Uncovering a positive risk-return relation: the role
of implied volatility index
Published online: 1 November 2012
Ó Springer Science+Business Media, LLC 2012
Abstract We report empirical evidence suggesting a strong and positive risk-return
relation for the daily S&P 100 market index if the implied volatility index is included as an
exogenous variable in the conditional variance equation. This result holds for alternative
GARCH speciﬁcations and conditional distributions. Monte Carlo evidence suggests that if
implied volatility is not included, whilst is should be, the risk-return relation is more likely
to be negative or weak.
Keywords S&P 100 Á Implied volatility index Á GARCH-M Á Risk-return relation
JEL Classiﬁcation G12 Á C22
This paper unveils the importance of the CBOE implied volatility index in uncovering a
strong and positive risk-return relation for the daily S&P 100 market index within the
framework of GARCH-in-Mean (GARCH-M) models. On one hand, empirical evidence on
the risk-return relation is conﬂicting, with recent studies ﬁnding a weak or negative relation
(Goyal and Santa-Clara 2003; Lettau and Ludvigson 2003).
On the other hand, there is
evidence supporting the ability of implied volatility to predict future volatility, highlighting
the information content of implied volatility (Guo and Whitelaw 2006; Day and Lewis
1992). This paper is an attempt to bridge these two pieces of literature: by adding the
implied volatility index (IVI) as an exogenous variable in conditional variance, it explores
A. Kanas (&)
Department of Economics, University of Piraeus, 80 Karaoli and Demetriou Str., 18534 Piraeus,
A large number of studies have examined the relation between returns and risk, including Cai et al. (2006),
Cheng and Smith (2012), Drew et al. (2007), Hobbes et al. (2007), Psychoyios et al. (2010), Arora et al.
(2009), and Kanas (2012).
Rev Quant Finan Acc (2014) 42:159–170