Volatility Estimated Based on the Holding-Period Return versus the Logarithmic Return: Their Difference Can Make a Difference

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.