Integrating volatility factors in the analysis of the hedge fund alpha puzzle

Abstract

Estimation of financial models of hedge fund returns often gives rise to abnormally high alphas. This phenomenon may be due to mis-specified models, but recently the introduction of volatility factors in hedge fund returns models (Kuenzi and Xu, 2007) has been viewed as a solution to solve the alpha puzzle. This paper shows that modelling the volatility of the innovation term of hedge fund return models might be another way to explain the alpha puzzle. The model proposed in this paper is a factor model that incorporates an 'alternative' factor, which is the return of a short put on the Standard & Poor's 500 whose volatility is the VIX. This paper takes an overall view to analyse the problem of specification errors in financial models. To account for specification errors, it proposes a new estimator based on the generalised method of moments (GMM) whose instruments are the higher moments of returns, the GMM-hm. Some transformations of the basic factor model, which are recommended in the financial literature to improve the estimation of the alpha, are considered the n-CAPM and the conditional model. Some GARCH and EGARCH specifications of our basic model of returns are also estimated. Our results show that modelling the volatility of the innovation is the best way to lower the alpha. The n-CAPM has also had some success in reducing the alpha. The alpha is not the only garbage bag of a returns model (Jaeger and Wagner, 2005), but the alpha and the innovation both constitute the garbage bag.