The Virtue of Complexity in Machine Learning Portfolios

102 Pages Posted: 15 Dec 2021 Last revised: 17 Dec 2021

See all articles by Bryan T. Kelly

Bryan T. Kelly

Yale SOM; AQR Capital Management, LLC; National Bureau of Economic Research (NBER)

Semyon Malamud

Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute

Kangying Zhou

Yale School of Management

Date Written: December 13, 2021

Abstract

We theoretically characterize the behavior of machine learning portfolios in the high complexity regime, i.e. when the number of parameters exceeds the number of observations. We demonstrate a surprising "virtue of complexity:" Sharpe ratios of machine learning portfolios generally increase with model parameterization, even with minimal regularization. Empirically, we document the virtue of complexity in US equity market timing strategies. High complexity models deliver economically large and statistically significant out-of-sample portfolio gains relative to simpler models, due in large part to their remarkable ability to predict recessions.

Keywords: Portfolio choice, machine learning, random matrix theory, benign overfit, overparameterization

JEL Classification: C3, C58, C61, G11, G12, G14

Suggested Citation

Kelly, Bryan T. and Malamud, Semyon and Zhou, Kangying, The Virtue of Complexity in Machine Learning Portfolios (December 13, 2021). Swiss Finance Institute Research Paper No. 21-90, Available at SSRN: https://ssrn.com/abstract=3984925 or http://dx.doi.org/10.2139/ssrn.3984925

Bryan T. Kelly

Yale SOM ( email )

135 Prospect Street
P.O. Box 208200
New Haven, CT 06520-8200
United States

AQR Capital Management, LLC ( email )

Greenwich, CT
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Semyon Malamud (Contact Author)

Ecole Polytechnique Federale de Lausanne ( email )

Lausanne, 1015
Switzerland

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Kangying Zhou

Yale School of Management ( email )

165 Whitney Ave
New Haven, CT 06511

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