A Conditional Higher-Moment CAPM

This paper investigates whether dynamic and moment extensions to the traditional CAPM can improve its empirical performance and offer some alternative explanation to the cross-section of average returns on portfolios of stocks double sorted on book-to-market ratios and size. We consider three extensions. First, we introduce time-varying factor loadings obtained from a multivariate GARCH and dynamic conditional correlations. Second, we extend the model to a four-moment CAPM, which incorporates coskewness and cokurtosis. Finally, we allow for time-varying risk premia, based on a Markov-switching process. Our results confirm that the higher-moment CAPM does not perform well in its unconditional version, but its performance is significantly improved when we introduce a conditional version that accounts for both time-varying factor loadings and time-varying risk premia. The four-moment CAPM tests lead to a positive total risk premium estimate of 0.67% per month over the period 1926-2021, with all risk premia (beta, coskewness, and cokurtosis) exhibiting the expected theoretical signs