In the previous chapters, we argued that behavioural considerations can contribute to an understanding of certain anomalies in the pricing of individual stocks as well as in the aggregate value of the stock market. Remember that anomalies are defined as empirical results that, unless adequately explained, seem to run counter to market efficiency. It turns out that, just as there are cross-sectional anomalies, there are also aggregate stock market puzzles. In this chapter, we will introduce some of the most famous financial anomalies and consider whether behavioural factors can help us account for these puzzles.


The January effect & Small-firm effect

The January effect is named after the phenomenon in which the average monthly return for small firms is consistently higher in January than any other month of the year. This is at odds with the efficient market hypothesis, which predicts that stocks should move at a “random walk” as explained in section 2.1. However, a 1976 study by Rozeff & Kinney found that from 1904-74 the average amount of January returns for small firms was around 3.5%, whereas returns for all other months was closer to 0.5%. This suggests that the monthly performance of small stocks follows a relatively consistent pattern, which is contrary to what is predicted by conventional financial theory. Therefore, some unconventional factor (other than the random-walk process) must be creating this regular pattern.

One explanation is that the surge in January returns is a result of investors selling loser stocks in December to lock in tax losses, causing returns to bounce back up in January, when investors have less incentive to sell. While the year-end tax sell-off may explain some of the January effect, it does not account for the fact that the phenomenon still exists in places where capital gains taxes do not occur. This anomaly sets the stage for the line of thinking that conventional theories do not and cannot account for everything that happens in the real world.

Similar to the study by Rozeff & Kinney (1976), Gultekin & Gultekin (1983) studied stock markets in 15 different countries and discovered a January effect in all of them. This implies that the January effect is not explicable in terms of the specific tax (or other institutional) arrangements in a country. Keim (1983) found that about half of the small-firm effect occurred in January. In fact about a quarter of the small-firm effect for the year was typically accomplished during the first five trading days in January.

Kato & Shallheim (1985) studied the Tokyo stock exchange and found excess returns for January and a strong relationship between size and returns (small firms substantially outperforming large firms). Fama (1991) reported results from the United States for the period 1941-81. Stocks of small firms averaged returns of 8.06% in January, whereas the stocks of large firms averaged January returns of 1.342% (in both cases the January returns exceeded the average return in the other months). For the period 1982-91 the January returns were 5.32% and 3.2% for the stocks of small and large firms respectively. One possible explanation of the January effect is “window dressing” by fund managers. They are often required to publish the details of the portfolios that they hold at the end of the year. It has been suggested that they prefer to show large, well-known companies in their published portfolios. Thus, they sell small company shares and buy large company shares in December,and then do the opposite in January. Hence, the prices of small company shares rise in January. Although this may explain the relative outperformance of smaller company shares in January, it does not explain the general January effect (unless the window dressing entails a relative move to bonds and cash in December). Cooper et al. (2006) discovered another January-related anomaly. They found that stock market returns in January were predictive of returns during the next eleven months. Strong January returns were indicative of strong returns during the rest of the year. The effect was referred to as the “other January effect”.

Cross (1973), French (1980) and others have documented a weekend effect. They found that the average returns to stocks were negative between the close of trading on Friday and the close of trading on Monday. Gibbons & Hess (1983) examined a 17-year period between 1962 and 1978 and found that, on average, Monday returns were negative on an annualised basis (33.5% p.a.). Keim & Stambaugh (1984) investigated the daily returns on the S&P 500 from 1928 to 1982 and found that,on average,Monday returns were negative. Kohers & Kohers (1995) also found a weekend effect,suggesting that there would be an advantage from buying on Mondays and selling on Fridays.

Calendar effects, such as the January effect and the weekend effect,have been brought into doubt by Sullivan et al. (1999).They claim to have shown that the calendar effects can be completely explained by what they refer to as “data snooping”. They found that the same data that was used to identify a calendar effect was also used to test for the existence of the effect. They also demonstrated that,although the small number of calendar effects that have been reported are statistically significant, there are about 9,500 conceivable calendar effects. From these 9,500 some can be expected to be statistically significant through chance. Malkiel (2003) concluded that anomalies do not persist in the long run since they lose their predictive power when they are discovered. As an example, he stated that as soon as evidence of the January effect was made public investors acted on the information and the effect disappeared. Gu (2003, 2004) provided evidence consistent with Malkiel’s view by showing a decline in the January effect and a reversal of the weekend effect. Some calendar anomalies may persist since it is difficult for arbitragers,and other traders,to make profits from them. One well-known strategy isto “Sell in May and walk away”. This is an old stock market adage, which was researched by Keppler & Xue (2003). They studied the 18 most developed national stock markets over the period 1970 to 2001. It was found that during the months November to April the average rate of stock price rise was 8.36% whereas the average rate of price rise during the months May to October was 0.37%. Not only were returns higher between November and April, but also risk was lower. Keppler & Xue (2003) suggested a number of explanations including the observation that bonuses tend to be paid around the endor at the beginningof the year. Research on saving behaviour has found that people find it easier to save and invest from a lump sum than from regular earnings. Investment of such lump sums would tend to increase demand for stocks, and hence their prices, during the period in which the bonuses are invested.

The winner's curse

One assumption found in standard finance and economics is that investors and traders are rational enough to be aware of the true value of some asset and will bid or pay accordingly. However, anomalies such as the “winner’s curse”, being a tendency for the winning bid in an auction setting to exceed the intrinsic value of the item purchased, suggest that this is not the case. Simply speaking, the winner’s curse is the problem that occurs when bidders of an auction have to estimate the true value of the good they are bidding for. Assuming that there are a reasonable number of bidders on the market, the average bid will be less than the true value (bidders are risk-averse), but the winning bid will be significantly higher (due to estimation errors). As the highest overestimation wins the auction, the winner will usually overpay in an auction. This observation contradicts the standard economic assumption of rationality and can be applied to various aspects of economic life. Rational-based theories assume that all participants involved in the bidding process will have access to all relevant information and will all come to the same valuation. Any differences in the pricing would suggest that some other factor not directly tied to the asset is affecting the bidding.

According to Robert Thaler’s 1988 article on winner’s curse, there are two primary factors that undermine the rational bidding process: the number of bidders and the aggressiveness of bidding. For example, the more bidders involved in the process means that you have to bid more aggressively in order to dissuade others from bidding. Unfortunately, increasing your aggressiveness will also increase the likelihood in that your winning bid will exceed the value of the asset.

Consider the example of prospective homebuyers bidding for a house. It’s possible that all the parties involved are rational and know the home’s true value from studying recent sales of comparative homes in the area. However, variables irrelevant to the asset (aggressive bidding and the amount of bidders) can cause valuation error, oftentimes driving up the sales price more than 25% above the home’s true value.

In this example, the curse aspect is twofold: not only has the winning bidder overpaid for the home, but now that buyer might have a difficult time securing financing.

Another interesting area where the winner’s curse is observed is the market for initialpublic offerings (IPOs). In fact, the prices for IPOs are not set to clear the market, butto guarantee an excess demand (to alleviate buyers from the winner’s curse). This willgenerally result in lower revenues for the IPOcompany.

The offset is that during anopen-outcry auction-type, information of the other bidders is revealed that may havepositive or negative effects on the resulting end-price. Such irrational effects were,for example, observed recently with the Facebook IPO.

Winner’s curse provides more proof that investors are not rational. Winner’s curse has a number of explainable causes related to behavioural finance theories including incomplete information and emotions. Regardless of the cause, the item being auctioned is awarded to the bidder with the greatest overestimation. Paying more for something than what is worth is not rational behaviour. Theoretically, if markets were efficient, no overestimation would occur. However, the market has historically experienced many overestimations and corrections. Stock bubbles, such as the dot-com or housing bubble, prove that people buy stocks and real-estate at irrational prices beyond their true values.

The equity premium puzzle

Much research has examined the equity premiumpuzzle, which was originally brought to light by Mehra & Prescott (1985) and ever since has left academics in finance and economics scratching their heads. The equity premium is defined as the gap between the expected return on the aggregate stock market and a portfolio of fixed-income securities.

Studies by Siegel (1998) among many others have shown that over a 70-year period, stocks yield average returns that exceed government bond returns by 6-7%. Stocksreal returns are 10%, whereas bonds real returns are 3%. However, academics believe that an equity premium of 6% is extremely large and would imply that stocks are considerably risky to hold over bonds. Note of course that according to the capital asset pricing model, investors that hold riskier financial assets should indeed be compensated with higher rates of returns. Conventional economic models have, nevertheless, determined that this premium should be much lower than what it really is. This lack of convergence between theoretical models and empirical results represents a stumbling task for academics to explain. Rietz (1988) proposed a solution to the equity premiumpuzzle that incorporates a small probability of alarge drop in consumption. He found that the risk freerate in such a scenario is much lower than there turn on an equity security. This model requires a 1 in 100 chance of a 25 percent decline in consumption to reconcile the equity premium with a risk-aversion parameter of 10. Such a scenario has not been observed in the United States for the past 100 years (the time for which there is data available). Nevertheless, one can evaluate the implications of the model. One implication is that the real interest rate and the probability of the occurrence of the extremeevent move inversely. For example, the perceived probability of a recurrence of a depression was probably high just after WWII, but subsequently declined over time. If real interest rates had risen significantly as the war years receded, that evidence would support the Rietz (1988) hypothesis. Similarly, if the low-probability event precipitating the large decline in consumption is interpreted to be e.g. anuclear war, the perceived probability of such an event has surely varied over the past 100 years. It must have been low before 1945, the first and only year the atom bomb was used, and it must have been higher before the Cuban missile crisis than after it. If real interest rates moved with these sentiments as predicted, that evidence would support Rietz’s disaster scenario. But interest rates did not move as predicted. So what then?

Constantinides et al. (2002) argued that the young part of the population, who should (in an economy scenario without frictions and with complete contracting) be holding equity, are effectively shut out of this market because of borrowing constraints. They have low wages; so, ideally, they would like to smooth lifetime consumption by borrowing against future wage income (consuming a part of the loan and investing the rest in higher-returning equity). They are prevented from doing so, however, because human capital alone does not collateralize major loans inmodern economies (for reasons of moral hazard and adverse selection among others). In the presence of borrowing constraints, equity is thus exclusively priced by middle-aged investors and the equity premium is high. If the borrowing constraint were to be relaxed, the youngwould borrow to purchase equity, thereby raisingthe bond yield. The increase in the bond yield would induce the middle-aged to shift their portfolio holdings from equity to bonds. The increase in the demand for equity by the young and the decrease in the demand for equity by the middle- aged would work in opposite directions. On balance, the effect in the Constantinides et al. (2002) model isto increase both the equity and the bond returnwhile simultaneously shrinking the equity premium. Furthermore, the relaxation of the borrowing constraint reduces the net demand for bonds, and the risk-free rate puzzle unfortunately re-emerges.

In conclusion, behavioural finance’s answer to the equity premium puzzle revolves around the tendency for people to have “short-sighted (myopic) loss aversion”, a situation in which investors, overly preoccupied by the negative effects of losses in comparison to an equivalent amount of gains, take a very short-term view on an investment. What happens is that investors are paying too much attention to the short-term volatility of their stock portfolios. While it is not uncommon for an average stock to fluctuate a few percentage points in a very short period of time, a short-sighted investor may not react too favourably to the downside changes. Therefore, it is believed that equities must yield a high-enough premium to compensate for the investor’s considerable aversion to loss. Thus, the premium is seen as an incentive for market participants to invest in stocks instead of marginally safer government bonds.

Value premium puzzle

Extensive academic research has shown that value stocks (that is, stocks with low market prices relative to such financial statement fundamentals as earnings and book value) have a tendency to outperform growth stocks (stocks with high market values relative to their fundamentals) in the long run. Numerous test portfolios have shown that buying a collection of stocks with low price/book ratios will deliver market-beating performance. Such a simplistic strategy seems to be evidence against the efficient market hypothesis, but what if value stocks are riskier than growth stocks, and what if their risk is insufficiently captured by the capital asset pricing model? Then we do not have an anomaly after all, but just an inappropriate asset pricing model.

Many of the earlier empirical studies that identify a significant and consistent “value premium” suggest that a zero-net investment strategy of short-selling growth stocks and holding long positions in value stocks will produce consistent positive returns over time. More recent evidence, however, suggests that the value premium may not be robust or stable over time. For example, the value premium seems to have disappeared for almost all of the 1990s in the run-up to the technology bubble, only to reappear in 2000 when the bubble burst. It then persisted for a stretch of six years until the recent financial crisis started in 2007.

The debate about the cause of the value premium has been going on for as long as the empirical evidence of the phenomenon has existed. But what drives the value premium? Current explanations could be put into two broad categories. One explanation, first provided by Fama & French in 1992, is that the value premium is a rational phenomenon and represents an investor’s compensation for systematic risk. Fama & French (1992) argue that the value premium is associated with a stock’s relative financial distress. In a weakening economy, investors require a higher risk premium on firms with distress characteristics; value stocks thus must offer a higher average return in reward for the extra systematic risk borne by the investor. As argued in Bansal & Yaron (2004), risks related to long-term growth lead to large reactions in stock prices and, hence, entail a significant risk compensation. Assets’ valuations and risk premia, therefore, by large depend on the amount of low-frequency risks embodied in assets’ cash flows. As documented by Kiku (2006), value firms are highly exposed to long-run consumption shocks. Growth firm fluctuations, on the other hand, are mostly driven by short-lived fluctuations in consumption and risks related to future economic uncertainty. Consequently, value firms exhibit higher elasticity of their price/dividend ratios to long-run consumption news (relative to growth assets) and have to provide investors with high ex ante compensation.

Another explanation of the value premium is based on behavioural finance investor behaviour in the capital markets. Some investors have tendency to overreact to positive and negative news, which causes prices to move by more than what is justified by the underlying fundamentals. Thus, value stocks that have done badly are oversold at some point in time and get corrected at another point in the future when investor sentiment switches. Although the value premium puzzle makes sense to a point (unusually cheap stocks should attract buyers’ attention and revert to the mean), this is a relatively weak anomaly. Though it is true that low price-to-book stocks outperform as a group, the individual performance is very idiosyncratic and it takes very large portfolios of low price-to-book stocks to see the benefits.

Other anomalies

The efficient market hypothesis implies that publicly available information in the form of analyses published by investment advisory firms should not provide means of obtaining rates of return in excess of what would normally be expected on the basis of the risk of the investments. However, stock rankings provided by “The Value Line Investment Survey” appear to provide information that could be used to enhance investors’ returns (Huberman & Kandel 1990). There is, interestingly, evidence that the market adjusts to this information within two trading days (Stickel 1985). Similarly, Antunovich & Laster (2003) and Anderson & Smith (2006) found that companies identified by Fortunemagazine, as the most admired, subsequently performed better than the S&P 500. The Antunovich & Laster (2003) study indicated that stock price reaction to the information is subject to drift, in that it takes a significant amount of time to occur, hence permitting investors to profit from the information. Conversely, Shefrin & Statman (1997) obtained the opposite result when analysing annual surveys of firm reputation published by Fortune magazine. They found that, on average, the shares of firms with good reputations turned out to be relatively poor investments whereas the shares of companies with poor reputations subsequently performed well.

Lee et al. (1991) suggest that the existence of investment trusts (closed-end funds) is an anomaly because rational investors would not be expected to buy new issues. The tendency for investment trusts to fall to a discount subsequent to issue appears to offer an early loss. Rational investors should not make an investment that is expected to result in an almost immediate loss. An anomaly that is consistent with the belief that markets in the shares of large firms are more likely to be efficient than the markets for small company shares is the “neglected firm effect”. Neglect means that few analysts follow the stock,or that few institutional investors hold it. So fewer market participants put new information into the market. Neglected stocks are more likely to be mispriced,and, hence, are more prone to offer profit opportunities. Arbel & Strebel (1983) found that an investment strategy based on changes in the level of attention devoted by security analysts to different stocks could lead to positive excess returns. Allen (2005) observed that institutional investment funds specialising in small capitalisation companies in the United States outperformed the Russell 2000 (a stock index for small companies) whereas the institutions underperformed stock indices when managing funds of large capitalisation stocks. Allen (2005) suggested that the outperformance in the small capitalisation sector was partly due to an “instant history bias” wherein performance figures are not reported unless there is a history of good performance prior to records being reported for the first time. However, the view was taken that the outperformance was primarily because small company stocks were often neglected and that the resulting mispricing offered fund managers profitable opportunities.

Merton (1987) showed that neglected firms might be expected to earn high returns as compensation for the risk associated with limited information. The information deficiency resulting from the limited amount of analysis renders neglected firms riskier as investments. The relative absence of investment analysis makes it less likely that all relevant information is reflected in the share price.There is greater likelihood that the stock is mispriced, and the mispricing could entail the stock being overpriced. Investors may require compensation for the risk that the stock is purchased at an overvalued price. This view sees the neglected firm premium as a form of risk premium rather than as a contradiction of the efficient market hypothesis. Investors require the higher returns as compensation for the additional risk, and the higher required rates of return entail lower prices. On a risk-adjusted basis, neglected firms do not provide returns above a normal level.

Doukas et al. (2005) observed that not only were the stocks of neglected firms likely to trade at relatively low prices, but also the shares of firms receiving excessive attention from analysts may trade at abnormally high prices. It was suggested that when an investment bank anticipates investment-banking business with a company, the coverage of that company by the bank’s investment analysts increases. If it were accepted that investment analysts tend to be overly optimistic about the stocks of firms which are prospective clients of their banks,the result of increased attention from analysts could be rises in the prices of such stocks. If a number of investment banks seek business with a firm, the result could be excessive attention from analysts and a resultant overpricing of its shares. Related to the small-firm effect (as presented in section 4.1) and the neglected firm effect is the effect of liquidity on returns. Amihud & Mendelson (1991) argued that investors demand a premium to invest in illiquid stocks that entail high transaction costs. They found that such stocks did provide relatively high rates of return. Since the shares of small and neglected firms tend to be relatively illiquid, the liquidity effect may constitute part of the explanation of their high returns. However, the lack of liquidity, and high transaction costs, may remove the potential to profit from the liquidity effect on stock returns.

Some of the anomalies that apply to stocks within countries also seem to apply to international stock markets. Selecting countries for overseas investment on the basis of the anomalies appears to have potential. Asness et al. (1997) noted that within the United States the relative performance of stocks was positively related to high book-to-market ratios, small firm size,and high past year returns. For a 20-year period ending in 1994 they found that countries satisfying those three characteristics outperformed countries that did not. Richards (1997) investigated 16 national markets over the period 1970-95 and found that the type of winner-loser reversals found for U.S. stocks also applied to other countries. In particular, he found that for periods up to a year, relatively strong performance persisted,whereas over longer periods past relative outperformers (winners) became underperformers (losers) and vice versa. Emanuelli & Pearson (1994) studied 24 national markets and separated them on the basis of relative earnings revisions. They found that a portfolio of stocks from the countries with the greatest relative experience of positive earnings revisions outperformed an average of the 24 countries. A portfolio from the countries with the lowest positive (highest negative) earnings revisions underperformed.

Back to Top