Market Efficiency and Anomalies

Study Session 13

Exam Focus

This topic review is fairly straightforward. Know the limitations to the claim that market prices should be perfectly efficient, and know the limitations on arbitrage as a mechanism for forcing securities prices to their informationally efficient levels. Know the main reasons that research evidence suggesting anomalous returns behavior may suffer from bias.

LOS 55.a: Explain the three limitations to achieving fully efficient markets.

There are three primary limitations on the market's ability to produce informationally efficient prices.

1. Processing new information has costs and takes time. If market prices are efficient, there are no returns to the time and effort spent on fundamental analysis. But if no time and effort is spent on fundamental analysis, there is no process for making market prices efficient. We can resolve this apparent conundrum by looking to the time lag between the release of new value-relevant information and the adjustment of market prices to their new efficient levels.

There must be an adequate return to fundamental analysis and trading based on new information to compensate analysts and traders for their time and effort. Those who act rapidly and intelligently to the release of new information will be rewarded. If stock prices adjust to their new efficient levels within minutes or hours of the release of new information, we can consider markets to be efficient. If this price-adjustment process takes days or weeks, stock prices are not efficient. In this case, we expect that more activity by analysts, traders, and arbitrageurs will tend to reduce the adjustment period over time.

2. Market prices that are not precisely efficient can persist if the gains to be made by information trading are less than the transaction costs such trading would entail. The difficulties associated with short sales can be viewed as relatively high transaction costs. This means that deviations from efficient prices on the upside (overvalued stocks) may be more prevalent than downside deviations (undervalued stocks) since the transaction costs of increasing long positions are low relative to those of short selling. In general, for securities with larger transaction costs, the deviations from informationally efficient prices should be greater.

3. There are limits on the ability of the process of arbitrage to bring about efficient prices. Arbitrage is frequently not riskless. Just because fundamentals indicate that one stock is overpriced relative to another, or absolutely over- or underpriced, does not mean that trading based on this information will be immediately profitable. For example, one risk of shorting overvalued stocks during the internet stock bubble of the late 1990s was that a shorted company might be taken over at a significantly higher stock price than the one at which a trader sold short. The fact that the acquiring firm paid too much for the shares offers no solace to short sellers who have to cover their positions at the takeover price.

LOS 55.b: Describe four problems that may prevent arbitrageurs from correcting anomalies.

The ability of arbitrage to correct anomalies is limited by four factors.

1. There is no guarantee concerning when, or even if, apparent mispricings will be corrected and prices will return to efficient equilibrium levels.

2. It may be difficult or impossible to find two securities with exactly the same risk so that a mispricing can be exploited by taking a long (short) position in an underpriced (overpriced) security and an offsetting position in a correctly priced security with the same risk. To the extent that the risks of the two securities are not exactly offsetting, such a strategy will have risk that may make it unattractive, so the mispricing can persist.

3. Arbitrageurs do not have unlimited funds. Given the limitations on the funds that investors make available for exploiting mispricings, only the more significant mispricings may be exploited while others are allowed to persist. During bull markets, this effect may be greater since investments seeking profit from small pricing errors will be less attractive relative to long (or leveraged long) positions just at a time when mispricings are more prevalent.

4. Arbitrageurs must depend on their sources of capital. The providers of capital to arbitrageurs may place limits on the arbitrage trades and position sizes that restrict the ability of arbitrageurs to completely exploit mispricings. Further, if the arbitrageur's strategies do not produce positive near-term results or lose money because mispricings get temporarily worse instead of better, capital will be withdrawn and new capital to devote to arbitrage activities will be in short supply.

LOS 55.c: Explain why an apparent anomaly may be justified and describe the common biases that distort testing for mispricings.

Some apparent mispricings may be justified by risk factors. Two examples of such risk-based justifications are presented here.

Risk Measurement and Abnormal Returns

One of the most persistent criticisms of studies that document anomalous returns based on firm characteristics is that the model used to estimate normal returns may be flawed. Researchers often use the CAPM to model normal returns based on estimated firm betas. The fact that small firms show positive abnormal (risk-adjusted) returns on average may indicate that small firms are persistently underpriced, or that investing in small firms entails risk that is not captured by the firms' betas. This is especially problematic when tests for abnormal returns involve returns over longer periods. Since normal returns over a day or a week are close to zero, measuring abnormal returns is not as heavily influenced by the returns model used. Using such factors as firm size and price-book values may mitigate such problems, but the theoretical support for these characteristics as risk factors is weak.

The bottom line here is that we must be aware that firm characteristics associated with positive abnormal returns may be characteristics associated with a type of risk that is not captured by the returns model estimates to which actual returns are compared. In this case, the apparent "mispricing" is justified.

Strategy Risk

In addition to the concerns with the inadequate specification of firm risk in estimating normal returns, investors should consider strategy risk. Capturing the abnormal returns of a trading strategy is not without risk, even if the anomalous returns behavior persists. If the strategy is based on returns over a 20-year period, abnormal returns may be positive in only some of those years. Investors seeking to exploit the predictability of abnormal returns may have one or more down years in a row, even if the firm characteristics upon which the strategy is based continue to have predictive power over the long term. Any strategy designed to exploit anomalous returns behavior has the inherent risk that the behavior will either not continue, or be significantly reduced by other investors pursuing similar or identical strategies. Additional strategy risk such as this must be rewarded with higher returns and can justify the persistence of some mispricings.

Bias in Abnormal Returns Estimation

Biases in tests for abnormal returns that offer evidence of systematic security mispricing may explain some anomalous results.

Data Mining Bias '

Recall from quantitative methods, that statistical tests have a probability of a type I error equal to their significance level. A test of the hypothesis that stock prices are efficient (no abnormal returns) at the 5% level of significance will be rejected at the 5% level of significance 1 out of 20 times by chance, even when it is actually true.

Consider a researcher who tests 20 different factors using the same sample of data. In each test he tries to determine whether abnormal returns could have been earned by forming portfolios based on one of these factors. Even if none of the factors is actually valuable in predicting abnormal returns, chances are that one of the tests will show a statistically significant relation between a factor and subsequent abnormal returns. Now imagine thousands of researchers doing a hundred thousand tests all on the same data sample. This results in a data mining problem.

There are certainly many relationships in the data resulting purely from chance. Standard statistical tests will identify these as statistically significant when they are in fact not driven by any real characteristics of markets and are unlikely to be repeated outside the sample period. While a less-than-ethical researcher could be guilty of purposely mining the data, a large number of independent skilled researchers who just use the same data (e.g., U.S. stock returns) can also be mining the data.

Survivorship Bias

When constructing samples, researchers must be careful not to include just surviving companies, mutual funds, or investment newsletters. Since survivors tend to be those that have done well (by skill or chance), samples of mutual funds that have 10-year track records, for example, will exhibit performance histories with upward bias. Mutual fund companies regularly discontinue funds with poor performance histories or roll their assets into better-performing funds.

Sample Selection Bias

Sample selection bias (of the unintentional variety) occurs when the method of selecting a sample is not truly random. It is present when the researcher has inadvertently selected a sample that exhibits characteristics that are not present, or not present to the same degree of significance, in the overall population. If a researcher finds evidence of an anomaly in sample data, but the data are predominantly from small firms because that was the only information available to the researcher, it could be a mistake to make inferences about characteristics of the whole population of publicly traded firms based on that sample.

Small Sample Bias

Inferences about an entire population drawn from tests on a small sample may be incorrect. One type of small sample bias is to use a short time period. What is true over one time period is not necessarily true over longer periods.

Nonsynchronous Trading

Closing stock prices in market data may be actual trading prices very close to the market close for large-cap, heavily traded stocks. For stocks that trade infrequently, closing prices may be prices from much earlier in the day. Using these "stale" prices can make strategies appear more attractive than they really are. Assuming that one could actually trade at closing prices at or near the close of the market, may make a strategy look profitable when the strategy could not really be implemented.

LOS 55.d: Explain why a mispricing may persist and why valid anomalies may not be profitable.

There are several reasons that pricing anomalies can persist, but all are rooted in the fact that the pricing anomaly is not quickly exploited by traders or arbitrageurs.

1. Lack of Theoretical Explanation

If the reasons underlying a persistent pricing anomaly are not well understood, it is difficult to exploit. Arbitrageurs will use their funds to exploit other mispricings which they believe they understand better and are, therefore, better able to exploit and profit from.

2. Transactions Costs

The trades necessary to exploit any apparent mispricing may not be profitable because the costs of the trades are greater than the potential abnormal returns. Transactions costs include the bid-ask spread, brokerage commissions, and the impact that larger trades may have on the price of the securities involved. Mispricings of the stocks of smaller companies will be more likely to persist because the transactions costs for smaller firms' stocks will typically include higher percentage bid-ask spreads and higher costs from price impact of trades due to their lower liquidity.

3. Small Profit Opportunities

The total profit to be gained by exploiting a mispricing may be small enough that it does not represent a significant profit opportunity to large funds. Again, mispricings of the stocks of smaller companies may be persistent because the small size of the positions that can be established limits the profits to be realized by exploiting the mispricing.

4. Trading Restrictions

Restrictions on short selling make some strategies impossible for some period of time. Note that when a stock is first offered to the public, it typically cannot be shorted immediately after the IPO since shares cannot be borrowed. Initial overpricing of a new IPO can persist for days because of traders' inability to short the shares.

5. Irrational Behavior

Investor tendencies of perception and analysis that run counter to rational trading and investing may lead to persistent mispricings that are not rapidly exploited by arbitrageurs for one or more of the reasons we have noted thus far.

6. Other Limits on Arbitrage

The limits on arbitrageur activities previously discussed (e.g., limited capital, strategy risk, investor short-term performance demands) also can explain the persistence of some market pricing anomalies.

There may be valid anomalies (persistent, backed by theory, and not the result of measurement bias) that do not or will not result in profitable trading strategies. One reason for this is that evidence of mispricings is typically based on average returns for large samples over significant time periods. While there may be evidence that the market initially underreacts to positive earnings surprises, for any particular stock or time period there is no guarantee that purchasing a stock after a positive earnings surprise will result in positive returns or positive abnormal returns.

A second reason that trades based on valid anomalies may not be profitable is that even when abnormal returns (returns adjusted for risk and overall market performance) are positive, raw (unadjusted) returns can be negative during periods of market decline.

A third reason that arbitrage based on valid anomalies may be unprofitable is that the conditions causing the mispricing may change. This is especially true when the accepted explanation for the anomalous pricing is not well understood or is mistaken. In this case a change in the conditions that actually are causing the mispricing may not be recognized, so arbitrageurs are seeking to exploit a pricing anomaly that will not occur in the future.

A final reason that attempting to exploit a documented pricing anomaly may be unprofitable is the fact that arbitrage itself may have eliminated the associated mispricing. If enough investors purchase stocks after positive earnings surprises, the

^ prices of these securities will rise to their efficient levels and the strategy of buying

"positive earnings surprise" stocks will no longer be profitable.

Lessons From The Intelligent Investor

Lessons From The Intelligent Investor

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