Two Skewed Risks
45 Pages Posted: 31 Mar 2020 Last revised: 1 Sep 2022
Date Written: May 18, 2020
We analyze the joint effects of skewness and correlation in a two-risky-asset framework. Returns follow the split bivariate normal distribution, which combines bivariate normal distributions with different standard deviations and provides a good empirical fit. We show that equilibrium risk premia deviate from the CAPM if assets differ in skewness. Moreover, if the more positively skewed asset is more volatile, it underperforms and its beta, maximum return, idiosyncratic and systematic skewnesses are all higher—consistent with empirical evidence. We also derive formulas and analyze the role of skewness for portfolio choice and recently proposed conditional risk metrics.
Keywords: Skewness, Portfolio Choice, Asset Pricing, Conditional Value-at-Risk, Conditional Expected Shortfall
JEL Classification: C58, G11, G12, G32
Suggested Citation: Suggested Citation