A Continuous Return Model for the Low-Volatility and
Low-Beta Anomalies

Abstract

This study shows that a “rational,” capital asset pricing model (CAPM) type of positive relationship between short-horizon expected arithmetic return and risk can lead to a negative long-horizon relationship between compound annual return and risk (whether risk is measured by volatility or beta). This result follows from the stochastic portfolio theory relationship that a stock’s growth rate is less than its expected arithmetic return by approximately one-half its variance of return. The negative long-horizon relationships between return mean and volatility/beta often have been noted and characterized as the low-volatility and low-beta anomalies. Thus, these characterizations may be problematic.