Characteristics Are Covariances: A Unified Model of Risk and Return

59 Pages Posted: 7 Sep 2017 Last revised: 24 Jan 2018

Bryan T. Kelly

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

Seth Pruitt

Arizona State University (ASU) - Finance Department

Yinan Su

University of Chicago, Booth School of Business, Students; University of Chicago, University of Chicago, Department of Economics, Students

Date Written: January 22, 2018

Abstract

We propose a new modeling approach for the cross section of returns. Our method, Instrumented Principal Components Analysis (IPCA), allows for latent factors and time-varying loadings by introducing observable characteristics that instrument for the unobservable dynamic loadings. If the characteristics/expected return relationship is driven by compensation for exposure to latent risk factors, IPCA will identify the corresponding latent factors. If no such factors exist, IPCA infers that the characteristic effect is compensation without risk and allocates it to an "anomaly" intercept. Studying returns and characteristics at the stock-level, we find that four IPCA factors explain the cross section of average returns significantly more accurately than existing factor models and produce characteristic-associated anomaly intercepts that are small and statistically insignificant. Furthermore, among a large collection of characteristics explored in the literature, only eight are statistically significant in the IPCA specification and are responsible for nearly 100% of the model's accuracy.

Keywords: Cross section of returns, latent factors, anomaly, factor model, conditional betas, PCA, BARRA

Suggested Citation

Kelly, Bryan T. and Pruitt, Seth and Su, Yinan, Characteristics Are Covariances: A Unified Model of Risk and Return (January 22, 2018). Available at SSRN: https://ssrn.com/abstract=3032013 or http://dx.doi.org/10.2139/ssrn.3032013

Bryan T. Kelly (Contact Author)

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

Seth Pruitt

Arizona State University (ASU) - Finance Department ( email )

W. P. Carey School of Business
PO Box 873906
Tempe, AZ 85287-3906
United States

Yinan Su

University of Chicago, Booth School of Business, Students ( email )

Chicago, IL
United States

University of Chicago, University of Chicago, Department of Economics, Students ( email )

Chicago, IL
United States

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