The Virtue of Complexity Everywhere

45 Pages Posted: 25 Jul 2022 Last revised: 2 Aug 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

Multiple version iconThere are 2 versions of this paper

Date Written: July 18, 2022

Abstract

We investigate the performance of non-linear return prediction models in the high complexity regime, i.e., when the number of model parameters exceeds the number of observations. We document a "virtue of complexity" in all asset classes that we study (US equities, international equities, bonds, commodities, currencies, and interest rates). Specifically, return prediction R2 and optimal portfolio Sharpe ratio generally increase with model parameterization for every asset class. The virtue of complexity is present even in extremely data-scarce environments, e.g., for predictive models with less than twenty observations and tens of thousands of predictors. The empirical association between model complexity and out-of-sample model performance exhibits a striking consistency with theoretical predictions.

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 Everywhere (July 18, 2022). Swiss Finance Institute Research Paper No. 22-57, Available at SSRN: https://ssrn.com/abstract=4171581 or http://dx.doi.org/10.2139/ssrn.4171581

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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