Using S&P 500 Index options data to measure market volatility, skewness, and kurtosis, the authors seek to determine whether innovations in these market moments help explain cross-sectional equity returns. Market skewness appears to be the most robust of the measures, with some evidence of market volatility also being robust earlier in the sample period. The effect of market kurtosis never comes through in a consistent conclusive manner.
In an exhaustive study, the authors measure the effects of market volatility, market skewness, and market kurtosis on the cross-section of equity returns. The authors obtain measures of these three moments from S&P 500 Index options, which means these measures are forward looking, rather than estimates based on historical data. Moment measures obtained from options prices are considered to be better because historical data may not be indicative of the ex ante return distribution of the market (i.e., what actually happened in the past may be different from what was expected to happen).
In many of the empirical tests, the authors find that market skewness appears to be a significantly priced risk factor for cross-sectional equity returns, after accounting for other noted risk measures: excess market return, size, book-to-market ratio, and momentum. Stocks with high exposure to the skewness factor have lower returns, on average. The authors find that the risk premium on the other market moment factors, volatility and kurtosis, are smaller in magnitude. Overall, the results provide evidence that the higher moments of market returns are important in asset pricing.
How Is This Research Useful to Practitioners?
Because of the possible effect of market skewness on equity returns, practitioners may need to think beyond variance when forecasting expected returns. Hopefully, recognizing this added dimension of risk will lead to better decisions or explain why certain types of existing hedges work so well.
Another benefit is the use of information implied from option prices beyond what is available from the Volatility Index (VIX). Option prices may provide a treasure chest of information that has not yet been fully exploited by the finance community.
How Did the Authors Conduct This Research?
The authors use daily S&P 500 options with 30-day maturities (1996 through 2007) to extract risk-neutral market measures of volatility, skewness, and kurtosis without the aid of a particular option pricing model. Because of very high correlation with the VIX, they use the VIX (a more tractable measure) instead of the original implied market volatility data. Furthermore, because of high correlation between skewness and kurtosis (i.e., if skewness exists, then kurtosis exists), they regress the market kurtosis measure against the market skewness measure to generate residual errors. These residual errors (i.e., the variations in market kurtosis that are not captured by variations in market skewness) are then used instead of the original market kurtosis data.
To determine the effect of these market measures on individual equity returns (all stocks available in CRSP), the authors follow a two-step procedure. First, they regress a security’s daily return in excess of the risk-free return over a 30-day period against the market premium with either (1) the change in a market measure of volatility, skewness, or kurtosis individually or (2) all three market measures simultaneously. Based on the magnitude of the coefficient for a particular market measure (regressed alone or with the other two measures present), the equities are sorted into quintiles (Quintile 1 being the lowest exposure).
Second, they create a value-weighted portfolio for each quintile and then generate each portfolio’s return for the following 30 days (called “post-ranking returns”). To measure portfolio alphas, the authors regress each portfolio’s post-ranking returns (and a portfolio that is long Quintile 5 and short Quintile 1) against previously noted risk factors (excess market return, size, book-to-market, and momentum). This procedure is also performed using longer time periods for the first step.
The authors find that market skewness appears to be a robustly priced risk factor. Market volatility appears to have some risk factor elements but is not very robust. Market kurtosis does not appear to be a significant risk factor. Finally, they use the portfolios to build a time series of risk factor measures for innovations in market volatility, market skewness, and market kurtosis. Again, market skewness appears to be a very robust risk factor when analyzed with other noted risk factors.
Skewness has been suspected for some time as being an important dimension of risk, but it has never been exposed as a risk factor in this manner. Furthermore, the method of implying information from option prices is intriguing. Because of option pricing model complexity, I think the industry has been too timid to fully exploit the information contained in option prices.