Measuring Factor Exposures Uses and Abuses

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Measuring Factor Exposures
    AQR Capital Management, LLC Two Greenwich Plaza Greenwich, CT 06830 p: +1.203.742.3600 f: +1.203.742.3100 w: Measuring Factor Exposures: Uses and Abuses Ronen Israel Principal Adrienne Ross Associate October 2015 A growing number of investors have come to view their portfolios (especially equity portfolios) as a collection of exposures to risk factors. The most prevalent and widely harvested of these risk factors is the market (equity risk premium); but there are also others, such as value and momentum (style premia). Measuring exposures to these factors can be a challenge. Investors need to understand how factors are constructed and implemented in their portfolios. They also need to know how statistical analysis may be best applied. Without the proper model, rewards for factor exposures may be misconstrued as alpha, and investors may be misinformed about the risks their portfolios truly face. This paper should serve as a practical guide for investors looking to measure portfolio factor exposures. We discuss some of the pitfalls associated with regression analysis, and how factor design can matter a lot more than expected. Ultimately, investors with a clear understanding of the risk sources in an existing portfolio, as well as the risk exposures of other portfolios under consideration, may have an edge in building better diversified portfolios. We would like to thank Cliff Asness, Marco Hanig, Lukasz Pomorski, Lasse Pedersen, Rodney Sullivan, Scott Richardson, Antti Ilmanen, Tobias Moskowitz, Daniel Villalon, Sarah Jiang and Nick McQuinn for helpful comments and suggestions.      Measuring Factor Exposures: Uses and Abuses   1   Introduction: Why Should Investors Care About Factor Exposures? Investors have become increasingly focused on how to harvest returns in an efficient way. A big part of that process involves understanding the systematic sources of risk and reward in their portfolios. “ Risk-based investing ”  generally views a portfolio as a collection of return-generating processes or factors. The most straightforward of these processes is to invest in asset classes, such as stocks and bonds (asset class premia). Such risk taking has been rewarded globally over the long term, and has historically represented the biggest driver of returns for investors. However, asset class premia represent just one dimension of returns. A largely independent, separate source comes from style premia. Style premia are a set of systematic sources of returns that are well researched, geographically pervasive and have been shown to be persistent. There is a logical, economic rationale for why they provide a long-term source of return (and are likely to continue to do so). 1  Finally, they can be applied across multiple asset classes. 2  The common feature of risk-based investing is the emphasis on improved risk diversification, which can be achieved by identifying the sources of returns that are underrepresented in a portfolio. Investors who understand what risk sources their portfolios are exposed to (and the magnitude of these exposures) may be better suited to evaluate existing and potential managers. Without an understanding of portfolio risk factor exposures, how else would investors be able to tell if their value manager, for example, is actually providing significant value exposure? Or 1  See  “How Can a Strategy Still Work if Everyone Knows About It?” accessed September 23, 2015, 2  Applying styles across multiple asset classes provides greater diversification. In addition, the effectiveness of styles across asset classes helps dissuade criticisms of data mining. Asness, Moskowitz and Pedersen (2013); Asness, Ilmanen, Israel and Moskowitz (2015). Past performance is not indicative of future results. whether a manager is truly delivering alpha, and not some other factor exposure? Or even, whether a new manager would be additive to their existing portfolio? These are important questions for investors to answer, but quantifying them may be difficult. There are many ways to measure and interpret the results of factor analysis. There are also many variations in portfolio construction and factor portfolio design. Even a single factor such as value has variations that an investor should consider —  it can be applied as a tilt to a long-only equity portfolio, 3  or it can be applied in a “pure r ” form through long/short strategies; it c an be based on multiple measures of value, or a single measure such as book-to-price; or it can span multiple asset classes or geographies. Simply put, even two factors that aim to capture the same economic phenomenon can differ significantly in their construction —  and these differences can matter. In this paper, we discuss some of the difficulties associated with measuring and interpreting factor exposures. We explore the pitfalls of regression analysis, describe the differences associated with academic versus practitioner factors, and outline various choices that can affect the results. We hope that after reading this paper investors will be better able to measure portfolio factor exposures, understand the results of factor models and, ultimately, determine whether their portfolios are accessing the sources of return they want in a diversified manner. A Brief History of Factors Asset pricing models generally dictate that risk factors command a risk premium. Modern Portfolio Theory quantifies the relationship between risk and expected return, distinguishing 3  The long-only style tilt portfolio will still have significant market exposure. This type of style portfolio is often referred to as a “smart beta” portfolio.  2 Measuring Factor Exposures: Uses and Abuses   between two types of risks: idiosyncratic risk (that which can be diversified away) and systematic risk (such as market risk that cannot be diversified away). The Capital Asset Pricing Model (CAPM) provides a framework to evaluate the risk premium of systematic market risk. 4  In the CAPM single-factor world, we can use linear regression analysis to decompose returns into two components: alpha and beta. Alpha is the portion of returns that cannot be explained by exposure to the market, while beta is the portion of returns that can be attributed to the market. 5  But studies have shown that single-factor models may not adequately explain the relationship between risk and expected return, and that there are other risk factors at play. For example, under the framework of Fama and French (1992, 1993) the returns to a portfolio could be better explained by not only looking at how the overall equity market performed but also at the performance of size and value factors (i.e., the relative performance between small- and large-cap stocks, and between cheap and expensive stocks). Adding these two factors (value and size) to the market created a multi-factor model for asset pricing. Academics have continued to explore other risk factors, such as momentum 6  and low-beta or low risk, 7  and have shown that these factors have been effective in explaining long-run average returns. In general, style premia have been most widely studied in equity markets, with some classic examples being the work of Fama and French referenced above. For each style, they use single, simple and fairly standard definitions —  they are described in Exhibit 1 . 8   4  CAPM says the expected return on any security is proportional to the risk of that security as measured by its market beta. 5  More generally, the economic definition of alpha relates to returns that cannot be explained by exposure to common risk factors (Berger, Crowell, Israel and Kabiller, 2012). 6  Jegadeesh and Titman (1993); Asness (1994). 7  Black (1972); Frazzini and Pedersen (2014). 8  Specifically, these factors are constructed as follows: SMB and HML are formed by first splitting the universe of stocks into two size categories (S and B) using NYSE market-cap medians and then splitting Exhibit 1: Common Academic Factor Definitions HML  “High M inus Low”: a long/short measure of value that goes long stocks with high book-to-market values and short stocks with low book-to-market values UMD  “Up M inus Down”  : a long/short measure of momentum that goes long stocks with high returns over the past 12 months (skipping the most recent month) and short stocks with low returns over the same period SMB  “Small M inus Big”: a long/short measure of size that goes long small-market-cap stocks and short large-market-cap stocks  Assessing Factor Exposures in a Portfolio Using these well-known academic factors, we can analyze an illustrative portfolio’s factor exposures. But before we do, we should emphasize that the factors studied here are not a definitive or exhaustive list of factors. We should also emphasize that different design choices in factor construction can result in very different measured portfolio exposures. Indeed, the fact that you can still get large differences based on specific design choices is much of our point; we will revisit these design choices later in the paper. A common approach to measuring factor exposures is linear regression analysis; it describes the relationship between a dependent variable (portfolio returns) and explanatory stocks into three groups based on book-to-market equity [highest 30%(H), middle 40%(M), and lowest 30%(L), using NYSE breakpoints].The intersection of stocks across the six categories are value-weighed and used to form the portfolios SH(small, high book-to-market equity (BE/ME)), SM(small, middle BE/ME), SL (small, low BE/ME), BH(big, high BE/ME), BM(big, middle BE/ME), and BL (big, low BE/ME), where SMB is the average of the three small stock portfolios (1/3 SH + 1/3 SM + 1/3 SL) minus the average of the three big stock portfolios (1/3 BH + 1/3 BM + 1/3 BL) and HML is the average of the two high book-to-market portfolios (1/2 SH+ 1/2 BH) minus the average of the two low book-to-market portfolios (1/2 SL + 1/2 BL). UMD is constructed similarly to HML, in which two size groups and three momentum groups [highest 30% (U), middle 40% (M), lowest 30% (D)] are used to form six portfolios and UMD is the average of the small and big winners minus the average of the small and big losers.  
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