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Improving New Investment Paradigm Or Yet Another Marketing Fad? An EDHEC-Risk Institute Publication Factor Investing: A Welfare- Improving New Investment Paradigm or Yet Another Marketing Fad? July 2015 with the support of Institute Table of Contents Executive Summary ......................................................................................................... 5 1. Introduction .................................................................................................................. 13 2. Risk Premia and the Stochastic Discount Factor in Asset Pricing Theory ....... 17 3. Theoretical Analysis of Factor Investing ................................................................. 43 4. Survey of Empirical Literature .................................................................................. 57 5. Empirical Analysis of Factor Investing ..................................................................109 Conclusion ........................................................................................................................177 Appendices .......................................................................................................................179 References ........................................................................................................................191 About Lyxor Asset Management ...............................................................................207 About EDHEC-Risk Institute ...................................................................................... 211 EDHEC-Risk Institute Publications and Position Papers (2012-2015) ..............215 Printed in France, July 2015. Copyright EDHEC 2015. 2 The opinions expressed in this study are those of the author and do not necessarily reflect those of EDHEC Business School. The authors can be contacted at [email protected]. Factor Investing: A Welfare-Improving New Investment Paradigm or Yet Another Marketing Fad? — July 2015 Table of Contents Foreword The present publication was produced as The study suggests that the most part of the “Risk Allocation Solutions” meaningful way to group individual research chair at EDHEC-Risk Institute, securities is not to form arbitrary asset in partnership with Lyxor Asset class indices, but rather to form replicating Management. This chair is examining portfolios for asset pricing factors that performance portfolios with improved can collectively explain cross-sectional hedging benefits, hedging portfolios differences in security returns. with improved performance benefits, and inflation risk and asset allocation In this paper, the authors found that the solutions. out-of-sample benefits of factor investing are potentially extremely large when The current paper, “Factor Investing: short-selling is allowed, and remain A Welfare-Improving New Investment substantial in the presence of long- Paradigm or Yet Another Marketing only constraints, especially when Fad?”, examines the relative efficiency improved weighting schemes are used in of standard forms of practical implementation. implementation of the factor investing paradigm based on commonly-used I would like to thank Professor Lionel factors in the equity, fixed-income and Martellini and Dr Vincent Milhau for commodity universes. their work on this research, and Laurent Ringelstein and Dami Coker for their Investment practice has recently witnessed efforts in producing the final publication. the emergence of a new approach known as factor investing, which recommends I would also like to extend particular that allocation decisions be expressed thanks to Lyxor Asset Management for in terms of risk factors, as opposed to their support of this research chair. standard asset class decompositions. To answer the question of whether factor We wish you a useful and informative investing is truly a welfare-improving read. new investment paradigm or whether it is merely yet another marketing fad, the paper identifies mathematical conditions under which it is expected to generate welfare gains for asset owners and Noël Amenc provides an empirical measure of such Professor of Finance gains. Director of EDHEC-Risk Institute An EDHEC-Risk Institute Publication 3 Factor Investing: A Welfare-Improving New Investment Paradigm or Yet Another Marketing Fad? — July 2015 About the Authors Lionel Martellini is Professor of Finance at EDHEC Business School and Scientific Director of EDHEC-Risk Institute. He has graduate degrees in economics, statistics, and mathematics, as well as a PhD in finance from the University of California at Berkeley. Lionel is a member of the editorial board of the Journal of Portfolio Management and the Journal of Alternative Investments. An expert in quantitative asset management and derivatives valuation, his work has been widely published in academic and practitioner journals and he has co-authored textbooks on alternative investment strategies and fixed-income securities. Vincent Milhau is Deputy Scientific Director of EDHEC-Risk Institute. He holds master's degrees in statistics (ENSAE) and financial mathematics (Université Paris VII), as well as a PhD in finance (Université de Nice-Sophia Antipolis). His research focus is on portfolio selection problems and continuous-time asset-pricing models. 4 An EDHEC-Risk Institute Publication Executive Summary An EDHEC-Risk Institute Publication 5 Factor Investing: A Welfare-Improving New Investment Paradigm or Yet Another Marketing Fad? — July 2015 Executive Summary A new approach known as factor We then survey a (vast) empirical literature investing has recently emerged in in order to identify the most consensual investment practice, which recommends factors in three major asset classes, that allocation decisions be expressed namely stocks, bonds and commodities. in terms of risk factors, as opposed to The second challenge in factor investing standard asset class decompositions. is the implementation of decisions in a While intuitively appealing, this approach cost-efficient way with investable proxies. poses a major challenge, namely the On the empirical front, our paper provides choice of the meaningful factors and an analysis of the welfare gains that can be the corresponding investable proxies. expected from the use of proxies for factors, and discusses the choice of long-only Simply put, factor investing proposes versus long-short factors, which is relevant regarding each constituent in an investor's for many investors given that they are not portfolio, and therefore the whole portfolio, allowed to take short positions. as a bundle of factor exposures. Obviously, factor models, such as those of Sharpe In asset pricing theory, the relevant (1963) and Fama and French (1993), and important factors are the "pricing have long been used for performance factors'', the exposures to which explain measurement purposes, and several factors all differences in expected returns across correspond to classical investment styles, assets. such as value-growth investing, trend following or short volatility, that were Asset pricing theory makes a distinction in use in the industry before they were between "pricing factors", which explain formally identified as asset pricing factors. differences in expected returns across In this context, the question arises whether assets, and "priced factors", which earn factor investing is truly a welfare-improving a premium over the long run. The theory, new investment paradigm or whether it is exposed in the textbooks of Duffie (2001) merely yet another marketing fad. and Cochrane (2005), expresses the risk premium on an asset, i.e. the expected return A first remark is that if there are as many on this asset in excess of the risk-free rate, factors as individual securities and the as a function of the covariance between factors are themselves portfolios of such the pay-off and an abstract quantity known securities, then thinking in terms of factors as the stochastic discount factor. The goal is strictly equivalent to thinking in terms of theoretical and empirical asset pricing of asset classes, and would therefore not models is to find a representation for this add any value. More relevant is the situation random variable in terms of economically where a parsimonious factor mode is used, interpretable variables. For instance, in with a number of factors smaller than the consumption-based models, the stochastic number of constituents. The first challenge discount factor is proportional to the posed to investors who decide to express marginal utility of consumption. This their decisions in terms of factor exposures conveys an important economic intuition: is then the identification of meaningful risk premia exist as rewards required by factors. In this perspective, the theoretical investors in exchange for holding assets section of this paper reviews the academic that have a low pay-off in "bad times", literature on asset pricing and makes a list of defined as times where investors' wealth conditions that such factors should satisfy. is low and marginal utility is high. 6 An EDHEC-Risk Institute Publication Factor Investing: A Welfare-Improving New Investment Paradigm or Yet Another Marketing Fad? — July 2015 Executive Summary Pricing factors arise when one attempts to problem coincides with an optimal linear find observable proxies for the aggregate combination of mean-variance efficient investor's marginal utility. In a factor model, benchmark portfolios invested in individual the risk premium on an asset is a linear securities if each individual security has combination of the
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