Volatility-of-Volatility Risk in Asset Pricing

Recent studies have shown that adding a volatility process to stock market volatility helps extract useful information. We extend this literature by developing an asset pricing model in which market risk, market volatility risk, and market volatility-of-volatility (VOV) risk determine the cross-sectional asset prices. Using high-frequency S&P 500 index option data to estimate a time series of the variance of market variance, we find that the VOV risk is particularly significant during large market downturns, and largely subsumes the valuation effect of volatility risk documented in previous studies. In particular, defensive stocks (whose returns co-vary less negatively with the VOV) have lower expected future returns while crash-prone stocks (whose returns co-move more negatively with the VOV) have higher expected future returns. A hedge portfolio long in crash-prone stocks and short in defensive stocks yields a significant average annual return of 10.5 percent. In sum, our model and test results suggest that VOV risk is a significant pricing factor for individual stocks and that VOV risk captures investors’ fear of market crash.