Swedroe: Why Some Anomalies Persist

September 15, 2014

The reasons some investment anomalies have staying power are varied and surprising.

The academic literature is filled with challenges to the efficient markets hypothesis. Perhaps the greatest among these challenges involves the existence of momentum and the poor performance of small-growth stocks and high-beta stocks.

Beta is defined as the measure of the systematic risk of a security or a portfolio in comparison to the market as a whole. It’s highly correlated with another measure of risk—volatility.

Among the behavioral explanations for these two anomalies are that investors aren’t perfectly rational, that they don’t learn or change their behavior, and that there are some with a preference for assets with lotterylike distributions.

Assets with lotterylike distributions are those that exhibit positive skewness. That means most of the returns are distributed to the left of the mean, and also that the returns to the right are much further from it. These challenges exist because, even after the discovery of the anomaly becomes well known, they continue to persist.

Academic research has tried in various ways to explain why these anomalies can continue to survive. Among the possible explanations is that there’s a limit to arbitrage, which prevents rational investors from exploiting the anomaly. For example:

  • Many institutional investors (such as pension plans, endowments and mutual funds) are prohibited by their charters from taking short positions.
  • Shorting can be expensive. Investors doing so have to borrow a stock to go short, and many stocks are costly to borrow because the supply available from institutional investors is low. The largest anomalies tend to occur in small stocks—which are costly to trade in large quantity, both long and especially short—when the volume of shares available to borrow is limited and when borrowing costs are often high.
  • Investors are unwilling to accept the risks of shorting because of the potential for unlimited losses. Even traders who believe that a stock’s price is too high know that they can be correct—the price may eventually fall—but also that they face the risk the price will go up before it goes down. Such a price move, requiring additional capital, can force traders to liquidate at a loss.

A 2010 study by Malcolm Baker, Brendan Bradley and Jeffrey Wurgler, “Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly,” proposed that another explanation might be at work: the typical institutional investor’s mandate to maximize the ratio of excess returns relative to a fixed benchmark without resorting to leverage.

Many institutional investors who are in a position to offset an irrational demand for risky assets have fixed benchmark mandates that are typically capitalization weighted, thus straying from the benchmarks to exploit anomalies creates career risk.


The authors explain: “A typical contract for institutional equity management contains an implicit or explicit mandate to maximize the ‘information ratio’ relative to a specific, fixed, capitalization-weighted benchmark, without using leverage. For example, if the benchmark is the S&P 500 Index, the numerator of the information ratio is the expected difference between the return earned by the investment manager and the return on the S&P 500. The denominator is the volatility of this return difference, also called the tracking error. The investment manager is expected to maximize this information ratio through stock selection and do so without using leverage.

This contract is widely used because it has several appealing features. Although the ultimate investor cares more about total risk, not tracking error, it is arguably easier to understand the skill of an investment manager, and the risks taken, by comparing returns to a well-known benchmark. Knowing that each manager will stick at least roughly to a benchmark also helps the ultimate investor keep track of his or her overall risk across many asset classes and mandates.”

The authors then note that “these advantages come at a cost.” A benchmark makes institutional investment managers less likely to exploit an anomaly. They go on to demonstrate this cost using mathematics. They further show that, in the absence of the ability to use leverage and “in empirically relevant cases, the manager's incentive is to exacerbate mispricings.”

They further observe that: “In practice, our assumption of a leverage constraint seems reasonable. Very few mutual funds for example allow leverage.” To further demonstrate that mutual funds generally don’t attempt to exploit the low-beta anomaly (the lowest quartile of stocks ranked by beta outperforms the highest quartile), they noted that the average mutual fund beta had a beta of 1.10 over the last 10 years.

Finally, the authors concluded: “The combination of irrational investor demand for high volatility and delegated investment management with fixed benchmarks and no leverage flattens the relationship between risk and return. Yet, sophisticated investors are to a large extent sidelined by their mandates of maximizing active return subject to benchmark tracking error.” Thus, the anomaly persists.

Larry Swedroe is the director of research for the BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.



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