Do fear indices help predict stock returns?

Abstract

This study investigates the forecasting power of implied volatility indices on forward looking returns. Prior studies document that negative innovations to returns are associated with increasing implied volatility of the underlying indices; thus, suggesting a possible relationship between extremely high levels of implied volatility and positive short term returns. We investigate this issue by examining the predictive power of three implied volatility indices, VIX, VXN and VDAX, on the underlying index returns. We extend previous research by also focusing on characterised selected stocks and examine the relationship between implied volatility indices and future returns across different sectors and classified portfolios. Our findings suggest that implied volatility indices are good predictors of 20-days and 60-days forward looking returns and illustrate insignificant predictive power for very short term (1-day and 5-days) returns.

Keywords:

• Implied volatility
• Financial crises
• Forward looking returns
• Realised volatility

JEL Classification:

• C5
• E3
• G1
• G12
• G14

Notes

¹ After the bear market of 2002 bottomed in September 2002, the S&P 500 index gained 101% over the subsequent five year period and peaked in September 2007. If one should have invested his/her money in the S&P 500 stock index from July 2002 till the 3rd quarter of 2007, he/she would have earned an average annual return of 8%. Therefore, we add July and August 2002 (before the bull period) in our analysis to incorporate the predictive ability of implied volatility indices towards the start of the bull period.

² The old VIX (VXO) is based on just eight at the-money options on the S&P 100; VIX on the other hand uses the wide range of strike prices of all outstanding options based on the more liquid S&P 500 index. Furthermore, VXO is a weighted average of implied volatilities based on the Black and Scholes model, i.e. implied volatilities which are dependent on an option pricing model. The new VIX, on the other hand, is not based on the Black and Scholes option pricing model and uses a model-free approach which is independent of any kind of model (Britten-Jones and Neuberger (2003) and Carr and Wu (2006)). The new implied volatility is therefore more representative of the entire US market and offers a methodology which is more in line with the way average investors value their volatility.

³ For a detailed explanation of the new VIX calculation, we refer to the CBOE website at www.cboe.com (The CBOE volatility index—VIX), Jiang and Yisong Tian (2007) and Carr and Wu (2006).

⁴ We classify stocks characterised by their beta, size and B/M ratio separately. First portfolio represents average returns of the 10% of stocks with the highest beta, highest B/M ratio or highest market value. Tenth portfolio represents average returns of the 10% of stocks with the lowest beta, lowest B/M ratio or lowest market value. For example, in the first case, we regress average returns of the 10% of stocks with the highest beta on the representative volatility index.

⁵ Banerjee et al. (2007); ‘If implied volatility is a risk factor of returns, then it should have forecasting ability on future returns of all portfolios, even after adjustment for other risk factors. On the other hand, if markets are inefficient, then alternative portfolios may have sporadic or random patterns of return responses to implied volatilities.’

⁶ Of the 12 regressions 8 show a positive relationship and 4 of them are significant. Furthermore, we observe four negative relationships with only one significant result.

⁷ We find more significant results for the bottom of deciles of the VDAX.

⁸ Nine of the twelve regressions show a negative relationship from which five demonstrate a significant result.