The Virtue of Complexity in Return Prediction

102 Pages Posted: 15 Dec 2021 Last revised: 26 May 2022

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


Contrary to conventional wisdom in finance, return prediction R2 and optimal portfolio Sharpe ratio generally increase with model parameterization, even when minimal regularization is used. We theoretically characterize the behavior of return prediction models in the high complexity regime, i.e. when the number of parameters exceeds the number of observations. Empirically, we document this "virtue of complexity" in US equity market prediction. 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 Return Prediction (December 13, 2021). Swiss Finance Institute Research Paper No. 21-90, Available at SSRN: or

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

Centre for Economic Policy Research (CEPR) ( email )

United Kingdom

Swiss Finance Institute

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

Kangying Zhou

Yale School of Management ( email )

165 Whitney Ave
New Haven, CT 06511

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