Downside Risk Neutral Probabilities

Centre Interuniversitaire sur le Risque, les Politiques Economiques et l'Emploi, Working Paper Series, No. 21, 2015

35 Pages Posted: 24 Nov 2015

See all articles by Pierre Chaigneau

Pierre Chaigneau

Queen's University; Queen’s University

Louis Eeckhoudt

Catholic University of Lille - IESEG School of Management

Multiple version iconThere are 2 versions of this paper

Date Written: November 1, 2015

Abstract

The price of any asset can be expressed with risk neutral probabilities, which are adjusted to incorporate risk preferences. This paper introduces the concepts of downside (respectively outer) risk neutral probabilities, which are adjusted to incorporate the preferences for downside (resp. outer) risk and higher degree risks. We derive new asset pricing formulas that rely on these probability measures. Downside risk neutral probabilities allow to value assets in a simple mean-variance framework. The associated pricing kernel is linear in wealth, as in the CAPM. With outer risk neutral probabilities, the pricing kernel is quadratic in wealth, and can be U-shaped.

Keywords: asset pricing, downside risk, quadratic pricing kernel, linear pricing kernel, prudence, risk neutral probabilities

JEL Classification: D81, G12

Suggested Citation

Chaigneau, Pierre and Eeckhoudt, Louis, Downside Risk Neutral Probabilities (November 1, 2015). Centre Interuniversitaire sur le Risque, les Politiques Economiques et l'Emploi, Working Paper Series, No. 21, 2015 , Available at SSRN: https://ssrn.com/abstract=2693041 or http://dx.doi.org/10.2139/ssrn.2693041

Pierre Chaigneau (Contact Author)

Queen's University ( email )

Smith School of Business - Queen's University
143 Union Street
Kingston, Ontario K7L 3N6
Canada

Queen’s University ( email )

Louis Eeckhoudt

Catholic University of Lille - IESEG School of Management ( email )

3 Rue de la Digue
Office: A321
Puteaux, 92800
France

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