Two Skewed Risks
59 Pages Posted: 31 Mar 2020 Last revised: 18 May 2020
Date Written: May 18, 2020
We analyze the effect of skewness in a simple two-asset framework. Returns follow the split bivariate normal distribution, which is a combination of bivariate normal distributions with different standard deviations. We show that expected returns deviate from the CAPM in equilibrium if assets differ in skewness. In addition, if the more positively skewed asset is more volatile, the high beta asset underperforms and has a higher max return, higher idiosyncratic skewness, and higher systematic skewness — consistent with empirical evidence. We also derive simple formulas and analyze the role of skewness for portfolio choice and recently proposed conditional risk metrics. Finally, we show that the distribution provides a good empirical fit and thereby calculate the standard error of co-skewness in closed form.
Keywords: Skewness, Co-Skewness, Conditional Expected Shortfall, Conditional Value-at-Risk, Portfolio Choice, Asset Pricing
JEL Classification: G11, G12, G32
Suggested Citation: Suggested Citation