Two Skewed Risks

62 Pages Posted: 31 Mar 2020 Last revised: 26 Feb 2022

See all articles by Arthur Beddock

Arthur Beddock

Frankfurt School of Finance & Management

Paul Karehnke

ESCP Business School

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, 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)

Frankfurt School of Finance & Management ( email )

Adickesallee 32-34
Frankfurt am Main, 60322

HOME PAGE: http://

Paul Karehnke

ESCP Business School ( email )

79 avenue de la République

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