2.1 The cross-section of average stock returns
We first consider the evidence on risk pricing and the pricing of other characteristics. In general, the evidence in favour of the notion that systematic risk matters in asset pricing remains quite tenuous at best. Other characteristics seem far more relevant in the cross-section of expected returns.
Early empirical studies by Black et al. (1972) and Fama and MacBeth (1973) suggest a significant positive cross-sectional relation between security betas and expected returns, and this evidence supports the capital asset pricing model (Sharpe, 1964; Lintner, 1965; Mossin, 1966). However, more recently, Fama and French (1992) find that the relation between return and market beta is insignificant. Internationally, Rouwenhorst (1999) finds no significant relation between average return and beta with respect to the local market index. Tests of the consumption-based capital asset pricing model (Breeden, 1979) have also led to inconclusive results; see, for example, Hansen and Singleton (1983). Jagannathan and Wang (1996) find a modest positive relation between conditional beta and expected returns when the market is expanded to include human capital.
On the importance of other variables, the evidence is much more compelling. A landmark study by Fama and French (1992) finds that size and the book-to-market ratio strongly predict future returns (returns are negatively related to size and positively to book-market). Fama and French (1993) provide evidence that a three-factor model based on factors formed on the size and book-market characteristics explains average returns, and argue that the characteristics compensate for ‘distress risk.’ But Daniel and Titman (1997) argue that, after controlling for size and book/market ratios, returns are not strongly related to betas calculated based on the Fama and French (1993) factors (see, however, Davis et al. (2000) for a contrary view). Ferson and Harvey (1997) find that book/market and the Fama-French loadings are both relevant for determining expected returns in the international context. More recently, Daniel and Titman (2006) argue that the book/market effect is driven by overreaction to that part of the book/market ratio not related to accounting fundamentals. The part of this ratio that is related to fundamentals does not appear to forecast returns, thus raising questions about the ‘distress-risk’ explanation based upon fundamentals.
Brennan et al. (1998) find that investments based on book/market and size result in reward-to-risk ratios which are about three times as high as that obtained by investing in the market. These seem too large to be consistent with a rational asset pricing model. Given the Euler equation for the representative investor, as Hansen and Jagannathan (1991) point out, a high Sharpe ratio implies highly variable marginal utility across states. Moreover, the returns of small and high book/market stocks would need to covary negatively with marginal utility. This implies that the returns would need to be particularly high in good times when marginal utility is low and vice versa. Lakonishok et al. (1994) do not find any evidence that this is true.
Rouwenhorst (1999) finds that firm size and book-to-market ratios predict returns in several emerging markets. Daniel and Titman (1997) also find that the common stocks of firms with higher book/market ratios are more liquid than vice versa, so that the book/market effect cannot be justified by way of an illiquidity premium.
Turning now to other effects, Jegadeesh and Titman (1993) provide evidence of the important ‘momentum anomaly,’ namely, the cross-sectional predictability of returns over 6–12 month horizons. Rouwenhorst (1998) finds out-of-sample evidence of a momentum effect in many European countries. The momentum anomaly has been analyzed extensively in subsequent literature, and there is little doubt that it is robust across time, and across many countries. While Conrad and Kaul (1998) attribute the momentum anomaly to time-variation in expected returns, Jegadeesh and Titman (2002) argue that methodological issues in their study negate their conclusions.
Haugen and Baker (1996) find that the strongest determinants of expected returns are past returns, trading volume and accounting ratios such as return on equity and price/earnings. They find no evidence that risk measures such as systematic or total volatility are material for the cross-section of equity returns. Lakonishok et al. (1994) show that the return performance of glamour stocks (measured by high price/fundamental ratios such as market/book) is not impressive and value stocks do better. Baker and Stein (2004) argue that the negative relation between returns and past volume is driven by optimistic investors generating volume, and their optimism getting reversed in subsequent periods. Due to short-selling constraints, pessimism does not adequately get reflected in stock prices. In a similar vein Diether et al. (2002) find that stocks with higher dispersion of analyst earnings forecasts earn lower returns than other similar stocks. They suggest this happens because while dispersion implies high optimism and pessimism, the latter does not get into prices because of short-selling constraints. Thus the negative relation between future returns and dispersion can obtain because the high optimism inherent in high dispersion gets reversed out in subsequent stock prices. Chen et al. (2002) provide a related argument by positing that low breadth of long ownership in a stock indicates that the short-selling constraint is binding, so that prices in these stocks become very high relative to fundamentals. This suggests that prices should reverse more in stocks experiencing reductions in breadth; they find some empirical support for this phenomenon.
Some recent papers shed light on the type of stocks in which mispricing may be most intense. For example, Baker and Wurgler (2006) define a number of investor sentiment proxies at the aggregate level. These include share turnover, the closed-end fund discount (used by Lee et al. (1991)) and first-day IPO returns (suggested by Ritter, 1991). They find that stocks that are difficult to arbitrage (e.g., small, highly volatile ones) exhibit the maximum reversals in subsequent months when investor sentiment is high in a given period. Similarly, Zhang (2006) argues that stocks with greater information uncertainty (e.g., those which are small and have low analyst following) exhibit stronger statistical evidence of mispricing in terms of return predictability from book/market and momentum within cross-sectional regressions. Finally, Nagel (2005) provides evidence that the mispricing is greatest for stocks where institutional ownership is lowest; here institutional ownership is a proxy for the extent to which short-selling constraints bind (the assumption is that short-selling is cheaper for institutions).
In sum, the evidence indicates that support for non-risk related characteristics as predictors of stock returns is far more compelling than risk-based ones. This has led to some prominent theoretical attempts to explain patterns in the cross-section of returns, as discussed in the next subsection.
2.2 Theoretical literature
Prominent attempts to explain patterns in stock returns are Daniel et al. (1998, 2001), Barberis et al. (1998), and Hong and Stein (1999). The first paper attempts to explain patterns using overconfidence and self-attribution. Overconfidence about private signals causes overreaction and hence phenomena like the book/market effect and long-run reversals., whereas self-attribution (attributing success to competence and failures to bad luck) maintains overconfidence and allows prices to continue to overreact, creating momentum. In the longer-run there is reversal as prices revert to fundamentals as a consequence of Bayesian updating by agents. In a related paper Gervais and Odean (2001) formally model self-attribution bias in a dynamic setting with learning, and show that if this bias is severe, it may prevent a finitely-lived agent from ever learning about his true ability.
The Barberis et al. (1998) theory states that extrapolation from random sequences, wherein agents expect patterns in small samples to continue, creats overreaction (and subsequent reversals), whereas conservatism, the opposite of extrapolation, creates momentum through underreaction. Hong and Stein (1999) suggest that gradual diffusion of news causes momentum, and feedback traders who buy based on past returns create overreaction because they attribute the actions of past momentum traders to news and hence end up purchasing too much stock, which, when positions are reversed, causes momentum. While Brav and Heaton (2002) use a model with uncertainty about model parameters such as the asset value's mean and rational Bayesian learning to explain predictable return patterns, it appears that their explanation relies on the specific nature of the prior uncertainty and its resolution to generate over- versus underreactions. For example, if agents are concerned with structural change in the mean and it does not occur, there will be overreaction due to too much weight on recent data. On the other hand, if agents are unsure whether structure change has occurred and it indeed has occurred there will be underreaction.
Hong et al. (2005) suggest a model where agents use overly-simplified models to evaluate stocks, ignoring the true, more complex model. They use this notion to explain a variety of phenomena including momentum and asset bubbles. For example, an agent who believes in a particular model uses this model to make persistent forecast errors while ignoring a persistent but pertinent information signal, which leads to momentum. Further, an agent using a particular model while seeing a sequence of positive earnings, can drastically re-evaluate his beliefs after seeing the sequence being broken, leading to dramatic changes in stock prices.
A notable recent addition to theoretical thought is Barberis and Shleifer (2003), which argues that the tendency of investors to heuristically categorize objects can lead to the emergence of style-based mutual funds. Further, assets within a style co-move more than those outside of that style. The paper by Barberis et al. (2005) follows up by documenting that S&P 500 betas of stocks go up when these stocks are added to the index, and, in effect, arguing that this comovement, at least in part, is simply because investors treat S&P stocks as belonging to one category.
Other empirical evidence on the theories is preliminary at this point. For example, Kausar and Taffler (2006) provide evidence supporting the Daniel et al. (1998) arguments. They show that stocks initially exhibit continuation in response to an announcement (a going-concern audit report) that the firm is in distress, but later exhibit reversals. Chan et al. (1996), however, argue that momentum is due to slow diffusion of news, because they do not find any evidence that high momentum stocks reverse later. Doukas and Petmezas (2005) find support for the self-attribution hypothesis in the market for corporate control. Specifically, they find that managers earn successfully smaller returns in each successive acquisition, suggesting they become more and more overconfident with each successful acquisition.
In other attempts at modelling behavioural biases, Barberis et al. (2001) and Barberis and Huang (2001) have attempted to incorporate the phenomenon of loss aversion into utility functions. Loss aversion refers to the notion that investors suffer greater disutility from a wealth loss than the utility from an equivalent wealth gain in absolute terms. Barberis and Huang (2001) show that loss aversion in individual stocks leads to excess stock price fluctuations, i.e., more than that justified by fluctuations in dividends (viz. Shiller, 1981). This happens because, for example, agents' response to past stock gains is to increase their desire to hold the stock and thereby, in effect, lower the discount rate, raising the stock price still further. Further, a book/market effect also obtains because stocks with high market/book are ones that have done well and thus require lower returns in equilibrium. Barberis et al. (2001) use similar arguments to justify aggregate phenomena of excess volatility. In essence, the high volatility leads excessive losses, that, in turn, cause the investor to require a high premium to hold stocks, which leads to an explanation of the equity premium puzzle. Grinblatt and Han (2005) argue that loss aversion can also help explain momentum. Specifically, past winners have excess selling pressure and past losers are not shunned as quickly as they should be, and this causes underreaction to public information. In equilibrium, past winners are undervalued and past losers are overvalued. This creates momentum as the misvaluation reverses over time.
Scheinkman and Xiong (2003) analyse the interaction of overconfidence and short-sale constraints. They show that agents with positive information may be tempted to buy overvalued assets because they believe they can sell that asset to agents with even more extreme beliefs. With short-sale constraints, negative sentiment is sluggish to get into prices, and this can lead to asset pricing bubbles. Hong et al. (2006) show that such phenomena can be exacerbated if assets have limited float (i.e., if a large number of shares are locked up with insiders who face selling restrictions. Hirshleifer and Teoh (2003) model the notion that individual investors may have limited attention spans and this may cause them to miss certain important aspects of financial statements (e.g., stock options) that are disclosed subtly and not directly. This may cause dramatic valuation shifts when full and direct disclosure is made. Bernardo and Welch (2001) show that overconfidence in an economy is beneficial because increased risk-taking by overconfident agents facilitates the emergence of entrepreneurs who exploit new ideas.
Can psychological arguments about investor biases be tested in an ex ante manner? In a recent attempt to do this Sorescu and Subrahmanyam (2006) test the argument of Griffin and Tversky (1992) that agents overreact to the strength of a signal (e.g., the warmth of a recommendation letter) and underreact to its weight (the letter-writer's reputation). Using analyst experience and the number of categories spanned by analyst revisions as proxies for weight and strength, respectively, they find some support for this hypothesis. This type of approach appears to have promise, but much work remains to be done along these lines.
2.3 Investor moods
A separate line of research documents the effects of moods on investors. Saunders (1993) documents that the NYSE stock market tends to earn positive returns on sunny days and returns are mediocre on cloudy days. Hirshleifer and Shumway (2003) confirm this evidence across a number of international markets. This suggests that investor mood (ostensibly negative on cloudy days) affects the stock market. Goetzmann and Zhu (2005) find suggestive evidence that this effect is not due to the trading patterns of individual investors, thus leaving open the possibility that it may arise from the moods of market makers.
Kamstra et al. (2000) document that returns around the weekend of the switch to standard time from daylight savings time are very negative, and suggest that induced depression from the switch amongst investors suffused with seasonal affective disorder causes the negative return. Edmans et al. (2005) indicate that outcomes of sporting events involving the country as a whole impact the stock market of the country. It is hard to imagine what else but mood could cause this effect.
Overall, the evidence in favour of inefficient financial markets is far more compelling than that in favour of efficient ones. It is noteworthy that just because there is evidence of predictable patterns in stock returns does not mean individual investors can make superior returns. In many of the studies, the magnitude of the effects are not large enough for retail investors to earn superior returns after accounting for transaction costs. However, institutions may well be able to take advantage of such pricing problems (in fact, casual empiricism indicates that many do).
2.4 Limits to arbitrage and the survival of irrational traders
If it is indeed the case that financial market prices are driven at least in part by irrational agents, then two issues arise: (i) why does arbitrage not remove any mispricing? (ii) why do irrational traders, who would lose money on average, not get driven out of the market in the long-run? Recently, progress has been made in answering both of the preceding questions. First, Shleifer and Vishny (1997) argue that arbitrage may be restricted because it is costly precisely when it would be useful in removing pricing inefficiencies. For example, because of marking-to-market, arbitrageurs may require more and more capital as prices diverge more and more from their efficient values. Furthermore, Daniel et al. (2001) argue that owing to risk aversion, arbitrageurs may not be able to remove all systematic mispricing.
There are at least three counter-arguments to the notion that irrational traders would cease to be influential in the long-run. First, DeLong et al. (1991) argue that irrational agents, being overconfident, can end up bearing more of the risk and can hence earn greater expected returns in the long-run. Second, Kyle (1997) argue that even if agents are risk-neutral, overconfidence acts as a precommitment to act aggressively, which causes the rational agent to scale back his trading activity. In equilibrium, this may cause overconfident agents to earn greater expected profits than rational ones. Finally, Hirshleifer et al. (2006) argue that when stock prices influence fundamentals by affecting corporate investment, irrational agents can earn greater expected profits than rational ones. This happens because irrational agents act on sentiment sequentially. Agents who act on sentiment early benefit from late arriving irrationals who push prices in the same direction as the early ones. If private information is noisy, this can result in situations where the irrationals as a group, outperform the rationals in terms of average profits. As we mention in the next section, however, if individual investors trade in financial markets just to obtain pleasure from trading as a consumption good, they may continue to trade even if they lose money on average.