Is the Relation between Volatility and Expected Stock Returns Positive, Flat or Negative?

Theoretical models, such as the CAPM, predict a positive relation between risk and return, but the empirical evidence paints a mixed picture. Positive, flat and negative relations have been reported in various empirical studies. In this paper we reconcile these seemingly conflicting results by showing how methodological choices can lead to different, or even opposite conclusions. In our 1963-2009 U.S. sample we find that the empirical relation between historical volatility and expected returns is negative, with an average quintile return spread of -3.7%.The relation becomes 2% less negative when small caps are excluded, but 3% more negative when compounding effects are taken into account. We also argue that the positive relation between volatility and expected return reported by some studies can be attributed to various kinds of look-ahead bias. Our results provide an empirical basis for low-volatility and minimum-variance investment approaches