This paper applies the methodology of Lambert and Hübner (2009) for creating fundamental risk factors and factor systematic variance, skewness, and kurtosis into returns from March 1989 to June 2008. The coskewness and cokurtosis premiums present significant monthly average returns of respectively 0.2% and 0.4% over the period. First, we show that our set of moment-related premiums consistently price 2 sets of 2x3 covariance/coskewness and of 2x3 covariance/cokurtosis portfolios. The model delivers for all portfolios low levels of specification errors, high levels of R2, and beta loadings consistent with the portfolio rankings. Second, we perform Fama and MacBeth (1973) cross-sectional regressions made of higher-moment market premiums and/or Fama and French (1993) factors on 25 and 100 two-dimensional portfolios sorted on size and bookto- market. Used separately, a four-moment factor model and a four-factor Fama and French (1993) and Carhart (1997) model have been shown to deliver similar model specification errors (alphas) for the size/BTM portfolios. The Four-Moment Asset Pricing Model captures however a higher proportion of the portfolio variability of size/BTM portfolios than an empirical Capital Asset Pricing Model. Finally, our study demonstrates that moment and empirical premiums present complementary significance over the period.
