Hedge Funds Returns: An Alternative Investment or An Alternative to Investment? (Part 4: To higher moments and beyond…)
by Dr Constantin Gurdgiev, Adjunct Assistant Professor of Finance with Trinity College, Dublin
You may find Part 1: Measuring What here, Part 2: Dealing with Biases here and Part 3: Dealing with Funds and Benchmarks Selection here.
As maintained throughout this series of posts1, comparative returns computed across asset classes often suffer from a host of biases, many related to valuation models’ shortcomings and data problems. The core CFA Alternative Investment and Investment Theory modules attempt to address some of these issues.
However, to make matters even less tractable, all of the factors covered in previous posts can be cointegrated across time and exhibit strong colinearity, rendering traditional models empirically weaker.
For example, Baquero and Verbeek (2015) study looked at the importance that hedge fund investors “attach to past information in the fund selection process”.2 The authors found that actual results are not consistent with models that “predict future expected fund returns, alphas or Sharpe ratios”. Instead, investors appear to be sensitive – contrary to the assertions in the business media3 – to funds’ performance.
Some business reports (including those cited in above) suggest that investors act irrationally by neglecting hedge funds underperformance measures in recent history. Baquero and Verbeek show that investors do reference funds performance in their decision to invest or not. But, more interestingly, they also argue that such referencing, not the absence of it, is irrational, since past performance metrics for the funds have a “limited predictive power regarding fund performance”. Being irrational, is not about omitting consideration of the past performance, but about taking such performance into account.4
In another example, Sabbaghi (2012) looked into “…the return performance of different investment strategies in the hedge fund sector, with a particular emphasis on the recent US financial crisis of 2007-2010.”5 The author explicitly investigated the comovement of hedge fund index returns based on “…the cross-sectional volatility, covariance, and correlation metrics”. The majority of the broadly defined hedge fund investment strategies “incurred record level losses and gains during the 2007-2010 period”. The crisis period was associated with a “decrease in average correlations” in hedge funds returns across various strategies, “stemming from an increase in hedge fund volatility”.
Beyond the first and second moments, however, hedge funds returns exhibit dependence on higher moments of returns distribution, such as skew, kurtosis, co-skew and co-kurtosis.6 As has been established a long time ago, hedge funds, often have “non-normally distributed returns”. Thus, assessing hedge funds returns, one should use “a higher moment-based distributional risk measure” as opposed to simple (two-moment based alphas).
All of this suggests the presence of systemic risks relating to the hedge fund sector. But it also suggests that hedge funds’ returns, like much of financial sector data, exhibit violations of the basic modeling frameworks, thus rendering returns comparatives based on traditional metrics, such as the Sharpe or Jensen ratios at best flawed, at worst biased.
Back in 2005, a group of researchers asked the question about hedge funds’ returns in a more structured way than today’s business media does.7 In addition to fitting normal OLS to generate alphas, the study estimated Bayesian measures to control for short-term variations potentially attributable to pure chance, as well as for the problem that the returns do not follow parametric normal distributions. The result: Bayesian measures “lead to superior performance predictability. Relative to sorting on OLS alphas, sorting on Bayesian alphas yields a 5.5 percent per year increase in the alpha of the spread between the top and bottom hedge fund deciles.”
And there is more. Bayesian returns measures imply that top hedge fund managers “possess asset selection skill”. In other words, there is a lot more to the hedge funds returns performance than simple alpha comparatives capture.8
To confuse matters even further, hedge fund returns exhibit correlation between the effects of survivorship bias (covered in our earlier posts) and the moments of returns distribution. A paper from Cass Business School shows that in a multi-moment setting, survivorship bias accounts for a small share of over-estimation of hedge funds’ returns. But the data also contains “significant survivorship bias in estimates of the standard deviation, skewness and kurtosis of individual hedge fund returns. When not corrected for, this will lead investors to seriously overestimate the benefits of hedge funds.”9
As the series of posts here show, there is tremendous complexity to the problem of properly measuring hedge funds’ relative and absolute performance over time and across various hedge funds’ strategies, databases and cross-sector comparatives. While snapshots of data today may suggest persistent hedge funds’ underperformance over the recent years, such comparatives rarely are based on robust enough data and econometric methods
References
1. Hedge Funds’ Returns: An Alternative Investment or An Alternative to Investment? Part 1: Measuring What?, Part 2: Dealing with Biases and Part 3: Dealing with Funds and Benchmarks Selection.
2. Baquero, Guillermo and Verbeek, Marno, “Hedge Fund Flows and Performance Streaks: How Investors Weigh Information”, January 28, 2015. ESMT Working Paper No. 15-01:
3. See Gregory Zuckerman “Hedge Funds Keep Winning Despite Losing“, Wall Street Journal, February 8, 2015, , and Barry Ritholtz “The Most Fascinating Investing Paradox” BloombergView, February 12, 2015,.
4. In fact, these findings are not new to the literature. For example, see Kat, Harry M. and Menexe, Faye, Persistence in Hedge Fund Performance: The True Value of a Track Record (May 6, 2002). Cass Business School Research Paper. This makes business media insistence on investors’ referencing past returns in relation to future expected returns as being a sign of investor rationality even more surprising.
5. Sabbaghi, Omid, “Hedge Fund Return Volatility and Comovement: Recent Evidence”. Managerial Finance, 38(1), 2012: 101-119:
6. Berenyi, Zsolt, Measuring Hedge Fund Risk with Multi-moment Risk Measures (April 2002): and a good primer on statistical properties of hedge funds’ returns here: Kat, Harry M. and Lu, Sa, An Excursion into the Statistical Properties of Hedge Fund Returns (May 1, 2002). Cass Business School Research Paper.
7. Kosowski, Robert and Naik, Narayan Y. and Teo, Melvyn, Do Hedge Funds Deliver Alpha? A Bayesian and Bootstrap Analysis (December 2005).
8. More on this here: Sherman, Mila Getmansky and Lo, Andrew W. and Makarov, Igor, An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns (March 1, 2003). MIT Sloan Working Paper No. 4288-03; MIT Laboratory for Financial Engineering Working Paper No. LFE-1041A-03; EFMA 2003 Helsinki Meetings.
9. Kat, Harry M. and Amin, Gaurav S., Welcome to the Dark Side: Hedge Fund Attrition and Survivorship Bias over the Period 1994-2001 (December 11, 2001). Cass Business School Research Paper.
