The RQE-CAPM: New Insights About the Pricing of Idiosyncratic Risk

35 Pages Posted: 16 Mar 2022

See all articles by Benoit Carmichael

Benoit Carmichael

Université Laval

Gilles Boevi Koumou

Université Mohammed VI Polytechnique

Kevin Moran

Laval University - Department of Economics

Date Written: February 4, 2022

Abstract

We use an equivalent form of Markowitz's mean-variance utility function, based on Rao's Quadratic Entropy (RQE), to enrich the standard capital asset pricing model (CAPM), both in the presence and in the absence of a risk-free asset. The resulting equilibrium, which we denote RQE-CAPM, offers important new insights about the pricing of risk. Notably, it reveals that the reason for which the standard CAPM does not price idiosyncratic risk is not only because the market portfolio is law of large numbers diversifed but also because the model implicitly assumes agents' total risk aversion and their correlation diversifcation risk preference balance each other exactly. We then demonstrate that idiosyncratic risk is priced in a general RQECAPM where agents' total risk aversion and their correlation diversifcation risk preference coeffcients are not necessary equal. Our general RQE-CAPM therefore offers a unifying way of thinking about the pricing of idiosyncratic risk, including cases where such risk is negatively priced, and is relevant for the literature assessing the idiosyncratic risk puzzle. It also provides a natural theoretical underpinning for the empirical tests of the CAPM or the pricing of idiosyncratic risk performed in some existence studies.

Keywords: Rao's Quadratic Entropy, Mean-Variance Model, Capital Asset Pricing Model, Idiosyncratic Risk, Correlation Diversiffcation

JEL Classification: D81, G11, G12

Suggested Citation

Carmichael, Benoit and Koumou, Gilles and Moran, Kevin, The RQE-CAPM: New Insights About the Pricing of Idiosyncratic Risk (February 4, 2022). Available at SSRN: https://ssrn.com/abstract=4026448 or http://dx.doi.org/10.2139/ssrn.4026448

Benoit Carmichael (Contact Author)

Université Laval ( email )

Quebec G1K 7P4
Canada

Gilles Koumou

Université Mohammed VI Polytechnique ( email )

Rabat
Morocco

Kevin Moran

Laval University - Department of Economics ( email )

2325 Rue de l'Université
Ste-Foy, Quebec G1K 7P4 G1K 7P4
Canada

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