Low-volatility anomaly

The low-volatility anomaly is the observation that low-volatility stocks have higher returns than high-volatility stocks in most markets studied. This is an example of a stock market anomaly since it contradicts the central prediction of financial theory. The Capital Asset Pricing Model (CAPM) predicts a positive relation between risk and return. The low-volatility anomaly falsifies the CAPM and other risk-based asset pricing models. It is also referred to as the low-beta, minimum-variance, minimum volatility anomaly. The CAPM was developed in the late 1960s and predicts that return should be a positive and linear function of beta, and nothing else. First, the return of a stock with average beta should be the average return of stocks. Second, the intercept should be equal to the risk-free rate. Then the slope can be computed from these two points. Almost immediately these predictions were empirically challenged. Studies find that the correct slope is either less than predicted, not significantly different from zero, or even negative. Black (1972) proposed a theory where there is a zero-beta return which is different from the risk-free return. This fits the data better since the zero-beta return is different from the risk-free return. It still presumes, on principle, that there is higher return for higher beta. Research challenging CAPM's underlying assumptions about risk has been mounting for decades. One challenge was in 1972, when Jensen, Black and Scholes published a study showing what CAPM would look like if one could not borrow at a risk-free rate. Their results indicated that the relationship between beta and realized return was flatter than predicted by CAPM.Shortly after, Robert Haugen and James Heins produced a working paper titled “On the Evidence Supporting the Existence of Risk Premiums in the Capital Market”. Studying the period from 1926 to 1971, they concluded that 'over the long run stock portfolios with lesser variance in monthly returns have experienced greater average returns than their ‘riskier’ counterparts'. The low-volatility anomaly has been documented in the United States over an extended 90-year period. Volatility-sorted portfolios containing deep historical evidence since 1929 are available in an online data library The picture contains portfolio data for US stocks sorted on past volatility and grouped into ten portfolios. The portfolio of stocks with the lowest volatility has a higher return compared to the portfolio of stocks with the highest volatility. A visual illustration of the anomaly, since the relation between risk and return should be positive. Data for the related low-beta anomaly is also online available. The evidence of the anomaly has been mounting due to numerous studies by both academics and practitioners which confirm the presence of the anomaly throughout the forty years since its initial discovery in the early 1970s. Examples include Baker and Haugen ( 1991),Chan, Karceski and Lakonishok (1999), Jangannathan and Ma (2003), Clarke De Silva and Thorley, (2006) and Baker, Bradley and Wurgler (2011). Besides evidence for the US stock market, there is also evidence for international stock markets. For global equity markets, Blitz and van Vliet (2007), Nielsen and Aylursubramanian (2008), Carvalho, Xiao, Moulin (2011), Blitz, Pang, van Vliet (2012), Baker and Haugen (2012), all find similar results.