Complexity in Factor Pricing Models

139 Pages Posted: 14 Mar 2023 Last revised: 22 Jan 2024

See all articles by Antoine Didisheim

Antoine Didisheim

The University of Melbourne; Swiss Finance Institute

Shikun Ke

Yale School of Management

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

Multiple version iconThere are 2 versions of this paper

Date Written: March 13, 2023

Abstract

We theoretically characterize the behavior of machine learning asset pricing models. We prove that expected out-of-sample model performance—in terms of SDF Sharpe ratio and test asset pricing errors—is improving in model parameterization (or “complexity”). Our empirical findings verify the theoretically predicted “virtue of complexity” in the cross-section of stock returns. Models with an extremely large number of factors (more than the number of training observations or base assets) outperform simpler alternatives by a large margin.

Keywords: Stochastic discount factor (SDF), asset pricing test, pricing error, alpha, cross section of returns, portfolio choice

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

Suggested Citation

Didisheim, Antoine and Ke, Shikun and Kelly, Bryan T. and Malamud, Semyon, Complexity in Factor Pricing Models (March 13, 2023). Swiss Finance Institute Research Paper No. 23-19, Available at SSRN: https://ssrn.com/abstract=4388526 or http://dx.doi.org/10.2139/ssrn.4388526

Antoine Didisheim

The University of Melbourne ( email )

Parkville, 3010
Australia
0435776821 (Phone)

Swiss Finance Institute ( email )

University of Melbourne
Melbourne, VA
Australia
0797605012 (Phone)

Shikun Ke

Yale School of Management ( email )

165 Whitney Ave
New Haven, CT 06511

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

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