Optimal Instrumental Variables Generators Based on Improved Hausman Regression, with an Application to Hedge Fund Returns

The findings presented in this article improve the existing methods for estimating financial models of returns and especially for estimating the parameters that are relevant for portfolio managers, such as the Jensen alpha, a popular measure for stock selection, and beta, a well-known systemic risk measure. The authors focus on the presence of measurement errors in these models. For instance, the risk factors in the Fama and French models or the market model are biased by measurement, or specification, errors. These measurement errors are related to the use of proxies for measuring risk factors, such as the risk premium, and other risk factors, which are approximated by mimicking portfolios. To tackle these specification problems, the authors propose new Hausman-based estimators lying on cumulants optimal instruments. Using these newly generated strong instruments in a generalized method of moments (GMM) setting, the authors obtain new GMM estimators that they call GMM-C and its homologue GMM-hm. They also extend the methodology to the standard two-stage least squares (TSLS) framework using new optimally generated instruments. These procedures improve the existing method of moments for estimating, or calibrating, the parameters of a financial model and, more generally, for treating the problem of endogeneity often encountered in financial studies. Moreover, this study leads to a new indicator that signals the presence of specification errors in financial models. The authors apply a battery of tests and estimators to a sample of 22 HFR hedge fund indices observed monthly over the period 1990–2005. Their tests reveal that specification errors bias parameter estimation of financial models of returns and that the ranking of hedge funds is very sensitive to the choice of estimators.