The information content of the implied volatility term structure on future returns

• Published date: 01 March 2019
• Author: Kuang‐Chieh Yen,Yaw‐Huei Wang
• DOI: http://doi.org/10.1111/eufm.12166
• Date: 01 March 2019

W

380 © 2017 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/eufm Eur Financ Manag. 2019;25:380–406.

DOI: 10.1111/eufm.12166

ORIGINAL ARTICLE

The information content of the implied volatility

term structure on future returns

Yaw-Huei Wang

|

Kuang-Chieh Yen

Department of Finance, College of

Management, National Taiwan

University, Taipei, Taiwan

Emails: quetiony@gmail.com;

wangyh@ntu.edu.tw

Funding information

Ministry of Science and Technology of

Taiwan

Abstract

We derive the theoretical relation between the term

structure of implied variance and the expected excess

returns of the underlying asset. Adopting three alternative

approaches to compile the variables representing the

information on the implied volatility index level and term

structure, we show the important role of the term structure in

determining future excess returns of the S&P 500 index.

Both the in-sample and out-of-sample analyses suggest that

the information content of the term structure variable is

significant and a strong complement to that of the level

variable, especially for shorter-term excess returns.

KEYWORDS

predictability, S&P 500 index returns, VIX term structure

JEL CLASSIFICATION

G13, G14

1

|

INTRODUCTION

According to the methodology proposed by the Chicago Board Options Exchange (CBOE) for the

implementation of the model-free implied volatility formula

1

the computation of the implied volatility

The authors acknowledge the helpful comments and suggestions by John Doukas (the editor), the anonymous referees,

Pai-Ta Shih, Chien-Ling Lo, and the participants of the 1st Conference on Recent Developments in Financial Econometrics

and Applications, the 22th Conference on the Theories and Practices of Securities and Financial Markets, and the 2016

European Financial Management Association annual meeting. The authors are grateful to the Ministry of Science and

Technology of Taiwan for the financial support provided for this study.

i

o

5

o

a

i

r

v

s

h

f

s

t

p

m

i

i

a

m

5

T

w

w

p

l

s

r

f

i

i

c

i

1

a

(

t

2

c

c

(

3

WANG AND YEN

|

3

381

6.

e

y

index (VIX) is based on consideration of all of the available market prices of the S&P 500 index

options. Such an approach facilitates the approximation of the expected aggregate volatility of the S&P

500 index during the subsequent 30 calendar-day period,

2

and indeed, this method has been used not

only as a measure of sentiment but also as an instrument for timing the market, particularly in the

aftermath of the subprime mortgage crisis.

Following Whaley (2000), who proposes the use of the VIX as an effective fear indicator, Giot (2005)

identifies a strongly negative correlation between contemporaneous changes and future market index

returns, along with a positive correlation between such future returns and current levels of the implied

volatility indices. Both Guo and Whitelaw (2006) and Banerjee, Doran, and Peterson (2007) report

similar findings. Zhu (2013) shows that VIX has the significant predictive power for extreme low and

high stock returns. Furthermore, Bekaert and Hoerova (2014) show that the variance risk premium (VRP)

from decomposing the squared VIX can predict stock returns. Overall, their results provide empirical

support for the predictive ability of the VIX-related variables on future portfolio returns.

Because the current version of the VIX is compiled for each maturity and incorporates almost all of

the available contracts, it should be more informative than the old version when used to investigate its

predictive ability on future equity returns. However, the VIX is dependent on maturity, with 30-day

maturity being the most frequently used. This dependence on maturity gives rise to the interesting and

important question of whether the VIX term structure contains any useful information for potential use

in the forecasting of returns.

3

Furthermore, because the literature clearly shows that volatility has some special stylized facts, such

as clustering and mean reversion, the relative positions of the VIX levels for different maturity periods

may imply the expectations of market participants on market volatility and, thus, on changes in the S&P

500 index due to the mean–variance relation in the conventional theory of the capital asset pricing model.

Therefore, this study contributes to the extant related literature by comprehensively investigating

whether the VIX term structure contains any useful information on future returns in the S&P 500 index.

Based on the stochastic volatility with correlated jumps (SVCJ) model proposed by Eraker (2004),

we refine the theoretical work of Banerjee et al. (2007) to derive a theoretical model that reveals a

positive relation between expected excess returns in the S&P 500 index and both the squared VIX

levels and the difference between forward and current squared VIX levels. Because the forward

squared VIX level can be computed from two squared VIX values with different horizons, it can be

regarded as a proxy for the squared VIX term structure. Hence, this model provides theoretical

fundamentals for the potential of the VIX term structure with regard to the prediction of excess returns

in the S&P 500 index.

We propose three alternative empirical methods to compile the variables representing the

information in both the squared VIX level and its term structure to investigate whether the information

content of the term structure contributes to the forecasting of future excess returns in the S&P 500

index. First, adhering closely to the theoretical model, we use the 30-day squared current VIX level and

1

The CBOE's revision of the methodology of the VIX formula was based largely on the results of Carr and Madan (1998)

and Demeterfi, Derman, Kamal, and Zou (1999) . Regarding the theoretical fundamentals, Britten-Jones and Neuberger

(2000) derive model-free implied volatility under the diffusion assumption, and Jiang and Tian (2005) subsequently extend

the model to the jump diffusion assumption.

2

When it was introduced in 1993, the VIX was compiled from the implied volatility of eight S&P 100 index options,

comprising near at-the-money and nearby and second nearby calls and puts; however, ever since 2003, the VIX has been

calculated from the prices of S&P 500 index options using a model-free formula with almost all of the available contracts

(i.e., with a wide range of strike prices).

3

See, for example, Bakshi et al. (2011), Feunou et al. (2014), Luo and Zhang (2017), and Andreou et al. (2017).