In this article, the authors propose a variance-dependent explanation for the contradiction between skewness preference and low expected return concerning lottery stocks. They emphasize an overlooked aspect of skewness as a risk measure: the return uncertainty of extreme events. They show that, during periods of low market volatility, investors dislike large-skewness securities owing to a fear of uncertain results. Thus, one observes a positive relation between skewness and expected return because the security is currently undervalued. Conversely, negative associations occur in high-volatility environments. This conditional skewness–return nexus is demonstrated to possess return predictability and can help in adjusting portfolios with profitable buying and selling decisions. Key Findings ▪ The authors propose variance-dependent skewness to reconcile the skewness preference for lottery stocks with their actual low expected returns. ▪ They emphasize skewness as a risk measure of the return uncertainty of extreme events. ▪ The authors construct portfolios based on the return predictability of skewness conditional on volatility and show that these portfolios remain profitable after considering transaction costs and restrictions on short sales.

This paper analyses the correlations between returns and HVs in the short and long terms while developing a risk measure designed to contain the impacts of

Estimation of true volatility is a crucial part of equity investment, and there are many strategies for realizing this objective (e.g., the Parkinson realized volatility, the GARCH projected volatility, and stochastic implied volatility). Instead of treating volatility estimates as alternatives to one another, a recent series of studies has emphasized the return prediction performances of their paired differences, such as the variance risk premium, which subtracts the implied variance from the realized variance under a nonparametric framework. This article proposes a novel method of differencing variances that are computed on the basis of the holding-period return versus the logarithmic return. Via this approach, the authors provide a satisfactory substitute for the variance risk premium in cases in which its requirements for intraday and options data are not satisfied. They argue that the volatility differences can capture the information contained in logarithmic returns that involve continuous transactions. This argument is supported by follow-up empirical results—the proxy is demonstrated to be able to foreshadow the next-month market return and to perform well in adjusting holdings in long–short portfolio construction strategies. TOPICS:Volatility measures, exchanges/markets/clearinghouses, risk management Key Findings • The authors build a variance difference measure that is based on the holding-period versus logarithmic return for capturing information obtained from continuous trading activities. • This measure retains the return predictability of differencing volatility estimates, thereby providing a satisfactory alternative to the variance risk premium when its stringent data requirements cannot be satisfied. • The long–short portfolio strategies that are developed according to their variance difference are shown to outperform the market index, especially during market downtrend periods.