The asymmetric absolute returns of absolute return hedge funds.

Author:Cao, Bolong

    In 2003, Alexander M. Ineichen published a book, called Absolute Returns (Ineichen, 2003), in which he emphasizes that absolute-return investing is different from relative-return investing in the sense that absolute-return investors seek capital preservation and growth, wherever relative-return investors focus on minimize tracking errors relative to a benchmark but they are willing to tolerate capital losses resulting from the decline of the benchmark. Ineichen deems that providing absolute returns should be the investing philosophy of hedge fund managers. In 2007, Ineichen published a second book in the same vine, called Asymmetric Returns (Ineichen, 2007), in which he further developed the idea of absolute returns into asymmetric returns. By asymmetric returns, Ineichen means that a distribution profile of returns of an actively managed portfolio should has its mean and/or median lies right to zero. Furthermore, with an asymmetric return profile, one can achieve the absolute return for the portfolio. In a related article, (Grotheer, 2006), Ineichen pointed out the asymmetric return profile has "equity-like returns on the upside and much more bond-like volatility on the downside". To be more accurate, I call this kind of return Asymmetric Absolute returns in this paper.

    Nowadays, more and more hedge funds, fund of funds and even mutual funds call themselves "absolute return" funds based on the idea of asymmetric absolute returns. In this paper, I attempt to find out whether there is any substance to this name for hedge funds. The challenge is, however, how to directly measure the asymmetric absolute returns. Popular performance measures, such as Sharpe ratio, are easy to calculate and useful in fund selection. Intuitively, asymmetric absolute return profile will yield a high Sharpe ratio; albeit a high Sharpe ratio does not necessarily account for equity-like upside returns and bond-like downside volatility. In this paper, I construct a performance measure, called AA Score, to capture the asymmetric absolute return performance of hedge funds. Then I apply both univariate analysis and multivariate analysis to examine whether the so called "absolute return" funds can actually deliver higher AA Score.

    The AA Score measures the frequency of a hedge fund obtaining the asymmetric absolute return status in a large bootstrapped sample of hedge fund holding period returns. The asymmetric absolute return status is achieved if the bootstrapped holding period return of the hedge fund is higher than the maximum of zero, the holding period returns in the same bootstrap sample for the S&P500 index and for the Barclays US Treasury Bond index (Formerly Lehman Brother US Treasury Bond Index). I choose to use the US Treasury bonds to represent the fixed income class so as to provide sufficient limit on the downside of the hedge fund returns. The bootstrap samples are created using the stationary bootstrap method (Politis and Romano, 1994) which can preserve both the cross-sectional correlations and serial correlations of the time series.

    When measuring asymmetric absolute return, ideally, we would like to compare some simple statistics of the positive monthly returns of the hedge funds and those of stocks; on the negative side, we can compare the same statistics for hedge funds and bonds. But this is like comparing apples to oranges since the return profiles of the investment opportunities explored by hedge funds are neither like stocks nor like bonds. For example, hedge funds may have infrequent but large negative returns but a bond portfolio may have frequent small negative returns. In contrast, the holding period returns generated from bootstrap samples can help us understand the impact of the frequency and size of these negative returns in the monthly hedge fund returns. I have several reasons to choose the holding period returns as the subject to compare. First, some negative returns may reflect the strategic positions the manager has taken, which may eventually payoff with large positive returns, examining holding period returns will not unfairly punish the fund managers for taking this kind of bets. Second, as previous researches have shown (Getmansky et al, 2004), the monthly hedge fund returns may have high serial correlation due to the illiquid positions taken by the managers, the holding periods we examine here are long enough to take these serial correlations into account. Finally, the lock-up period for investing in hedge fund exists so examining the holding period returns has practical relevance.

    To understand whether the AA Score provide new information that is different from other performance measures, I compare it with the Sharpe ratio. As shown by Eling and Schuhmacher (2007), Sharpe ratio provides virtually identical rank ordering across hedge funds when compared with twelve other popular performance measures. In contrast, the AA Score has nearly zero correlation with the Sharpe ratio. So, the AA Score indeed is a new performance measure that examines the hedge fund performance from a different angle than most existing measures. Of course, the other most important performance measure is the alpha calculated based on regressing the hedge fund returns on various benchmark index or risk factor returns. However, as pointed out by Ineichen, alpha is a relative return measure but not an absolute return measure thus is inappropriate to use in this context.

    Comparing to the non-absolute return funds, the absolute return funds do achieve significantly higher AA Score but their Sharpe ratio is also lower and the difference is statistically significant in the univariate analysis. In the multivariate analysis, I control the size, growth rate, age, fund investment features and fee structure plus fund strategies. The absolute return funds still show some significant ability in generating higher AA Scores but the difference in the Sharpe ratio between the absolute return funds and nonabsolute return funds disappeared due to the overwhelming effect of fund age. In my sample, older funds tend to generate higher Sharpe ratio.

    The next section relates this paper to the existing literature. Section 3 describes the data used in this study and the construction of the variables. Section 4 analyzes the empirical results and Section 5 concludes the paper.


    Even though, to my best knowledge, there is no rigorous academic research on the asymmetric absolute returns, there are numerous articles on the performance of hedge funds, such as Fung and Hsieh (2002), Fung and Hsieh (2004), Agarwal and Naik (2004), Capocci and Hubner (2004), and Bollen and Whaley (2009), just to name a few. These papers all employ various risk factors to explain the performance of hedge funds. In Fung and Hsieh (2002) and Fung and Hsieh (2004), the returns of lookback straddles on various assets, credit spreads, yield changes, return spreads between large cap and small cap U.S. stocks and the S&P500 returns are used as asset-based style factors. Agarwal and Naik (2004) use option return based factors. Capocci and Hubner (2004) employs the factors in Carhart (1997), Agarwal and Naik (2004), Fama and French (1998) and an emerging market...

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