A Higher Moment Downside Framework for Conditional and Unconditional CAPM in The Russian Stock Market

Abstract

The article presents an empirical validation for mean-variance CAPM, using a Downside and Higher-moment framework of CAPM in the Russian stock market. The authors test the unconditional and conditional CAPM specifications on a sample of weekly returns of the most liquid Russian stocks over the financially stable period of 2004-2007 and over the crisis period of 2008-2009. The primary contribution of this study is ranking the models with respect to their explanatory power of cross-sectional return variations. The unconditional classical CAPM (where market risk is approximated by the beta coefficient) is compared to the downside (mean semivariance) CAPM extended to incorporate the third (skewness) and fourth (kurtosis) moments. The ranking methodology is based on Fama and MacBeth’s (1973) two-stage estimation procedure. The unconditional CAPMs prove to have low explanatory power for the financially stable period and test results that are not statistically significant for the crisis period. Incorporating additional risk measures of the third and fourth moments and adopting one-sided risk measures only slightly increases the explanatory power. The highest explanatory power is offered by the unconditional CAPM of the Harlow-Rao downside systematic risk measure with zero benchmark. Our study confirms the feasibility of employing conditional CAPMs extended for systematic asymmetry (co-skewness) and systematic kurtosis (co-kurtosis) for the Russian stock market since these models display better explanatory power for cross-sectional return variations.

Keywords: downside CAPM, higher moment CAPM, conditional CAPM

JEL Classification: G11, G12