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. However, empirical studies have found the actual relationship to be flat, or even negative. Over the last 50 years, the most “defensive” stocks have delivered higher returns than the most “aggressive” stocks.
Additionally, defensive strategies, at least those based on volatility, have delivered significant Fama-French three-factor (beta, size and value) and Carhart four-factor (adding momentum) alphas.
The superior performance of low-volatility stocks was first documented in the literature back in the 1970s—by Fischer Black in 1972 among others—before the size and value premiums were “discovered.” The low-volatility anomaly has been demonstrated to exist in equity markets around the globe. What’s interesting is that this finding holds true not only for stocks but for bonds as well. In other words, it has been pervasive.
Explaining The Low-Volatility Advantage
One of the assumptions of the CAPM is that there are no constraints on either leverage or short-selling. But in the real world, many investors are constrained against the use of leverage (by their charters) or have an aversion to its use. The same is true of short-selling, and the borrowing costs for some difficult-to-borrow stocks can be quite high. Such limits to arbitrage, combined with an aversion to shorting and the high costs of shorting certain stocks, can prevent arbitrageurs from correcting the pricing mistake.
Another assumption made by the 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 the ones with the highest costs of shorting.
The explanation for the low-volatility anomaly, then, is that, faced with constraints and frictions, investors looking to increase their return choose to tilt their portfolios toward high-beta securities to capture more of the equity risk premium. This extra demand for high-beta securities, and reduced demand for low-beta securities, may explain the anomaly of a flat or even inverted relationship between risk and expected return relative to the predictions of the CAPM.
