Portfolio Optimisation within a Wasserstein Ball

37 Pages Posted: 8 Feb 2021 Last revised: 21 Jun 2022

See all articles by Silvana M. Pesenti

Silvana M. Pesenti

University of Toronto

Sebastian Jaimungal

University of Toronto - Department of Statistics

Date Written: May 5, 2021

Abstract

We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy's risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal wealth lie within a Wasserstein ball surrounding a benchmark's -- being distributionally close -- and that have a specified dependence/copula -- tying state-by-state outcomes -- to it. The investor then chooses the alternative strategy that minimises a distortion risk measure of terminal wealth. In a general (complete) market model, we prove that an optimal dynamic strategy exists and provide its characterisation through the notion of isotonic projections.

We further propose a simulation approach to calculate the optimal strategy's terminal wealth, making our approach applicable to a wide range of market models. Finally, we illustrate how investors with different copula and risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped, and lower- and upper-tail distortion risk measures as examples. We find that investors' optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving the benchmark's structure.

Keywords: Portfolio Allocation, Behavioural Finance, Wasserstein Distance, Tail Value-at-Risk, Benchmark

JEL Classification: C61,G11, C44

Suggested Citation

Pesenti, Silvana M. and Jaimungal, Sebastian, Portfolio Optimisation within a Wasserstein Ball (May 5, 2021). Available at SSRN: https://ssrn.com/abstract=3744994 or http://dx.doi.org/10.2139/ssrn.3744994

Silvana M. Pesenti (Contact Author)

University of Toronto ( email )

100 St. George Street
Toronto, Ontario M5S 3G8
Canada

Sebastian Jaimungal

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://http:/sebastian.statistics.utoronto.ca

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