Realized Semi Betas in Currency markets and other asset classes

CAPM does not perform well in pricing the cross-sectional returns from the currency carry trade and factors such as volatility innovation (Menkhoff et all, 2011) or downside risk (Dobrynskaya, 2014) have been used to solve this problem. 

In this paper, we argue that market return could be used as the solo factor to price the cross-sessional carry trade – however it needs to be decomposed into four semibetas that depend on the signed covariation between the market and individual asset returns.