One of the biggest problems facing 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. Empirical studies have found that the actual relationship is flat, or even negative.
But the superior performance of low-volatility stocks was documented in the literature as far back as the 1970s—by Fischer Black, among others—even before the size and value premiums were officially “discovered.” The low-volatility anomaly has been shown to exist in equity markets around the globe. What’s interesting is that this finding is true not only for stocks, but for bonds as well.
When examining this anomaly, Robert Novy-Marx—in his September 2014 paper, “Understanding Defensive Equity,” which covered the period from 1968 through 2013—found that when ranking stocks in quintiles, either by volatility or beta, the highest-quintile stocks dramatically underperform, while the performance of the remaining four quintiles are very similar and marketlike.
Explaining The Anomaly
David Blitz, Eric Falkenstein and Pim van Vliet—authors of “Explanations for the Volatility Effect,” which appears in the Spring 2014 issue of The Journal of Portfolio Management—provided a broad overview of the literature that addresses the explanations for this volatility effect.
The authors begin by explaining that an empirical failure of the CAPM must be attributable to a violation of one or more of the model’s underlying assumptions. While models can help us understand how markets work and set prices, by definition they’re flawed or wrong. Otherwise they would be called laws, as we have in physics.
One of the assumptions of the CAPM is that there are no constraints on leverage and short-selling. In the real world, many investors actually are either constrained against the use of leverage (by their charters) or have an aversion to its use.
And the research has shown that as leverage constraints tighten, market betas get compressed to 1. Limits to arbitrage (constraints) and an aversion to shorting, as well as the high cost of shorting such stocks, can prevent arbitrageurs from correcting the pricing mistake.
Another assumption of 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. And the evidence shows the stocks that are most mispriced are the ones with the highest shorting costs.
The explanation for the low-volatility anomaly, then, is that 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 anomaly behind a flat or even inverted relationship between risk and expected return relative to the predictions of the CAPM model.
The Impact Of Constraints
Regulatory constraints can also cause the anomaly. As the authors explain, “Regulators typically do not distinguish between different types of stocks, but merely consider the total amount invested in stocks for determining required solvency buffers. Examples are the standard models in the Basel II and III frameworks (which set a fixed capital charge of 23.2 percent for equity holdings), Solvency II (which sets a fixed capital charge of 32 percent for equity holdings) and the FTK for pension funds in the Netherlands (which prescribes a fixed capital buffer of 25 percent for equity holdings). Investors who wish to maximize their equity exposure but minimize the associated capital charge under such regulations are drawn to the high volatility segment of the equity market, as this effectively gives [the] most equity exposure per unit of capital charge.”
The academic literature has long posited that constraints on short-selling can cause stocks to be overpriced. The authors go on to explain why high-risk stocks can indeed become overpriced: “In a market with little or no short selling, the demand for a particular security will come from the minority who hold the most optimistic expectations about it. This phenomenon is also referred to as the winner’s curse. As divergence of opinion is likely to increase with risk, high-risk stocks are more likely to be overpriced than low-risk stocks, because their owners will have the greatest bias.”
The Human Factor
Another assumption under the CAPM is that investors are risk-averse, maximize the expected utility of absolute wealth, and care only about the mean and variance of return.
But we know that assumption doesn’t hold. In the real world, there are investors who have a “taste,” or preference, for lotterylike investments—investments that exhibit positive skewness and excess kurtosis. This leads such investors to “irrationally” invest in high-volatility stocks (which have lotterylike distributions) despite the poor returns.