Option‐implied betas and the cross section of stock returns

• Published date: 01 January 2019
• Date: 01 January 2019
• Author: Xuguang Li,Fang Qiao,Richard D. F. Harris
• DOI: http://doi.org/10.1002/fut.21936

Received: 29 September 2017

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Revised: 12 May 2018

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Accepted: 13 May 2018

DOI: 10.1002/fut.21936

RESEARCH ARTICLE

Option‐implied betas and the cross section of stock returns

Richard D. F. Harris

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Xuguang Li

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Fang Qiao

3

1

Xfi Centre for Finance and Investment,

University of Exeter, Exeter, UK

2

The People’s Bank of China Shanghai

Head Office, Shanghai, China

3

PBC School of Finance, Tsinghua

University, Beijing, China

Correspondence

Fang Qiao, PBC School of Finance,

Tsinghua University, 43 Chengfu Road,

Haidian District, Beijing 100083, China.

Email: qiaof@pbcsf.tsinghua.edu.cn

We investigate the cross‐sectional relationship between stock returns and a

number of measures of option‐implied beta. Using portfolio analysis, we show

that the method proposed by Buss and Vilkov (2012, The Review of Financial

Studies, 2525, 3113–3140) leads to a stronger relationship between implied beta

and stock returns than other approaches. However, using the Fama and

MacBeth (1973, Journal of Political Economy, 8181, 607–636) cross‐section

regression methodology, we show that the relationship is not robust to the

inclusion of other firm characteristics. We further show that a similar result

holds for implied downside beta. We, therefore, conclude that there is no robust

relation between option‐implied beta and returns.

KEYWORDS

cross section, downside beta, option‐implied beta, stock returns

JEL CLASSIFICATION

G12

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INTRODUCTION

The capital asset pricing model (CAPM), developed independently by Sharpe (1964), Lintner (1965), and Mossin (1966),

predicts that the expected return of a stock should be a positive linear function of its market beta, and unrelated to all

other characteristics of the stock. These predictions of the CAPM have been empirically tested in many studies.

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However, these studies typically estimate the unobserved beta using historical data on stock returns. As noted by

McNulty, Yeh, Schulze, and Lubatkin (2002), the use of historical stock returns to estimate market beta is problematic,

since it leads to sensitivity to minor changes in the sample period used.

In an attempt to reduce the estimation error that arises from the use of historical data, a number of studies have

developed estimators of market beta that exploit information about the covariance matrix of stock returns that is

contained in option prices. French, Groth, and Kolari (1983; FGK) introduce a hybrid method to estimate market beta

that combines an estimate of the correlation between the stock return and the market return from historical data with

the ratio of stock‐to‐market implied volatility. Chang, Christoffersen, Jacobs, and Vainberg (2011; CCJV) use both

option‐implied skewness and volatility to estimate market beta. They find that the CCJV beta performs relatively well

and can explain a sizeable proportion of cross‐sectional variation in expected returns. Buss and Vilkov (2012; BV)

compute option‐implied beta using option‐implied correlation and volatility. They find that in support of the CAPM,

there is a monotonically increasing relation between BV beta and returns.

Buss and Vilkov (2012) compare their approach with both historical beta, and other option‐implied betas, using tests

based on portfolio sorting, and conclude that the BV beta performs best. In this paper, we investigate the robustness of these

findings with respect to the inclusion of other firm‐specific characteristics. We employ options on the S&P 500 index and its

J Futures Markets. 2019;39:94–108.wileyonlinelibrary.com/journal/fut94

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© 2018 Wiley Periodicals, Inc.

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See, for example, Fama and French (1992), who find that the relation between market betas and average returns disappears during the more recent 1963–1990 period of U.S. stock return data even

when beta is the only explanatory variable.