To identify volatilities and other risk factors corresponding to specific option maturities, the authors apply a term structure of risk methodology to decompose option prices. Their findings demonstrate that the term structure of risk implicit in option prices reveals two predictors of the bond, equity, and variance premiums.
The authors’ objective is to show that the term structure of risk (also referred to as the “maturity structure of uncertainty”) that is implicit in option prices can reveal certain useful risk factors. A structural or no-arbitrage asset-pricing model is used to derive risk factors. The authors contribute to the literature by proposing a new approach to measuring risk factors priced in the option market; they demonstrate that option prices can be used to provide forward-looking measures of risk.
How Is This Research Useful to Practitioners?
The authors explore the factor structure of time-varying expected returns and provide a partial explanation for it. They study option prices to understand the factor structure of time-varying expected returns and find that two factors summarize the compensation for risk implicit in the term structure of option-implied variance and that the same risk factors are associated with common predictability of equity, variance, and bond risk premiums. They interpret the risk factors via their relationship with 124 financial and economic indicators. The estimated factors proxy for actual economic risks.
The variance term structure reveals two risk factors for each economic and financial variable. These factors exhibit significant predictability for the bond, equity, and variance premiums, and the predictive content is robust and strong within short time horizons. The variance risk factors imply countercyclical risk-premium variations, which is evidenced by data showing that fewer than one-third of the variance risk factor variations can be explained by macroeconomic indicators. The authors find an R2 between 20% and 25% for only three economic and financial variables: number 24 (LHELX), which represents employment; number 111 (FYAAAC), which represents the Moody’s AAA corporate bond yield; and number 114 (FYAVG), which represents the Moody’s average corporate bond yield.
The authors’ approach of using option-implied information in forecasting return predictability is most closely related to Bakshi, Panayotov, and Skoulakis (Journal of Financial Economics 2011); they also study the predictive content of the one- and two-month forward variances for the S&P 500 Index and T-bill returns. In the final analysis, the authors ask several more questions, inviting more research.
How Did the Authors Conduct This Research?
The data for excess returns are obtained from CRSP to compute end-of-the-month equity returns on the S&P 500 at horizons of 1, 2, 3, 6, 9, and 12 months. Longer-horizon returns are obtained by summing monthly returns. The authors use the Fama–Bliss zero-coupon bond prices from CRSP to compute bond excess returns, whereas the excess equity returns are computed using risk-free rates from CRSP.
They obtain the data for the excess variance by summing monthly realized variances and also by following Britten–Jones and Neuberger’s (Journal of Finance 2000) methodology to compute expected integrated variance under the risk-neutral measure from option prices. The excess variance is computed as the difference between the realized variance under the historical measure and the ex ante measure of the conditional variance under the risk-neutral measure.
The data for the risk-neutral variance are obtained from the OptionMetrics database of European options written on the S&P 500. The authors include 85,385 observations covering the period from January 1996 to October 2008.
Their first step in exploring the variance term structure, which predicts the bond and equity premiums, is to measure the variance using options on S&P 500 futures across a range of maturities based on the standard model-free measure from Bakshi and Madan (Journal of Financial Economics 2000). The research also shows that the variance term structure exhibits a low-dimensional factor structure. Next, the authors estimate how many factors from the variance structure are sufficient to summarize its predictive content for bond and equity returns, jointly.
They then estimate these factors via a multivariate reduced-rank regression of returns on the variance term structure, in which the rank of the coefficient matrix corresponds to the number of linear combinations that are sufficient to summarize the information content. Their final step is to show formally that the variance term structure is also linked to the variance premium.
The authors leverage prior research from notable publications and delve deeper into an analysis of the term structure of risk, risk premiums, and the variance premium. This quantification is interesting to consider because it is similar to the use of the familiar term structure of interest rates to derive implied forward interest rates from spot rates. In this case, however, the authors derive option volatilities associated with option maturities to identify equity and bond risk premiums. The research provides analysts with a tool to better consider volatility and risk–return trade-offs when making short-term and long-term portfolio management decisions.