To Hedge Or Not To Hedge: Factor Dependence And Skill Among Hedge Funds by Causeway


Do you know how your hedge fund generates returns? As average hedge fund performance continues to wane, investors are increasingly seeking objective criteria to distinguish talented managers from the herd. Differentiating the contributions of systematic and idiosyncratic factors in a fund’s return stream is one way to accomplish this goal. In this paper, we combine two related, but distinct, methods of measuring these variables. Using the Fama-French-Carhart 4-factor approach, we find that hedge funds with the highest 4-factor alpha (a proxy for skill) and lowest r-squared to the four factors (a proxy for factor dependence) produce the strongest subsequent returns. We also find that those managers with high trailing 4-factor alpha have lower exposure to systematic risk factors in general.

Investment returns, whether on individual stocks or entire portfolios, are widely considered the payoffs to systematic and security-specific risks.  When hedge funds posted impressive returns in the late 1990s and early 2000s, investors lacked many of the tools to differentiate between the two types of risk.  More recently, however, competitive pressures and regulatory changes[1] have eroded hedge fund returns, and investors now seek informative methods to identify the small percentage of managers with true talent.  Fundamental to this process is determining to what extent systematic risks are responsible for generating returns.

The Capital Asset Pricing Model (CAPM) was the first model to assume that expected returns are not entirely specific to an individual stock.  According to CAPM, part of a stock’s expected return is due to its systematic covariance with the market’s return (the stock’s beta).  Since CAPM was developed, research has uncovered additional systematic factors that influence expected returns beyond the market’s movements.  Specifically, researchers identified systematic excess returns to value companies over growth companies,[2] small stocks over large stocks,[3] and recent “winners” (as measured by price change over the last 3, 6, or 12 months) over recent “losers.”[4]  But the excess expected returns to these factors arise from taking additional risks.  Generally speaking, smaller companies tend to be riskier than larger companies, undervalued stocks tend to be unpopular investments, and momentum stocks with recent steep price climbs are prone to reversals.

In decomposing hedge fund portfolio returns, a portion will be explained by exposure to these systematic sources, but successful managers should also contribute skill in the form of unique alpha sources.  By isolating the effects of these systematic factors – equity beta, value, size, and momentum – when analyzing a fund’s returns, an investor can more effectively distinguish the skilled-based, active returns (what we call “4-factor alpha”) from the systematic, passive returns.  Since most hedge funds have no benchmark (an effective 0% hurdle), they earn performance fees for any positive return ? regardless of the attribution between passive and active sources.  Despite this fact, many investors seem comfortable with high exposure to systematic factors (chiefly equity beta and exposure to small caps) in their hedge fund portfolios.  Figure 1 tracks the average exposure to the four Fama-French-Carhart style factors (equity beta, value, size, momentum) over time across all equity hedge funds in Hedge Fund Research’s HFRI returns database.  These numbers represent the average month-to-month multivariate coefficient using a 24-month rolling regression window.

Hedge Funds Skill

Review of Past Research

Previous research has explored similar issues of factor dependence and skill among mutual funds and hedge funds.  Professors Sheridan Titman and Cristian Tiu hypothesized that specific “hedge funds…will choose greater exposure to priced factors if they have less confidence in their abilities to generate abnormal returns from the active component of their portfolios.”[5]  In other words, those that lack skill will seek to hide this fact by relying mostly on standard factors to produce returns.  To test this, the authors sorted hedge funds by r-squared to standard risk factors, and they found that funds with lower r-squareds have higher alphas, attract more capital, and charge higher fees.  Zheng Sun, Ashley Wang, and Lu Zheng used an alternate measure of strategy distinctiveness – a fund’s past correlation to its peer average – to sort hedge funds, and found that funds with lower correlation to their peers had better subsequent performance.[6]

Most recently, Professors Yakov Amihud and Ruslan Goyenko sorted the mutual fund universe by two variables/characteristics.  They not only sorted mutual funds based on trailing r-squared but also by trailing 4-factor alpha, and found that funds that sorted into the lowest quintile of r-squared and the highest quintile of 4-factor alpha went on to produce the highest subsequent alphas. [7]  Additionally, they found that those funds with high r-squared measures were larger, were run by managers with shorter tenures, and had lower fees.

Our Approach

Assessing funds using both 4-factor alpha and r-squared is more revealing than focusing on one dimension alone.  Therefore, we sought to apply the same methodology used by Amihud/Goyenko to hedge funds rather than mutual funds.  Conveniently, both of these dimensional measures – r-squared and 4-factor alpha ? are outputs of the same regression.  When we regress hedge fund returns against returns to these four factors (equity beta, value, size, and momentum), we can derive the r-squared (or “coefficient of determination”) of the regression, which will tell us the percentage of variation in fund returns that is attributable to variation in the factor returns.  Additionally, the regression output will include an alpha term, which is the return over and above (or under and below) what would be expected from a fund’s average factor exposures alone.  This “4-factor alpha” will measure the alpha relative to a benchmark tailored specifically for that fund’s recent exposures.  It’s also worth noting that 4-factor alpha, in addition to capturing stock selection skill, will capture factor timing skill provided that factor exposures are adjusted more frequently than the window size (24 months in our analysis).

The r-squared highlights a fund’s factor dependence (the higher the r-squared, the more a fund is relying on factors to produce returns), while the 4-factor alpha is a proxy for skill, which, in this case, will capture stock selection skill and higher-frequency factor timing skill.  There exists a misguided notion that hedge funds with demonstrated skill also come with high levels of systematic factor exposures – that skill and factor dependence come as a “package deal.”  The relatively steady run-up in equities over the past six years has supported this notion, since many of the funds with the highest recent returns (and therefore perceived skill) have also had high exposure to equity beta.  But while recent experience might suggest otherwise, skill is independent of factor exposure.  An individual manager has a fixed level of skill (or lack of skill), but factor exposure and timing are within a manager’s control.  In other words, a manager has the choice to layer factor exposures on top of the skill-based returns.  In Figure 2, we propose a high-level classification framework for hedge funds based on the relative measures of these two variables.

Hedge Funds Skill

We assume that all fund managers seek to deploy their maximum level of skill (and, by extension, 4-factor alpha since

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