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Is stellar hedge fund performance for real?
Authors: R. Kosowski, N.Y. Naik and M. Teo
Source: Working Paper
Date: June 2004

This paper examines hedge fund returns from the angle of a bootstrap method, in order to test whether they can be explained by luck alone. A short performance persistence analysis, focused on alpha, is also conducted.

The database contains datasets provided by CISDM, HFR, MSCI and TASS. It gives a more complete picture of the hedge fund universe. The period is from January 1991 to December 2002.

A Bera Jarque test indicates that 70% of returns are not normally distributed. Such results underline the relevance of bootstrapping in the context of hedge fund performance measurement. Moreover, serial correlation of returns and heteroscedasticity of residuals are found.

To specify the model, a stepwise regression is carried out on the excess return earned by passive option-based strategies and that earned by buy-and-hold strategies. This gives a generalised asset class factor model where the alpha (the intercept obtained from the regression) represents the value added by a hedge fund over the regression time period.

Firstly, on the entire sample and on the whole period, funds are ranked successively by their estimated alphas (i.e. their abnormal returns) and by their estimated alpha t-statistics (i.e. the consistency of their abnormal performance). In the extreme deciles, the bootstrap p-values imply that returns are not the result of random chance. By adjusting for backfill bias, similar results are found. On the basis of the Okunev and White (2003)* approach, a smoothed sample is constructed to control for serial correlation. A similar conclusion is reached.

Secondly, bootstrap tests are separately conducted on six investment categories: directional trader, relative value, security selection, multi-process, equity long/short (subset of security selection) and fund of funds. Each category contains funds that conssistently outperform or underperform their benchmark. Focusing on funds that stop reporting, close or terminate, it appears that in some cases the reason for the disappearance is not poor performance.

The robustness of the results obtained via the simple bootstrap is evaluated by applying four more complex bootstrap techniques, i.e. a factor residual resampling bootstrap, a bootstrap procedure that accommodates cross-sectional dependence in residuals, a bootstrap produre where a Monte Carlo simulation is used to simulate a potentially omitted factor, and a stationary bootstrap procedure to allow explicitly for the time series dependence in the residuals. Whatever the extension to the bootstrap method used, p-values confirm that abnormal returns are not the result of random chance.

Drivers of the superior performance exhibited by the top twenty equity long/short funds are examined. On average, it is stated that the top three return observations explain about 40% of fund alpha. On the other hand, the difficulty of investing in the top funds is underlined by a low mean monthly inflow of about 1.8%.

The persistence tests conducted in this study have the specific characteristic of being focused on alphas. These tests are motivated by the previous bootstrap results, suggesting that superior abnormal returns are not due to chance. Funds are successively sorted based on an alpha from one year, two year, three year and four year formation periods in ten deciles (decile 1 comprises the top funds).

Concerning top decile funds, whatever the length of the formation period, in the subsequent period these funds exhibit an abnormal post fee return that is statistically greater than zero. The bottom decile funds display an alpha that is insignificantly different from zero. After that, in decile 1 the top 3 observations are removed to calculate formation period alphas, while in decile 10 the bottom 3 observations are removed. In the test period, alphas of the top decile funds are reduced, but they are more significantly positive.

To verify that top decile funds do not exhibit good post-fee alphas only because they charge lower incentive and managerial fees than in the bottom decile funds, pre-fee alphas are calculated. The previous results are confirmed.

*Okunev, J., and D. White, “Hedge Fund Risk Factors and Value at Risk of Credit Trading Strategies”, Working Paper, 2003.