Two Essays on the Low Volatility Anomaly

I find the low volatility anomaly is present in all but the smallest of stocks. Portfolios can be formed on either total or idiosyncratic volatility to take advantage of this anomaly, but I show measures of idiosyncratic volatility are key. Standard risk-adjusted returns suggest that there is no low volatility anomaly from 1996 through 2011, but I find this result arises from model misspecification. Caution must be taken when analyzing high volatility stocks because their returns have a nonlinear relationship with momentum during market bubbles. I then find that mutual funds with low return volatility in the prior year outperform those with high return volatility by about 5.4% during the next year. After controlling for heterogeneity in fund characteristics, I show that a one standard deviation decrease in fund volatility in the prior year predicts an increase in alpha of about 2.5% in the following year. My evidence suggests that this difference in performance is not due to manager skill but is instead caused by the low volatility anomaly. I find no difference in performance or skill between low and high volatility mutual funds after accounting for the returns on low and high volatility stocks