Range-based volatility, expected stock returns, and the low volatility anomaly

One of the foundations of financial economics is the idea that rational investors will discount stocks with more risk (volatility), which will result in a positive relation between risk and future returns. However, the empirical evidence is mixed when determining how volatility is related to future returns. In this paper, we examine this relation using a range-based measure of volatility, which is shown to be theoretically, numerically, and empirically superior to other measures of volatility. In a variety of tests, we find that range-based volatility is negatively associated with expected stock returns. These results are robust to time-series multifactor models as well as cross-sectional tests. Our findings contribute to the debate about the direction of the relationship between risk and return and confirm the presence of the low volatility anomaly, or the anomalous finding that low volatility stocks outperform high volatility stocks. In other tests, we find that the lower returns associated with range-based volatility are driven by stocks with lottery-like characteristics.