Style consistency of hedge fund indexes across providers

Abstract

This article investigates the consistency of style returns of hedge funds across eight providers of style indexes. We select 10 style categories which are defined in a relatively consistent way across the various providers, so that the natural null hypothesis is that the returns should behave very similarly. We compare the results of a principal component analysis with tests of the hypothesis that unconditional mean returns and first order autocorrelation coefficients of returns are equal across the different providers for the same style. Our findings reveal a substantial degree of heterogeneity of index returns within the same style and cast serious doubts on their usefulness as benchmarks in the asset management industry.

Acknowledgements

The suggestions of two referees of this Journal have substantially improved the article and are gratefully acknowledged. Moreover, we would like to thank the Verein zur Förderung des WWZ for partial financial support under project No. D-114.

Notes

¹ This practice, however, was only observed in a minority of cases in the database used in this study.

² We did not consider other hedge fund index providers due to the following reasons: their indexes start later than January 1999 (Morgan Stanley Capital International (MSCI), Dow Jones, Eurekahedge, HF Intelligence, Feri/ARIX, MondoHedge); the main index consists of very few funds, and style indexes are not available or their number is too limited (Standard & Poor's (S&P), Bernheim, EACM Advisors); or because they provide indexes of indexes (Edhec).

³ Small funds exhibit relatively larger weights in equally weighted indexes. Based on the observation by e.g. Harri and Brorsen (2004) that large hedge funds exhibit statistically significant lower risk-adjusted returns, returns on equally weighted indexes should be higher than returns on capitalization weighted indexes. According to Table 1, equally weighted indexes are predominantly used in the industry.

⁴ In this article, we use style consistency and style homogeneity as synonyms.

⁵ From the 10 styles and eight providers, four series are missing: Altvest supplies no style categories for convertible arbitrage, equity market neutral and FI arbitrage, and Center for International Securities and Derivatives Markets (CISDM) provides no short selling index.

⁶ Unfortunately, to the best of our knowledge, no test is available to test the hypothesis of equal principal component loadings for the first component.

⁷ The presence of serial correlation not only emerges from univariate autocorrelation coefficients, but is robust to alternative estimation procedures. For example, Beltratti and Morana (2008) find strong persistence in hedge fund returns (and flows) in a latent Vector Autoregression (VAR) model for nine style categories.

⁸ The unconditional mean of an AR(1) process is μ = a ₀/(1−a ₁).

⁹ For some of the styles we have only data of seven providers and therefore only six restrictions.

¹⁰ As we are in the framework of a (nonlinear) system estimation, we get asymptotically valid χ²-distributions under the hypothesis of equality of coefficients across equations instead of F-distributions as in the standard linear regression model.

¹¹ Brooks and Kat (2002) found (highly significant) first order autocorrelation of convertible arbitrage index returns across providers.

¹² Notice that the test statistic for the third arbitrage style (FI) is insignificant on the 95% confidence level, but the null hypothesis of equal mean returns cannot be rejected on the 99% level.