Specification Errors in Financial Models of Returns

This article uses a new set of instruments based on higher statistical moments to discard the specification errors that might be present in the Fama and French model. It shows that the usual instruments perform quite poorly in comparison to higher moments. It estimates the Fama and French model on a sample of 22 HFR hedge funds indices and 111 HFR individual hedge funds over the period 1990-2005. To do so, it compares many instrumental variables methods as the two-stage least squares and the generalized method of moments. The results show that there are few problems of specification errors on the side of the indices but this level of aggregation hides the errors. Indeed, the estimations of the sample of 111 funds reveal specification errors for the loadings of the market premium and the factor SMB which seem understated. The message to retain is that the individual investor must consider specification errors when modelling the returns of hedge funds as he does not buy the indices but the stocks of individual hedge funds. This article shows an investor how to correct the traditional measures of performance, which are alphas and factor loadings, to guide him towards a better decision process.