A Robust Estimation of the CAPM with a Heavy-tailed Distribution

Abstract

This study quantitatively explores the linear standard capital asset pricing model (CAPM) and a non-linear CAPM by using ten US representative firms’ monthly stock returns. By the maximum likelihood estimation, we derive the following useful findings. (1) First, when the stock return distribution is fat-tailed, our non-linear CAPM application is highly effective. Because our non-linear CAPM parameters very well capture the behavior of fat-tailed returns, the non-linear CAPM estimation derives more reliable beta value estimates than the standard linear CAPM. (2) Second, conducting the Wald tests based on both the standard linear CAPM and non-linear CAPM estimators, we clarify that when the stock return distribution is fat-tailed, the Wald test result based on the non-linear CAPM estimators is more reliable than that based on the standard linear CAPM estimators.