The Distribution of Cross Sectional Momentum Returns When Underlying Asset Returns Are Student’s t Distributed

Abstract

In Kwon and Satchell (2018), a theoretical framework was introduced to investigate the distributional properties of the cross-sectional momentum returns under the assumption that the vector of asset returns over the ranking and holding periods were multivariate normal. In this paper, the framework is extended to derive the corresponding results when the asset returns are multivariate Student’s t. In particular, we derive the probability density function and the moments of the cross-sectional momentum returns and examine in detail the special case of two underlying assets to demonstrate that many of the salient features reported in the empirical literature are consistent with the theoretical implications.