One of the problems for the first formal asset pricing model developed by financial economists, the Capital Asset Pricing Model (CAPM), was that it predicted a positive relationship between risk and return. But empirical studies have found the actual relationship to be flat, or even negative.

Only adding to the issues that can arise with CAPM is that, over the last five decades, the most “defensive” (low-volatility, low-risk) stocks have delivered higher risk-adjusted returns than the most “aggressive” (high-volatility, high-risk) stocks. In addition, defensive strategies, at least the ones based on volatility, have delivered significant Fama-French three-factor and four-factor alphas.

The superior performance of low-volatility stocks was first documented in the literature in the 1970s, by Fischer Black (in 1972) among others, before the size and value premiums were “discovered.” The low-volatility anomaly has been shown to exist in equity markets around the globe. Interestingly, this finding holds true not only for stocks, but for bonds as well. In other words, it has been pervasive.

One of CAPM’s assumptions is that there are no constraints on either leverage or short selling. In the real world, many investors are, in fact, constrained against the use of leverage (through their charters) or have an aversion to its use. The same is true of short selling. Plus, the borrowing costs for certain difficult-to-borrow stocks may be quite high. Such limits can prevent arbitrageurs from correcting the pricing mistake. Another assumption made by CAPM is that markets have no frictions, meaning there are neither transaction costs nor taxes. Of course, in the real world, there are costs. The evidence shows that the most mispriced stocks are those with the highest costs of shorting.

The explanation for the low-volatility anomaly is that when faced with constraints and frictions, investors looking to increase their returns choose to tilt their portfolios toward high-beta securities to garner more of the equity risk premium. This extra demand for high-beta securities, and reduced demand for low-beta securities, may explain the flat or even inverted relationship between risk and expected return relative to the predictions of CAPM.

More recent research on the low-volatility anomaly has found that once profitability is included as a factor, low-volatility performance is well explained by controlling for the common investment factors of size, value and profitability. In addition, research has also found that low-volatility strategies have exposure to term risk (the duration factor). This should not be a surprise because, generally speaking, low-volatility (or low-beta) stocks are more “bond like.” They are typically large stocks, the stocks of profitable and dividend-paying firms, and the stocks of firms with mediocre growth opportunities. In other words, they are stocks with the characteristics of safety, as opposed to risk and opportunity. Thus, they show higher correlations with long-term bond returns.

Joost Driessen, Ivo Kuiper and Robbert Beilo contribute to the literature with their 2016 study, Does Interest Rate Exposure Explain the Low Volatility Anomaly? Their study covered the period from July 1963 through December 2014. They found that low-volatility portfolios do have a strong exposure to interest rate risk. The following is a summary of their findings:

• The duration of the lowest-volatility decile corresponds to a 30 percent weight to bonds.
• The duration of the highest-volatility decile corresponds to a position of 100 percent short bonds.
• Term risk helps explain the low-volatility anomaly.
• Depending on the methods chosen, term exposure explains between 19 percent and 99 percent of the monthly return difference between the lowest-volatility and the highest-volatility deciles.
• Interestingly, they found that exposure of low-volatility stocks to term risk varied over time. In the 1970s, low-volatility stocks were no different in their exposure to term risk than high-volatility stocks. However, beginning in the mid-1980s, the exposure to term risk began to increase and has since remained high.
• Their basic conclusions were not altered when different bond maturities were used for the term factor.

The literature now contains a number of studies showing that low-volatility stocks contain term risk. In contrast to the rest of the literature on the anomaly, term risk exposure provides a rational explanation for the superior performance of low-volatility stocks, as they have benefited from a more than 30-year secular decline in interest rates. Given this knowledge, mutual fund investors in low-volatility strategies should be sure to take their bond exposure into account when considering the overall risks of their portfolio.