A Simple Skewed Distribution with Asset Pricing Applications

53 Pages Posted: 18 Aug 2015 Last revised: 28 Jul 2016

See all articles by Frans de Roon

Frans de Roon

Tilburg University - Department of Finance

Paul Karehnke

ESCP Europe - Department of Finance

Date Written: July 6, 2016

Abstract

Recent research has identified skewness and downside risk as one of the most important features of risk. We present a new distribution which makes modeling skewed risks no more difficult than normally distributed (symmetric) risks. Our distribution is a combination of the "downside" and "upside" half of two normal distributions, and its parameters can be calculated in closed-form to match a given mean, variance, and skewness. Value-at-risk, expected shortfall, portfolio weights, and risk premia have simple expressions for our distribution and show economically meaningful deviations from the normal case already for very modest levels of skewness. An empirical application suggests that our distribution fits the data well.

Keywords: Skewness, Value-at-Risk, Expected Shortfall, Portfolio Choice, Asset Pricing

JEL Classification: G10, G11

Suggested Citation

de Roon, Frans A. and Karehnke, Paul, A Simple Skewed Distribution with Asset Pricing Applications (July 6, 2016). Review of Finance, Forthcoming; 28th Australasian Finance and Banking Conference. Available at SSRN: https://ssrn.com/abstract=2646297 or http://dx.doi.org/10.2139/ssrn.2646297

Frans A. De Roon

Tilburg University - Department of Finance ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 1 3466 8361/3025 (Phone)
+31 1 3466 2875 (Fax)

Paul Karehnke (Contact Author)

ESCP Europe - Department of Finance ( email )

Paris Campus
79, Avenue de la Republique
Paris, 75011
France

HOME PAGE: http://https://sites.google.com/site/paulkarehnke/

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