Two Stochastic Portfolio Theory Models of a Low Beta Anomaly

The finance literature has established that portfolios of low beta stocks have higher growth rates (long-term return rates) than portfolios of high beta stocks. The literature largely concludes from this that low beta stocks have higher growth rates than high beta stocks and that investors are irrational. This paper presents two Stochastic Portfolio Theory models of a Low Beta Anomaly that do not require irrational investor behavior and do not require that low beta stocks have higher growth rates than high beta stocks. Both models imply a Low Beta Anomaly that is due to reconstitution relative volatility capture. One of the models implies outperformance of portfolios of low beta stocks for all benchmarks used to define stocks’ betas. The other implies outperformance or underperformance of portfolios of low beta stocks according to whether the benchmark is such that the equal weight portfolio’s beta is less than or greater than 1.