Beta Risk in the Cross-Section of Equities

86 Pages Posted: 3 Mar 2017 Last revised: 23 Jul 2019

See all articles by Ali Boloorforoosh

Ali Boloorforoosh

Concordia University; TD Asset Management

Peter Christoffersen

University of Toronto - Rotman School of Management; Copenhagen Business School; Aarhus University - CREATES

Mathieu Fournier

HEC Montreal

Christian Gourieroux

University of Toronto - Department of Economics; Center for Interuniversity Research and Analysis on Organization (CIRANO); Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE); National Bureau of Economic Research (NBER)

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Date Written: July 22, 2019

Abstract

We develop a conditional capital asset pricing model in continuous-time that allows for stochastic beta exposure. When beta co-moves with market variance and the stochastic discount factor (SDF), beta risk is priced, and the expected return on a stock deviates from the security market line. The model predicts that low-beta stocks earn high returns because their beta co-moves positively with market variance and the SDF. The opposite is true for high-beta stocks. Estimating the model on equity and option data, we find that beta risk explains expected returns on low- and high-beta stocks, resolving the "betting against beta" anomaly.

Keywords: Factor Models, Stochastic Beta, Option-Implied Beta, Wishart Processes

JEL Classification: G10, G12, G13

Suggested Citation

Boloorforoosh, Ali and Christoffersen, Peter and Fournier, Mathieu and Gourieroux, Christian, Beta Risk in the Cross-Section of Equities (July 22, 2019). Rotman School of Management Working Paper No. 2926511. Available at SSRN: https://ssrn.com/abstract=2926511 or http://dx.doi.org/10.2139/ssrn.2926511

Ali Boloorforoosh

Concordia University ( email )

John Molson School of Business
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HOME PAGE: http://aliboloor.com

TD Asset Management ( email )

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Peter Christoffersen

University of Toronto - Rotman School of Management ( email )

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Copenhagen Business School

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Denmark

Aarhus University - CREATES

School of Economics and Management
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DK-8000 Aarhus C
Denmark

Mathieu Fournier (Contact Author)

HEC Montreal ( email )

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Montreal, Quebec H2X 2L3 H3T 2A7
Canada

Christian Gourieroux

University of Toronto - Department of Economics ( email )

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Canada
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416-978-6713 (Fax)

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

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Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE) ( email )

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France
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National Bureau of Economic Research (NBER)

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United States

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