As I have discussed before, one of the major problems for the first formal asset pricing model developed by financial economists, the capital asset pricing model (CAPM), was that it predicts a positive relation between risk and return. But empirical studies have found the actual relation to be flat, or even negative.

Over the past five decades, the most “defensive” stocks have furnished 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.

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Low-Volatility Strategies

The superior performance of low-volatility stocks (as well as closely related low-beta stocks) 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 around the globe, not only for stocks, but for bonds. In other words, it has been pervasive.

One of the CAPM’s assumptions is that there are no constraints on either leverage or short-selling. In reality, however, 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.

[drizzle]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. 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.

Supporting studies

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 wrote in their paper that when using their five-factor model, the “returns of low volatility stocks behaved 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.

David Blitz and Milan Vidojevic contributed to the literature on the low-volatility anomaly with their July 2016 paper, “The Profitability of Low Volatility,” which covers the period July 1963 through December 2015.

While they did not question the empirical results of the Fama and French and Novy-Marx papers, the authors do argue that direct evidence of a linear, positive relationship between market beta and returns, which is assumed in the aforementioned models, is still lacking.

They wrote: “We are unable to construct high-beta portfolios with high returns and low-beta portfolios with low returns by controlling for factors such as profitability, while it should be possible to do so if the low-beta anomaly is fully explained by such factors.”

They also found “more pronounced mispricing for volatility than for beta. This suggests that the low-volatility anomaly is stronger than the low-beta anomaly, and, given that the two are closely related, that the low-volatility anomaly is the dominant phenomenon.”

Blitz and Vidojevic noted that they did include momentum as one of the control factors in their analyses because it is widely recognized as an important driver of stock returns in the cross section of returns.

In addition, they found that the results held across all size groups. The authors concluded that “exposure to market beta in the cross-section is not rewarded with significantly higher returns, regardless of whether one controls for the additional factors proposed by Fama and French.”

They then go on to add: “These results imply that the relation between risk and return in the cross-section is flat instead of positive. We also find that the mispricing is even more pronounced for volatility than for beta.”

Finally, Blitz and Vidojevic end with the following caveat: “The results in this paper represent just one attempt at obtaining a positive risk-return relation by controlling for the factors that supposedly explain the low-risk anomaly. The fact that this attempt is unsuccessful does not rule out that portfolios constructed in a different manner do exhibit a clear positive risk-return relation consistent with the predictions of the Fama and French and Novy-Marx models. For instance, the market betas or factor exposures used in this paper might not be appropriate, and it is possible that a different methodology would lead to different conclusions. But as long as the data indicates that portfolios with higher risk do not generate higher returns, it is premature to conclude that the low-risk anomaly has been resolved.”

Before you draw any conclusions, however, let’s look at some of the other evidence.

By Larry Swedroe, read the full article here.