Downside Risk Neutral Probabilities

15 Pages Posted: 19 Feb 2015 Last revised: 26 Sep 2018

See all articles by Pierre Chaigneau

Pierre Chaigneau

Queen's University; Queen’s University

Louis Eeckhoudt

Facultes Universitaires Catholiques de Mons (FUCAM)

Multiple version iconThere are 2 versions of this paper

Date Written: September 2018


We show that there exists a probability measure under which the CAPM formula for expected returns holds for general utility functions and probability distributions. This probability measure, the ``downside risk neutral'' measure, is adjusted to incorporate the effects of downside risk and higher degree risks. It thus belongs to the same family as the risk neutral measure, which is also a risk-adjusted measure. Using risk preference theory, we interpret this change in probability measure in terms of risk substitution.

Keywords: downside risk, prudence, risk aversion, risk neutral probabilities, risk substitution

JEL Classification: D81, G12

Suggested Citation

Chaigneau, Pierre and Eeckhoudt, Louis, Downside Risk Neutral Probabilities (September 2018). Available at SSRN: or

Pierre Chaigneau (Contact Author)

Queen's University ( email )

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

Queen’s University ( email )

Louis Eeckhoudt

Facultes Universitaires Catholiques de Mons (FUCAM) ( email )

Chaussee de Binche, 151
Mons 7000

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