Second-order stochastic dominance, reward-risk portfolio selection, and the CAPM

Enrico De Giorgi; Thierry Post

doi:10.1017/s0022109000003616

Second-order stochastic dominance, reward-risk portfolio selection, and the CAPM

Enrico De Giorgi, Thierry Post

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

Starting from the reward-risk model for portfolio selection introduced in De Giorgi (2005), we derive the reward-risk Capital Asset Pricing Model (CAPM) analogously to the classical mean-variance CAPM. In contrast to the mean-variance model, reward-risk portfolio selection arises from an axiomatic definition of reward and risk measures based on a few basic principles, including consistency with second-order stochastic dominance. With complete markets, we show that at any financial market equilibrium, reward-risk investors' optimal allocations are comonotonic and, therefore, our model reduces to a representative investor model. Moreover, the pricing kernel is an explicitly given, non-increasing function of the market portfolio return, reflecting the representative investor's risk attitude. Finally, an empirical application shows that the reward-risk CAPM captures the cross section of U.S. stock returns better than the mean-variance CAPM does.

Original language	English
Pages (from-to)	525-546
Number of pages	22
Journal	Journal of Financial and Quantitative Analysis
Volume	43
Issue number	2
DOIs	https://doi.org/10.1017/s0022109000003616
Publication status	Published - Jun 2008
Externally published	Yes

Funding

∗De Giorgi, [email protected], University of Lugano, via Buffi 13, CH-6900 Lugano, Switzerland; Post, [email protected], Erasmus School of Economics, Erasmus University Rotterdam, Room H14-11, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands. Financial support from the Foundation for Research and Development at the University of Lugano, the National Center of Competence in Research “Financial Valuation and Risk Management” (NCCR-FINRISK), the Tinbergen Institute, the Erasmus Research Institute of Management, and the Erasmus Center of Financial Research is gratefully acknowledged. We received useful comments from Thorsten Hens, Olivier Scail-let, Fabio Trojani, Terry Rockafellar, Pim van Vliet, Philippe Versijp, and Mark Schroder and Lance Young (the referees). An earlier version of the paper was presented at the NCCR-FINRISK Research Day in Berne, at the International Conference on Risk Management and Quantitative Approaches in Finance in Gainesville, Florida, and at the 14th European Workshop on General Equilibrium Theory in Zurich. We thank the participants for their helpful comments and suggestions. Pim van Vliet is credited for making the data available.

ASJC Scopus subject areas

Accounting
Finance
Economics and Econometrics

Access to Document

10.1017/s0022109000003616

Cite this

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title = "Second-order stochastic dominance, reward-risk portfolio selection, and the CAPM",

abstract = "Starting from the reward-risk model for portfolio selection introduced in De Giorgi (2005), we derive the reward-risk Capital Asset Pricing Model (CAPM) analogously to the classical mean-variance CAPM. In contrast to the mean-variance model, reward-risk portfolio selection arises from an axiomatic definition of reward and risk measures based on a few basic principles, including consistency with second-order stochastic dominance. With complete markets, we show that at any financial market equilibrium, reward-risk investors' optimal allocations are comonotonic and, therefore, our model reduces to a representative investor model. Moreover, the pricing kernel is an explicitly given, non-increasing function of the market portfolio return, reflecting the representative investor's risk attitude. Finally, an empirical application shows that the reward-risk CAPM captures the cross section of U.S. stock returns better than the mean-variance CAPM does.",

author = "\{De Giorgi\}, Enrico and Thierry Post",

note = "Funding Information: ∗De Giorgi, [email protected], University of Lugano, via Buffi 13, CH-6900 Lugano, Switzerland; Post, [email protected], Erasmus School of Economics, Erasmus University Rotterdam, Room H14-11, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands. Financial support from the Foundation for Research and Development at the University of Lugano, the National Center of Competence in Research “Financial Valuation and Risk Management” (NCCR-FINRISK), the Tinbergen Institute, the Erasmus Research Institute of Management, and the Erasmus Center of Financial Research is gratefully acknowledged. We received useful comments from Thorsten Hens, Olivier Scail-let, Fabio Trojani, Terry Rockafellar, Pim van Vliet, Philippe Versijp, and Mark Schroder and Lance Young (the referees). An earlier version of the paper was presented at the NCCR-FINRISK Research Day in Berne, at the International Conference on Risk Management and Quantitative Approaches in Finance in Gainesville, Florida, and at the 14th European Workshop on General Equilibrium Theory in Zurich. We thank the participants for their helpful comments and suggestions. Pim van Vliet is credited for making the data available.",

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N2 - Starting from the reward-risk model for portfolio selection introduced in De Giorgi (2005), we derive the reward-risk Capital Asset Pricing Model (CAPM) analogously to the classical mean-variance CAPM. In contrast to the mean-variance model, reward-risk portfolio selection arises from an axiomatic definition of reward and risk measures based on a few basic principles, including consistency with second-order stochastic dominance. With complete markets, we show that at any financial market equilibrium, reward-risk investors' optimal allocations are comonotonic and, therefore, our model reduces to a representative investor model. Moreover, the pricing kernel is an explicitly given, non-increasing function of the market portfolio return, reflecting the representative investor's risk attitude. Finally, an empirical application shows that the reward-risk CAPM captures the cross section of U.S. stock returns better than the mean-variance CAPM does.

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Second-order stochastic dominance, reward-risk portfolio selection, and the CAPM

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