Optimally Weighting Higher-Moment Instruments to Deal with Measurement Errors in Financial Return Models

Abstract

Factor loadings are often measured with errors in financial return models. However, these models find applications in many fields of economics and finance. We present a new procedure to optimally weight two well-known cumulant (higher moments) estimators originally designed to deal with errors-in-variables. We develop a new version of the Hausman test which relies on these new instruments in order to build an indicator of measurement errors providing information about the extent of the bias for an estimated coefficient. We apply our new methodology to a well-known financial return model, i.e. the Fama and French (1997) model, over a sample of HFR hedge fund returns, whose distribution is strongly asymmetric and leptokurtic. Our experiments suggest that the market beta is biased by measurement errors, especially at the level of hedge fund strategies. Nevertheless, the alpha puzzle remains robust to our cumulant instruments.