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 that firms use stock splits as a means of attracting attention and inducing information production to correct price distortion caused by investors’ 52-week high anchoring bias. Our analysis shows that firms are more likely to split stocks when their prices are near 52-week highs, especially if they are highly profitable and undervalued. After splits, undervaluation gradually disappears. Moreover, these splits are associated with a slower market reaction and a more positive post-split drift, consistent with the notion that investors’ anchoring bias hinders price adjustment, leading to a gradual price correction. In addition, the likelihood of such splits increases with CEO wealth-performance sensitivity, and investment-price sensitivity increases following splits. Our evidence suggests that firms utilize stock splits to correct mispricing induced by investors’ 52-week high anchoring bias.

We hypothesize that managers use stock splits to attract more uninformed trading so that market makers can provide liquidity services at lower costs, thereby increasing investors’ trading propensity and improving liquidity. We examine a large sample of stock splits and find that, consistent with our hypothesis, the incidence of no trading decreases and liquidity risk is lower following splits, implying a decline in latent trading costs and a reduced cost of equity capital. Further, split announcement returns are correlated with the improvements in both liquidity levels and liquidity risk. Our analysis suggests nontrivial economic benefits from liquidity improvements, with less liquid firms benefiting more from stock splits.

We hypothesize that high stock price levels impede informed trading on the stocks and reduce price informativeness. This is because uninformed trading is needed to facilitate informed trading, and high stock prices may impose budget constraints on uninformed investors. Indeed, we find, for high-price firms, (i) options to stock trading volume (O/S), an informed trading measure in options market, is higher, (ii) price informativeness about future earnings is lower, and (iii) investment sensitivity to price is lower. We also find these patterns reverse after stock splits, suggesting that firms can use splits to improve informed trading and enhance price informativeness.