Wasserstein-Kelly Portfolios: A Robust Data-Driven Solution to Optimize Portfolio Growth

16 Pages Posted: 3 Mar 2023

See all articles by Jonathan Yu-Meng Li

Jonathan Yu-Meng Li

Telfer School of Management, University of Ottawa

Date Written: February 27, 2023

Abstract

We introduce a robust variant of the Kelly portfolio optimization model, called the Wasserstein- Kelly portfolio optimization. Our model, taking a Wasserstein distributionally robust optimization (DRO) formulation, addresses the fundamental issue of estimation error in Kelly portfolio optimization by defining a “ball” of distributions close to the empirical return distribution using the Wasserstein metric and seeking a robust log-optimal portfolio against the worst-case distribution from the Wasserstein ball. Enhancing the Kelly portfolio using Wasserstein DRO is a natural step to take, given many successful applications of the latter in areas such as machine learning for generating robust data-driven solutions. However, naive application of Wasserstein DRO to the growth-optimal portfolio problem can lead to several issues, which we resolve through careful modelling. Our proposed model is both practically motivated and efficiently solvable as a convex pro- gram. Using empirical financial data, our numerical study demonstrates that the Wasserstein-Kelly portfolio can outperform the Kelly portfolio in out-of-sample testing across multiple performance metrics and exhibits greater stability.

Suggested Citation

Li, Jonathan Yu-Meng, Wasserstein-Kelly Portfolios: A Robust Data-Driven Solution to Optimize Portfolio Growth (February 27, 2023). Available at SSRN: https://ssrn.com/abstract=4372148 or http://dx.doi.org/10.2139/ssrn.4372148

Jonathan Yu-Meng Li (Contact Author)

Telfer School of Management, University of Ottawa ( email )

136 Jean-Jacques Lussier Street
Ottawa, Ontario K1N 6N5
Canada

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