### 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 |

Publication status | Published - Jun 2008 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Finance
- Accounting
- Economics and Econometrics

### Cite this

*Journal of Financial and Quantitative Analysis*,

*43*(2), 525-546.

**Second-order stochastic dominance, reward-risk portfolio selection, and the CAPM.** / De Giorgi, Enrico; Post, Thierry.

Research output: Contribution to journal › Article

*Journal of Financial and Quantitative Analysis*, vol. 43, no. 2, pp. 525-546.

}

TY - JOUR

T1 - Second-order stochastic dominance, reward-risk portfolio selection, and the CAPM

AU - De Giorgi, Enrico

AU - Post, Thierry

PY - 2008/6

Y1 - 2008/6

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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=46849110164&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=46849110164&partnerID=8YFLogxK

M3 - Article

VL - 43

SP - 525

EP - 546

JO - Journal of Financial and Quantitative Analysis

JF - Journal of Financial and Quantitative Analysis

SN - 0022-1090

IS - 2

ER -