Two Skewed Risks

59 Pages Posted: 31 Mar 2020 Last revised: 18 May 2020

See all articles by Arthur Beddock

Arthur Beddock

Université Paris Dauphine - Department of Finance; Tilburg University - Department of Finance

Paul Karehnke

ESCP Europe - Department of Finance

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

Beddock, Arthur and Karehnke, Paul, Two Skewed Risks (May 18, 2020). Available at SSRN: or

Arthur Beddock (Contact Author)

Université Paris Dauphine - Department of Finance ( email )

Place du Maréchal de Lattre de Tassigny
Paris Cedex 16, 75775

Tilburg University - Department of Finance ( email )

P.O. Box 90153
Tilburg, 5000 LE

Paul Karehnke

ESCP Europe - Department of Finance ( email )

Paris Campus
79, Avenue de la Republique
Paris, 75011


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