Asset Pricing with Omitted Factors

39 Pages Posted: 8 Nov 2016 Last revised: 17 Sep 2019

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

Multiple version iconThere are 2 versions of this paper

Date Written: September 14, 2019

Abstract

Standard estimators of risk premia in linear asset pricing models are biased if some priced factors are omitted. We propose a three-pass method to estimate the risk premium of an observable factor, which is valid even when not all factors in the model are specified or observed. We show that the risk premium of the observable factor can be identified regardless of the rotation of the other control factors, as long as they together span the true factor space. Motivated by this rotation invariance result, our approach uses principal components of test asset returns to recover the factor space and additional cross-sectional and time-series regressions to obtain the risk premium of the observed factor. Our estimator is also equivalent to the average excess return of a mimicking portfolio maximally correlated with the observed factor using appropriate regularization. Our methodology also accounts for potential measurement error in the observed factor and detects when such a factor is spurious or even useless. The methodology exploits the blessings of dimensionality, and we therefore apply it to a large panel of equity and non-equity portfolios to estimate risk premia for several workhorse factors.

Keywords: Three-Pass Estimator, Regularized Mimicking Portfolio, Latent Factors, Omitted Factors, Measurement Error, Fama-MacBeth Regression, Principal Component Regression

Suggested Citation

Giglio, Stefano and Xiu, Dacheng, Asset Pricing with Omitted Factors (September 14, 2019). Chicago Booth Research Paper No. 16-21, Available at SSRN: https://ssrn.com/abstract=2865922 or http://dx.doi.org/10.2139/ssrn.2865922

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

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