Investment Choices, and Risk-adjusted Performance Measures with Skewness

Liang Tang, George Xiang and Larry Zhang

Asset returns are involved with multi-dimensional risks and therefore any good risk-adjusted performance measure (RAPM) should incorporate these risks. We extend the risk-adjusted performance measure theory developed by Xiang, Liu and Wang (2012) to include multiple risks. The following models are derived in this paper: a RAPM with skewness under individual equilibrium for an individual investor, a RAPM that comprises the skewness under market equilibrium for all investors using a three-moment asset pricing model. Both the individual and market RAPMs show that investors prefer a positive skewness to a negative skewness, ceteris paribus. We prove that the RAPM is the Sharpe ratio when the return doesn’t show any skewness. Finally this paper provides a theoretical justification to the relationships between investment choices, an asset pricing model, an individual RAPM, and a market RAPM.

DOI : https://doi.org/10.21102/irbrp.2018.09.142.06