Stochastic Portfolio Theory and the Low Beta Anomaly

Abstract

Many studies have found that portfolios of low beta stocks have higher growth rates than portfolios of high beta stocks and have concluded that low beta stocks have higher growth rates than high beta stocks. Since rational investor behavior is thought to imply that additional risk is rewarded with additional return, the alleged higher growth rates of low beta versus high beta stocks has been termed a “Low Beta Anomaly” (LBA). However, it is premature to conclude that these observed LBAs are due to stocks’ differential growth rates, because the tested portfolios are traded. Stochastic Portfolio Theory (SPT) shows that traded portfolios’ growth rates can exceed the growth rates of their stocks. This paper presents several SPT models of an LBA that do not require investment constraints, irrational investor behavior, or that low beta stocks have higher growth rates than high beta stocks. These LBAs are due to reconstitution relative volatility capture that favors portfolios of low vs. high beta stocks. They result from trading profit, not differential growth rates between low and high beta stocks. Monte Carlo simulations demonstrate a reconstitution relative volatility capture Low Beta Anomaly that is consistent with the models and the literature.