The robustness of asset pricing models: Coskewness and cokurtosis

We consider the robustness of the least-squares inference of linear asset pricing models. We evaluate the asymptotic covariance matrices of the least-squares estimator of alphas and betas when the joint distribution of factors and error terms is independently and identically distributed without making any specific distributional assumptions. When the standard assumption of conditional homoskedasticity for the conditional covariance matrix of error terms given factors does not hold, we show the asymptotic covariance matrix for betas depends only on cokurtosis of factors and error terms while the asymptotic covariance matrix for alphas depends on cokurtosis as well as coskewness of factors and error terms. This implies the inference of betas is not affected by skewness of the underlying joint distribution. Numerical examples are provided using Fama and French's benchmark portfolio returns and factors.