The capm with measurement error: 'There's life in the old dog yet!'

Abstract

This paper takes a closer look at the consequences of using a market index as a proxy for the latent market return in the capital asset pricing model. In particular, the consequences of two major sources of misspecification are analyzed: (i) the use of inaccurate weights and (ii) the use of only a subset of the asset universe to construct the index. The consequences resulting from the use of a badly chosen market proxy reach from inconsistent parameter estimates to misinterpretation of test outcomes indicating the existence of abnormal returns. A minimum distance approach of estimating the CAPM under measurement error is presented, which identifies the CAPM parameters by exploiting the cross-equation cross-sectional restrictions resulting from a common measurement error. The new approach allows for quantifying the impact of measurement error and for testing the presence of spurious abnormal returns. Practical guidelines are presented to mitigate potential biases in the estimated CAPM parameters.