Portfolio selection in quantile decision models
Portfolio selection in quantile decision models
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-à-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.
Optimal asset allocation, Portfolio theory, Quantile preferences, Risk attitude
133-181
Castro, Luciano De
66a58404-79c5-4690-8cb1-e1454d14a334
Galvao, Antonio F.
6f2af55a-e340-404e-a787-cb2f90c87ebd
Montes-rojas, Gabriel
69548d5d-9e1f-4f6c-8453-6c2675b8dc21
Olmo, Jose
706f68c8-f991-4959-8245-6657a591056e
June 2022
Castro, Luciano De
66a58404-79c5-4690-8cb1-e1454d14a334
Galvao, Antonio F.
6f2af55a-e340-404e-a787-cb2f90c87ebd
Montes-rojas, Gabriel
69548d5d-9e1f-4f6c-8453-6c2675b8dc21
Olmo, Jose
706f68c8-f991-4959-8245-6657a591056e
Castro, Luciano De, Galvao, Antonio F., Montes-rojas, Gabriel and Olmo, Jose
(2022)
Portfolio selection in quantile decision models.
Annals of Finance, 18 (2), .
(doi:10.1007/s10436-021-00405-4).
Abstract
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-à-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.
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Accepted/In Press date: 6 October 2021
e-pub ahead of print date: 29 March 2022
Published date: June 2022
Additional Information:
Funding Information:
The authors would like to express their appreciation to the Editor-in-Chief Anne Villamil, an anonymous reviewer, Nabil Al-Najjar, Hide Ichimura, Derek Lemoine, Richard Peter, Tiemen Woutersen, María Florencia Gabrielli and seminar participants at the University of Iowa, INSPER, JOLATE Bahía Blanca, RedNIE, Southampton Econometrics Conference, and Universidad de Buenos Aires for helpful comments and discussions. Luciano de Castro acknowledges the support of the National Council for Scientific and Technological Development – CNPq. Computer programs to replicate the numerical analyses are available from the authors.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Keywords:
Optimal asset allocation, Portfolio theory, Quantile preferences, Risk attitude
Identifiers
Local EPrints ID: 457706
URI: http://eprints.soton.ac.uk/id/eprint/457706
ISSN: 1614-2446
PURE UUID: 2864ba9a-9ecd-497e-b47c-0e194a1d16e8
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Date deposited: 16 Jun 2022 00:10
Last modified: 17 Mar 2024 07:19
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Contributors
Author:
Luciano De Castro
Author:
Antonio F. Galvao
Author:
Gabriel Montes-rojas
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