Benchmarks as Limits to Arbitrage: Understanding the Low Volatility Anomaly

Abstract

Over the past 41 years, high volatility and high beta stocks have substantially underperformed low volatility and low beta stocks in U.S. markets. We propose an explanation that combines the average investor's preference for risk and the typical institutional investor’s mandate to maximize the ratio of excess returns and tracking error relative to a fixed benchmark (the information ratio) without resorting to leverage. Models of delegated asset management show that such mandates discourage arbitrage activity in both high alpha, low beta stocks and low alpha, high beta stocks. This explanation is consistent with several aspects of the low volatility anomaly including why it has strengthened in recent years even as institutional investors have become more dominant.