The low volatility anomaly is an intriguing unexplained anomaly in the finance literature which questions a fundamental aspect of financial theory. The anomaly, built on work done by Ang et. al (2006) claims that stocks with the lowest volatility have the highest returns and stocks with the highest volatility have the lowest returns.
This completely contradicts conventional finance theory in that the main proxy for "risk" in financial markets is volatility. So these results suggest that stocks with lower "risk" are earning a higher return than stocks with higher levels of "risk."
In other words, while financial theory suggests a positive relationship between risk and return, the low volatility anomaly indicates the opposite. A direct implication of this anomaly is that investing in low volatility stocks and shorting high volatility stocks may produce large risk-adjusted returns.
To understand the volatility anomaly, it is important that investors understand what financial economists have learned about the factors that are responsible for stock returns. Prior to the 1990s, stock returns were thought to be due to a stock's beta – the correlation between a stock and the broader market.
Today, it is well accepted that stock returns cannot be explained by beta alone.
Fama and French (1992, 1993) show that other factors like size and market-to-book ratio explain the cross-section of stock returns better than beta. Jegadeesh and Titman (1993) find that a stock's return is also driven by its momentum, or the amount of price appreciation a stock has experienced in the last 12 months compared to its peers.Jegadeesh and Titman (2001) claim that momentum is generated by delayed overreactions in the market.
The volatility anomaly builds on past factors in stock returns showing that the stocks that perform the best are actually the least risky as well. That's like telling an investor "you can have your cake and eat it too!"
The original study in this area from Ang, Hodrick, Xing, and Zhang (2006) found that "size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility."
The most common method of determining a firm's idiosyncratic volatility is described in Ang, Hodrick, Xing, and Xhang (2009).They calculate idiosyncratic volatility for a stock as the standard deviation of the residuals from regressing a firm's daily returns over the past month on the three Fama and French (1993) factors and a momentum factor. Consistent with Miller (1977), firms with high idiosyncratic volatility have lower returns. Even if you are cautious about higher returns from the volatility anomaly, the strategy is still useful, though.
For instance, the volatility anomaly can be used as a risk reduction tool to give investors a market rate of return with less risk. This strategy can be especially effective if one is pursuing a factor based investment strategy that results in higher betas – by adding in a low beta component, the portfolio's overall beta falls, potentially, without sacrificing market return.
So why does the volatility anomaly work?
Hou and Loh (2016) simultaneously test many explanations and find that lottery preferences, short-term return reversals, and earnings shocks together explain 60 to 80% of the negative relationship between returns and idiosyncratic volatility. Lottery preference alone can explain 48 to 67% of the relationship.
