Uncovering a positive risk-return relation: the role of implied volatility index

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).

Guo and Whitelaw (2006) found that omitting the ‘hedge component’ of stock returns from the estimation methodology of the risk-return relation causes a large downward bias in the estimate of relative risk aversion. These authors estimated the hedge component using a linear function of a vector of state variables including the dividend yield, the yield spread between Baa-rated and Aaa-rated bonds, and the yield spread between the 6-month commercial paper and the 3-month Treasury Bill rate. Using a GMM estimation approach and employing past realized volatility or implied volatility as instruments for conditional volatility, these authors found that incorporating the previously defined hedge component reveals a positive risk-return relation. The present study differs from Guo and Whitelaw (2006) in several ways. Firstly, we adopt a GARCH-in-Mean estimation framework, with the conditional variance being estimated on the basis of a GARCH-type specification and not being approximated using instruments. Secondly, in the present study, IVI is not used as an instrument variable for conditional variance but as an important variable for the specification of the conditional variance equation. Thirdly, we illustrate that it is the IVI, and not the hedge component, the important variable which is capable of revealing a positive risk-return relation.

The CBOE implied volatility index is also known as VIX. There exist an old VIX series (distributed under the new ticker VXO) which is highly correlated with the former VIX series (Banerjee et al. 2007).

Day and Lewis (1992, Tables 2 and 3, pages 277, 280).