Are the hypotheses supported by the data? Are there market patterns that lead to abnormal returns more often than not?

A market anomaly is a security price distortion in the market that seems to contradict the efficient market hypothesis. There are different categories of market anomalies.

Time-Series Anomalies

Calendar anomalies raise the question of whether some regularities exist in the rates of return during the calendar year that would allow investors to predict returns on stocks.

The January anomaly, also called small-firm-in-January effect, says that many people sell stocks that have declined in price during the previous months to realize their capital losses before the end of the tax year. Such investors do not put the proceeds from these sales back into the stock market until after the turn of the year. At that point the rush of demand for stock places an upward pressure on prices that results in the January effect.

The effect is said to show up most dramatically for the smallest firms because the small-firm group includes stocks with the greatest variability of prices during the year (and the group therefore includes a relatively large number of firms that have declined sufficiently to induce tax-loss selling).

Another possible reason for the January effect on stock markets is strategic selling by institutional investors at the end of their reporting periods. Portfolio managers may be reluctant to report holdings of stocks in their annual reports that have performed poorly in the previous period. Therefore, the managers sell these stocks at the end of their accounting periods (usually the end of December). This so-called "window-dressing" was suggested as a source of the January effect by Haugen and Lakonishok (1988).

Despite numerous studies, the January anomaly poses as many questions as it answers.

Other calendar anomalies include the monthly effect, weekend or day-of-the-week effect, and intraday effect.

Momentum and Overreaction Anomalies. The debate surrounding investor overreaction and contrarian investing is one of the most extensive and controversial areas of research in finance. The overreaction anomaly, evidenced by long-term reversals in stock returns, was first identified by De Bondt and Thaler (1985), who showed that stocks which have performed poorly in the past three to five years demonstrate superior performance over the next three to five years compared to stocks that have performed well in the past. The study provided evidence that abnormal excess returns could be gained by employing a strategy of buying past losers and selling short past winners, or the contrarian strategy.

Although the overreaction anomaly and market momentum do seem to exist, researchers have argued that the existence of momentum is rational, and the additional return (based on the contrarian investment strategy) would come simply at the expense of increased risk.

Cross-Sectional Anomalies

If the semi-strong EMH is true, all securities should have equal risk-adjusted returns because security prices should reflect all public information that would influence the security's risk. Using public information, is it possible to determine what stocks will enjoy above-average, risk-adjusted returns?

The size effect relates to the impact of size (measured by total market value) on risk-adjusted rates of return. Some researchers found that small firms outperformed large firms after considering risk and transaction costs.

Basu's study concluded that publicly available P/E ratios conveyed valuable information, and that the risk-adjusted returns for stocks in the lowest P/E ratio quintile were superior to those in the highest P/E ratio quintile. This is known as the value effect.

Fama and French found that both size and BV/MV ratio are significant when included together, and that their importance dominates that of other ratios. The dramatic dependence of returns on market-to-book ratio is independent of beta, suggesting either that low market-to-book-ratio firms are relatively underpriced or that the market-to-book ratio is serving as a proxy for a risk factor that affects equilibrium expected returns.

Other Anomalies

Closed-End Investment Fund Discounts. Closed-end funds usually trade at substantial discounts relative to their net asset values. There are several explanations:

• Agency costs. The existence of management fees (from 0.5% to 2%) implies that funds will sell at a discount. However, open-end funds also charge fees. Boudreaux (1973) suggested that since fund managers buy and sell securities, discounts might reflect their differential ability to perform this task. However, this explanation does not explain why funds trade, on average, at discounts.

• Taxes. When a fund realizes a capital gain it must report this, and the tax liability is borne by the existing shareholders at the time the gain is realized. So if you buy a fund today and it realizes a large capital gain tomorrow, you must pay a tax even if you have not made any money. This implies that a fund with large unrealized capital appreciation is worth less than its net asset value to both existing and potential shareholders, and should thus sell at a discount. This explanation, like the others, has some apparent merit but fails to explain all the facts.

• Liquidity. One way in which a portfolio might be misvalued is if the fund held large quantities of stocks that cannot be freely sold in the open market. Such stocks, some have argued, are valued too highly in the calculation of net asset value. However, most closed-end funds hold little or no restricted stock and yet still sell at discounts.

When closed-end funds are terminated, either through a merger, liquidation, or conversion to an open-end fund, prices converge to reported net asset value.

In summary, a number of reasons have been put forth to explain closed-end fund discounts in the context of the efficient market hypothesis and rational agents. Several of these factors do have some merits, but taken together, these factors explain only a small portion of the total variation in discounts.

Earnings surprises. Price changes tend to persist after initial announcements. Stocks with positive surprises tend to drift upward; those with negative surprises tend to drift downward. Some refer to the likelihood of positive earnings surprises to be followed by several more earnings surprises as the "cockroach" theory; when you find one, there are likely to be more in hiding.

Research shows that the post-earnings-announcement drift occurs mainly in highly illiquid stocks, which have high trading costs and market impact costs, supporting the argument that transaction costs could be the source of the drift.

Initial public offerings. Because of uncertainty about price and the risk involved in underwriting stocks of previously closely held companies, it has been hypothesized that underwriters tend to under-price these new issues. Although there is some under-pricing of IPOs (about 15%) when they are offered, the price adjustment takes place within one day after the offering. Investors who acquire the stock after the initial adjustment do not experience abnormal returns.

Predictability of returns based on prior information. Finding that stock returns are related to prior information, such as interest rates, inflation rates, and dividend yields, would not result in abnormal trading returns.

Summary

Most empirical evidence supports the semi-strong form EMH. The test results of the strong-form EMH are mixed.