Portfolio Selection in Quantile Utility Models

57 Pages Posted: 13 Dec 2019

See all articles by Luciano I. de Castro

Luciano I. de Castro

Tippie College of Business

Antonio F. Galvao

University of Arizona

Gabriel Montes-Rojas

City University of London

Jose Olmo

Universidad de Zaragoza; University of Southampton

Date Written: November 27, 2019

Abstract

This paper develops a model for optimal portfolio allocation for an investor with quantile preferences. The investor chooses optimal allocation of weights to maximize the τ-quantile of the utility of the portfolio, for τ ∈ (0,1). A central characteristic of this model is that the portfolio choice is independent of the utility function and related exclusively to the risk attitude, which is captured by the quantile τ. We derive conditions under which the optimal portfolio decision has an interior solution that guarantees diversification vis-a-vis fully investing in a single risky asset. For some families of popular distribution functions the optimal portfolio decision is characterized by two regions: a first region given by the lower quantiles in which diversification is optimal and a second region given by the upper quantiles in which the optimal portfolio allocation is characterized by no diversification. The presence of a risk-free asset produces an all-or-nothing optimal response of the investor to the risky asset that depends on the investors' quantile preferences. This result entails a different interpretation of standard mutual fund separation theorem. In an empirical application we compare the optimal asset allocation of expected utility and quantile utility individuals for a tactical portfolio of stocks, bonds and a risk-free asset.

Keywords: Optimal asset allocation, Expected Utility, Quantile Utility, Portfolio Theory, Risk Attitude

JEL Classification: G11

Suggested Citation

de Castro, Luciano I. and Galvao, Antonio F. and Montes-Rojas, Gabriel and Olmo, Jose, Portfolio Selection in Quantile Utility Models (November 27, 2019). Available at SSRN: https://ssrn.com/abstract=3494601 or http://dx.doi.org/10.2139/ssrn.3494601

Luciano I. De Castro

Tippie College of Business ( email )

108 Pappajohn Building
Iowa City, IA 52242
United States

HOME PAGE: http://https://lucianodecastro.net/

Antonio F. Galvao (Contact Author)

University of Arizona ( email )

McClelland Hall, Room 401 1130 E. Helen Street
Tucson, AZ 85721
United States

Gabriel Montes-Rojas

City University of London ( email )

Northampton Square
London, EC1V OHB
United Kingdom

Jose Olmo

Universidad de Zaragoza ( email )

Gran Via, 2
50005 Zaragoza, Zaragoza 50005
Spain

University of Southampton ( email )

Southampton
United Kingdom

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