Tail risk, beta anomaly, and demand for lottery: what explains cross-sectional variations in equity returns?

This study investigates the tail-risk and returns relationship in an emerging equity market—India. We observe both the beta and the tail risk anomalies at the univariate portfolio level. However, after controlling for the lottery effects (MAX and idiosyncratic volatility), the relationship between the systematic tail risk measures and the expected returns turns positive for some of the proxies of tail risk, while the relationship between beta and expected returns becomes flat. The lottery effect explains the tail risk anomaly reported in the literate. These results suggest that investors care for probabilities of extreme changes in stock prices but do not care much about moderate variations in stock returns. Emerging markets have a significant presence of individual investors, who consider investing in the stock market as an opportunity to gamble and earn lottery-like payoffs, which results in an overvaluation of lottery stocks. Since these stocks also have high systematic risk and a high probability of extreme negative returns, we observe that the expected returns are negatively correlated with beta and left tail risk measures before controlling for the lottery effects. These results are robust after controlling for other relevant variables such as the size of the firm, book-to-market ratio, momentum, retail ownership, and illiquidity.