The Invisible Hand of Factors - Lazard Asset Management...diversification has motivated practitioners to search for more efficient methods to optimize asset class exposures in a portfolio

Investment Research

The Invisible Hand of Factors

Erianna Khusainova, Senior Vice President, Portfolio Manager/Analyst

The role of factors in investing has greatly deepened and broadened since the 1960s, as key theoretical concepts have evolved with research and application. For capital allocators, in particular, advances in factor understanding have driven new ways to optimize portfolios and express highly specific investment theses. However, when theory meets practice, complexity increases. We highlight the value of applying a factor framework to capital allocation, risk control, long-term alpha generation, and idea implementation. We also discuss the challenges of a factor approach in each of these four areas.

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Factor theory has changed the way many asset allocators today view and manage capital. The concept was first introduced in the 1960s through the capital asset pricing model (CAPM). CAPM attempted to explain the behavior of an asset’s return and concluded that it was largely a function of its exposure to systematic risk—and thus the world’s first investment “factor” was identified. Understanding of this subject has deepened significantly, gaining usefulness based on the past 50 years of research by academics and industry practitioners. A large number of factors have been identified since, while the scope for using them in the investment process has broadened.

We define a factor as a source of common exposure or a characteristic shared by a group of securities that helps explain their risk and return behavior, both individually and collectively. Borrowing a classic metaphor from Adam Smith’s The Wealth of Nations, we liken factors to many “invisible hands” at work in markets and portfolios. For asset allocators seeking a more efficient way to manage their exposures, a factor-based framework can help them view their portfolio differently in four important areas: capital allocation, risk control, alpha generation, and idea implementation. Factor analysis can result in valuable insights not available through a purely asset-class-based approach.

1 Capital Allocation: Correcting Blind Spots

For decades, asset classes have been the basic inputs for asset allocation, reflecting the widespread adoption of mean-variance optimization (MVO) techniques.1 A key principle in MVO is asset class diversification, and this states that uncorrelated asset classes can be combined to improve the risk-return trade-off. (See the Appendix for more detail.) As investors discovered, this theory contains a flaw: Correlations between asset classes are generally not

stable over time and can, in fact, change dramatically. Since 1976, the correlation of US large cap equities and US debt has been as low as -0.47 and as high as +0.64 (Exhibit 1). Over a similar time frame, US large cap equities and non-US large-cap equities went through intervals when they were virtually uncorrelated (+0.11) and almost perfectly correlated (+0.94).

One explanation for why correlations may increase in certain market environments is the existence of shared exposures between dissimilar asset classes. Factor analysis is helpful to identify those common exposures and can aid in correcting these “blind spots.” In emerging markets, for example, some “equity-typical” exposures, such as quality, size, or sensitivity to the equity market, are present in certain debt instruments over the medium term (Exhibit 2).2 An equity-only portfolio of high-growth companies may have fixed income duration exposure due to expected cash flows modeled farther away in time.3 Correlations also tend to increase during periods of financial stress and some factors tend to dominate others during these intervals.

Return variability among asset classes tends to be dominated by a factor that captures the extent to which investment capital is at risk. This can be demonstrated via a principal component

Exhibit 1Asset Class Correlations Can Change

-1.0

-0.5

0.0

0.5

1.0

US Eq LC to

EAFE Eq LC

US Eq LC to

US Debt

DM Eq LC to

Glob Debt

EAFE LC to

EAFE SC

EM Eq to

EAFE Eq

EM Eq to

EMD Hard

EM Eqto

EMD Loc

EM Eq to

EM FX

Rolling 3-Year Correlations

Upper Limit

Lower Limit

As of 30 November 2017

Beginning dates: US Eq LC (S&P 500 Index) to EAFE Eq LC (MSCI EAFE Index), 31 December 1969; US Eq LC (S&P 500 Index) to US Debt (Bloomberg Barclays US Aggregate Bond Index), 31 December 1975; DM Eq LC (MSCI World Index) to Glob Debt (Bloomberg Barclays Global Aggregate Bond Index), 31 December 1989; EAFE LC (MSCI EAFE Index) to EAFE SC (MSCI EAFE Small Cap Index), 31 December 1992; EM Eq (MSCI Emerging Markets Index) to EAFE Eq (MSCI EAFE Index), 31 December 1987; EM Eq (MSCI Emerging Markets Index) to EMD Hard (JP Morgan EMBI Global Diversified Index), 31 December 1993; EM Eq (MSCI Emerging Markets Index) to EMD Loc (JP Morgan GBI-EM Global Diversified Index), 31 December 2002; EM Eq (MSCI Emerging Markets Index) to EM FX (JP Morgan ELMI+), 31 December 1993.

Source: Lazard, Bloomberg, J.P. Morgan, MSCI

We define a factor as a source of common exposure or a characteristic shared by a group of securities that helps explain their risk and return behavior, both individually and collectively.

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analysis of the monthly returns of 16 asset classes: developed equities, small cap developed equities, emerging markets equities, Treasuries, government-related bonds, inflation-protected bonds, investment grade debt, high yield debt, European securitized debt, US securitized debt, emerging markets debt, emerging markets currencies, infrastructure, REITs, oil, and commodities (excluding energy). Our analysis spans January 1999 to September 2017, representing the most extensive dataset available for all 16 asset classes.4

Throughout the analyzed time period, the first principal component (PC1)—a factor we infer to be broad market risk—explained 49% of the variation in the asset class returns (Exhibit 3, left). However, when looking at the rolling 5-year sub-periods, we see that while PC1 continues to explain a large portion of the return variation, its contribution spiked from about 34% in early 2000 to about 60% around the time of the 2008 global financial crisis. The dominance of this factor remained elevated in the backdrop of global quantitative easing and started to gradually subside as monetary policy began to normalize in certain parts of the world.

The requirement to better manage aggregate portfolio risk (especially in the wake of the global financial crisis) and improve diversification has motivated practitioners to search for more efficient methods to optimize asset class exposures in a portfolio. The solution to this challenge, we believe, is to transform a multi-asset portfolio into a factor exposure portfolio.5 This should allow practitioners to account for, and minimize, overlapping exposures between assets. The choice and number of factors to use in the conversion can differ by portfolio. Ultimately, the allocator’s goals are to identify outsize or insufficient exposures, determine the desired allocation, and implement that view.

Using asset classes as the sole optimization inputs may at times lead to a false perception that a portfolio has been adequately diversified when, in reality, latent factor overlaps can create blind spots in a portfolio. A factor-based approach can give practitioners a more comprehensive view of their portfolio by allowing holdings to be sorted by shared risk drivers. This permits an asset allocator to have more control over the portfolio’s aggregate factor exposures, creating room to improve its diversification.

2 Risk Control: Minimizing Unintended Exposures

Factor analysis is used extensively to monitor portfolio risk and can aid in minimizing unintended exposures. Once the type of risk is identified and described, a supplemental portfolio can be constructed to minimize it. We call this a “factor-completion portfolio.” It is important to emphasize that the success of a factor-completion approach depends on first clearly defining the type or types of risk that should be mitigated. Core to this endeavor is identifying unintended bets in a portfolio, particularly as they relate to areas that are outside of the investor’s expertise.

Consider the following example. Portfolio A, a developed equity portfolio with alpha driven by security selection, is benchmarked to the MSCI World Index. Our analysis showed that Portfolio A had significant—and unintended—sector and country risk

Exhibit 2Disparate Asset Classes Can Share Common Exposures

Multivariate Regression betas, three years ending 31 October 2017

EM Equity Market Style (G-V) Size (L-S) Quality Credit EM Currencies Duration

EM Growth Equity 1.00 0.49

EM Value Equity 1.00 -0.51

EM Small Cap Equity 0.99 -0.91 -0.05

EM Debt Local -0.76 1.44 0.46

EM Debt Hard 0.16 0.11 -2.28 0.51

EM Corporate Debt 0.12 -0.09 0.08 -1.03 0.28

Based on weekly returns. Statistically insignificant values have been omitted.

Source: Lazard, J.P. Morgan, MSCI

Exhibit 3Broad Market Risk Is a Key Driver of Asset Class Returns

PC Contribution (%) PC Contribution, Rolling 5 Years (%)

0

25

50

75

100

Jan 99–Sep 17

PC7–16PC6PC5PC4PC3PC2PC1

20172015201320112009200720052003

traft As of 31 October 2017

Source: Lazard, J.P. Morgan, MSCI

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(Exhibit 4). Its overweight to technology stocks was at times as high as 11.6%, while its active weight in US stocks ranged from -6% to +6%. These unintentional bets exposed the portfolio to the possibility of significant fluctuations that were inconsistent with the portfolio’s objectives, keeping in mind the portfolio was not constructed with any intent to exploit sector or macroeconomic dislocations. Additionally, ongoing exposure to these sources of systematic risk was not compensated with a risk premium.

To mitigate these unintended sector and country exposures, we constructed a factor-completion portfolio (Portfolio FC), leveraging our proprietary quantitative alpha model with bottom-up stock selection capabilities and designing a process to avoid unwanted top-down exposures. We limited active weights at the industry, sector, and country levels, while integrating turnover penalties to avoid unwarranted and excessive trading costs. As a result of overlaying Portfolio FC onto Portfolio A, unintended sector and country active bets were minimized in Portfolio A

and remained stable over time (Exhibit 5). The active weight in technology of the combined portfolio was range-bound between -2% and +2% and its active exposure to US stocks was limited to 0% and -3.5%.

We were careful to ensure that Portfolio A’s alpha was undiluted and continued to be explained by stock selection. It is worth noting, however, that we did not set out to maximize stock-specific risk, as this does not necessarily improve returns.

The factor-completion portfolio maintained a similar composition of idiosyncratic and systematic risk (Exhibit 6). Before, Portfolio A’s idiosyncratic (stock-specific) risk contributed 75% on average to its predicted tracking error,6 while systematic (factor) risk accounted for the remaining 25%. The combined portfolio utilized the active risk budget more efficiently. The contribution of idiosyncratic risk to predicted tracking error rose modestly to 80%, reducing systematic risk’s share to 20%.

Exhibit 4Unintended Exposures Posed Material Risk

Sector Active Weight Relative to MSCI World Index Country Active Weight Relative to MSCI World Index

(%)

-8

-4

0

4

8

12

InformationTechnology

Industrials

Financials

Consumer Staples

2017201620152014

(%)

-6

-3

0

3

6

United States

United Kingdom

Netherlands

2017201620152014


Source: Lazard, MSCI, Northfield

Exhibit 5We Dampened Outsized Exposures…

Information Technology Active Weight Relative to MSCI World Index United States Active Weight Relative to MSCI World Index

(%)

-4

0

4

8

12

Portfolio A + Portfolio FC

Portfolio A

2017201620152014

(%)

-8

-4

0

4

8

Portfolio A + Portfolio FC

Portfolio A

2017201620152014


For illustrative purposes only. The portfolios represented are not available products.


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A closer look at the sources of systematic risk7 shows that concen-trated region and sector risks were minimized (Exhibit 7).

We would point out that neutralizing sector and region exposures using an effective factor completion approach limits accidental downside and upside. Additionally, it is not possible to immunize the portfolio from all sources of systematic risk. However, a factor completion portfolio can better align investment results and invest-ment objectives over time, while remaining within the limits of a predetermined risk budget.

3 Alpha Generation: Harvesting Factor Risk Premiums

Factor investing is based on the idea that excess returns can be gener-ated through exposure to certain factors with positive risk premiums. An investor who knows which “invisible hands” may be associated with consistent positive, long-term returns could try to establish exposure to them. “Smart-beta” investment products are based on this concept. Booming demand for these portfolios has launched

smart beta to the ranks of the most recognizable, but possibly least understood investment catchphrases of the past decade.

We believe the concept is sound—certain factors have had persistent risk premiums. Application, however, is where smart-beta products can at times fall short. In the early days of passive investing, market cap–weighted indices were used to replicate the returns of particular market segments. Since this approach did not involve security selection, these passive, index-based portfolios were regarded as “beta” products. When regressing the return of a passive product against its reference index, the product should have a beta of one to that index, with little residual noise, or alpha.

As research emerged demonstrating that indices with alternative constructs—equal-weighted or weighted by volatility or fundamen-tals, for example—outperformed their cap-weighted counterparts, quantitative methods were developed to reconstruct these exposures in portfolios. As practitioners enhanced “regular” beta to improve the risk-return trade-off, the resulting product was dubbed smart beta.

Exhibit 6…While Preserving Security Selection Capabilities

Risk Decomposition: Portfolio A Risk Decomposition: Portfolio A + Portfolio FC

(%) (%)

0

25

50

75

100

0

1

2

3

4

2017201620152014

(%) (%)

0

25

50

75

100

0

1

2

3

4

2017201620152014

Idiosyncratic Risk [LHS] Systematic Risk [LHS] Est. Tracking Error [RHS]As of 30 November 2017


Exhibit 7Concentration Risk Was Minimized

Systematic Risk Decomposition: Portfolio A Systematic Risk Decomposition: Portfolio A + Portfolio FC

-5

0

10

20

30

2014 2015 2016 2017

(%)

2014 2015 2016 2017

(%)

-5

0

10

20

30

Global MarketValue–Growth Blind Factor

Region Super Sector Economic SizeAs of 30 November 2017


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As time passed, it became evident that smart beta was not without risks. (See Six Sins of Smart Beta.) Examples of these risks include:

• Macro association risk: A low-volatility factor portfolio can have an excessive weight in stocks with a steady cash flow profile, such as utility companies. That causes the portfolio to exhibit a bond-like sensitivity to interest rates, resulting in underperformance during periods of rising rates.

• Construction methodology risk: Equal-weighting a portfolio’s holdings essentially introduces a small cap bias. Small cap stocks can be less liquid, which can create difficulties when rebalancing the portfolio and result in high transaction costs.

• Specification risk: A portfolio with a value focus needs to express itself using the right metrics in order to minimize specification risk. A low P/E stock, for example, is not synonymous with an undervalued stock and the ability to tell the difference between a value trap and a truly undervalued stock is critical in constructing a value factor. Additionally, single-factor returns exhibit cyclicality, and it often takes longer to generate those returns than some investors anticipate or ideally want.

To address these risks, the next generation of smart-beta strategies deployed more than one factor. Factor construction and factor blending methodologies continue to evolve and, currently, the debate revolves around factor selection (which factors deliver positive premiums), factor specification (how to best express a given factor), as well as implementation of factor allocation (whether or not to time an individual factor, allocate among several, or use a hybrid approach).

When selecting factors with positive risk premia, two questions to ask are why a particular factor might command a premium and what sustains that premium over time. While a multitude of factors are crucial in explaining sources of risk, not all of them earn a persistent premium associated with taking these risks. For example, a large sector or country weight in a portfolio exposes that portfolio to the systematic risks associated with those expo-sures. Continual exposure to these sector and country factors does not necessarily result in a sustainable premium, however. Robust research is critical to establish a solid rationale for why certain factors work better than others.

A few theories attempt to explain the existence and persistence of risk premia. Proponents of efficient markets attribute factor anomalies to the additional risks embedded in investments that embody these factors, such as the illiquidity premium for small companies. Alternatively, it is also thought that different sensitivi-ties of certain stocks to changing macroeconomic drivers can cause dislocations that cannot be arbitraged. Other theories point to irrational investor behaviors (such as home bias, loss aversion, or return-chasing, among many others) or mismatched investor regu-latory or institutional constraints.

Factor versus Asset ClassOpinions are sharply divided about whether factor-based approaches are superior to asset-class-based approaches. Here, we respond to the two main criticisms of factor-based approaches:8

1. Several studies comparing factor-based and asset-based allocations utilized different opportunity sets. If the same opportunity set had been specified, then the efficient frontiers of the two approaches should be similar.

While the point about equal comparison is valid, this criticism often assumes a narrow definition of factors, implying that they can only be formed from asset classes. When accounting for other types of factors, such as changes in production, tradable proxies may not exist. So the opportunity set cannot be solely explained at the asset class level and that results in dissimilarity of the two approaches. See the Appendix for more detail on different types of factors.

2. Some studies applied different constraints to the two allocation types: Shorting was allowed in a factor-based portfolio, but it was not permitted in the asset-class-based portfolio. As a result, the correlation profile was improved for the former, which led to the questionable conclusion that a factor-based approach is preferable.

We support the idea of a like-to-like comparison. The more important observation, however, is that removing the long-only constraint offers higher diversification potential, which is valuable.

Some studies testing the equivalence of the two approaches assume that mapping between factors and assets is fully fungible, i.e., the returns of assets can be perfectly explained through returns of factors. We believe this assumption is hardly practical, as it is not possible to identify all systematic drivers of returns; there will always be translational noise and errors. This assumption also implies transformations that are not subject to constraints. In reality, investment constraints vary significantly from most restrictive, with mandated exposure to certain assets, to least restrictive, which allows for illiquid investments or the deployment of leverage. To illustrate, European pension plan assets are skewed towards fixed income9 due to local regulatory requirements while assets of large US endowments and foundations tend to have higher allocations to alternative investments.10

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Although levels of agreement vary, the investment community has broadly identified the following factors as having positive return premium potential: value, small cap, quality, momentum, and low volatility. Even in cases where some have found weak empirical support for certain factors’ alpha,11 these factors still have attractive attributes for investors. Interestingly, the growth factor has courted the most controversy due to specification challenges. Lack of uniformity in definitions and measures of growth have contributed to its lower standing among factor peers. Nonetheless, the growth factor has exhibited periods of outperformance, and its diversification potential can improve the consistency of returns (See The Case for Growth).

Once an economically sensible rationale for a factor is established, it is critical to evaluate its accessibility. This includes ease of measurement, the ability to model the factor using financial instru-ments, and implementation costs. Additionally, restrictions on shorting or type of instrument (e.g., derivatives) imposed by either the client and/or regulators may add further constraints. Outcomes could vary significantly as result of how the factor is specified and rebalanced. (This poses a trade-off between factor “purity” and the need to curb trading costs necessary to avoid factor drift.)

To illustrate our point, we compare the performance of three popular value indices. These indices have different construction methodologies and have yielded different patterns of performance (Exhibit 8).

From a deployment standpoint, several strategies are available to investors. One is to engage in factor timing, with the task being to identify one or two factors that are expected to outperform in a given environment, rotating into and out of them. The drawback of this approach is the challenge of correctly timing inflection points. Another is factor diversification. To mitigate potential losses and address the cyclicality of factor returns, long-term strategic exposure to a set of fairly uncorrelated factors can be established, with periodic rebalancing. The combination can help to smooth returns while mitigating drawdown risk. This approach is not without its shortcomings as factor diversification can dilute some of the premium upside.

A hybrid of the two approaches, factor tilting, presents a third option. An investor starts with a strategic allocation specific to their objectives and subsequently leans into factors that tend to outperform in certain types of macroeconomic environments. An advantage of this approach is that the process is tethered to desired risk-return objectives while tapping into additional alpha sources.

4 Idea Implementation: Creating Custom Factors

A factor construct represents an important breakthrough, potentially as a more precise way to create custom exposures. As investors pursue alternative sources of return, factors fill a void left by traditional asset categories, which often are not suited to

expressing highly specific investment ideas, such as capturing a productivity factor or capitalizing on a long-term macro trend such as emerging markets reforms.

We see a growing demand for the monetization of “high-hanging” factors, which are more complex and difficult to specify, measure, and implement. Indeed, the difficulty of measurement rises with a factor’s complexity (Exhibit 9). Successful implementation requires multiple investment capabilities, from in-depth industry knowl-edge to macroeconomic and quantitative expertise. Technological advances have increased the availability of new and unconventional digital datasets (examples include online employee reviews of their employers and company management or consumer reviews of products and services), which aid the task. We believe managers with the ability to augment their investment process—be it funda-mental bottom-up, top-down, or quantitative—with insights from these unorthodox datasets are in a better position to capture alter-native investment themes.

Exhibit 9The More Complex a Factor, the Harder It Is to Measure

Mea

sure

men

t D

ifficu

lty

Complexity

SectorSize

Country

BetaValue

Volatility

Momentum

Quality

Growth

Scarcity

Productivity

Longevity

Care

Experience

PricingPower

Security

For illustrative purposes.

Source: Lazard

Exhibit 8Different Factor Definitions, Different Outcomes

(US$)

100

400

700

1000

2017201420112008200520021999199619931990

S&P Developed LargeMidCap ValueMSCI World Value Index

MSCI World Value Weighted


Source: Lazard, MSCI, S&P

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The Way AheadFactor-based analysis continues to transform the way that inves-tors manage their portfolios, providing significant benefits from long-term alpha generation to risk management, capital allocation, and idea implementation. We believe that factor frameworks’ ability to complement more orthodox asset-class approaches is part of their usefulness. Notably, factor-based analysis can help capital allocators account for overlapping exposures between assets, creating room to improve diversification. Additionally, unintended bets could be minimized with a factor completion portfolio. This permits a practitioner to have more control over the portfolio’s risk budget.

The attractive risk premiums that some factors offer are a clear benefit, although we believe care must be taken to identify the structural drivers of the risk premium. Correctly expressing the factor using the right choice of investment metric could also have a big impact on the pattern of returns. For investors seeking alterna-tive sources of return, advances in factor understanding and data technology have meant that they can now more precisely express niche investment theses. Understanding of factors may eventually be commoditized, but that is still far from the present reality. For present-day investors, innovations in factor research and applica-tion create exciting new possibilities.

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APPENDIXThe principles of the seminal work of Markowitz (1952) continue to be at the core of portfolio construction exercises today. Particularly, one of the most important approaches was viewing investments in the context of a portfolio as opposed to on a standalone basis. The critical insight of this method was the improvement in portfolio’s diversification potential and risk-return trade-off when it was composed of non-correlated investments. While this work was originally developed using individual securi-ties to build a traditional portfolio, the findings were later applied to construct multi-asset portfolios exploring correlation dynamics of different asset classes.

Exhibit A illustrates the point. We constructed a hypothetical port-folio consisting of the following asset classes:

(%)

US Equity 30

International Equity 20

Emerging Markets Equity 10

Global Fixed Income 30

Emerging Markets Debt (Hard Currency) 5

Emerging Markets Debt (Local Currency) 5

Then we calculated volatility contributions of each asset over the past 5 years without taking into consideration their correlations. Without diversification benefit, the hypothetical portfolio’s vola-tility would have been 9.97% instead of 7.53%. However, due to moderate-to-negative correlations among some assets, as demon-strated in Exhibit B, overall volatility was reduced by 2.45%.

Factors: Old and NewAny number of factors can exist and there are numerous ways of grouping them. One of the most intuitive classifications was provided by Connor (1995), who grouped factors into macroeco-nomic, fundamental, and statistical categories.12 To account for a broader scope of the factor definition and increased data avail-ability, we are expanding on this classification.

Fundamental: Captures factors associated with a security’s funda-mentals, such as balance sheet and income statement–based ratios and security valuations, both on a trailing and estimated basis. These factors are typically estimated via cross-sectional regression or by ranking securities by the desired characteristics (ROE, P/B, Dividend Yield) and selecting the top-ranked percentiles (e.g., tertile, quintile) to build a factor-mimicking portfolio. The advantage of these factors is that they are observable and relatively easy to measure.

Macroeconomic: Refers to factors that measure the economic characteristics of countries and commodities. They help to assess the sensitivity of securities to macroeconomic shocks. Economic time series are commonly used to estimate betas via regression

analysis. While the time series are observable, keep in mind that structural global economic shifts (e.g., de-pegging of some emerging markets currencies from the US dollar, globalization, commodity cycles) may render historical data less descriptive of the future. In other words, ex-post betas will have a less predictive power to accurately represent ex-ante beta.

Statistical: These are factors derived from statistical techniques such as principal component analysis. The goal is to find uncorre-lated variables that account the most for variation in the data sets. While many statistical packages offer this analysis, the drawback of this approach is that factors are not specified. This makes it harder to assimilate statistical factors in an overall study.

Exhibit A

(%)

0

4

8

12

Div

ersi

fied

Port

folio

Vol

atili

ty

Div

ersi

ficat

ion

Ben

efit

EM H

ard

Deb

t

EM L

ocal

Deb

t

Glo

bal D

ebt

EM E

quity

EAFE

Equ

ity

US

Equ

ity

7.53

2.450.350.511.52

1.56

2.76

3.27


Source: Lazard, J.P. Morgan, MSCI, S&P

Exhibit B

US Equity

EAFE Equity

Global Debt

EM Equity

EM Debt Local

EM Debt Hard

US Equity 1.00 0.68 -0.19 0.59 0.35 0.36

EAFE Equity 0.68 1.00 0.10 0.79 0.63 0.51

Global Debt -0.19 0.10 1.00 0.17 0.54 0.42

EM Equity 0.59 0.79 0.17 1.00 0.75 0.64

EM Debt Local 0.35 0.63 0.54 0.75 1.00 0.76

EM Debt Hard 0.36 0.51 0.42 0.64 0.76 1.00


Source: Lazard, J.P. Morgan, MSCI, S&P

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Binary Descriptors: These describe a security’s attributes, such as sector or country classification. These attributes tend to capture sources of systematic risk that do not carry a risk premium. These factors are observable; however, the methodology and granularity of the breakdowns can vary significantly. In fixed income, even though sector granularity is less of an issue, a much higher degree of sector customization is prevalent.

Market Technicals: These refer to factors that capture price trends attributed to market-based trading mechanics. Typically, they represent the technical aspect of asset price movements and trading volumes data, such as volatility of security returns, price momentum, and beta.

Evolution of Analytical Factor FrameworksUnderstanding return drivers is an ongoing exercise for invest-ment practitioners. Different return decomposition approaches have been developed over time and multiple models have been constructed to explain what factors drive investment returns.

The Capital Asset Pricing Model (CAPM), the product of the work of several financial theorists13 in the 1960s essentially represents a single-factor model that describes an asset’s expected return as a func-tion of its exposure to one factor, that is, market or systematic risk. This model takes into account the different sensitivities, or betas, of investments to systematic risk to estimate expected returns.14

The introduction of Arbitrage Pricing Theory15 fifteen years later provided an analytical framework for multi-factor models. Even though this model did not specify what factors would be best suited to explain asset returns, it enabled further research and testing of numerous multi-factor models that aimed to identify appropriate return drivers.

More ground was broken with the Fama–French three-factor model for stocks.16 This extended CAPM by incorporating two additional variables in addition to market risk: exposure to size (small vs. big) and style (value vs. growth). The Carhart four-factor model built on this model by introducing the momentum factor.17

Exhibit C

Factor Type Examples of Typical Measurements

Security Fundamentals Value P/E, P/B, EV/EBIT (reciprocals of these ratios are often used)

Growth EPS growth, sales growth, cash flow growth

Quality/Profitability ROE, ROIC, earnings stability, debt/equity (leverage), accruals, profit margins

Dividend Yield Dividend yield, dividend growth, dividend payout ratio

Credit/Default CDX spreads, high yield over government bond spread

Duration or Term Structure Difference between returns of long-term and short-term government bonds

Macroeconomic GDP growth GDP growth

Inflation CPI

Real rates Changes in real rates

Industrial production Industrial production growth

Unemployment Unemployment rate change

Consumption Per capita consumption growth

Currency DXY index, ELMI index

Oil WTI Crude Oil

Macroeconomic liquidity Loan growth

Statistical Factors are not pre-specified

Binary Descriptors Sector/Industry Specific to various index providers. Examples include GICS, ICB, ASX for stocks; Bloomberg Barclays, BofA Merrill Lynch, J.P.Morgan for bonds.

Country Specific to various index providers. Country of major revenue, regulatory risk, incorporation, stock exchange.

Market Technicals Momentum Price momentum (1mo, 6mo, 12mo), RSI

Volatility Standard deviation of time series

Dispersion Cross-sectional volatility

Size Market capitalization

Market liquidity Bid-ask spread, ADV

Market risk Beta (3 month, 6 month, 12 month), downside volatility

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As the number and nature of variables in multi-factor models exploded (Exhibit C), the factor concept was adopted across the investment ecosystem. Portfolio risk and analytics providers devel-oped sophisticated risk models to explain the risk exposures of a portfolio using factors. Similarly, style-based attributions or hold-ings decompositions available via third-parties gained popularity with investors.

A suite of rules-based, quantitatively managed investment strate-gies was developed, primarily to take advantage of the risk premia associated with some factors. Over time, this broad category has become highly heterogeneous in terms of construction meth-odology. Despite this, performance among practitioners who claimed to exploit the same factor differed significantly. As a result, managers began to differentiate themselves on construction competencies. Later on, some of these strategies were marketed as “smart beta” products.

As index providers caught on, they rolled out their versions of factor indices to act as benchmarks for factor portfolios. The avail-ability of exchange-traded funds (ETFs) to replicate those indices also increased accessibility to some investment styles and helped

popularize factor terminology. As such, the term’s ubiquity may come as little surprise.

Exhibit D shows correlations of different asset classes over approximately 13 years prior to the global financial crisis (GFC). Within asset sub-groups, correlations are elevated: EAFE equity small cap has a correlation of 0.82 with EAFE equity large cap; EAFE equity large cap’s correlation with US equity large cap is 0.76, while it is 0.69 for US debt and global debt.18 On the other hand, the uncorrelated nature of debt and equity return patterns provides more opportunity for diversification. For example, US equity large cap is virtually uncorrelated with US debt and US equity small cap’s correlation to global debt is slightly negative at -0.04.

When looking at the same asset class correlations during the GFC from the market’s peak on 9 October 2007 to its trough on 9 March 2009 (Exhibit E), it becomes evident that while there is still scope for diversification, correlations have broadly increased. Because we used a monthly time series, we adjusted the time period to span 30 September 2007–28 February 2009.19

For comparison, Exhibit F shows correlations spanning 23 years, which include the GFC.

Exhibit D

(31 May 1994–31 August 2007)

US Equity Large

US Equity Small

EAFE Equity Large

EAFE Equity Small

EM Equity Large

EM Equity Small

US Debt

Global Debt

EM Debt Hard

CurrencyEM

Currencies Cash

US Equity Large 1.00

US Equity Small 0.72 1.00

EAFE Equity Large 0.76 0.69 1.00

EAFE Equity Small 0.54 0.61 0.82 1.00

EM Equity Large 0.66 0.68 0.73 0.71 1.00

EM Equity Small 0.54 0.58 0.65 0.71 0.92 1.00

US Debt -0.01 -0.11 -0.12 -0.12 -0.15 -0.20 1.00

Global Debt -0.01 -0.04 0.13 0.12 -0.06 -0.07 0.69 1.00

EM Debt Hard Currency 0.51 0.49 0.44 0.38 0.65 0.52 0.23 0.12 1.00

EM Currencies 0.44 0.42 0.54 0.50 0.66 0.64 -0.04 0.27 0.52 1.00

Cash 0.06 -0.03 -0.09 -0.21 -0.16 -0.20 0.13 -0.06 0.00 -0.12 1.00

As of 31 August 2007

Source: Lazard, Bloomberg, Citigroup, J.P.Morgan, MSCI

12

Exhibit E (28 September 2007–28 Februrary 2009)

US Equity Large

US Equity Small

EAFE Equity Large

EAFE Equity Small

EM Equity Large

EM Equity Small

US Debt

Global Debt

EM Debt Hard

CurrencyEM

Currencies Cash





EM Equity Large 0.80 0.75 0.94 0.96 1.00

EM Equity Small 0.76 0.73 0.91 0.95 0.97 1.00

US Debt 0.38 0.32 0.52 0.52 0.39 0.49 1.00

Global Debt 0.37 0.37 0.56 0.56 0.43 0.50 0.88 1.00


EM Currencies 0.72 0.73 0.83 0.79 0.77 0.75 0.54 0.71 0.72 1.00

Cash 0.31 0.26 0.20 0.11 0.14 0.03 0.08 0.20 0.06 0.40 1.00

As of 28 February 2009

Source: Lazard, Bloomberg, Citigroup, J.P. Morgan, MSCI

Exhibit F (31 May 1994–30 November 2017)

US Equity Large

US Equity Small

EAFE Equity Large

EAFE Equity Small

EM Equity Large

EM Equity Small

US Debt

Global Debt

EM Debt Hard

CurrencyEM

Currencies Cash





EM Equity Large 0.73 0.70 0.80 0.79 1.00

EM Equity Small 0.65 0.64 0.77 0.80 0.94 1.00

US Debt 0.01 -0.09 0.01 0.01 -0.01 -0.01 1.00

Global Debt 0.15 0.07 0.32 0.31 0.21 0.21 0.70 1.00


EM Currencies 0.56 0.50 0.69 0.65 0.74 0.72 0.12 0.51 0.57 1.00

Cash 0.02 -0.02 -0.02 -0.10 -0.05 -0.08 0.14 0.05 0.05 0.09 1.00


Source: Lazard, Bloomberg, Citigroup, J.P. Morgan, MSCI

13

LR29518

References:Bender, Jennifer, Remy Briand, Dimitris Melas, and Raman Aylur Subramanian. Foundations of Factor Investing. (2013)

French, Craig W. “The Treynor Capital Asset Pricing Model.” Journal of Investment Management. Vol. 1, no. 2 (2003)

Fama, Eugene F. and French, Kenneth R. (2015). Dissecting Anomalies with a Five-Factor Model. (2015)

Gregory Connor. The Three Types of Factor Models: A Comparison of Their Explanatory Power. (1995)

FTSE Russell. The Evolution of Factor Investing. (2016)

Connor, Gregory and R.A. Korajczyk. A Test for the Number of Factors in an Approximate Factor Model. (1993)

Grinold, Richard and Ronald N. Kahn. BARRA. “Multiple-Factor Models for Portfolio Risk.” (1994)

Idzorek, Thomas M. and Maciej Kowara. Factor-Based Asset Allocation vs. Asset-Class-Based Asset Allocation. (2013)

Lee, W. “Risk-Based Asset Allocation: A New Answer to an Old Question.” The Journal of Portfolio Management. Vol. 37, no. 4 (2011)

Cocoma, P., M. Czasonis, M. Kritzman, and D. Turkington. “Facts about Factors.” Working Paper. SSRN. (2016)

Clarke, R.G., H. de Silva, and R. Murdock. “A Factor Approach to Asset Allocation.” The Journal of Portfolio Management. Vol. 32, no. 1 (2005)

Bender, Jennifer, Remy Briand, Frank Nielsen, and Dan Stefek. “Portfolio of Risk Premia: A New Approach to Diversification.” Journal of Portfolio Management 36. (2010)

Page, Sébastien and Mark A. Taborsky. “The Myth of Diversification: Risk Factors vs. Asset Classes.” Journal of Portfolio Management. Vol. 37, no. 4. (2011)

Bass, Robert, Scott Gladstone, and Andrew Ang. “Total Portfolio Factor, Not Just Asset, Allocation.” (2017)

Menchero, Jose. Characteristics of Factor Portfolios. (2010)

Podkaminer, Eugene L. Risk Factors as Building Blocks for Portfolio Diversification: The Chemistry of Asset Allocation. (2013)

Williams, Jason. “The Six Sins of Smart Beta.” (2017)

Lazard Quantitative Equity Team. “The Case for Growth.” (2017)

Beck, Noah, Jason Hsu, Vitali Kalesnik, and Helge Kostka. “Will Your Factor Deliver? An Examination of Factor Robustness and Implementation Costs.” (2016)

Notes1 In addition to the traditional Sharpe ratio–optimized MVO, the following optimization methods can be treated as special cases of the traditional MVO: 1) variance and 2) volatility-based risk

parity–implies correlation of 0 among assets, 3) volatility minimization, and 4) equal risk contribution. All four variations also treat return means as being equal in value.

2 Represents betas to the respective factors with a p-value less than 0.05. Calculated as multivariate regression over 3 years as of 31 October 2017 using weekly observations. Asset classes are represented by MSCI and J.P. Morgan indices.

3 This sensitivity is not seen in this particular example, which is based on indices. However, some implementations of growth strategies may show a duration bet.

4 Returns are in US dollars. A correlation matrix was used in PCA computation. Returns were scaled by the standard deviation of each vector. A covariance matrix can be used as well, where variables with higher variances will be allocated a larger weight.

5 Clark et al (2005), Bender et al (2010), Page and Taborsky (2011), Podkaminer (2013), Bass et al (2017)

6 Measured as ex-ante tracking error using the Northfield Global risk model.

7 We grouped factors in the Northfield Global risk model into seven categories for easier data interpretation.

8 Lee (2011), Idzorek and Kowara (2013), Cocoma et al (2016)

9 Mercer European Asset Allocation Report

10 Pensions & Investments. http://www.pionline.com/article/20160909/INTERACTIVE/160909860/eampf-asset-allocation11 Beck et al (2016) find the robustness of quality and small cap factors to be lacking.

12 Connor, Gregory. “The Three Types of Factor Models: A comparison of Their Explanatory Power.” (1995)

13 Treynor (1961); Sharpe (1964); Lintner (1965); Mossin (1966).

14 Unsystematic risk, or idiosyncratic risk associated with individual securities, is diversifiable in the context of mean-variance efficient portfolios.

15 Ross (1976a,b)

16 Fama and French (1992, 1993). For the bond market, these two factors were used: maturity and default risks. Additionally, a five-factor model for stocks, which includes profitability and investment factors, was introduced by Fama and French (2015).

17 Carhart (1997)

18 US debt represents about 40% of the global debt universe and this partially explains the high correlation.

19 We maintained monthly data intervals for a like-to-like comparison with Table D, although we recognize that 17 observations affect the statistical significance of the results.

Important InformationPublished on 21 February 2018.

This document reflects the views of Lazard Asset Management LLC or its affiliates (“Lazard”) based upon information believed to be reliable as of 16 February 2018. There is no guarantee that any forecast or opinion will be realized. This document is provided by Lazard Asset Management LLC or its affiliates (“Lazard”) for informational purposes only. Nothing herein constitutes invest-ment advice or a recommendation relating to any security, commodity, derivative, investment management service or investment product. Investments in securities, derivatives and commodities involve risk, will fluctuate in price, and may result in losses. Certain assets held in Lazard’s investment portfolios, in particular alternative investment portfolios, can involve high degrees of risk and volatility when compared to other assets. Similarly, certain assets held in Lazard’s investment portfolios may trade in less liquid or efficient markets, which can affect investment performance. Past performance does not guarantee future results. The views expressed herein are subject to change, and may differ from the views of other Lazard investment professionals.

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