Portfolio Optimisation within a Wasserstein Ball

36 Pages Posted: 8 Feb 2021

See all articles by Silvana M. Pesenti

Silvana M. Pesenti

University of Toronto

Sebastian Jaimungal

University of Toronto - Department of Statistics

Date Written: August 10, 2020


We consider the problem of active portfolio management where a loss-averse and/or gain-seeking investor aims to outperform a benchmark strategy's risk profile while not deviating too much from it. Specifically, an investor considers alternative strategies that co-move with the benchmark and whose terminal wealth lies within a Wasserstein ball surrounding it. The investor then chooses the alternative strategy that minimises their personal risk preferences, modelled in terms of a distortion risk measure. In a general market model, we prove that an optimal dynamic strategy exists and is unique, and provide its characterisation through the notion of isotonic projections. Finally, we illustrate how investors with different risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped distortion risk measures, and lower- and upper-tail 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 some aspects of the benchmark.

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 (August 10, 2020). 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

Sebastian Jaimungal

University of Toronto - Department of Statistics ( email )

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

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

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