Test Assets and Weak Factors

101 Pages Posted: 12 Jul 2021

See all articles by Stefano Giglio

Stefano Giglio

Yale School of Management; National Bureau of Economic Research (NBER); Centre for Economic Policy Research (CEPR)

Dacheng Xiu

University of Chicago - Booth School of Business

Dake Zhang

University of Chicago - Booth School of Business

Multiple version iconThere are 4 versions of this paper

Date Written: July 8, 2021

Abstract

Estimation and testing of factor models in asset pricing requires choosing a set of test assets. The choice of test assets determines how well different factor risk premia can be identified: if only few assets are exposed to a factor, that factor is weak, which makes standard estimation and inference incorrect. In other words, the strength of a factor is not an inherent property of the factor: it is a property of the cross-section used in the analysis. We propose a novel way to select assets from a universe of test assets and estimate the risk premium of a factor of interest, as well as the entire stochastic discount factor, that explicitly accounts for weak factors and test assets with highly correlated risk exposures. We refer to our methodology as supervised principal component analysis (SPCA), because it iterates an asset selection step and a principal-component estimation step. We provide the asymptotic properties of our estimator, and compare its limiting behavior with that of alternative estimators proposed in the recent literature, which rely on PCA, Ridge, Lasso, and Partial Least Squares (PLS). We  find that the SPCA is superior in the presence of weak factors, both in theory and in  nite samples. We illustrate the use of SPCA by applying it to estimate the risk premia of several tradable and nontradable factors, to evaluate asset managers' performance, and to de-noise asset pricing factors.

Keywords: Supervised PCA, SPCA, PCA, risk premium, factor models, APT, Ridge, Lasso, stochastic discount factor

Suggested Citation

Giglio, Stefano and Xiu, Dacheng and Zhang, Dake, Test Assets and Weak Factors (July 8, 2021). University of Chicago, Becker Friedman Institute for Economics Working Paper No. 2021-79, Available at SSRN: https://ssrn.com/abstract=3882815 or http://dx.doi.org/10.2139/ssrn.3882815

Stefano Giglio

Yale School of Management ( email )

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

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
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Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

Dacheng Xiu (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

Dake Zhang

University of Chicago - Booth School of Business ( email )

5807 S Woodlawn Ave
Chicago, IL 60637
United States

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