White Paper 6 Strategic Asset Allocation

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<ul><li><p>W h i t e P a P e r</p><p>S T R A T E G I C </p><p>A S S E T A L L O C A T I O N</p><p>March 2011</p><p>Issue #6</p><p>Karl EychenneResearch &amp; DevelopmentLyxor Asset Management, Pariskarl.eychenne@lyxor.com</p><p>Stphane MartinettiResearch &amp; DevelopmentLyxor Asset Management, Parisstephane.martinetti@lyxor.com</p><p>Thierry RoncalliResearch &amp; DevelopmentLyxor Asset Management, Paristhierry.roncalli@lyxor.com</p></li><li><p>Q u a n t R e s e a R c h b y Ly x o R 1</p><p>s t r at e g i c a s s e t a l l o c at i o nissue # 6</p><p>Foreword</p><p>The primary goal of a Strategic Asset Allocation (SAA) is to create an asset mix whichwill provide an optimal balance between expected risk and return for a long-term investmenthorizon. SAA is often thought as a reference portfolio which will be tactically adjusted basedon short-term market forecasts, following a process often called Tactical Asset Allocation(TAA). Many empirical studies support that SAA is the most important determinant of thetotal return and risk of a broadly diversified portfolio.</p><p>As a matter of fact, long-term allocation needs long-term assumptions on assets risk/re-turn characteristics as a key input. With 30 years in mind as a typical horizon, the issue ofdetermining expected returns, volatilities and correlations for equity, bond, commodity andalternative asset classes is a complex task, faced by most institutions. Two main routes canbe explored to address this issue.</p><p>The first one basically consists in stating that past history will repeat itself similarly andhistorical figures can serve as a reliable guide for the future. This method, sometimes referredas unconditional, determines expected returns based on historical returns, disregarding anyworld shocks or structural economic changes that could arise. As a result, this approachappears unsatisfactory and not adapted to the SAA problem.</p><p>A second route consists in relating long-run financial expected returns to long-run macro-economic scenarios. The assumption here is that market prices do not differ, on the longterm, from their so called fundamental value which is determined by the returns of physicalassets. Hence, this fair value methodology consists in first, establishing a link betweenfinancial prices and economic fundamentals and second, determining the long-run value ofthose fundamentals.</p><p>This sixth white paper explores the second route. First, the long-run short rate is definedbased upon macro-economic quantities such as the long-run inflation and real potentialoutput growth. Using this long-run short rate as a reference numeraire, risk-premium ofbonds, equities and some alternative asset classes are then successively derived. Eventually,using a typical mean-variance framework, numerical results are obtained.</p><p>Overall, the approach described herein provides an original line of thought to addressallocation issues in a consistent set-up. The traditional segmentation between SAA andTAA, which could appear artificial, finds a clear justification. In the SAA step, allocation isbuilt to adapt to the expected long-term stationary state of the economy. In turn, the TAAstep allows for local fluctuations (business cycle) around this steady-state to be taken intoaccount. We hope you will find this article both interesting and useful in practice.</p><p>Nicolas GausselGlobal Head of Quantitative Asset Management</p></li><li><p>2</p></li><li><p>Q u a n t R e s e a R c h b y Ly x o R 3</p><p>s t r at e g i c a s s e t a l l o c at i o nissue # 6</p><p>Executive Summary</p><p>IntroductionStrategic asset allocation is the first and most important choice that a long-term or institu-tional investor must make. It is in fact a key concept for anybody who hopes to receive apension in retirement.</p><p>Strategic asset allocation is the choice of equities, bonds,or alternative assets that the investor wishes to hold forthe long-run, usually from 10 to 50 years.</p><p>Nowadays, with the growing conviction that future asset returns are unlikely to match thoseof the last 25 years, this decision plays a central role. Indeed, this period has been marked byunprecedented performances of government bonds, while the dot.com and subprime criseshave weighted on equities. Most of all, the world is facing structural changes, with an ageingpopulation, globalization, and ever-increasing demands on natural resources.</p><p>To build a consistent strategic allocation, one has to answer the two following questions:</p><p>(i) What is the long-run scenario for the next 50 years?</p><p>(ii) In what proportions should equities, bonds, and possibly alternative assetsbe chosen to build a long-run portfolio consistent with this scenario?</p><p>Our paper addresses these two questions, starting with the paradigm that long-run assetreturns should be consistent with long-run fundamentals.</p><p>Misunderstanding. . .A key feature of strategic asset allocation is its long-term horizon. Does this mean that theinvestor should ignore business cycles and financial crises? These questions reveal confusionregarding the nature of the decisions. Strategic asset allocation (SAA) is often defined asthe opposite of tactical asset allocation (TAA).</p><p>TAA is a short to medium-termdecision. It is assimilated asmarket timing decisions relatedto business cycles and/or mar-ket sentiment. Typically, the in-vestor modifies the asset mix inthe portfolio conditionally to theeconomic news flow or technicalfactors.</p><p>SAA is a long-term decision.Over this horizon, the influenceof financial crisis and business cy-cles is supposed to be less im-portant. Then, long-run expec-tations obey to structural factorslike the population growth (or de-mographic change), governmentpolicies and productivity.</p></li><li><p>4The long-run scenario for 2050Long-run asset returns are determined by the long-run fundamentals of the economy. Theeconomic argument is that asset prices vary with business cycles over the medium term, andconverge to a fundamental value over the long run.</p><p>The long-run fundamentals of the economyIt is nowadays widely admitted that these fundamentals are two-fold, namely output (alsocalled GDP) and inflation. During business cycles, these two pillars are closely linked, withperiods of faster output growth triggering an acceleration of inflation.</p><p>Over the long run, the influence of the business cycle declines. Output should then convergeto so-called potential output, while long-run inflation should be influenced by the ability ofCentral Banks to control the inflation expectations of economic agents.</p><p>Long-run GDP (Solow model)</p><p>Over the medium term, the outputgrowth is varying with the stage of thebusiness cycles. During economic ex-pansions, the output growth is acceler-ating, during economic recessions it iscontracting.</p><p>Over the long run, the Solow modelstates that economies tend to a steady-state, which is defined as:</p><p>GDP Growth = ProductivityGrowth + Employment Growth</p><p>Long-run inflation (Phillips curve)</p><p>A fundamental concept in inflation anal-ysis is the relationship between inflationand unemployment. The lower the un-employment in an economy, the higherthe rate of inflation.</p><p>Over the long run, the unemploymentrate converges to the NAIRU, which isthe non-accelerating inflation rate ofunemployment. Then, long-run infla-tion only depends on the inflation ex-pectations of economic agents, and otherstructural or exogenous factors.</p><p>Unemployment</p><p>Inflation</p><p>NAIRU</p><p>Economic modeling of asset returnsEquity prices rise during periods of economic expansion, and bond prices fall during periodsof high inflation. In short, asset returns vary with business cycles. Assuming a world withno risks and no uncertainty related to the future, it would be reasonable to equate all assetreturns to a single return, the same for all investors, which we could call a risk-free return. If</p></li><li><p>Q u a n t R e s e a R c h b y Ly x o R 5</p><p>s t r at e g i c a s s e t a l l o c at i o nissue # 6</p><p>however we return to reality and acknowledge the uncertainty of the future world, it wouldalso be reasonable to add an additional term which we call the risk premium, in referenceto the risk aversion of investors. A practical way to understand the mechanism is to breakasset returns down into these two terms:</p><p>Asset returns = Risk-Free Rate + Risk Premium</p><p>A risk-free return is traditionally described as the guaranteed return obtained over a sethorizon: the short-term rate for a short-term horizon, or the bond yield for a long-termhorizon. During periods of economic expansion, it increases as Central banks hiketheir short rates in order to restrain demand and so limit inflationary pressures. Over thelong run, the risk-free return should equate potential output growth, through the Goldenrule.</p><p>The risk premium could be interpreted as the return required by investors in excess ofthe risk-free return, in order to cushion them against uncertainty. During periods ofeconomic expansion, the risk premium decreases, as investors become less risk averseand are willing to accept a lower excess return. Over long-term horizons, risk premiumsshould converge to values that depend solely on the nature of the underlying asset. Standardmodels derived from asset pricing theory then help us identify the specific fundamentaldeterminants tied to a specific asset class.</p><p>To determine long-run assumptions, we adopt a fundamental fair value approach.</p><p>The Two Economic Pillars</p><p>Potential Growth</p><p>Inflation</p><p>Long-run Returns on Asset Classes</p><p>Short Rate =</p><p>Government Bonds =</p><p>Equities</p><p>Corporate Bonds</p><p>Commodities</p><p>Other Asset Classes</p><p>2050: lower bond returns, and a return to standard equity risk pre-miumsAfter the initial step of choosing asset returns models, we use simple statistical tools tocalibrate long-run relationships, and then forecast long-run asset returns in a systematicway. We can then answer the first question: what is the long-run scenario for the next 50years?</p><p>Our results highlight a much more favorable outlook for equities than for bonds when com-pared to figures observed over the last 25 years.</p></li><li><p>6Asset Classes 2020 2030 2050US 10Y 1.9% 3.5% 4.3%EURO 10Y 1.8% 3.2% 4.0%</p><p>Bonds EM 10Y 5.6% 7.6% 9.0%US IG 6.1% 6.2% 6.3%US HY 8.9% 9.6% 9.9%US 9.2% 8.4% 9.1%EURO 9.7% 8.2% 8.7%</p><p>Equities JPY 8.8% 4.9% 5.6%EM 10.7% 10.4% 10.8%Small cap 12.2% 11.4% 12.1%Commodity 8.4% 8.6% 9.0%</p><p>Alternative Hedge funds 7.1% 7.3% 7.4%Investments Real estate 8.2% 7.4% 8.1%</p><p>Private equity 12.5% 11.7% 12.1%</p><p>We obtain an annualized returnof 4.3% for US bonds and 4.0%for Euro bonds at the 2050 hori-zon, a figure contrasting withthe 9% annualized performanceposted since 1980, thanks to thedisinflation regime.</p><p>Regarding equities, when mea-sured in excess of bond returns,equity risk premium forecasts arehigher than the ones obtainedduring the last decade, at 4.8%for US and Euro equities, withthe exception of Japan whichcomes lower, at 3%.</p><p>Our long-run volatility forecasts are much lower than the values obtained during the two lastdecades, which have been marked by two severe economic recessions. On the other hand,our long-run correlation forecasts highlight two key facts. First, the correlation betweenequity and bond returns should remain low or slightly negative, as it was during the twolast decades in a regime of limited inflation risks. Second, the correlation between equitiesor between bonds should remain high, in line with increasing globalization.</p><p>Strategic allocation for 2050</p><p>The equity/bond asset mix decisionThe equity/bond asset mix is certainly the most challenging decision for pension funds andlong-term investors. If we compare pension funds in different countries, we observe significantdifferences. However, following the subprime crisis, most European pension funds have cuttheir strategic exposure to equities below 30%, with the exception of United Kingdom. Usingour quantitative model, we construct strategic allocations that are conditional on differentlevels of risk aversion for the investor, as measured by its ex-ante required volatility. We findthat the optimal allocation is a portfolio composed by 70% in bonds and 30% in equities ifwe consider a standard risk-aversion parameter for long-term investors. A balanced portfolioof 50% in bonds and 50% in equities is reached for a 7% ex-ante volatility.</p><p>Is there a place for alternative assets?Another major issue faced by long-term investors is the place of alternative investmentsin strategic asset allocation. We have observed that incorporating alternative investments</p></li><li><p>Q u a n t R e s e a R c h b y Ly x o R 7</p><p>s t r at e g i c a s s e t a l l o c at i o nissue # 6</p><p>improves the portfolio return for a given level of risk aversion. We have also noticed thatthe weightings of bonds are fairly similar. Alternative investments are therefore a substitutefor equities.</p><p>Interestingly, we find that these optimal weightings of alternative investments are higher thanthe ones implemented in practice. The lack of liquidity of such investments is commonly citedas an explanation. Nevertheless, we can demonstrate that even if we take this drawback intoaccount, the place of alternative investments in strategic asset allocation today is certainlyunder-estimated.</p><p>We can now answer the second question about strategic allocation: in whichproportions should equities, bonds, and possibly alternative assets be chosento build a long-term portfolio consistent with this scenario?</p><p> The strategic equity/bond asset mix allocation derived from our long-runassumptions highlights an equity exposure close to 30% for a standardrisk-aversion parameter. This allocation is close to the one exhibited bymost European pension funds, following the subprime crisis.</p><p> There is a place for alternative assets in this strategic allocation. Specif-ically, we find that the weightings of alternative assets could reach 1/3of the overall risky assets, which is higher than the one implemented inpractice. But the lack of liquidity of such investments is a negative factorin implementing tactical asset allocation.</p><p>ConclusionThe recent crisis has one great merit. It has reminded us that strategic allocation is akey issue that any institutional investor must address. A long-term strategy needs to beconsistent with a long-run economic scenario. By consistency we mean a strategy thatreflects the world we live in: ageing populations, globalization and ever increasing demandson natural resources. These key themes will have an impact on global output and assetreturns for the years to come. Our quantitative framework accounts for these phenomenonand provides strategic allocations that match a long-run scenario.</p></li><li><p>8</p></li><li><p>Q u a n t R e s e a R c h b y Ly x o R 9</p><p>s t r at e g i c a s s e t a l l o c at i o nissue # 6</p><p>Table of Contents</p><p>1 Introduction 11</p><p>2 Economic modeling of risk premiums 132.1 The two economic pillars . . . . . . . . . . . . . . . . . . . . . . 152.2 Modeling asset returns . . . . . . . . . . . . . . . . . . . . . . . 172.3 Assessing market risks . . . . . . . . . . . . . . . . . . . . . . . 23</p><p>3 Empirical estimation of risk premiums 253.1 Potential output and inflation . . . . . . . . . . . . . . . . . . . 253.2 Asset returns . . . . . . . ....</p></li></ul>

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