Risk and the Volatility Anomaly

Is the long-term volatility anomaly a function of risk measure choice? Using such symmetric risk measures as beta and variance, the volatility anomaly is apparent in the United States and 21 other global equity markets. This study finds less support for the volatility anomaly when symmetric risk measures are replaced with their asymmetric risk counterparts: relative variance (negative semivariance minus variance) and relative beta (downside beta minus beta). When relative variance is the sorting variable, the expected positive risk–return relationship is restored. Strategies of buying low-variance or low-beta stocks and shorting high-variance or high-beta stocks generate positive monthly risk-adjusted returns in nearly one-third of the sample. These results reverse or disappear, however, when relative variance or relative beta are the sorting variables. Portfolio matching shows that portfolios sorted on variance versus relative variance are truly different portfolios, and the same result holds true for portfolios sorted on beta versus relative beta.