Two Skewed Risks

58 Pages Posted: 31 Mar 2020 Last revised: 23 Jun 2021

See all articles by Arthur Beddock

Arthur Beddock

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

Paul Karehnke

ESCP Business School

Date Written: May 18, 2020


We analyze the joint effects of skewness and correlation in a simple two-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, 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 Business School ( email )

79 avenue de la République

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