Portfolio Selection in Quantile Decision Models

62 Pages Posted: 13 Dec 2019 Last revised: 6 Aug 2020

See all articles by Luciano I. de Castro

Luciano I. de Castro

Tippie College of Business; IMPA

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


This paper develops a model for optimal portfolio allocation for an investor with quantile preferences, i.e., who maximizes the τ-quantile of the portfolio return, for τ ∈ (0,1). Quantile preferences allow to study heterogeneity in individuals' portfolio choice by varying the quantiles, and have a solid axiomatic foundation. Their associated risk attitude is captured entirely by a single dimensional parameter (the quantile τ), instead of the utility function. We formally establish the properties of the quantile model. The presence of a risk-free asset in the portfolio produces an all-or-nothing optimal response to the risk-free asset that depends on investors' quantile preference. In addition, when both assets are risky, 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. We also derive conditions under which the optimal portfolio decision is characterized by two regions: full diversification for quantiles below the median and no diversification for upper quantiles. These results are illustrated in an exhaustive simulation study and an empirical application using a tactical portfolio of stocks, bonds and a risk-free asset. The results show heterogeneity in portfolio diversification across risk attitudes.

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 Decision 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 )

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

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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

University of Southampton ( email )

United Kingdom

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