This paper develops a general equilibrium model and provides empirical support that the market volatility-of-volatility (VOV) predicts market returns and drives the time-varying volatility risk. In asset pricing tests with the market, volatility, and VOV as factors, the risk premium on VOV is statistically and economically significant and robust. Market and volatility risks are not priced in unconditional models, but, consistent with theory, their factor loadings, conditional on VOV, are priced. The pricing impact of VOV strengthens during market crashes, suggesting that VOV is particularly relevant during market turmoil, when investors demand increased compensation for VOV risk.

We propose a latent-variables approach to recover extrapolative beliefs from asset prices. We estimate a present-value model of the price–dividend ratio of the market that embeds both return extrapolation and cash-flow extrapolation, alongside discount rates and rational expectations of dividend growth. This approach allows us to measure extrapolation bias without having to rely on survey data, and it inherently guarantees that the researcher focuses on a set of beliefs that matter for price formation. We show that extrapolative beliefs extracted from prices are highly correlated with surveys and that survey-based and price-based extrapolative beliefs share similar predictive properties for future returns, with the former improving upon the latter.