Brice Bénaben, Stefania A. PerrucciNew Sky Capital

Emerging countries have been pioneers in the inflation market.Brazil, Israel and Iceland issued their first inflation-linked bond in1964; Chile and Colombia issued their first in 1967. For such pio-neers, issuing inflation-linked debt provided one of the few viablelong-term funding options to support on-going infrastructure andagriculture projects in the backdrop of the persistent high inflationenvironment of the 1960s, 1970s and 1980s (Figure 20.1). This con-trasts with what occurred in developed countries. At the time ofwriting, the latter are the largest issuers of inflation-linked debt, buttheir inflation-linked programmes started much later,1 and, with theexception of the UK, not as a way to counteract high inflation butin order to meet investors’ demand for stable yields and portfoliodiversification.

Although emerging countries’ inflation-linked debt accounts foronly 20% of the total (Figure 20.2), it grew at a rapid pace from theearly 2000s onwards, especially in Latin American countries (whichtogether comprise three-quarters of emerging markets’ inflation-linked issuance), particularly Brazil, where such growth was spurredby brisk economic activity combined with relatively high inflation.At the same time, the evolution of domestic pension funds and insur-ance companies has also created additional structural demand forreal return assets. In addition, while emerging markets’ inflation-linked debt has traditionally been absorbed by local demand, this hasgradually changed, and growing interest on behalf of internationalinvestors has indeed been one of the reasons behind the growth in

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Figure 20.1 Year-on-year inflation rate in emerging countries

140

120

100

80

60

40

20

0

%

1969

1970

1972

1974

1976

1978

1980

1981

1983

1985

1987

1989

1991

1992

1994

1996

1998

2000

2002

2003

2005

2007

2009

2011

Sources: International Monetary Fund (2004), New Sky Capital.

Figure 20.2 Size of inflation-linked debt: developed versus emergingmarkets

Emergingmarkets

20%Australia

1%Canada

3%

Japan2%

Italy 5%

Germany2%

France9%

UK22%

US35%

Sources: Bloomberg, New Sky Capital; data as of March 2012.

issuance, a phenomenon we have observed across several emergingcountries not just in Latin America, but in Asia as well.

In this chapter, we analyse the key developments in inflation-linked markets in emerging countries. In the first part, we focuson the historical development of the inflation indexation mecha-nism, with a focus on Latin American countries, which were the

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early issuers of inflation-linked debt and, together, account for most(about three-quarters) of emerging markets’ inflation-linked debtoutstanding. Although these countries still dominate the emergingmarkets’ inflation-linked debt sector, we also mention the positiveprospects for the growth we see elsewhere, particularly in Asia.

The second part of the chapter discusses the detailed characteris-tics of several of the inflation-linked instruments issued in emergingcountries, covering not only the common features but also the speci-ficities of each market. Given that, from Latin America to Africa andAsia, about 20 emerging countries have issued inflation-linked debt(and more are adding to the count, eg, Hong Kong, Thailand andRussia, or considering resuming issuance again, eg, India), a com-prehensive treatment of every traded instrument would be tediousand beyond the scope of this chapter. Therefore, we shall focus onthe inflation-linked products that offer the most liquid opportunitiesin the space, as these are the instruments on which foreign investors’demand is likely to concentrate.

THE EVOLUTION OF INFLATION INDEXATION IN EMERGINGMARKETSIn this section, we focus on the history and development of themodern-era inflation indexation mechanism, with a focus on LatinAmerican countries, which have been the pioneers in issuing in-flation-linked debt and, together, still account for the vast major-ity of emerging markets’ inflation-linked debt outstanding. Nextwe discuss the evolution of the inflation indexation mechanism inother emerging markets, specifically in Asia, where inflation-linkedissuance is still small and, in many aspects, in its infancy, and yet wesee potential for significant growth in the years to come.

When it comes to inflation indexation, history, for example, inLatin America, has exposed some weaknesses and practical limi-tations of this risk transfer mechanism, especially when it comesto consumer products. However, the benefits of indexed financialproducts for pension funds and insurance companies are also wellrecognised, and these have contributed substantially to the demandfor these products across the globe. At the same time, the overallregulatory framework regarding inflation indexation has evolvedquickly, especially in the area of risk and asset–liability manage-ment, with inflation-linked instruments becoming a key hedging

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tool: a development that contributes further to structural demand inthe sector.

Another reason that, in our opinion, the developments of infla-tion-linked instruments will be sustained is the intrinsic uncertaintyaround inflation, even in the instances where monetary policy hasbeen successful in anchoring long-term expectations. Indeed, non-core components of inflation, ie, energy and food products, whichare the hardest to predict, have shown increased volatility in thefirst decade of the 21st century, thus contributing to higher volatil-ity in headline inflation, through first- and second-order effects. Theunderlying causes are complex and multiple (weather, global warm-ing, geopolitical tensions, changes in food consumption in countriessuch as China, population growth, globalisation of economies) andmore likely than not to continue. In addition, these effects are ampli-fied by the fact that, as seen in Chapter 3, food products in consump-tion baskets in emerging markets have, on average, more than twicethe weight of those in developed countries. This provides an addi-tional challenge to monetary policy in emerging markets, and hasbecome a topical issue of discussion in both financial and academiccircles.

Because of all these factors, a plausible outcome is the continu-ation of the trend we saw at the end of the 2000s, with developedand emerging countries promoting liquidity and issuance in boththeir nominal and real debt markets. In other words, Latin Ameri-can countries, historically the pioneers of inflation indexation, have,over time, thanks to more stable economies and prices levels, startedto develop their nominal debt markets as well. In contrast, the USand several European and Asian countries, where high inflation hasbeen less of an issue in the past and which have a large nominal debtmarket, have started to develop inflation indexation as an alterna-tive funding mechanism, in the wake of increasing investor demand,in particular from insurance companies and pension funds.

Latin AmericaLatin American countries have some of the oldest and most ad-vanced inflation-linked financial markets, which include severalactive agents (such as the domestic government, local banks, pen-sions funds and insurance companies) and several inflation instru-ments (such as inflation-linked sovereign bonds, and inflation-linked mortgage/consumer loans and securities).

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From the 1960s to the 1990s, most Latin American countries expe-rienced high inflation, and even hyperinflation, often caused bythe running of large structural fiscal deficits, which were financedby “printing money”. In turn, excessive money growth resulted inhigher prices, and higher inflation expectations; the latter are animportant factor, as the “de-anchoring” of inflation expectationsexplains the persistence of very high inflation in Latin Americancountries for the greatest part of this period. According to Bernanke(2005), the root of the problem was in the implementation of so-called“structuralist” theories of development, which involve the protec-tion of domestic companies from international competition. Domes-tic governments played an important role in this, by implementingmeasures to prevent foreign competitors from entering local mar-kets, and by heavily subsidising entire sectors of the economy. How-ever, this came at the cost of chronic budget deficits, expansion inmonetary aggregates and mounting inflationary pressure.

Indeed, inflation indexation policies arose within the context ofhigh and persistent inflation, with domestic governments havinglittle choice but to issue inflation-linked debt as a way to securelong-term funding in local currency. For example, after its creationin 1953, the State Bank of Chile issued bonds to finance an ambitiousprogramme of development in the country’s agriculture and infra-structure sectors. Due to investors’ concerns about inflation and theChilean currency, these bonds were initially indexed to the US dol-lar. Then, in 1967, the authorities introduced a new unit of account,the “Unidad de Fomento” (UF), tied to the “Índice de Precios alConsumidor” (IPC), the Chilean Consumer Price Index. Such anindexed unit of account has been the subject of several academicpapers (see, for example, Shiller 1998) and finds its roots in themonetarist theory of Irving Fisher (1911). In the case of Chile, infla-tion indexation was soon applied not just to government bonds,but also to a host of other financial transactions, including bankdeposits, residential rents, mortgage loans, house and commercialproperty prices, alimony and child support payments and taxes.Several Latin American countries followed a similar path. Ecuadorcreated the “Unidad de Valor Constante” in 1993; Mexico establishedthe “Unidad de Inversion” in 1995; Colombia created the “Unidadde Poder Adquisitivo Constante” in 1972 and Uruguay adopted the“Unidad Reajustable” in 1968.

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From the 1990s onwards, faced with the negative impact of per-sistent high inflation, Latin American countries began to focus theireconomic policies on the task of stabilising prices. Currency pegswere introduced in several countries as a way to enforce fiscal dis-cipline and anchor inflation expectations, a necessary condition forlong-term price stability. Mexico pegged its currency in 1987, as didArgentina in 1991, while Brazil adopted a crawling band regimein 1994. Although there were some early successes and inflationrates decreased, currency-targeting policies could not be sustainedfor a host of reasons. First, local governments in these emergingcountries lacked credibility in their fiscal and monetary policies. Inaddition, currency pegs created barriers in the free movement ofcapital across borders, thus affecting the stability of the domesticeconomies. Furthermore, these pegged currencies were perceivedas over-valued and became the subject of intense market specula-tion. All of these factors forced governments to give up the currencypegs (Mexico in 1994, Brazil in 1999 and Argentina in 2002) anddevaluate. Of course, this raised prices dramatically, but inflationrates stayed below the peaks reached in previous decades. Thesecurrency-devaluation episodes did not change the Latin Americancountries’ focus on lowering and stabilising inflation. Following theexample of several developed (eg, New Zealand) and developingeconomies (eg, Chile in 1990), most Latin American countries shiftedtheir monetary policy framework from exchange rate targeting toinflation targeting. Peru did so in 1994, with Brazil, Mexico andColombia following in 1999, after which inflation rates did indeeddecrease and stabilise.

In reality, the successful reining in of inflation was not simply theconsequence of inflation targeting monetary policies, but the resultof a more complex combination of factors. As Ben Bernanke saidduring a speech at the Stanford Institute:

I do not mean to claim, however, that Latin America conqueredinflation simply by choosing a particular framework for monetarypolicy. Rather, my more fundamental point is that inflation hasdeclined in Latin America because new ideas and new politicalrealities have fostered the development of economic institutionsand policies that promote macroeconomic stability more gener-ally. Recent changes in the policy environment have been especiallyimportant in three areas: fiscal policy, banking regulation, and cen-tral bank independence. No monetary policy regime, including

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inflation targeting, will succeed in reducing inflation permanentlyin the face of unsustainable fiscal policies – large and growingdeficits.

(Bernanke 2005)

Interestingly enough, the stabilisation of inflation rates inducedsome Latin American countries to raise concerns on, and reconsider,their indexation policies. For example, one issue with the linkage ofwages to inflation is that, as explained by Shiller (1998), indexationmight result in higher inflation expectations. This is a consequenceof the natural reluctance of individuals to accept a nominal salary cutduring low-inflation periods, while, on the opposite side of the coin,it is easier, in non-indexed economies, not to raise nominal wagesin line with the full increase in inflation. In this case, a nominalincrease in salary, which still results in a lower real income, is psy-chologically easier to accept (the so called “money illusion” effect).A second issue is the spillover of inflation risk and indexation intocredit risk. As we have seen, in Latin American countries, inflationindexation was applied to a host of financial transactions, includ-ing consumer loans and mortgages. When local currencies devalu-ated and inflation rose, the nominal size of that debt increased sig-nificantly, putting extreme pressure on households and consumersand triggering credit defaults. Social and political pressure on localgovernments to “fix” these problems also mounted. For example,in Chile, farmers, whose loans were UF-indexed, forcefully lobbiedthe government to “freeze” the index of account. Some governmentstried to correct the indexation by fine-tuning indexes to better reflectwages, but this did not resolve the public outcry against indexation.

However, these abrupt developments did not eliminate the useof inflation indexation in Latin American financial markets. Indeed,although some debate is still going on, especially in regard to thetopic of indexation of consumer loans, the sovereign inflation-linkedbond market is alive and well, with governments taking advantageof long-term funding opportunities, and demand from institutionalinvestors growing stronger by the day.

The Latin American experience is of great historical and practicalimportance in that it not only jump-started modern-era inflation-linked markets, but also created a standard for indexation of bothinflation-linked bonds and derivatives. Furthermore, the introduc-tion of “units of account” as the translation mechanism between

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Figure 20.3 Year-on-year Inflation in Asia

18

16

14

12

10

8

6

4

2

0

%

Jan

1980

Mar

198

1M

ay 1

982

Jul 1

983

Sep

198

4N

ov19

85Ja

n 19

87M

ar 1

988

May

198

9Ju

l 199

0S

ep 1

991

Nov

1992

Jan

1994

Mar

199

5M

ay 1

996

Jul 1

997

Sep

199

8N

ov19

99Ja

n 20

01M

ar 2

002

May

200

3Ju

l 200

4S

ep 2

005

Nov

200

6Ja

n 20

08M

ar 2

009

May

201

0Ju

l 201

1

Sources: International Monetary Fund (2004), New Sky Capital.

the nominal and indexed economies brought about the concept of“currency analogy”, which has proved fruitful in the modelling ofinflation-linked products, further contributing to the understandingand acceptance of such instruments by financial and non-financialagents around the world.

Asia: a sleeping giant?As shown in Figure 20.3, Asia experienced high inflation rates overmost of the 20th century, with a peak in 1998 during the Asian Crisis.In fact, after the “economic miracle” of the 1980s and 1990s, whenAsian economies experienced high growth and large foreign capitalinflows, the crisis started in 1997, triggered by a massive speculationagainst the pegging of the Thai baht to the US dollar. The crisis alsoquickly spread to other Asian countries, on the wings of a massivewithdrawal of foreign capital, which caused a credit crunch. Therewere several economic factors (Kaufman et al 1999) that triggeredthese events, but a key one was the sharp volatility and devalua-tion of several Asian currencies, and the consequent rise in inflation.Between June 1997 and July 1998, the currency Thai baht/US dol-lar rate depreciated by 70% and the South Korean won/US dollarrate depreciated by 54%, while the Indonesian rupiah/US dollar raterose from 2,450 to 14,750!

More recently, inflation in Asia rose again to reach about 8% in2008 and 7% in 2011, mostly as a consequence of higher commodity

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prices and the dependence of these countries on oil and food imports.However,Asian economies are also evolving, with domestic demandgrowing considerably and playing a stronger role as a determinantof inflation. In fact, according to Osorio and Unsal (2011):

The relative roles of key inflation drivers appear to be changingover time. The role of supply shocks in driving inflation appearsto have fallen slightly in recent years, while the role of outputgaps has increased. The impact of monetary shocks on inflation inAsia has diminished, particularly in economies that have relativelyclear monetary objectives and flexible exchange rate regimes (suchas Indonesia, Korea, the Philippines, and Thailand).

Osorio and Unsal also mention that demand-driven inflation spill-over effects from China to the rest of Asia are significant, and arisefrom both higher imported goods and commodity prices. Theseforces are likely to continue, thus contributing to both inflation andits volatility in the foreseeable future.

However, despite the historically high and volatile inflation expe-rienced in many Asian countries, the inflation-linked market is stillin its infancy, with the size of the outstanding inflation-linked debtaccounting for only a very small percentage of the overall total (Fig-ure 20.4). South Korea and Thailand have recently issued inflation-linked bonds (Table 20.1), but again the size of issuance is under-whelming. This might be the consequence of the relatively smallsize of the fixed income market in these countries, with local gov-ernments prioritising the development of the nominal rate market.Another possible explanation is that pension fund schemes and theinsurance sectors are still at a fairly embryonic stage in many of thesecountries; thus, the demand side has still to fully develop.

There are signs that Asian inflation-linked markets have thepotential to flourish, and room to expand, in the future. First, theevolution and growth of pension schemes and the insurance sectormight take time but they are unavoidable, and they will create solidstructural demand for inflation-linked products. Indeed, when, in2011, Thailand issued its first inflation-linked bond, private and pub-lic pension funds were the main investor targets. Secondly, althoughpractical obstacles to foreign investors entering the space (such aswithholding the tax that applies to South Korean inflation-linkedbonds) are still present, a lively debate has ensued in official cir-cles as to how to eliminate such impediments and thus broaden the

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INF

LA

TIO

N-S

EN

SIT

IVE

AS

SE

TS

Table 20.1 Main issuers of inflation-linked bonds in emerging markets

Country First issuance Inflation index Index ticker (Bloomberg) Market value (US$ bn)

Israel 1964 Israel CPI 2010 = 100 ISCPINM 41Brazil 1964 Brazil CPI IPCA BZPIIPCA

281FGV Brazil General Prices IGPIBREIGPM

Colombia 1967 Colombia Consumer Prices Index COCPI 2Chile 1967 Chilean Consumer Price Index CLCPI 14Argentina 1972 Argentina CPI ARCPI 13Mexico 1989 Mexico CPI MXCPI 53Poland 1992 Poland CPI Inflation Linked Bond POCPILB 7Turkey 1997 Turkey CPI TUCPI 48South Africa 2000 South Africa CPI 2008 = 100 SACPI 31South Korea 2007 South Korea CPI 2010 = 100 KOCPI 6Thailand 2011 Thailand CPI All Items 2007 = 10 THCPI 2

Total 499

Sources: Deacon et al (2004), Bloomberg, Barclays Capital, New Sky Capital.

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investor base. Finally, the appeal of inflation-linked bonds for debtmanagement purposes and as an important instrument in supportof an expanding pension system has been increasingly recognised.One of the conclusions of the IMF working paper by Poirson et al(2007) was that

debt management agencies and regulators can support the provi-sion of new instruments for retirement savings by ensuring liquidgovernment bonds (that serve an important benchmark functionfor the private sector) and issuing price indexed bonds (to supportthe issue of price-indexed annuities).

Indeed, large Asian countries such as India have the potential tobecome important issuers of inflation-linked bonds. India issuedits first five-year maturity Capital Index Bond in December 1997,for which only the principal repayments at maturity were linked toinflation. In 2010, the Reserve Bank of India launched a consultationpaper to reissue inflation-linked bonds. In a technical paper,2 a newstructure for the inflation-linked bonds was defined, where bothinterest and principal payments were to be linked to inflation (simi-larly to US Treasury Protected Securities (TIPS)), through the WholePrice Index, with a four-month lag. As of spring 2012, India had infact authorised the issuance of inflation-linked bonds. Such a deci-sion reflects not only the desire to address the issue of high inflationrates, but also a strong motivation in providing financial instrumentsthat might help to build a solid domestic pension system.

All these signs indicate that Asia may not remain a sleepinggiant forever, and could quickly become an important player in theinflation-linked market.

EMERGING MARKETS INFLATION-LINKED PRODUCTSAfter analysing the evolution of inflation indexation in emergingmarkets, in this section we focus on inflation-linked products, theirstructure and their liquidity, as well as some of the inflation strategiesemployed by specialised asset managers and hedge funds. About20 emerging market countries have issued inflation-linked bonds,but we shall not cover all of them. Rather, we shall focus on thecountries and instruments that offer the most liquid opportunitiesand are fairly accessible to foreign investors.

Figure 20.4 shows a breakdown of outstanding inflation-linkeddebt by country, and additional information is provided in Table 20.1

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Figure 20.4 Emerging market inflation-linked bonds outstanding bycountry

Brazil56%

Argentina3%Israel

8%

South Africa6%

Poland1%

Turkey10%

Colombia0%

Chile3%

Mexico11%

Thailand1%

South Korea1%

Sources: Bloomberg, New Sky Capital.

(sorted by first issuance date). Brazil has the largest stock of inflation-linked bonds (US$281 billion equivalent), followed by Mexico,Turkey and Israel.

As seen in Table 20.1, Israel and Latin American countries pio-neered inflation indexation and, as a result, these markets offer awider range of inflation-linked products, ie, bonds and derivativesas well as several underlying indexes, and an array of domestic andforeign investors, from pension funds to insurance companies andasset managers, active in the space. Other countries are newer toinflation indexation, and their markets are somewhat less sophis-ticated, with fewer products available, the latter typically beingsovereign inflation-linked bonds with a structure similar to US TIPS.However, even these countries (one example being South Africa)have been developing quickly in line with a parallel evolution oftheir pension fund sectors sponsoring demand for these products.

At the same time, foreign demand has also risen considerably.International institutional investors are actively allocating a por-tion of their assets to global inflation products, including emerg-ing markets. Other emerging market investors are also considering

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inflation-linked strategies. Finally, pension funds, especially thoseof multinational companies with employees in emerging countries,are also strategically investing in the sector. Although investing inemerging markets still has many obstacles (such as currency deliver-ability, local and foreign tax treatment), demand for inflation-linkedproducts has also been supported by the creation of global inflationindexes and new vehicles, such as exchange-traded funds (ETFs),that offer exposure to such indexes.3

Brazil

Brazil has one of the oldest and largest inflation markets, offeringa variety of instruments including inflation-linked government andcorporate bonds and inflation-linked derivatives such as swaps.

Sovereign bonds are clearly the most liquid inflation products,and they have been central to the Brazilian National Treasury’s fund-ing strategy. This strategy has hinged on promoting inflation-linkedand fixed rate issuance while reducing the share of floating ratebonds, with the objective of lengthening the average maturity of thedebt,4 thus reducing the need for short-term refinancing. Indeed, theNational Treasury also establishes targets for different types of debtoutstanding, based on its analysis of funding costs and risks (TesouroNacional 2011). From Table 20.2, we can see that in 2011, the NationalTreasury of Brazil estimated a long-term target of about one-thirdof inflation-linked debt to be optimal (that is a range between 30%and 35%). Interestingly enough, this figure is in line with similaranalysis conducted, and conclusions adopted, by several other largesovereign inflation-linked issuers worldwide.

Inflation-linked bonds play an important role in the manage-ment of sovereign debt, with their virtues eloquently highlightedby Tesouro Nacional (2011):

Although a significant share of the debt is indexed to inflation, therisks associated to that indexing factor are attenuated by a seriesof other factors. In the first place, changes in price indices provokealterations in nominal federal public debt stock, but not in thereal value of the outstanding debt measured as a percentage of theGDP. Secondly, an important share of federal government revenuesshows a high correlation with inflation, thus providing a hedge tothe share of the debt indexed to inflation. Thirdly, in an inflationtarget system, one expects that the index used as a reference bemaintained under control over time, with volatility well below

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Table 20.2 Brazil: federal public debt breakdown in 2011 and targetranges

Target range︷ ︸︸ ︷2011 Lower Upper

Type weights (%) limit (%) limit (%)

Fixed rate 36.6 40 50inflation linked 26.6 30 35Floating rate 31.6 10 20Foreign currency 5.2 5 10

Sources: National Treasury of Brazil, New Sky Capital.

Figure 20.5 Asset allocation of different financial and economic agents

18%

27%

53%

2%

25%

52%

24%

17%

63%

20% 54%

25%

21%

41%

33%

2%

24%

70%

11%

19%

15%

4%63%

Financialinstitutions

Funds Pensions Non-residents

Govern-ment

Insurers Other

Other Floating Fixed-rate Inflation-linked

Sources: National Treasury of Brazil, New Sky Capital.

that observed in other financial variables such as interest rates andexchange rate.

Another important role has to do with domestic institutionalinvestors, especially pension funds and insurance companies, whohave long-term liabilities often linked to inflation. For these twotypes of investor, inflation-linked bonds provide a natural hedge,and this is indeed reflected in their asset allocation (Figure 20.5).

In contrast to the vibrant domestic market, access to Brazilianinflation-linked bonds provides challenges to offshore investors,given that the Brazilian real is not fully convertible into the major

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Table 20.3 Brazilian price indexes

IPC-A IGP-M

Price index Average cost of livingin 11 major Braziliancities for families withincome from 1x up to40x minimum wage

Market General PriceIndex

Publisher Instituto Brasiliero deGeografiaeEstatistica(sponsored byFederal Government)

Fundacao GetulioVarga (independentfoundation)

Period covered First to last day of themonth

21st of the previousmonth to the 20th ofthe month ofreference

Publication The inflation for agiven month isreported on the 15thday of the followingmonth

The index for a givenmonth can bepublished at orbefore month end

Bloomberg ticker BZCLVLUE IBREIGPM

Breakdown 70% markets, 30%administered prices

60% wholesale, 30%consumer and 10%of construction prices

Base Dec 1993 = 100 Aug 1994 = 100

Seasonality Non-seasonallyadjusted

Sources: Bloomberg, New Sky Capital.

currencies and foreign investment in fixed-income products is con-tingent to the payment of an upfront withholding tax (typically 1.5%of notional). These factors are at the root of the developments of theinflation swap market in Brazil, as we shall discuss later on.

As for the mechanics of sovereign Brazilian inflation-linkedbonds, several indexes and indexation methods have been usedsince the start of the market in the 1960s. For example, in the early1970s, indexation was based on a combination of both realised andprojected (by the government) inflation rates (Deacon et al 2004),

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Figure 20.6 Brazilian annual inflation rates (IPC-A) and policy targets

02468

101214161820

%Ja

n 19

99A

ug 1

999

Mar

200

0D

ec 2

000

Dec

200

1M

ay 2

001

Jul 2

002

Feb

200

3S

ep 2

003

Apr

200

4N

ov 2

004

Jun

2005

Jan

2006

Aug

200

6M

ar 2

007

Dec

200

8Ju

l 200

9F

eb 2

010

Sep

201

0A

pr 2

011

Nov

201

1

YoY inflationInflation target

Source: Bloomberg.

in an effort to minimise feedback effects from past to future infla-tion. Later, a fixed equilibrium rate replaced future projections. Inthe mid 1970s, “supply shocks” corrections were introduced, whicheffectively reduced government funding costs, but to the detrimentof investors.

As of spring 2012, two types of sovereign inflation-linked bondsremain outstanding, the Notas de Tesouro Nacional-C (NTN-C) andthe NTN-B. The NTN-Cs, linked to the IGP-M index (Table 20.3),were first issued in 1990 during the implementation of the “Col-lor Plan I”, aimed at stabilising the economy and inflation. Theirissuance was suspended in 1994 with the introduction of the “PianoReal”, but resumed in 1999. The NTN-Bs, linked to the IPC-A index,were introduced in 2002. At the time of writing they constitute mostof the inflation-linked debt outstanding (Table 20.4), as a result ofthe Brazilian government focusing issuance on a single price index,that is the IPC-A, in order to improve market depth and liquidity.Indeed, the NTN-C’s share of inflation debt decreased from 75% in2004 to 13% in 2011.

The choice of the IPC-A index is natural when we consider thatthis is the same index adopted by the Brazilian Central Bank (BCB) inconducting its inflation-targeting policy. This policy framework wasintroduced in July 1999, six months after the BCB adopted a float-ing exchange rate system. Since then, the government has definedinflation targets for the coming years (Figure 20.6) and given to BCB

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Table 20.4 Brazilian government inflation-linked debt

NTN-B NTN-C

First issuance 2002 1990

Outstanding (R, billions) 209 25

Inflation index IPC-A IGPM

Bloomberg index ticker BZCLVLUE IBREIGPM

Auction Up to two auctionsper month and swapauction (buy shortterm and sell longerterm)

Irregular

Coupon Semiannual at 6% Semiannual at 6% or12%

Floor No No

Quotation Nominal dirty Nominal dirty

Date count fraction Business/252 Business/253

Number of bonds 15 3

Maturity 2012,. . . ,2050 2012, 2017, 2032

Bloomberg ticker BNTNB BNTNC

Sources: Bloomberg, New Sky Capital.

the responsibility (and the operational independence) to conductmonetary policy in pursue of those targets, with the goal of pro-moting economic growth in an environment of price stability andsustainable employment rate.

The format of NTN-Bs and NTN-Cs is the standard one used formost inflation-linked bonds where the notional amount is linkedto an inflation index.5 The coupon is calculated by multiplying afixed rate by the inflation-accruing bond notional amount and is paidsemi-annually. At maturity, the full inflated notional is paid down,and for Brazilian bonds there is no deflation floor, unlike for US TIPS.Another specificity of Brazilian inflation-linked bonds is the absenceof inflation lag in the bond index.6 This raises the issue of how toconvert nominal into real prices. In Brazil, the NTN-Bs and NTN-Csare quoted in dirty nominal prices at time t, for settlement at time t+1.However, the index is not known at settlement. Therefore, to obtainreal prices and yields, the market convention is to use the indexvalue assumption, as published twice per month by the Andima,

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INF

LA

TIO

N-S

EN

SIT

IVE

AS

SE

TS

Table 20.5 From nominal dirty price to clean price

Linker NTN-B 6%, August 15, 2040

Settlement date May 21, 2012Quoted price (nominal dirty price for a par value of 1,000) 2,870(1) Base Bond Index (at bond issuance) 1614.62Latest IPCA: (April 2012) 3467.46Number of business days in the accrual period (from May 15 to June 15) 22Number of business days accrued (from May 15 to May 21) 4IPCA assumption (published by Andima) 0.46(2) Bond index at settlement date: 3467.46× (1+ 0.46%)4/22 = 3,470.35(3) Bond index ratio: (2)/(1) 2.14933Real dirty price = 2,870/(3) 1335.3Semi-annual coupon (1+6%)0.5− 1 2.956%Number of days since the last coupon date 64Number of days between two coupon dates 125(4) Real accrued coupon: 2.956× 64/125 = 15.14Nominal accrued coupon: (4)× (3) 32.541Real clean price 1,320.16

Sources: Bloomberg, New Sky Capital.

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the Brazilian National Association of Financial Market Institutions.When the actual index value is released, it replaces the assumptionby Andima. Table 20.5 provides an example of price calculation.

Inflation swaps are also traded in Brazil, in addition to cash bonds.Demand from foreign investors has been key to the development ofthese instruments, whose structure resembles total return swaps,rather than the zero-coupon format which is the structure of choicecatered to pension funds’ demand in Europe and the US. In a Brazil-ian inflation swap, the inflation-linked leg mirrors the cashflows ofinflation-linked bonds, while the floating leg is linked to money mar-ket rates, specifically the CDI rate published by CETIP, the BrazilianOver-the-Counter Securities and Derivatives Association. All cash-flows are settled in US dollars, and the market convention is touse the PTAX800 exchange rate, as quoted by the Banco Central doBrasil. Note that, because Brazilian inflation swaps involve both theinflation index and the exchange rate, their valuation is rather com-plex, akin to a “quanto”, where we need to consider the stochasticevolution of both stochastic variables as well as their correlation.

Chile

As discussed previously, Chile has been a pioneer in inflation index-ation, having introduced in the 1960s the “Unidad de Fomento”(UF), still in use at the time of writing. The UF is a daily price indexpublished by the Chilean government, and based on the “Índice dePrecios al Consumidor” (IPC), the Chilean Consumer Price Index.

As shown in Figure 20.4, the size of Chilean sovereign inflation-linked debt is much smaller than the similar outstanding debt inother emerging market countries, such as Brazil and Mexico. Indeed,overall sovereign debt in Chile was on a downwards trend untilthe 2008–9 global financial crisis (for example, as a percentage ofGDP). In addition, as the country’s economy has followed a pathof stabilisation and lower inflation, some emphasis has been shiftedto the development of a liquid nominal debt market in local cur-rency. Despite these effects, the inflation-linked market in Chilehas preserved good liquidity and, notably, since the crisis its sizestill accounts for about two-thirds of total sovereign inflation-linkedmarket in the country.

The two main inflation-linked bonds in Chile are the “Bonos de laTesorería General de la República en Unidad de Fomento” (BTUs)

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Table 20.6 Chilean sovereign inflation-linked debt outstanding

BTUs BCUs

Debt outstanding (UF million) 401 354

Sources: Bloomberg, Barclays, New Sky Capital.

and the “Bonos del Banco Central de Chile” (BCUs). The BTUs areissued by the government, which uses the central bank as its agent.In general, the government issuance follows a budget-stabiliser typeof strategy, which means an increase in net issuance when the eco-nomic activity is below its potential, and vice versa. As a result, theissuance of BTUs decreased between 2000 and 2008, only to thenincrease again afterwards. BTUs maturities range from 5 to 30 years.The BCUs are issued by the central bank rather than the govern-ment. They play an important role in conducting monetary policy,for example, in sterilised interventions, which aim at controlling theforeign exchange rate.7 BCUs’ maturities range from 2 to 20 years.Investors in BTUs and BCUs are typically domestic institutions, pen-sion funds and insurance companies in particular. In general, tax-ation on interests and capital gains continues to be an obstacle formost offshore investors (Barclays Capital 2012).

Similarly to sovereign bonds, the vast majority (92% of issues)of corporate bonds are denominated in UF. In addition, deriva-tives instruments also trade with good liquidity. For short maturities(within 18 months), forwards contracts on the UF index trade dailyvia electronic platforms. In these contracts, one counterpart agreesto pay the UF index in exchange for the variable short-term rate“Camara”, which represents the average funding cost for domesticfinancial institutions and is published daily by the Chilean Bank-ing Association. For longer maturities (1Y, 5Y, 10Y and up to 30Y),two types of real rate swaps are traded, with the real leg mirroringthe cashflows of inflation-linked bonds. One is the “UF/Camara”swap, denominated in local currency. The other is the “UF/Libor”swap, which settles in US dollars and has the “quanto” features wepreviously hinted at when discussing Brazilian swaps.

MexicoMexico has the second largest stock (after Brazil) of inflation-linkedbonds in emerging markets countries. The first inflation-linked

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Table 20.7 List and outstanding size of UDIBonos

Maturity Issue OutstandingCoupon date date (Ps, billion)

3.25 Jun 2012 Jan 2009 7.25.5 Dec 2012 Jan 2003 9.03.5 Dec 2013 Jan 2004 10.24.5 Dec 2014 Jan 2005 15.15 Jun 2016 Jul 2006 10.83.5 Dec 2017 Jan 2008 13.34 Jun 2019 Jul 2009 10.22.5 Dec 2020 Mar 2011 11.84.5 Dec 2025 Jan 2006 8.64.5 Nov 2035 Jan 2006 24.34 Nov 2040 Mar 2010 20.3

Total 141.0

Sources: Bloomberg, New Sky Capital.

bonds were issued in 1996, two years after the Mexican pesoscrisis. Over time, with inflation stabilising and a nominal domes-tic debt market developing, the percentage of inflation-linked debthas decreased from a peak of about 30% in the 1990s to about 20%as of 2012. Given the importance of these instruments in meetingdemand from domestic institutions, and the government’s focus onsupporting the evolution of a modern pension system, issuance ofsovereign inflation-linked bonds is here to stay.

In Mexico all inflation products are linked to the Unidad deInversion (UDI), which is an official index computed by the centralbank every two weeks. This index tracks the changes in the “ÍndiceNacional de Precios al Consumidor” (INPC).8

Mexican sovereign inflation-linked bonds are called UDIBonos(Table 20.7). Their structure is similar to the TIPS structure, wherea real coupon rate is applied to an UDI-inflated notional. The cen-tral bank, Banxico, acts as an agent of the Treasury and auctionsthe bonds. To maintain a good level of market liquidity, the govern-ment runs a regular issuance schedule as well as auctions, wherelong-dated bonds are exchanged for short-dated ones. Demand isdriven by domestic institutions, such as pension funds and insurancecompanies, with long-term inflation-sensitive liabilities. Demandfrom offshore investors, albeit on the rise at the time of writing,

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remains below 10% (Barclays Capital 2012) in spite of favourabletax treatment.9

The inflation-linked swap market is well developed with bothonshore and offshore institutional players. As in most Latin Ameri-can countries, there are two swap formats, one catering to domesticinvestors and the other to foreign investors. In the first, the USI/TIIEswap, a real UDI fixed rate is exchanged for the benchmark Mexi-can interbank deposit rate (TIIE). Principals are also exchanged atthe start and the end of the swap contract. The second structure,the UDI/Libor swap, is aimed at offshore investors and combinesa real swap with a cross-currency swap. In this swap, the fixed legpays USI real rate in pesos, and receives a floating Libor rate on a USnotional. Principals in the two currencies are exchanged at the startand end of the swap contract.

IsraelIsrael is one of the oldest issuers of inflation-linked bonds. Indeed,the evolution of its market shares many similarities with the eco-nomic realities faced by Latin American countries, ie, chronic infla-tion in the 20th century and the subsequent policy responses (Barneaand Liviatan 2008).

The first issuance of indexed bonds by the Israeli governmentoccurred in 1964, a time marked by high inflation and substantialgovernment financing needs. In such an environment, the govern-ment could effectively fund itself only by issuing in hard currency(US dollars) or indexing to inflation. Indeed, by the 1980s, a periodwhen inflation rates ranged between 100% and 450% per annum, thevast majority of government debt was indexed. In 1985, the govern-ment started a reform programme aimed at stabilising the economyand reducing inflation. The role of the government in the economywas reduced, and so were the fiscal deficit and public debt. In addi-tion, more independence was given to the central bank (Deacon etal 2004).

Consequently, the share of indexed bonds started to decrease. In1992, a new law clearly defined the objective of monetary policyas “to maintain price stability in order to help to create a businessenvironment that supports sustainable economic growth”.10 Infla-tion targeting was adopted, with the short-term rate as the monetarypolicy tool of choice, controlled by the Bank of Israel. The dramaticeffect of these policy reforms is clear from Figure 20.7.

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Figure 20.7 Reduction in annual inflation rates in Israel from 1995

14

12

10

8

6

4

2

0

–2Jan

1994Jan

1996Jan

1998Jan

2000Jan

2002Jan

2004Jan

2006Jan

2008Jan

2010Jan

2012

Sources: Bloomberg, New Sky Capital.

In the wake of these developments, the government funding strat-egy has gradually shifted on establishing a liquid nominal bond mar-ket. The share of inflation-linked bonds as a percentage of overallgovernment debt has been decreasing and at the time of writing it hasstabilised just above 40%. However, the demand for real rate assetsremain strong, as it is clear from the fact that about 70% of the corpo-rate debt market is also indexed to inflation. According to BarclaysCapital (2012), the total stock of inflation-linked bonds in Israel wasNIS405 billion at the end of 2011, split between government inflation-linked bonds (NIS170 billion) and corporate inflation-linked bonds(NIS235 billion).

Israeli Government inflation-linked bonds come in two flavours,both linked to the Consumer Price Index (CPI). The Galil bonds haveboth principal and interest indexed to the CPI and floored. Theiroriginal maturities ranged between 2 years and 30 years, but thelongest outstanding issue has (at the time of writing) only 12 yearsto maturity. Since 2006, a new type of inflation-linked bond has beenissued (also up to 30 years’ maturity), the main difference beingthe absence of principal and coupon floors. This is partly due tothe historical large fluctuations of inflation rates in Israel, and thegovernment’s reluctance to sell such deflation floors.

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CONCLUSIONS

Several of the most advanced inflation-indexed markets are to befound in emerging countries.

Indexation pioneers include Brazil and Israel, which issued theirfirst linkers in 1964, and Chile, which started issuance in 1967. To putthe timeline into perspective, this was about 20 years earlier than theoccurrence of similar developments in the UK, the first developedcountry to start an inflation-linked programme in the modern era.

For many emerging markets, the issuance of inflation-linkedbonds was a piece of a much larger jigsaw. These countries had intro-duced a new inflation-linked accounting measure, which affected allthe aspects of economic activity from linking salaries to inflation tomortgage and corporate debt. Indeed, these measures were aimedat mitigating the effects of chronically high inflation, partly causedby a “structuralist” economic approach, where the government sub-sidised industries, creating chronic deficit and high inflation in theprocess. Indeed, inflation-linked bonds were one of the few viableoptions for funding long-term local currency debt in these economiccircumstances.

In the 1990s, the focus of policymakers in emerging countriesturned to lowering and controlling inflation. After the failure of cur-rency pegs in Mexico, Argentina and Brazil, inflation-targeting mon-etary policies were adopted in these countries and others. Their suc-cess had important consequences. The drop in inflation was coupledwith an anchoring of inflation expectations around the inflation tar-get. Lower and more stable inflation expectations and less volatilityin inflation drove down market inflation break-evens significantlyacross most countries. This initiated a de-indexation phase in sev-eral emerging market economies, and in countries such as Brazil,Israel and Chile the focus gradually moved to the development ofthe nominal yield curve. However, this did not mean the beginningof the end of inflation markets. On the contrary, the rapid growthand social development experienced by most developing countriessince the 2000s has seen the evolution of modern pension and insur-ance systems, which, together with important changes in the regula-tory framework, has gradually created a large structural demand forlong-dated real return assets. Consequently, governments have beenreshaping their inflation-linked debt, through issuance or auctions,eg, by extending duration in order to better match pension funds’

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demand. This, together with increased market liquidity and simpli-fied offer processes, has helped to lower long-term real yield and alsocontributed to the development of a corporate inflation-linked bondmarket in countries such as Israel, Brazil, South Africa and Chile,whereas such markets remain limited in developed countries.

When it comes to inflation indexation, it is interesting to note howthe path followed by developed countries (the UK starting issuanceof inflation-linked debt in 1981, followed by the US in 1997 andFrance in 1998) is quite different. These countries developed a nom-inal debt market first, and for them indexation was motivated bythe desire to capture the inflation risk premium, and thus achievebetter funding rates, rather than being dictated by chronic high infla-tion. Indeed, for most developed countries, the growth of sovereigninflation-linked bonds has been exponential but occurred in a lowand stable inflation environment (with the exception of the UK). Onthe demand side, the evolution of the market in developed countrieswas driven in part by regulations that encouraged pension funds andinsurance companies to hedge their inflation-sensitive liabilities.

Despite the difference in historical and economic paths betweendeveloped and emerging markets, at the time of writing we are wit-nessing a certain degree of convergence in global fixed income mar-kets. After establishing a liquid nominal curve first, developed coun-tries have, since the late 1990s, established or completed the realcurve as well. Conversely, several emerging countries, for whichindexation has traditionally been the only viable long-term fund-ing option, have also established (or extended the maturity of) theirnominal programmes. In all cases, rising structural demand forinflation-linked products (from pension funds and insurance com-panies) has been supporting indexation, often being a major causefor issuance (eg, in South Africa and Thailand). We expect this tocontinue to be a positive factor globally, and for Asian countries (eg,India) in particular.

The gradual integration of emerging countries inflation marketsinto the overall market is translating into more complex flows at theglobal level, with new products (such as inflation focused mutualfunds and exchange-traded funds) being engineered in order to meetnew demand. Strong global demand for inflation-linked productshas translated into lower real rates, but more complex flows can alsoplant the seeds for higher volatility, as the new sources of demand

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can be more variable, especially compared with the traditional mar-ket activities of domestic pension funds and insurance companies.Other macroeconomic factors, such as the rising volatility of com-modity prices (an important factor, especially for emerging coun-tries’ price baskets), add to the uncertainty, especially in the short endof the inflation curve. Furthermore, the monetary policies adoptedin response to the 2008–9 recession, ie, exceptionally low rates andquantitative easing, might come into question in the future and alsoraise uncertainty about the future path of inflation globally.

All of these points make us believe that inflation markets will offeropportunities as well as investment solutions to these very topicalissues. And, in this respect, the long history of inflation indexationin emerging countries may indeed make them better prepared forwhat is likely to be an uncertain future.

1 The UK Government started issuing inflation-linked bonds in 1981, the US Treasury startedin 1997 and France followed in 1998.

2 See “Capital Indexed Bonds” at http://rbidocs.rbi.org.in/rdocs/PublicationReport/Pdfs/53629.pdf.

3 In 2010, State Street Global Advisors launched an ETF tracking the Deutsche Bank Global Gov-ernments Ex-US Inflation-Linked Bond Capped Index. This index measures the total returnof inflation-linked government bonds of both developed and emerging market countries out-side the US. As of May 31, 2010, the index was composed of 17 government inflation-linkedbenchmark indexes: Australia, Brazil, Canada, Chile, France, Germany, Greece, Israel, Italy,Japan, Mexico, Poland, South Africa, South Korea, Sweden, Turkey and the UK.

4 The National Treasury of Brazil issues long-maturity (10Y, 30Y and 40Y) inflation-linkedbonds.

5 The exact calculation can be found in “Federal Government Bonds: Methodology for Calculat-ing Federal Government Bonds Offered in PrimaryAuctions” at http://www.tesouro.gov.br/.

6 In most countries the inflation index is published with a lag. In addition, the index used forsettlement of inflation-linked bonds typically contains a lag and/or is an interpolated valuebetween lagged inflation index values.

7 Chile has had a floating exchange rate regime since 1999, but intervenes if the exchange ratelevel deviates significantly from its equilibrium.

8 The INPC is released twice a month, on the 9th (accruing inflation between the 15th of themonth and the last day of the previous month) and on the 24th (accruing inflation betweenthe 1st and the 15th of the current month).

9 Foreign investors are not subject to withholding taxes or any other Mexican taxes (BarclaysCapital 2012).

10 See “The Functions of the Bank of Israel” at http://www.bankisrael.gov.il/abeng/1-4eng.htm.

REFERENCES

Barclays Capital, 2012, “Global Inflation-Linked Products: A User’s Guide”, BarclaysCapital Inflation-Linked Research, May.

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INFLATION INDEXATION AND PRODUCTS IN EMERGING MARKETS

Barnea, E., and N. Liviatan, 2008, “The Chronic Inflation Process: A Model and Evidencefrom Brazil and Israel”, Journal of Economic Policy Reform 11(2), 151–162.

Bénaben, B., and H. Cros, 2008, “Global Inflation Derivatives Markets”, in B. Bénaben andS. Goldberg (eds), Inflation Risks and Products: The Complete Guide, Chapter 11 (London: RiskBooks).

Bernanke, B. S., 2005, “Inflation in Latin America: A New Era?”, Speech at the Stan-ford Institute for Economic Policy Research Economic Summit, Stanford, California,February 11, URL: http://federalreserve.gov/boarddocs/speeches/2005/20050211/.

Chow, K., and R. Segreti, 2008, “Inflation Products in Emerging Markets”, in B. Bénabenand S. Goldberg (eds), Inflation Risks and Products: The Complete Guide, Chapter 10 (London:Risk Books).

Deacon, M., A. Derry and D. Mirfendereski, 2004, Inflation Indexed Securities (Chichester:Wiley Finance).

Fisher, I., 1911, The Purchasing Power of Money (New York: Macmillan).

International Monetary Fund, 2004, “Chile: Selected Issues”, IMF Country Report 04/292.

Kaufman, G. G., T. H. Krueger and W. C. Hunter, 1999, The Asian Financial Crisis: Origins,Implications and Solutions (Springer).

Osorio, C., and F. D. Unsal, 2011, “Inflation Dynamics in Asia: Causes, Changes, andSpillovers from China”, IMF Working Paper WP11/257.

Poirson, H. K., 2007, “Financial Market Implications of India’s Pension Reform”, IMFWorking Paper WP/07/85.

Shiller, R., 1998, “Indexed Units of Account: Theorey and Assessment of HistoricalExperience”, Cowles Foundation Discussion Paper 1171.

Tesouro Nacional, 2011, “Optimal Federal Public Debt Composition: Definition of a Long-Term Benchmark”, URL: http://www.tesouro.fazenda.gov.br/.

Tesouro Nacional, 2012, “Federal Public Debt:Annual Borrowing Plan 2012”, URL: http://www.tesouro.fazenda.gov.br/.

505

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Index

(page numbers in italic type relate to tables or figures)

A

ABP, 19additive year-over-year inflation

swap, 126affine term structure models,

215–16real and nominal, 248–50see also models

airports, 74–6see also infrastructure assets

alternative calibration exploitingcurrency analogy, 169–70,173–4

American International GroupCommodity Index(AIGCI), 18

arbitrage trade, 471–2Archer Daniels Midland

Company, 85Art Market Research indexes, 427assessment of liquidity in

inflation swaps andoptions, 163

asset-class models to factormodels, 402–6

asset prices:and inflation, 277–96and money-neutrality

hypothesis, 284–5asset returns:

and inflation, 8–9equilibrium-basedtheories of, 306–9stock-price-based theoriesof, 309–13

and lagged inflation, 48asset and sector rotation,

hedging through, 325–46,333, 334, 337, 341, 343

and broad asset classes,impulse response, 336–42

and core asset classes,impulse response, 332–6

and data, 331–2and investment implications,

342–5and model specification,

328–31and previous research,

learning from, 326–8asset swaps (ASWs) and

inflation asset swaps,128–33, 129

and effect of interest rate,spread and inflationbreak-even changes, 132

TIPS, 130Australia, mining investments

in, as percentage of GDP,36

B

Bank of Canada, 196Monetary Policy Report

(2011), 192Bank of England, 196

Inflation Report (2011), 192Bank of Finland, 196Bank of Israel, 183, 500

interest-rate forecast, 183Bank of Japan, 263Bankers Trust Commodity Index

(BTCI), 18Bernanke, Ben, 185, 484Blue Chip Economic Indicators

Survey, 225, 226bond prices in discrete time,

238–9bonds, inflation-linked, 103–5,

116–25non-government, 123–5, 124pricing distortions and

opportunities in, 116–23

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INFLATION-SENSITIVE ASSETS

and lack of investmentindex sponsorship, 121–2and market pricing drivenby real rates levels, 120–1and other inefficiencies,122and risk-adjusted inflationbreak-even rate, 122–3

see also TIPSbonds, investment-linked, asset

allocation with, 113–16bonds, n-period expected return,

239–40“busted” convertible securities,

96–100

C

California Public Employees’Retirement System(CalPERS), 417

Chase Physical CommodityIndex, 18

Chicago Fed National ActivityIndex, 354

Chicago Mercantile Exchange,413

Church and Dwight, 94, 95Colliers International Luxury

Residential Index, 426commodities:

as best-performing coreasset-class hedge, 335

and growth, 33–7and inflation, 25–30, 26misunderstood nature of, 16and pensions, as investment

strategy, 415–17prices of, and Chinese

non-food inflation, 29prices of, and European core

inflation, 28prices of, and US core

inflation, 28risky nature of, 15see also commodity investing

commodities shocks, andinflation, 13–23

commodity investing, 37–40and growth, 39–40and inflation, 37–9as inflation hedge, 21–2mainstream status of, 19–20see also commodities

commodity price indexes:evolution of, 18–19first investable, 16–18and futures, 14–16growth in, 18–19

commodity prices:and inflation and monetary

policy, 255–75econometric findings,269–73in financial crisis, 262–4overshooting, 267–9targeting, 257–62

Commodity Research Bureau, 27and commodity price

indexes, 14comparison between historical

and implied volatility,164–6, 166

constant-volatility affine AR(1)models, 216, 240

see also modelsConsumer Price Index (CPI)

(European Harmonised),413

Consumer Price Index (CPI)(US), 17, 43, 108, 272

Colliers International LuxuryResidential Indexcompared to, 426

distribution of annualisedsix-month rates, 49

and food and energy, 31Higher Education Price Index

compared to, 426Liv-ex Fine Wine Index

against, 427Consumer Price Index – All

Urban Consumers (CPI-U)(US), 5, 5, 369

and stock performance, 418

508

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INDEX

convertible securities, “busted”96–100

Copernicus, Nicolaus, 278core projection models, 193–8

different types of, 195–6and parsimony, 193and policy reaction function,

196–8and robustness to policy

errors, 194–5top-down approach to, 193–4

cost-of-living adjustment(COLA), 390–1, 397

CPI, see Consumer Price IndexCredit Suisse Commodity

Benchmark (CSCB), 18, 37currency analogy, 167–70, 168

alternative calibrationexploiting, 169–70, 173–4

Jarrow–Yildirim model,167–9, 168, 173–4

Czech National Bank:Inflation Report (2011), 192three-month Pribor rate

forecast, 183

D

Daiwa Physical CommodityIndex (DPCI), 18

deflation/inflation debate in US,474–6

see also inflationdeveloped-market equities:

equity investing andinflation, sensibleapproach to, 335

and growth versus valuestyles, 340

sector indexes, 338–40development of zero-coupon

inflation options, 160–2directional trade, 470–1Dow Jones, and commodity

price indexes, 14, 18Dow Jones Industrial Average,

445and break-even inflation, 444

Dow Jones UBS CommodityIndex (DJUBSCI), 18, 20,37

E

Economist, The, 14emerging markets:

developed versus, forecastinginflation for, 365–6

developed versus, size ofinflation-linked debt, 481

federal public debt, Brazil,492

food inflation in, 365higher mean inflation in, 302inflation in, as percentages, 31

inflation indexation andproducts in, 479–504

evolution of: Asia, 486–9evolution of: Latin America,

482–6inflation-linked products in,

489–501, 490Brazil, 491–7Chile, 497–8Israel, 500–1Mexico, 498–500

inflation rates, Brazil, 494inflation rates, Israel, 501

and inflation targeting, 260largest inflation in, 31money markets, bonds and

equities, 341–2price indexes, Brazil, 493sovereign inflation-linked

debt, Chile, 495year-on-year inflation rate in,

480energy and water utilities, 71–2equilibrium-based theories of

inflation and asset returns,306–9

equities:developed-market, as

worst-performing coreasset-class hedge, 335

509

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INFLATION-SENSITIVE ASSETS

and emerging markets,money markets andbonds, 341–2

and pensions, as investmentstrategy, 417–18

equity–inflation puzzle, 305–20and equilibrium-based

theories of inflation andasset returns, 306–9

and high- and low-inflationdifferences, 319–20

and stock-price-basedtheories of inflation andasset returns, 309–13

and stock returns, empiricalevidence, 313–20

equity investing and inflation,sensible approach to,85–100

and “busted” convertiblesecurities, 96–100

and leveraged companiesand deleveragingmechanisms, 90–6, 92, 93

and real-estate companies,89–90

and royalty companies, 86–8and spread-based companies,

88–9equity investments:

and inflation, 79–102prices, 79–85, 80, 81

equity prices:and inflation, 79–85, 80, 81,

287–9and expectations onprices, 83–5and interest rates andcosts, 82–3

equity returns:and inflation, 299–321

expected versusunexpected, 304–5and Fisher’s hypothesis,303–4

nominal and real, 300nominal and real annual, 301

European Central Bank, 25, 33,151, 185, 256, 278, 393

European Harmonised Index ofConsumer Prices, 413

excess inflation, summarysample statistics(1947–2011), 407

excess inflation, summarysubsample statistics, 409

exchange rates, and inflation,286–7

expectation hypothesis andno-arbitrage models,212–13

expected inflation:and expectation hypothesis

and no-arbitrage models,212–13

implications for investorsand policymakers, 233–5

versus risk premium, 233and term structure of interest

rates, 209–51and term structure

modelling, basic conceptsof, 209–20; see also models;term structure modellingand probability measures,211–12

and term structure models,literature on, reviewed,224–9

versus unexpected, 304–5see also inflation

F

factor framework, modellinginflation in, 406–11

factor volatilities and correlationmatrix, 409

Feldman, Jay, 27final-goods inflation, 264–7Financial Times, 14first investable commodity price

index, 16–18Fisher, Irving, 299, 303–4

and unemployment, 353

510

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INDEX

floors in inflation-linkedgovernment bonds, 156–7

food inflation, 362–3, 362forecasting inflation:

in developed versusemerging markets, 365–6

practical models for, 351–67,352, 354, 358, 359in developed versusemerging markets, 365–6and food, 362–3, 362fundamental, bottom-up,356–63fundamental, top-down,351–6and household energy,361–2and petroleum, 359–60and shelter, 360technical time-series,363–5

technical time-series modelsfor, 363–5

forecasting and policy analysissystems (FPAS), 186–93

and forecasting horizons,different models for,187–8, 187

major components in, 188–91,188

forward inflation curve:granular, 154–5monthly, 150–6yearly, 150

FPAS, see forecasting and policyanalysis systems

Franco-Nevada, 86, 87fundamental models for

forecasting inflation:bottom-up models, 356–63top-down models, 351–6

futures, and commodity priceindexes, 14–16

G

global financial crisis, 34–5, 369,460

and inflation market, 444–5inflation markets since, 444–5and inflation volatility, 439and low yields from, 428monetary policy in, 262–4

Goldman Sachs CommodityIndex (GSCI), 18

Gordon growth model, 309Gordon, Myron, 309government-issued

inflation-linked bonds,412–13

granular forward inflationcurve, 154–5

“Great Inflation”, xix, 277, 282,287–8

and portfolio shift, 292, 293,295

“Great Moderation”, 4, 188“Great Recession” (2008–9), see

global financial crisisgrowth:

and commodities, 33–7and commodity investing,

39–40forecasts of, embedded in

equity and industrialcommodity prices, 9

H

hard awakening of riskmanagement in inflationoption books, 158–60

hedging:assets for, and an efficient

frontier, 381–4ASW strategy, 458, 458commodity investing as, 21–2and developed-market

equities, asworst-performing coreasset-class hedge, 335

effectiveness of, andinflation-sensitivity, 47–8

with illiquid real-estateinvestments, 63–5

511

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INFLATION-SENSITIVE ASSETS

by pension funds andinsurance companies,441–2, 441

and real-estate investments,45–8

through asset and sectorrotation, 325–46, 333, 334,337, 341, 343and broad asset classes,impulse response, 336–42and core asset classes,impulse response, 332–6and data, 331–2and investmentimplications, 342–5and model specification,328–31and previous research,learning from, 326–8

and zero-coupon inflationswaps, 457, 458

Higher Education Price Index,426

historical and implied volatility,comparison between,164–6

household energy inflation,361–2

I

IBM, 15implied and historical volatility,

comparison between,164–6

income, nominal and real, effectsof taxation on, 289–95

index, proxy, modelling assetsand liabilities with, 400

indexation lag, 231–2indexation of pension plans,

390–2, 391indexed bonds, real bonds and

TIPS, 242–5inflation, 279–84

annual rates of:Brazil, 302, 494Germany, 4, 302

Japan, 4, 302Mexico, 302UK, 4US, 4, 302

annual, and policy targets, inBrazil, 494

Art Market Research indexesversus, 427

and asset prices, 277–96and money-neutralityhypothesis, 284–5

and asset returns, 8–9equilibrium-basedtheories of, 306–9stock-price-based theoriesof, 309–13

basic concepts of, 5–6break-even, for, 10-year TIPS,

407–8, 408break-even, versus Dow

Jones Industrial Average(2011) 444

in China, non-food, andcommodity prices, 29

and commodities, 25–30, 26and commodities shocks,

13–14commodity investing as

hedge against, 21–2; seealso inflation-sensitiveassets

and commodity investments,37–9

compensation: expectationand risk premium, 459–62,460

and CPI, see Consumer PriceIndex

core, commodity prices’correlation with, 30

core, and money supply, 355cumulative, 371derivatives, 126, 413–14derivatives, with linear

payouts, 125–8different causes of, 6–8duration, and real rate

duration, 399

512

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INDEX

and equity investments,79–102prices, 79–85sensible approach to,85–100

and equity prices, 287–9and equity, puzzle

concerning, seeequity–inflation puzzle

and equity returns, 299–321and Fisher’s hypothesis,303–4nominal and real, 300nominal and real annual,301

European, and commodityprices, 28

excess, summary samplestatistics (1947–2011) 407

excess, summary subsamplestatistics, 409

and exchange rates, 286–7expected:

implications for investorsand policymakers, 233–5versus risk premium, 233and term structure ofinterest rates, 209–51versus unexpected, 304–5

as feared economicphenomenon, 137

on final goods, 264–7food, 362–3, 362government-issued bonds

linked to, 412–13, 412hedging for, through asset

and sector rotation,325–46, 333, 334, 337, 341,343and broad asset classes,impulse response, 336–42and core asset classes,impulse response, 332–6and data, 331–2and investmentimplications, 342–5and model specification,328–31

and previous research,learning from, 326–8

hedging strategies for,tailoring, 384–6

history and outlook, 369–73household energy, 361–2and indexation and products

in emerging markets,479–504evolution of: Asia, 486–9evolution of: LatinAmerica, 482–6

and infrastructure assets,69–77airports, 74–6defining, 69–70energy and water utilities,71–2impact on, 70–1tollroads, 72–4, 73

and investable commodityindexes, 13–23

lagged, and asset returns, 48market models of, 170–2markets linked to, 103–35

bonds, 103–5, 116–25TIPS, 105–13, 111, 113, 115

markets, portfolio manager’sperspective on, 435–76; seealso inflation markets

measures of, 281–4modelling, in factor

framework, 406–11as monetary phenomenon,

279–80and monetary policy, 32–3and monetary policy and

commodity prices, 255–75econometric findings,269–73and final goods, 264–7in financial crisis, 262–4overshooting, 267–9“super-cycle” possibility,257targeting, 257–62

and nominal interest rates,285–6, 285

513

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INFLATION-SENSITIVE ASSETS

and non-monetary factors,280–1

as non-stationary stochasticprocess, 447–9, 448

options, 147options, historical

perspective on, 156–62options, US-traded, 413–14,

414and pensions, 389–420

and asset-class and factormodels, 402–6, 404brief history, 392–4contributions affected byliability changes, 394–7correlation matrix, 401investment strategies for,see investment strategiesand risk-factor correlationmatrix, 405surplus in, risk-factorloadings for, 405surplus variancedecomposition, 401variance decomposition,401and variancedecomposition by riskfactor and factor-modelsurplus volatility, 406

periods of, a brief history,392–4

and personal consumption,282

petroleum, 359–60protecting insurance

portfolios from, 369–88,374asset allocation details, 376and capital adequacy/credit rating, 385and decomposition ofvariance of economicvalue, 377and different assets ininflationary periods,379–81

and economic variancedecomposition, 375–8and efficient investmentfrontiers for economicvalue, 383and hedging strategies,tailoring, 384–6history and outlook,369–73and impact on insurers’equity value, 378–9, 378and inflation-hedgingassets and efficientfrontier, 381–4and insurers’ equity value,383and investment income,386and liabilities, long-tailversus short-tail, 385liability compositiondetails, 377and life insurancecompanies, 386–7and risk to property andcasualty companies, 373–4and risk tolerance, 386and risk and return ofvarious asset classes, 382simulation approach,374–5

protection, 48–56, 52optimal portfolioallocation for, 57and portfolios, balancedapproach to, 56–61success rate, 50, 52tactical asset selection for,48–54tactical asset selection for,effectiveness of, 48–51tactical asset selection for,robustness of, 51–4tactical portfolio allocationfor, 54–6

and real-estate investments,43–68and hedging, 45–8

514

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INDEX

and real stock prices, 387“recycling”, from project

finance deal to pensionfund, 143

risk of, for life insurancecompanies, 386–7; see alsoinsurance portfolios

risk of, for property andcasualty companies, 373–4

risk premium, 10-year, 460risk premium, 10-year

(estimate) 461sensitivity, and hedge

effectiveness, 47–8shelter, 360and sovereign debt, 438, 438,

491, 497, 498and stock returns, empirical

evidence, 313–20hedge effectiveness,313–17high- and low-inflationdifferences, 319–20tactical asset allocation,317–19tactical asset allocation inrelation to, 317–19

tailoring hedging strategiesfor, 384–6

and term structure models,literature on, reviewed,224–9

and ultra-high-net-worth(UHNW) investors, 423–34definition, 424and legacy and timehorizon, 425and leverage, 432–3and liabilities, 525–6and real-asset life cycle,430and real assets, 428–9and risks and returns,430–2, 432

and unemployment, 7, 7,352–6 passim, 352

US, 370US, annual rate of, 393

and US banking system, 6US, and commodity prices, 28US, rolling annual

(1948–2010) 380US, stability of, 369US, strong autoregressive

properties of, 334year-on-year, Asia, 486

inflation asset swaps, 128–33,129

and effect of interest rate,spread and inflationbreak-even changes, 132

TIPS, 130see also inflation swaps

inflation cashflows of astructured note, 144

inflation/deflation debate in US,474–6

inflation demand, 439–42inflation derivatives with linear

payouts, 126inflation expectation versus risk

premium, 233inflation forecasting:

in developed versusemerging markets, 365–6

practical models for, 351–67,352, 354, 358, 359in developed versusemerging markets, 365–6and food, 362–3, 362fundamental, bottom-up,356–63fundamental, top-down,351–6and household energy,361–2and petroleum, 359–60and shelter, 360technical time-series,363–5

technical time-series modelsfor, 363–5

inflation-linked bonds, 103–5,116–25

floors in, 156–7non-government, 123–5, 124

515

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pricing distortions andopportunities in, 116–23and lack of investmentindex sponsorship, 121–2and market pricing drivenby real rates levels, 120–1and other inefficiencies,122and risk-adjusted inflationbreak-even rate, 122–3

inflation-linked markets, 103–35,126

bonds, 103–5, 116–25non-government, 123–5,124pricing distortions andopportunities in, 116–23

characteristics of, 106and investment-linked

bonds, 113–16TIPS, 105–13, 111, 113, 115

inflation markets, 437carry calculations concerning,

462and demand, 439–42and global financial crisis,

444–5and global financial crisis

(2008–9), 444–5, globalfinancial crisis

and impact of hedging bypension funds andinsurance companies,441–2, 441

and inflation compensation:expectation and riskpremium, 459–62

and macroeconomic models,447–55, 452growth and real rates,453–4monetary policy, 452–3scenario analysis, 454–5,455

and option models, 465–9portfolio manager’s

perspective on, 435–76; seealso inflation markets

and pricing andcompensation in swap andcash market, 455–9

and pricing models, 455–69role of market makers in,

442–4and seasonality, 462–5, 463and sovereign debt, 438strategies, in action, 469–72,

471, 472; see alsoinvestment strategiesexamples: arbitrage trade,471–2examples: directionaltrade, 470–1

and supply, 438–9inflation option books, hard

awakening of riskmanagement in, 158–60

inflation options:at-the-money, 147historical perspective on,

156–62and floors ininflation-linkedgovernment bonds, 156–7and hard awakening ofrisk management ininflation option books,158–60and structured inflationnotes market andyear-on-year inflationoptions, 157–8and zero-coupon inflationoptions, 160–2

market, understanding:year-on-year, 162zero-coupon, 162–3, 163

models, 167–72Jarrow–Yildirim, andcurrency analogy, 167–9,168macroeconomic, 167

US-traded, 413–14, 414zero-coupon, 160–2, 162–3,

163

516

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INDEX

inflation premium and real-termpremium, 245–8

inflation products, 446–7in emerging markets, 489–501

Brazil, 491–7Chile, 497–8Israel, 500–1Mexico, 498–500

see also inflation markets:strategies, in action;investment strategies

inflation-protected portfolio,balanced approach to,56–61

inflation-sensitive assets, 3–11and basic concepts of

inflation, 5–6and evaluation of assets, 3–4as new asset class, 9–11and other instruments, 10see also inflation

inflation-structured notes:and retail demand, 143–4year-on-year, 157–8, 157

inflation supply, 438–9inflation swaps:

different market conventionsfor, 146

historical perspective on,138–44, 139investment banks:managing inflation risk,142–3pension funds: hedgingliabilities’ inflation risk,138–42; see also inflationasset swapsretail demand andinflation-structured notes,143–4

and historical and impliedvolatility, comparisonbetween, 164–6

market, understanding,144–56and monthly forwardinflation curve, 150–6year-on-year, 145–50

year-on-year, complexityadjustments in, 145–50and yearly forwardinflation curve, 150zero-coupon, 144–5

and options, assessment ofliquidity in, 163

and options, understandingand trading, 137–74, 165,166and currency analogy,167–70; see also currencyanalogyand development ofzero-coupon inflationoptions, 160–2and hedging year-on-yearswap with twozero-coupon swaps, 148and historical and impliedvolatility, comparisonbetween, 164–6and inflation-structurednotes, 157–8, 157

zero-coupon, 144–5inflation targeting and emerging

markets, 260inflation targeting and modern

monetary policymaking,257–62

inflationary periods, briefhistory of, 392–4

infrastructure assets:airports, 74–6defining, 69–70energy and water, 71–2high leverage on,

implications of, 76–7and inflation, 69–77

impact of, 70–1tollroads, 72–4, 72

insurance companies, impact ofinflation hedging by,441–2, 441

insurance portfolios:protection of, from inflation,

369–88, 374asset allocation details, 376

517

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and capitaladequacy/credit rating,385and decomposition ofvariance of economicvalue, 377and different assets ininflationary periods,379–81and economic variancedecomposition, 375–8and efficient investmentfrontiers for economicvalue, 383history and outlook,369–73and impact on insurers’equity value, 378–9, 378and inflation-hedgingassets and efficientfrontier, 381–4and inflation-hedgingstrategies, tailoring, 384–6and insurers’ equity value,383and investment income,386and liabilities, long-tailversus short-tail, 385liability compositiondetails, 377and life insurancecompanies, 386–7and risk tolerance, 386and risk and return ofvarious asset classes, 382simulation approach,374–5

interest, Fisher’s theory of, 299,303–4

interest rates:Bank of Israel forecast

concerning, 183forecasts of, drivers of change

in, 200and inflation break-even

changes, effect of, 132

nominal, and inflation, 285–6,285

Reserve Bank of NewZealand, 90-day forecastconcerning, 181

rising, impact of, 82–3and spread changes, effect of,

129term structure of, and

expected inflation, 209–51;see also expected inflation

investable commodity indexes,and inflation, 13–23

investment-linked bonds, assetallocation with, 113–16

investment strategies, 411–18commodities, 415–17equities, 417–18government-issued

inflation-linked bonds,412–13, 412

inflation derivatives, 412–13see also inflation markets:

strategies, in action;inflation products

investments:equity, and inflation, 79–102long- versus short-term, 295mining, as percentage of GDP

(Australia) 36real-estate, 43–68, 64

illiquid, 63–5Iran Revolution, 13

J

Japan, “lost decade” in, 3Jarrow, Robert, 157Jarrow–Yildirim models and

currency analogy, 167–9,168, 173–4

JP Morgan Commodity FuturesIndex, 18

JP Morgan Commodity Index(JPMCI), 18

JP Morgan Emerging LocalMarkets Index Plus(ELMI+), 332

518

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INDEX

JP Morgan Emerging MarketBond Index Plus (EMBI+),332

L

leverage, 432–3along real asset value chain, 433of companies, and deleverage

mechanisms, 90–6, 92, 93high, implications of, on

infrastructure assets, 76–7liabilities, long-tail versus

short-tail, 384–6life insurance companies,

inflation risk for, 386–7; seealso insurance portfolios

linear payouts, inflationderivatives with, 125–8,126

liquidity effects in TIPS, 229–31liquidity in inflation swaps and

options, 163Liv-ex Fine Wine Index, 427Livingston Survey, 225, 408

M

market makers, role of, 442–4market models of inflation,

170–2markets, inflation-linked,

103–35, 126bonds, 103–5, 116–25

non-government, 123–5,124pricing distortions andopportunities in, 116–23

characteristics of, 106and investment-linked

bonds, 113–16TIPS, 105–13, 111, 113, 115

Merrill Lynch Energy andMetals Index (ENMET), 18

mining investments, aspercentage of GDP(Australia) 36

modelling inflation in a factorframework, 406–11

models:affine term structure, 215–16affine term structure, real and

nominal, 248–50asset-class to factor, 402–6constant-volatility affine

AR(1), 216, 240how used, 199for inflation forecasting,

351–67, 352, 354, 358, 359in developed versusemerging markets, 365–6and food, 362–3, 362fundamental, bottom-up,356–63fundamental, top-down,351–6and household energy,361–2and petroleum, 359–60and shelter, 360technical time-series,363–5

and interest-rate forecast,drivers of change in, 200

and latent factors andmacroeconomic variables,219–20

multi-factor, of the short rate,214–15

multivariate, for near-termforecasting, 201–2

no-arbitrage, and expectationhypothesis, 212–13

option, and inflation markets,465–9

and pensions, 402–6pricing, and inflation

compensation in swap andcash market, 455–9, 456

projection, core, 193–8different types of, 195–6and parsimony, 193and robustness to policyerrors, 194–5top-down approach to,193–4

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INFLATION-SENSITIVE ASSETS

real term structures, literatureon, reviewed, 224–9

of real and nominal-termstructures, 221–3, 228

role of, in modern monetarypolicy, 179–206Bank of Israel interest rateforecast, 183Czech National Bankthree-month Pribor rateforecast, 183forecast productionprocess, 191–3forecasting andpolicy-analysis systems,186–93how used, 198–9, 199Norges Bank policy rateforecast, 182Reserve Bank of NewZealand, 90-day interestrate forecast, 181Riksbank (Sweden) reporate, 182

single-factor, of the short rate,313

stochastic volatility, 216–19stylised, semi-structural flow,

for open economy, 202–5term structure, basic concepts

of, 209–20; see also termstructure modelling andprobability measures,211–12

modern monetary policy:role of models in, 179–206

Bank of Israel interest rateforecast, 183forecast productionprocess, 191–3forecasting andpolicy-analysis systems,186–93how used, 198–9, 199Norges Bank policy rateforecast, 182projection, core, 193–8

Reserve Bank of NewZealand, 90-day interestrate forecast, 181Riksbank (Sweden) reporate, 182

monetary policy, and inflation,32–3

money-neutrality hypothesis,284–5

money supply, and coreinflation, 355

monthly forward inflationcurve, 150–6

multi-factor models of the shortrate, 214–15

see also modelsmultiplicative inflation swap,

126multivariate models for

near-term forecasting,201–2

N

neutral money, 278Newmont Mining, 82–4, 87Nixon, Richard, 13nominal interest rates, and

inflation, 285–6, 285nominal and real income, effects

of taxation on, 289–95non-government

inflation-linked bonds,123–5, 124

Norges Bank, 183, 196, 198policy rate forecast, 182

O

OAPEC oil embargo, 13oil-price shocks, 13, 30, 473–4,

474Ontario Teachers’ Pension Plan,

19operating costs, rising, impact

of, 82–3Oppenheimer Commodity

Strategy Total ReturnFund, 19

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INDEX

Oppenheimer Real Asset Fund,19

optimised investment portfolios,historical performance of,59

overshooting, a theory of, 267–9

P

pension funds, impact ofinflation hedging on,441–2

pension plans:California Public Employees’

Retirement System(CalPERS), 417

contributions to, affected byliability changes, 394–7

discount curve and othercharacteristics of, 396

duration contributions, 398and inflation, 389–420

and asset-class and factormodels, 402–6, 404correlation matrix, 401investment strategies for,see investment strategiesmodelling, in factorframework, 406–11surplus variancedecomposition, 401variance decomposition,401

inflation indexation of, 390–2,391

and inflationary periods,brief history of, 392–4

and liabilities, inflationsensitivity of, 398–9

and liabilities, interest-ratesensibility of, 397–8

and risk budgeting, 399–402and risk-factor correlation

matrix, 405surplus in, risk-factor

loadings for, 405US, private, example of, 397

and variance decompositionby risk factor andfactor-model surplusvolatility, 406

People’s Bank of China, 25petroleum inflation, 359–60PGGM, 19Phillips, William, 353portfolio allocation:

optimal, 57, 60tactical, 54–6

property types, different,inflation-sensitivity of,61–3

proxy index, modelling assetsand liabilities with, 400

R

real-asset life cycle and valuechain, 430

real-asset value chain, risks andreturns along, 432

real bonds, indexed bonds andTIPS, 242–5

real-estate investments, 64,89–90

home versus consumerprices, 415

illiquid, inflation hedgingwith, 63–5

and inflation, 43–68and hedging, 45–8

public and private, and otherreal assets, 414–15

real and nominal income, effectsof taxation on, 289–95

real and nominal-termstructures, modelling,221–3

real-term premium and inflationpremium, 245–8

real yields versus zero-couponTIPS yields, 229–32

and deflation floor, 232and indexation lag, 231–2and liquidity effects, 229–31

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“recycling” inflation, fromproject finance deal topension fund, 143

REITs, see real-estateinvestments

Reserve Bank of New Zealand,196

90-day interest rate forecast,181

retail demand andinflation-structured notes,143–4

Reuters, 14Reuters–Commodity Research

Bureau Price Index, 17Riksbank, 182, 183, 196

Monetary Policy Report(2011), 192

repo rate, 181risk factor:

and factor-model surplusvolatility, variancedecomposition by, 406

loadings, and variancedecomposition, 410

risk, market price of, 236risk premium versus inflation

expectation, 233risks and returns along real asset

value chain, 432Royal Gold, 86royalty companies, 86–8“Russian wheat deal” 13

S

single-factor models of the shortrate, 213

see also modelsSoss, Neal, 27sovereign inflation-linked debt,

438, 438, 491, 497in Chile, 498

spread-based companies, 88–9stagflation, 3, 257Standard & Poor’s Goldman

Sachs Commodity Index(SPGSCI), 18, 20, 37–8, 53

stochastic volatility models,216–19

see also modelsstock-price-based theories of

inflation and asset returns,309–13

Gordon growth modelconcerning, 309

structured inflation notesmarket and year-on-yearinflation options, 157–8

structured note, inflationcashflows of, 144

stylised semi-structural flowmodel for an openeconomy, example of,202–5

Survey of ProfessionalForecasters, 225, 226, 371,459, 460

T

tactical asset selection:effectiveness of, 48–51robustness of, 51–4

taxation, effects of:on nominal and real income,

289–95on real earnings, 291–5on real rate of interest, 290–1

Taylor, John, 259Taylor rule, 140, 204, 259, 452–3,

453term structure modelling:

and price of risk, 210–11, 211and probability measures,

211–12from short rate to yield curve,

209–10TIPS, see US Treasury Inflation

Protected Securitiestollroads, 72–4, 72, 73

see also infrastructure assetsTreasury Inflation Protected

Securities (TIPS), see USTreasury InflationProtected Securities

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U

ultra-high-net-worth investors,423–34

definition of, 424inflation threat to, 424–5and legacy and time horizon,

425and leverage, 432–3and liabilities, 425–6and real-asset life cycle,

429–30, 430and real assets, 428–9and risks and returns, 430–2,

432unemployment, and inflation, 7,

7, 352–6 passim, 352United Nations Food and

Agriculture World FoodPrice Index, 30

US aggregate bonds, 335US bond sector indexes, 337–8US Bureau of Labor Statistics, 5,

105, 331US Federal Reserve, 25, 33, 185,

193, 195, 234, 256, 263, 314Open Market Committee of,

191, 278quantitative easing

programmes of, 372unexpected steps taken by, 369

US Treasury Inflation ProtectedSecurities (TIPS), 10, 47,50–60 passim, 105–13, 111,113, 115, 220–1, 220, 381,454

and deflation floor, 232indexation lag in, 231–2liquidity effects in, 229–31and real bonds and indexed

bonds, 242–5ten-year, break-even inflation

for, 407–8, 408zero-coupon yields, versus

real, 229–32see also bonds,

inflation-linked

V

variance decomposition by riskfactor and factor-modelsurplus volatility, 406

variance decomposition and riskfactor loadings, 410

Volcker, Paul, xix

W

water and energy utilities, 71–2see also infrastructure assets

Weimar Republic, xix

Y

year-on-year caps and floorsquotes, 162

year-on-year inflation-structurednotes, 157–8

issuance of, 157year-on-year inflation swaps,

145–50convexity adjustments in,

147–50hedging, 148

yearly forward inflation curve,150

Yildirim, Yildiray, 157

Z

zero-coupon bond prices, 236–8calculation of, 238

zero-coupon caps and floorquotes, 163

zero-coupon inflation options,160–2

development of, 160–2zero-coupon inflation swaps,

126, 144–5and hedging strategies, 457,

458, 458quotes, 152–3

zero-coupon TIPS yields versusreal yields, 229–32

and deflation floor, 232and indexation lag, 231–2and liquidity effects, 229–31see also TIPS

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