Market anomalies: calendar, momentum, size, value and more

What is a market anomaly?

A market anomaly is a price pattern that cannot be linked to relevant information and seems to offer abnormal returns. If a pattern persisted and could be exploited, it would be an exception to efficiency.

Researchers sort anomalies by how they were found.

Market anomaliesreturn patterns that seem to offer abnormal returns

• Time-series Memorize found in a series of returns over time
  • Calendar January, turn-of-the-month, day-of-the-week, weekend, holiday
  • Momentum short-run winners keep winning
  • Overreaction 3 to 5 year losers beat winners
• Cross-sectional Memorize found by comparing companies that differ on a characteristic
  • Size effect small caps outperform
  • Value effect low P/E, low P/B, high yield beat growth
• Other Memorize found by event studies and other means
  • Closed-end fund discount price below net asset value
  • Earnings surprise drift after the announcement
  • IPOs day-one underpricing, weak long run
  • Predictability from prior information interest rates, inflation, volatility

The list is long, and the rest of this lesson covers the ones the curriculum names. Throughout, keep one question in mind: is this pattern real, and could you earn it after costs?

Which anomalies show up in time series?

Calendar effects. The January effect (also called the turn-of-the-year effect) is the finding that returns in January, especially in its first five trading days, were higher than in other months. It is strongest for small-cap shares. No news explains it, so it contradicts efficiency. Two explanations are offered. In tax-loss selling , investors sell losing shares in December to realize losses that offset gains, depressing prices, and buy back in January. In window dressing , managers sell riskier shares before year-end reports to look less risky, then buy them back. Each explains part of the effect, not all. After adjusting for risk, the January effect produces no abnormal returns.

Other calendar effects include the turn-of-the-month, day-of-the-week (Monday returns lower), weekend and holiday effects. Most have faded over time, which fits the view that they were exploited and arbitraged away.

Momentum and overreaction. Momentum is the tendency of shares that did well recently to keep doing well over the next short period. Because it uses past prices alone, it contradicts the weak form if profitable. A rational explanation is that shocks to expected growth cause short-lived serial correlation.

The overreaction effect runs the other way over a longer horizon. Investors overreact to unexpected news, pushing prices too far. Shares that were the biggest losers over the previous three to five years then outperform the previous winners. Critics say statistical problems may account for the result.

Which anomalies show up across companies?

Size. The size effect is the finding that small-cap shares outperform large-cap shares on a risk-adjusted basis. It was documented in the early 1980s but not confirmed in later studies. If it were real, investors acting on it would have competed it away. It also seems to be limited to the smallest, micro-cap shares, and may have been a chance outcome of the original sample.

Value. The value effect is the finding that shares with below-average price-to-earnings and price-to-book ratios and above-average dividend yields (value shares) beat growth shares over long periods. The classifying information is public, so if it persists it contradicts the semi-strong form. But Fama and French showed that a model adding size and book-to-market factors to the market return makes the value effect disappear. On that view, value shares carry extra risk, and the extra return is compensation.

What other anomalies are there?

Closed-end fund discounts. A closed-end fund issues a fixed number of shares that then trade on an exchange. Net asset value (NAV) per share is the market value of its holdings less liabilities, divided by shares outstanding. The closed-end fund discount is the tendency of fund shares to trade below NAV, by 4 to 10% on average. In principle you could buy every share, liquidate and keep the difference.

$$D = \frac{P - NAV}{NAV}$$

Why it may not be free money: taxes on unrealized gains inside the fund and illiquid holdings explain part of the discount. Fees and the manager’s expected performance are often suggested, but evidence does not support them. Most importantly, the costs of buying all the shares and liquidating would eat the profit, and discounts tend to move back toward zero anyway.

Earnings surprise. An earnings surprise is the unanticipated part of an earnings announcement, the part that merits a price change. Most studies find the price reacts quickly, but part of the adjustment comes after the announcement. Companies with the largest positive surprises then outperform, and those with negative surprises underperform. Buying on public news would then earn abnormal returns, contradicting the semi-strong form. But other studies find the gains disappear once transaction costs and risk are controlled for.

IPOs. In an initial public offering, the shares are priced with an investment bank. On average the offer price is set too low, so the price jumps on the first day. IPO underpricing is the percentage difference between the issue price and the first-day close.

$$U = \frac{C - O}{O}$$

Predictability from prior information. Returns have been linked to earlier interest rates, inflation, volatility and dividend yields. That is not evidence of inefficiency, because it likely reflects changing risk premiums. The links are also unstable: the relationship between returns and dividend yield has changed sign between periods.

Is it really an anomaly?

Often not. Three problems recur.

Data mining. Data mining (or data snooping) means searching the data for patterns before forming a hypothesis. Test enough rules and some will look significant by chance. Proper research starts with an economic reason, then tests it on objectively chosen data.

$$K = T \times \alpha$$

Risk and costs. A pattern may be a reward for risk, or it may vanish after spreads, commissions and price impact.

Persistence. A real anomaly lasts over long periods and in samples that were not used to find it. Many have disappeared since they became known.

Tests for a true anomaly

• Persists over long periods Use it and in samples not used to find it
• Survives risk adjustment Use it not just compensation for extra risk
• Survives trading costs Use it spreads, commissions, price impact
• Not a product of data mining Use it a reason for the pattern before testing it

Most researchers conclude that anomalies are not violations of efficiency but a product of statistical methods, and that when the methods are corrected most disappear. Overreactions occur, but so do under-reactions, so on average the market is still efficient. Few investors would trust a strategy of buying on Mondays and selling on Fridays with no economic reason behind it.

Go deeper Fama–French in one paragraph

The capital asset pricing model (CAPM) explains a share’s return with one factor, its beta to the market. The Fama–French model adds two: company size (market value of equity) and book-to-market (book value of equity divided by market value). When the value effect is tested against this three-factor model instead of the CAPM, it disappears. The model captures risk dimensions the CAPM misses, which suggests value shares earn more because they are riskier.