Asymmetric Effects of Volatility Risk on Stock Returns: Evidence from VIX and VIX Futures

• DOI: http://doi.org/10.1002/fut.21772
• Author: Matteo Sandri,Mark B. Shackleton,Xi Fu
• Published date: 01 November 2016
• Date: 01 November 2016

Asymmetric Effects of Volatility Risk on

Stock Returns: Evidence from VIX and

VIX Futures

Xi Fu*, Matteo Sandri and Mark B. Shackleton

First, to separate different market conditions, this study focuses on how VIX spot (VIX), VIX

futures (VXF), and their basis (VIX VXF) perform different roles in asset pricing. Secondly,

this study decomposes the VIX index into two parts: volatility calculated from out-of-the-money

call options and volatility calculated from out-of-the-money put options. The analysis shows

that out-of-the-money put options capture more useful information in predicting future stock

returns. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 36:1029–1056, 2016

1. INTRODUCTION

Since the introduction of th e Capital Asset Pricing Model (CAPM) by Sharpe (1964),

Lintner (1965), and Mossin (196 6), the market risk premium, de fined as the

compensation required by in vestors to bear market risk , has been investigated. In a ddition

to the market risk premium, v arious empirical studies (Arisoy, Salih, & Akdeniz, 2007;

Bakshi & Kapadia, 2003; Bollersle v, Gibson, & Zhou, 2011; Bollerslev, Tauc hen, & Zhou,

2009; Carr & Wu, 2009; Mo & Wu, 2007) do cument the existence of a premiu m for

bearing volatility risk; thi s supports the hypothesis that vo latility is another importa nt

pricing factor in equity mark ets. Ang, Hodrick, Xing, and Zha ng (2006) and Chang,

Christoffersen, and Jaco bs (2013) show that the ag gregate volatility risk (m easured by

changes in volatility indices ) is important in explaining the cros s-section of returns: stocks

Xi Fu (Lecturer) is at the Department of Economics, Finance and Accounting, University of Liverpool

Management School, University of Liverpool, Liverpool, United Kingdom. Matteo Sandri, and Mark B.

Shackleton (Professor) are at the Department of Accounting and Finance, Lancaster University Management

School, Lancaster University, Lancaster, United Kingdom. We would like to thank Robert I. Webb (the

Editor), the anonymous referee, Torben Andersen, Tristan Linke, Ingmar Nolte, Ser-Huang Poon, Stephen

Taylor, and all participants at 1st KoLa Workshop on Finance and Econometrics in Lancaster University,

2014 FMA European Conference Doctoral Student Consortium, 2014 FEBS International Conference,

EFMA 2014 Conference, and ESRC NWDTC AccFin Pathway Event: Ph.D. Student Workshop in Finance

and Accounting, SoFiE Financial Econometrics Spring School 2015, and 7th International IFABS

Conference for helpful comments.

JEL Classification: G12

*Correspondence author, Department of Economics, Finance and Accounting, University of Liverpool

Management School, University of Liverpool, Chatham Street, Liverpool L69 7ZH, United Kingdom. Tel: þ44

(0)151 795 3000, Fax: þ44(0)151 795 3005, e-mail: Xi.Fu@liverpool.ac.uk.

Received December 2014; Accepted November 2015

The Journal of Futures Markets, Vol. 36, No. 11, 1029–1056 (2016)

© 2016 Wiley Periodicals, Inc.

Published online 4 February 2016 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21772

that fall less as volatility rises have low average returns because they provide protection

against crisis movements in financial markets.

1

Additionally, many empirical studies also reveal that the influence of market risk is not

symmetric. For instance, Ang, Chen, and Xing (2006) show the existence of a downside risk

premium (approximately 6% per annum), where stocks with higher market covariance during

recession periods provide higher average returns compared to those that exhibit lower

covariance with the market.

2

Given that market risk has an asymmetric effect on equity

returns, it is interesting to ask whether the influence of volatility risk on equity returns is also

asymmetric. By using delta-hedged option portfolios, Bakshi and Kapadia (2003) provide

evidence in support of an overall negative volatility risk premium. These empirical results also

reveal time-variation of the volatility risk premium (i.e., the underperformance of delta-

hedged strategies is greater during times of high volatility). DeLisle, Doran, and Peterson

(2011) use innovations in the VIX index to measure volatility risk and focus on its asymmetric

effect. To be more specific, their study shows that sensitivity to VIX innovations is negatively

related to stock returns when volatility is expected to increase, but it is unrelated when

volatility is expected to decrease. Based on the ICAPM (Merton, 1973), Campbell (1993,

1996), and Chen (2003) argue that an increment in aggregate volatility can be interpreted as

a worsening of the investment opportunity set. More recently, Farago and Tedongap (2015)

claim that investors’disappointment aversion is relevant to asset pricing theory, conjecturing

that a worsening opportunity set may result either from a decrease in the market index or from

an increase in the volatility index. Empirical results in their study show that these undesirable

changes (decreases in market and increases in volatility indices) motivate significant

premiums in the cross-section of stock returns. In order to understand the asymmetric effect

due to market or volatility risks, it is important to distinguish between different cases: positive

or negative market returns, and increments or reductions in the aggregate volatility,

especially by using forward-looking measures of volatility.

This study first concentrates on the unconditional relationship between an asset’s

return and its sensitivity to volatility risk through a quintile portfolio level analysis. This study

uses the VIX index itself to construct a volatility factor, that is, innovations in the squared VIX

index. In addition, this study introduces VIX index futures into asset pricing models. Thus,

this study uses innovations in squares of the VIX index or VIX futures to measure changes in

the volatility risk, and further tests the unconditional relationship between portfolio returns

and sensitivity to volatility risk factors.

This study also focuses on the asymmetric effect of volatility risk. In order to do so, the

empirical analysis follows the method used in DeLisle et al. (2011) and defines a dummy

variable to distinguish different situations. To contribute beyond previous studies, this study

defines a dummy variable based on the VIX futures basis (i.e., the difference between the

VIX spot and VIX futures) instead of daily changes in the VIX index. Daily innovations in the

VIX index reflect how it changes from its level on the previous trading day. However, the VIX

futures basis reflects how the spot VIX index deviates from its risk-neutral market

1

In the previous literature, historical data are used to calculate the aggregate volatility. However, if economic

conditions change, historical data no longer reflect the current and future expectations. As it is known that option

prices incorporate market expectations, the introduction of forward-looking information into asset pricing models

becomes extremely valuable. In fact, information, such as volatility, incorporated into options reflects market

expectations of future conditions. Given that several previous studies provide supportive evidence that option-

implied information outperforms historical in volatility prediction (Blair, Poon, & Taylor, 2001; Christensen &

Prabhala, 1998; Muzzioli, 2011; Poon & Granger, 2005; Taylor, Yadav, & Zhang, 2010), using a volatility index

constructed from using option data is expected to incorporate more information about aggregate volatility.

2

The measure of downside risk used in Ang, Chen, et al. (2006) was originally introduced by Bawa and Lindenberg

(1977).

1030 Fu, Sandri, and Shackleton