Return Dispersion and the Cross-Section of Stock Returns

Abstract

Stock returns can have positive and negative sensitivity to the cross-sectional standard deviation of returns or return dispersion (RD). To capture asymmetric RD effects, we propose a new asset pricing model dubbed the ZCAPM that takes into account beta risk associated with the market factor and zeta risk related to positive and negative RD factor movements. To deal with the unobservable sign of the RD sensitivity, the expectation-maximization (EM) algorithm is used to fit the ZCAPM to data. Out-of-sample cross-sectional tests of U.S. stock portfolios yield highly significant estimates for the market price of zeta risk with t-statistics normally in the range of 3 to 6. Our results for zeta risk dominate loadings of popular multifactors, which are less significant across different test assets and sample periods. Strikingly, cross-sectional regression R-squared values for the ZCAPM as high as 94 percent are obtained for size and book-to-market sorted portfolios. Moreover, estimates of the market premium for zeta risk are economically substantial. We conclude that the ZCAPM represents a major innovation in asset pricing for academic research and investment practice.

Keywords: Asset pricing, Cross-sectional stock returns, Expectation-maximization (EM) algorithm, Return dispersion

JEL Classification: G12, C20