One of the significant problems for the first formal asset pricing model developed by financial economists, the capital asset pricing model (CAPM), was that it predicts a positive relationship between risk and return. However, empirical studies have found the actual relationship to be flat, or even negative.
Over the past five decades, the most “defensive” stocks have delivered higher returns than the most “aggressive” stocks. In addition, defensive strategies (at least those based on volatility) have delivered significant Fama-French three-factor and four-factor alphas.
The superior performance of low-volatility stocks (as well as low-beta stocks, which are closely related) was initially documented in the academic literature in the 1970s, before even the size and value premiums were “discovered.” The low-volatility anomaly has been found to exist in equity markets across the globe, and not only for stocks but for bonds. In other words, it has been pervasive.
CAPM & Its Assumptions
One of the CAPM’s assumptions is that there are no constraints on either leverage or short-selling. In reality, though, many investors are constrained against employing leverage (by their charters) or have an aversion to its use.
The same is true of short-selling, and the borrowing costs for some hard-to-borrow stocks can be high. Such limits to arbitrage 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 seeking to increase their returns elect to tilt their portfolios toward high-beta securities to garner more of the equity risk premium.
High & Low Demand
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 CAPM’s predictions.
Some recent papers (Robert Novy-Marx’s 2016 study, “Understanding Defensive Equity,” and Eugene Fama and Kenneth French’s 2015 study, “Dissecting Anomalies with a Five-Factor Model”) argue that the low-volatility and low-beta anomalies are well-explained by asset pricing models that include the newer factors of profitability and investment (in addition to market beta, size and value).
For example, Fama and French write in their paper that when using their five-factor model, the “returns of low volatility stocks behave like those of firms that are profitable but conservative in terms of investment, whereas the returns of high volatility stocks behave like those of firms that are relatively unprofitable but nevertheless invest aggressively.”
They add that positive exposure to RMW (the profitability factor, or robust minus weak) and CMA (the investment factor, or conservative minus aggressive) also go a long way toward capturing the average returns of low-volatility stocks whether volatility is measured by total returns or residuals from the Fama-French three-factor model.