The Coskewness Puzzle in the Cross-Section of Industry Portfolio Returns

Abstract

I derive the beta-pricing representation of Harvey and Siddique (2000) conditional 3M-CAPM and demonstrate the restrictions that it imposes on a quadratic market factor model. I confirm that, while the latter is surprisingly successful at capturing the cross-sectional variation of the returns on the Fama and French (1995) 30 US industry-sorted portfolios, the 3M-CAPM coskewness premium for the period 1952-2002 turns out to be too large for non satiation, risk aversion and non-increasing absolute risk aversion to hold. I demonstrate however that a representative investor with this type of preferences would still find the market portfolio to be in sample more efficient than individual industry portfolios. I also show that Fama and French (1995) 3-factor model cannot match the explanatory power of a quadratic market factor model for the cross section of industry-sorted portfolio returns. Thus, I propose to use an APT-type quadratic market factor model with an upper bound on the volatility of the implied stochastic discount factor. This approach allows the explanatory power of the quadratic specification to be salvaged yet avoiding fitting unexpected extreme outcomes rather then pricing patterns.