5. The Low-Volatility Anomaly

A direct relationship between risk and return—in the sense that return should vary positively and proportionately to volatility—is so essential that this should be designated as the first law of finance. Investors otherwise would never be induced to commit capital to risky assets. In reality, low-volatility stocks offer abnormally high returns relative to their riskier counterparts. By undermining conventional assumptions about the relationship between risk and return, the low-volatility anomaly arguably represents the most significant challenge to mathematical finance. The value premium in the Fama and French’s three-factor model is arguably a special case of the low-volatility premium, attributable to the costly reversibility of physical investments and human capital during recessions and economic downturns. The literature of strategic management has identified a similar effect, called Bowman’s paradox. That discipline identifies managerial culture, especially corporate and social responsibility, as a possible explanation for abnormal returns on low-volatility stocks.