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.
In other words, they pay a premium to gamble. Among the stocks that fall into this category of “lottery tickets” are IPOs; small growth stocks that aren’t profitable; penny stocks; and stocks in bankruptcy. Limits to arbitrage and the costs or fear of shorting prevent rational investors from correcting the mispricings.
The CAPM also assumes that investors maximize the expected utility of their own personal wealth. Yet research shows that individuals care more about relative wealth. For example, the authors cite a study which found that an “overwhelming majority of people would rather earn $100k when others earn $90k, than $110k when others earn $200k, i.e. people prefer the higher relative, lower absolute wealth option.”
They note that the presence of both absolute- and relative-return-oriented investors implies a partial flattening of the security market line. The degree of flattening depends on the number of relative-return investors versus the number of absolute-return investors.
The CAPM also assumes that agents will maximize option values. But this may not always hold in the real world. For example, “portfolio managers are typically paid a base salary, on top of which they receive a bonus if performance is sufficiently high.”
This compensation arrangement “resembles a call option on the portfolio return, the value of which can be increased by creating a more volatile portfolio. In other words, there is a conflict of interest between professional investors, who have an incentive to engage in risk-seeking behavior, and their clients, who are more likely to be risk-averse as assumed by the CAPM.”
The authors explain that the optionality argument can be taken one step further “by arguing that the rewards to being recognized as a top manager are much larger than the rewards for, say, second quintile managers. For example, top managers receive a disproportionate share of attention from outside investors, such as making it to the front cover of Bloomberg magazine. In order to become a top investment manager one needs to generate an extreme, outsized return. This has the additional benefit of signaling to potential future investors and employers that one is truly skilled, as it is virtually impossible to distinguish between skill and luck in case of a modest outperformance. Delegated portfolio managers focused on realizing an extreme return in the short run may be willing to accept a lower long-term expected return on the high-risk stocks which enable such returns.”
Assumptions Of Rationality
The CAPM also assumes that investors have complete information, and that they rationally process the available information. But we know this also isn’t always the case in the real world. The research documents that mutual funds and individual investors tend to hold firms appearing more frequently in the news. They buy attention-grabbing stocks that experience high abnormal trading volume, as well as stocks with extreme recent returns.
The idea is that attention-driven buying may result from the difficulty investors have researching the thousands of stocks they could potentially buy. Such purchases can temporarily inflate a stock’s price, leading to poor subsequent returns. Attention-grabbing stocks are typically high-volatility stocks, while boring low-volatility stocks suffer from investor neglect. The attention-grabbing phenomenon is therefore another argument supporting the existence of the volatility effect.
The research also shows that investors (including active fund managers) are overconfident, another violation of the CAPM’s assumption of rational information processing.
The impact on the volatility effect is that, if an active manager is skilled, it makes sense for that manager to be particularly active in the high-volatility segment of markets, because that segment offers the largest rewards to skill. However, this results in excess demand for high-volatility stocks.
An Anomaly With Legs?
As you can see, the academic literature is filled with a large number of possible explanations. What does seem clear is that many of the explanations come from either constraints or agency issues that drive managers toward higher-volatility stocks.
Given that there doesn’t seem to be anything on the horizon that would have an impact on these issues, it seems likely that the anomaly can persist. In addition, human nature doesn’t change easily. Thus, there doesn’t appear to be any reason to believe that investors will abandon their preference for “lottery tickets.” And the limits to arbitrage, and fear and costs of margin, make it difficult for arbitrageurs to correct mispricings.
Finally, it’s important to remember that the anomaly is much more about the underperformance of high-volatility (or high-beta) stocks, and not so much about the outperformance of low-volatility (or low-beta) stocks. Because of this, one way to take advantage of the anomaly is simply to avoid high-volatility/high-beta stocks or invest in funds that screen them out.
Larry Swedroe is the director of research for the BAM Alliance, a community of more than 150 independent registered investment advisors throughout the country.