1. Market-Wide Anomalies

2. Outline Puzzles in the Aggregate Market-wide Data Behavioral Modeling
Equity Premium Puzzle
Excessive Volatility Puzzle
Behavioral Modeling
Belief-based Models: BSV(1998), DHS(1998),
Hong and Stein (1990)
Preference-based Models: Barberis, Huang, and Santos (2001)

3. Puzzles in the Aggregate Market-wide Data
Chapter 5 focuses on the consequences of behavioral biases to the capital market as a whole. There are two major anomalies in the aggregate market-wide data, that is, the equity premium puzzle and the excessive volatility puzzle.
Equity premium puzzle
The discussion was initiated by Mehra and Prescott (1985) who claimed that the average historical amount of premium on the US stock market, which stood at 6.2 percent in 1889–1978, was much too high given what had been theoretically predicted

4. Puzzles in the Aggregate Market-wide Data
based on changes in aggregated consumption.
The influence of fluctuations on the stock market on changes in aggregated consumption is not strong enough to justify such high levels of the risk premium.
In order to account for the high-risk premium observed historically, investors would have to display unrealistically high coefficients of relative risk aversion. It follows that very high risk-aversion coefficients would mean that investors should try to even out the consumption level intertemporally.

5. Puzzles in the Aggregate Market-wide Data
If common, this attitude should result in high real interest rates. In practice, however, real historical returns on risk-free assets are surprisingly low (Weil, 1989).
Numerous theoretical attempts to explain the equity premium puzzle questioned the assumptions adopted by Mehra and Prescott. The discussion focused on the following major areas: models accounting for additional risk; models assuming market segmentation; arguments of market incompleteness, transaction costs, and other market

6. Puzzles in the Aggregate Market-wide Data
imperfections; as well as behavioral models based on modified utility functions and referring to investor psychology.
Reitz (1988) suggested that the high equity premium may be explained if we assume that, over the studied period, investors were afraid of the slightly probable severe economic crash that could have happened but did not. That is why the ex post premium for shares seems so high.

7. Puzzles in the Aggregate Market-wide Data
Mankiw and Zeldes (1991) and Haliassos and Bertaut (1995) suggest that the reason the equity premium might seem too high compared to fluctuations of consumption is because market segmentation has not been factored in.
Mehra and Prescott (1985) used aggregated data on American consumption forgetting that almost three quarters of Americans do not invest in shares at all.
Such caveats solve the problem only partially. Even with market segmentation taken into account, equity premium still seems too elevated.

8. Puzzles in the Aggregate Market-wide Data
A large part of discussion in the literature focuses on ways to modify the utility function used to evaluate changes in the consumption level.
Constantinides (1990) suggests a habit formation model. Abel (1990) and Campbell and Cochrane (1999) claim that current consumption should be evaluated not against its past levels but rather the present consumption of other market players with whom the decision maker compares his own situation. These models can explain low real returns on safe instruments.

9. Puzzles in the Aggregate Market-wide Data
Fama and French (2002a) tried to explain the puzzle looking at changes in fundamental values—the rate of dividend and the price-to-earnings ratio. It turned out that the equity premium stemming from an increase in fundamental factors in the second half of the twentieth century should stand at 2.6 percent for the dividend-based model and 4.3 percent for the one based on the price-to-earnings ratio, significantly below the actual empirical values in the same period.

10. Puzzles in the Aggregate Market-wide Data
Behavioral finance offers its own explanation of the equity puzzle.
Benartzi and Thaler (1995) point out that mental accounting coexists with strong loss aversion. Being myopic in their attitude, investors frame and mentally account returns of each period separately. Hence, the high equity premium is a reward for taking the risk of short-term fluctuations and, as such, is necessary to overcome short-term loss aversion investors commonly experience.

11. Puzzles in the Aggregate Market-wide Data
Barberis, Huang, and Santos (2001) propose a formal model to explain the equity puzzle by myopic loss aversion.
Drawing on the prospect theory, they assume that investors evaluate utility not only on the basis of the total level of consumption, but also changes in wealth, and that they are more sensitive to losses than gains.
It is additionally assumed that the degree of risk aversion depends on previous investor’s experience, as earlier noticed by Thaler and Johnson (1990).

12. Puzzles in the Aggregate Market-wide Data
The model predicts that the equity premium in 1926–1995 should theoretically amount to 4.1 percent annually in real terms. In other words, it can explain a major part of the actually observed real premium, which, at the time, stood at about 6 percent per annum.
Another psychological phenomenon that may make investors expect higher equity premiums is ambiguity aversion whereby people are reluctant to take part in lotteries with undefined probability distribution (Olsen and Troughton, 2000).

13. Puzzles in the Aggregate Market-wide Data
Excessive Volatility Puzzle
Another phenomenon affecting the aggregated stock market that the classical theory of finance struggles to explain is excessive volatility of prices compared to observed fluctuations of fundamental values, such as earnings or dividends, or changes in expected consumption.
LeRoy and Porter (1981) and Shiller (1981) find that price variance is much higher than what might have been justified by changes in dividend levels.

14. Puzzles in the Aggregate Market-wide Data
If the variance of the returns is higher than the variance of dividends, it is obvious that there must be fluctuations of the price-to-dividend ratio (P/D).
The theoretical explanation for the fluctuations of P/D
Changing expectations of future dividends or changes in discount rates
Changes in discount rates, in turn, might stem from changing expectations related to returns on risk-free assets, changes in the expected level of risk, or changing risk aversion.

15. Puzzles in the Aggregate Market-wide Data
Campbell and Shiller (1988), Campbell (1991), and Fama and French (2002a) document that historical P/D levels do not translate into real dividend growth rates. Neither does the P/D ratio explain changes in the risk-free rate or fluctuations of risk levels in historical time series.
Therefore, the only factor that potentially can influence fluctuations of the P/D ratio and, consequently, explain higher variance for prices compared to dividends is the changing degree of risk aversion.

16. Puzzles in the Aggregate Market-wide Data
Campbell and Cochrane (1999) propose a model in which people are relatively slow to get used to a specific level of consumption.
If current consumption is higher than what consumers are accustomed to, risk aversion will decrease. Conversely, when current consumption is likely to fall below the habit level, risk aversion will increase.
Changes in the attitude to risk are reflected in the level of discount rates and, as a consequence, cause fluctuations in the P/D ratio.

17. Puzzles in the Aggregate Market-wide Data
Behavioral finance offers a number of potential explanations that could be roughly divided into two groups: those related to irrational investor beliefs and those based on instability of preferences.
1. The first group includes a representativeness bias in the form of the short-series error, which leads to the extrapolation bias and a belief in trends. Another mistake that may contribute to high price volatility is overconfidence combined with selective attribution.

18. Puzzles in the Aggregate Market-wide Data
Representativeness bias. Having observed a firm with a consecutive series of higher-than-expected earnings, investors underestimate the probability that the situation might be random and become mistakenly convinced that a permanent change has taken place and the observed growth will continue in the future. These expectations are reflected in current prices causing irrational fluctuations in the P/D ratio.
Overconfidence. Attaching too much importance to

19. Puzzles in the Aggregate Market-wide Data
privately acquired knowledge to the detriment of public information triggers price fluctuations that are not justified by real changes in earnings or dividends (Odean (1998b) and Daniel, Hirshleifer, and Subrahmanyam (1998, 2001)).
2. The second group includes irrational instability of investor preferences and shifts in the degree of risk aversion.
Barberis et al. (2001) suggest investors will change their preferences depending on the results of their former choices.

20. Puzzles in the Aggregate Market-wide Data
Following previous positive experiences, falling risk aversion should be observed and vice versa— after adverse events, investors will be more sensitive to risk. Shifts in the degree of risk aversion will result in applying different discount rates to forecasted cash flows resulting in periodical under- and overvaluation.

21. Behavioral Modeling
This section presents early attempts of behavioral modeling based on beliefs and preferences of market participants to explain the phenomena observed empirically on the market.
Model of Investor Sentiment
Barberis, Shleifer, and Vishny (1998)(BSV) suggest a model where attitudes of investors correspond to two behavioral patterns found in the literature: mean- reverting regime and trend earnings regime.

22. Behavioral Modeling
An investor convinced of the validity of the first pattern (mean-reverting) will react to new information slowly. Consequently, price adjustment to the new information is delayed and returns may periodically continue to follow a trend. Barberis et al. (1998) associate such investor behaviors with cognitive conservatism documented by Edwards (1968) and others.
On the other hand, investors who follow the second pattern (trending regime) attach great importance to the latest results and excessively extrapolate them into the future.

23. Behavioral Modeling
BSV (1998) associate this attitude with the phenomenon generally referred to by psychologists as the representativeness heuristic (Kahneman and Tversky, 1973; Tversky and Kahneman, 1974; Grether, 1980).
According to BSV (1998), the aforementioned mechanism, which is based on delayed changes in prevalence between the two alternative regimes, may explain the simultaneous occurrence of market underreaction in the short term and overreaction in the long term.

24. Behavioral Modeling
Daniel, Hirshleifer, and Subrahmanyam Model
DHS(1998) assume that investors can be divided into two categories: the informed and the under-informed. Informed traders may influence the market through their overconfidence. They overestimate the precision and overstate the importance of private information (calibration error) as compared to the weight of the information available publicly. Besides they try to attribute failures to other factors (attribution error).
If an investor assesses perspectives of a given company as positive and later on the assessment is

25. Behavioral Modeling
confirmed by good financial results or higher stock quotes, the investor’s confidence in his own skills will usually be reinforced.
In a reverse situation (i.e., if a given corporation does not measure up to expectations), investors will usually seek explanations other than self error. Only a compilation of multiple public contradictory signals, usually received over an extended period of time, may prevail over the original private signal and change the opinion of the investor.

26. Behavioral Modeling
As a result, DHS(1998) show that investor overconfidence will result in overreaction to private information, whereas distortions related to incorrect attribution of events are responsible for under- reaction to public signals. Such investor behavior may cause short-term continuations and long-term reversals in stock returns.

27. Behavioral Modeling Hong and Stein’s Model
Hong and Stein (1999) formulate a hypothesis that the market is composed of two categories of investors: (1) the supporters of fundamental analysis (“news watchers”) and (2) the momentum traders. Additionally, they assume fundamental information is distributed among new watchers gradually, which causes a certain delay in the reaction of the entire market.
Based on these assumptions, Hong and Stein show that when market is dominated by new watchers,

28. Behavioral Modeling
prices adjust to the new information gradually and the market reaction is usually slightly delayed.
Gradual inclusion of fundamental information results in continuation of returns and the occurrence of a trend. This, in turn, is a signal to the momentum traders, who bring the prices of assets to the proximity of their intrinsic values.
The actions of momentum traders are stimulated by increasingly clear price changes and will trigger overreaction of the market.

29. Behavioral Modeling
The growing mispricing will motivate news watchers to take action. At some point, activities of the news watchers will induce a correction and the general direction of market price changes will reverse.
Similarly to the BSV (1998) and DHS (1998), Hong and Stein (1999) appropriately handle the explanation of short-term continuations and long- term reversals. As in the case of the other models, long-term post-announcement drift after selective events is a source of certain difficulty for this model.

30. Behavioral Modeling Model of Shifting Risk Attitude
Barberis, Huang, and Santos (2001) propose a model drawn on three main ideas. First, investors care about fluctuations in the value of their financial wealth. Second, they are much more sensitive to reductions in their wealth than to increases. Third, people are less risk averse after prior gains and more risk averse after prior losses (Thaler and Johnson, 1990).
According to this model, a positive fundamental signal will generate a high return which lowers the

31. Behavioral Modeling
investors’ risk aversion. Therefore, investors apply a lower discount rate to the future dividend stream, giving stock prices an extra push upward. A similar mechanism holds for a bad fundamental signal.
One result of this effect is that stock returns are much more volatile than dividend changes. Normally, this pattern could be viewed as exhibiting market overreaction to initial good/bad news. Stock returns are made up of two “justified” components: one due to fundamental signals and the other to a change in risk aversion.

32. Behavioral Modeling
BHS(2001) demonstrate that their model fits well with several empirical observations. P/D ratios are inversely related to future stock returns. The returns are predictable in time series, weakly correlated with consumption, and have a high mean. The equity premium is justified because loss-averse investors require a high reward for holding a risky or excessively volatile asset.
Barberis and Huang (2001) further elaborate the model and focus on firm-level returns.