Return Explanatory Ability and Predictability of Non-Linear Market Models

Recent literature supports the pricing of higher-order systematic co-moments of returns. This paper provides some support for the quadratic-market model that is consistent with the three-moment CAPM in explaining time-series returns of the winner and the smallest size portfolios. This study further uses three innovative methodologies in analysing the ability of the linear CAPM, the quadratic- and the cubic-market models in predicting one-period- ahead returns on individual stocks, equally- and value-weighted portfolios of momentum, size and country sorts. The results are surprising but important that the higher-moment CAPM market models do not outperform the linear CAPM in the return predictability tests.