N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 317 In the context at hand,Griffin and Tversky's theory suggests that individuals might underweight the information contained in isolated quarterly earnings announcements,since a single earnings number seems like a weakly informative blip exhibiting no particular pattern or strength on its own.In doing so,they ignore the substantial weight that the latest earnings news has for forecasting the level of earnings,particularly when earnings are close to a random walk.At the same time,individuals might overweight consistent multiyear patterns of notice- ably high or low earnings growth.Such data can be very salient,or have high strength,yet their weight in forecasting earnings growth rates can be quite low. Unfortunately,the psychological evidence does not tell us quantitatively what kind of information is strong and salient(and hence is overreacted to)and what kind of information is low in weight(and hence is underreacted to).For example, it does not tell us how long a sequence of earnings increases is required for its strength to cause significant overpricing.Nor does the evidence tell us the magnitude of the reaction(relative to a true Bayesian)to information that has high strength and weight,or low strength and weight.For these reasons,it would be inappropriate for us to say that our model is derived from the psychological evidence,as opposed to just being motivated by it. There are also some stock trading experiments that are consistent with the psychological evidence as well as with the model presented below.Andreassen and Kraus(1990)show subjects(who are university undergraduates untrained in finance)a time series of stock prices and ask them to trade at the prevailing price.After subjects trade,the next realization of price appears,and they can trade again.Trades do not affect prices:subjects trade with a time series rather than with each other.Stock prices are rescaled real stock prices taken from the financial press,and sometimes modified by the introduction of trends Andreassen and Kraus's basic findings are as follows.Subjects generally 'track prices',i.e.,sell when prices rise and buy when prices fall,even when the series they are offered is a random walk.This is the fairly universal mode of behavior,which is consistent with underreaction to news in markets.However, when subjects are given a series of data with an ostensible trend,they reduce tracking,i.e.,they trade less in response to price movements.It is not clear from Andreassen and Kraus's results whether subjects actually switch from bucking trends to chasing them,although their findings certainly suggest it. De Bondt(1993)nicely complements Andreassen and Kraus's findings.Using a combination of classroom experiments and investor surveys,De Bondt finds strong evidence that people extrapolate past trends.In one case,he asks subjects to forecast future stock price levels after showing them past stock prices over unnamed periods.He also analyzes a sample of regular forecasts of the Dow Jones Index from a survey of members of the American Association of Indi- vidual Investors.In both cases,the forecasted change in price level is higher following a series of previous price increases than following price decreases, suggesting that investors indeed chase trends once they think they see them
In the context at hand, Griffin and Tversky’s theory suggests that individuals might underweight the information contained in isolated quarterly earnings announcements, since a single earnings number seems like a weakly informative blip exhibiting no particular pattern or strength on its own. In doing so, they ignore the substantial weight that the latest earnings news has for forecasting the level of earnings, particularly when earnings are close to a random walk. At the same time, individuals might overweight consistent multiyear patterns of noticeably high or low earnings growth. Such data can be very salient, or have high strength, yet their weight in forecasting earnings growth rates can be quite low. Unfortunately, the psychological evidence does not tell us quantitatively what kind of information is strong and salient (and hence is overreacted to) and what kind of information is low in weight (and hence is underreacted to). For example, it does not tell us how long a sequence of earnings increases is required for its strength to cause significant overpricing. Nor does the evidence tell us the magnitude of the reaction (relative to a true Bayesian) to information that has high strength and weight, or low strength and weight. For these reasons, it would be inappropriate for us to say that our model is derived from the psychological evidence, as opposed to just being motivated by it. There are also some stock trading experiments that are consistent with the psychological evidence as well as with the model presented below. Andreassen and Kraus (1990) show subjects (who are university undergraduates untrained in finance) a time series of stock prices and ask them to trade at the prevailing price. After subjects trade, the next realization of price appears, and they can trade again. Trades do not affect prices: subjects trade with a time series rather than with each other. Stock prices are rescaled real stock prices taken from the financial press, and sometimes modified by the introduction of trends. Andreassen and Kraus’s basic findings are as follows. Subjects generally ‘track prices’, i.e., sell when prices rise and buy when prices fall, even when the series they are offered is a random walk. This is the fairly universal mode of behavior, which is consistent with underreaction to news in markets. However, when subjects are given a series of data with an ostensible trend, they reduce tracking, i.e., they trade less in response to price movements. It is not clear from Andreassen and Kraus’s results whether subjects actually switch from bucking trends to chasing them, although their findings certainly suggest it. De Bondt (1993) nicely complements Andreassen and Kraus’s findings. Using a combination of classroom experiments and investor surveys, De Bondt finds strong evidence that people extrapolate past trends. In one case, he asks subjects to forecast future stock price levels after showing them past stock prices over unnamed periods. He also analyzes a sample of regular forecasts of the Dow Jones Index from a survey of members of the American Association of Individual Investors. In both cases, the forecasted change in price level is higher following a series of previous price increases than following price decreases, suggesting that investors indeed chase trends once they think they see them. N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343 317
318 N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 4.A model of investor sentiment 4.1.Informal description of the model The model we present in this section attempts to capture the empirical evidence summarized in Section 2 using the ideas from psychology discussed in Section 3.We consider a model with a representative,risk-neutral investor with discount rate 8.We can think of this investor's beliefs as reflecting the 'consen- sus',even if different investors have different beliefs.There is only one security, which pays out 100%of its earnings as dividends;in this context,the equilib- rium price of the security is equal to the net present value of future earnings,as forecasted by the representative investor.In contrast to models with heterogen- eous agents,there is no information in prices over and above the information already contained in earnings. Given the assumptions of risk-neutrality and a constant discount rate,returns are unpredictable if the investor knows the correct process followed by the earnings stream,a fact first established by Samuelson(1965).If our model is to generate the kind of predictability in returns documented in the empirical studies discussed in Section 2,the investor must be using the wrong model to form expectations. We suppose that the earnings stream follows a random walk.This assumption is not entirely accurate,as we discussed above,since earnings growth rates at one-to three-quarter horizons are slightly positively autocorrelated(Bernard and Thomas,1990).We make our assumption for concreteness,and it is not at all essential for generating the results.What is essential is that investors some- times believe that earnings are more stationary than they really are-the idea stressed by Bernard and captured within our model below.This relative misper- ception is the key to underreaction. The investor in our model does not realize that earnings follow a random walk.He thinks that the world moves between two 'states'or 'regimes'and that there is a different model governing earnings in each regime.When the world is in regime 1,Model 1 determines earnings;in regime 2,it is Model 2 that determines them.Neither of the two models is a random walk.Rather,under Model 1,earnings are mean-reverting;in Model 2,they trend.For simplicity,we specify these models as Markov processes:that is,in each model the change in earnings in period t depends only on the change in earnings in period t-1.The only difference between the two models lies in the transition probabilities.Under Model 1,earnings shocks are likely to be reversed in the following period,so that a positive shock to earnings is more likely to be followed in the next period by a negative shock than by another positive shock.Under Model 2,shocks are more likely to be followed by another shock of the same sign. The idea that the investor believes that the world is governed by one of the two incorrect models is a crude way of capturing the psychological phenomena
4. A model of investor sentiment 4.1. Informal description of the model The model we present in this section attempts to capture the empirical evidence summarized in Section 2 using the ideas from psychology discussed in Section 3. We consider a model with a representative, risk-neutral investor with discount rate d. We can think of this investor’s beliefs as reflecting the ‘consensus’, even if different investors have different beliefs. There is only one security, which pays out 100% of its earnings as dividends; in this context, the equilibrium price of the security is equal to the net present value of future earnings, as forecasted by the representative investor. In contrast to models with heterogeneous agents, there is no information in prices over and above the information already contained in earnings. Given the assumptions of risk-neutrality and a constant discount rate, returns are unpredictable if the investor knows the correct process followed by the earnings stream, a fact first established by Samuelson (1965). If our model is to generate the kind of predictability in returns documented in the empirical studies discussed in Section 2, the investor must be using the wrong model to form expectations. We suppose that the earnings stream follows a random walk. This assumption is not entirely accurate, as we discussed above, since earnings growth rates at one- to three-quarter horizons are slightly positively autocorrelated (Bernard and Thomas, 1990). We make our assumption for concreteness, and it is not at all essential for generating the results. What is essential is that investors sometimes believe that earnings are more stationary than they really are — the idea stressed by Bernard and captured within our model below. This relative misperception is the key to underreaction. The investor in our model does not realize that earnings follow a random walk. He thinks that the world moves between two ‘states’ or ‘regimes’ and that there is a different model governing earnings in each regime. When the world is in regime 1, Model 1 determines earnings; in regime 2, it is Model 2 that determines them. Neither of the two models is a random walk. Rather, under Model 1, earnings are mean-reverting; in Model 2, they trend. For simplicity, we specify these models as Markov processes: that is, in each model the change in earnings in period t depends only on the change in earnings in period t!1. The only difference between the two models lies in the transition probabilities. Under Model 1, earnings shocks are likely to be reversed in the following period, so that a positive shock to earnings is more likely to be followed in the next period by a negative shock than by another positive shock. Under Model 2, shocks are more likely to be followed by another shock of the same sign. The idea that the investor believes that the world is governed by one of the two incorrect models is a crude way of capturing the psychological phenomena 318 N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343
N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 319 of the previous section.Model 1 generates effects identical to those predicted by conservatism.An investor using Model 1 to forecast earnings reacts too little to an individual earnings announcement,as would an investor exhibiting conser- vatism.From the perspective of Griffin and Tversky (1992),there is insufficient reaction to individual earnings announcements because they are low in strength. In fact,these announcements have extremely high weight when earnings follow a random walk,but investors are insensitive to this aspect of the evidence. In contrast,the investor who believes in Model 2 behaves as if he is subject to the representativeness heuristic.After a string of positive or negative earnings changes,the investor uses Model 2 to forecast future earnings,extrapolating past performance too far into the future.This captures the way that representa- tiveness might lead investors to associate past earnings growth too strongly with future earnings growth.In the language of Griffin and Tversky,investors overreact to the information in a string of positive or negative earnings changes since it is of high strength;they ignore the fact that it has low weight when earnings simply follow a random walk. The investor also believes that there is an underlying regime-switching pro- cess that determines which regime the world is in at any time.We specify this underlying process as a Markov process as well,so that whether the current regime is Model 1 or Model 2 depends only on what the regime was last period. We focus attention on cases in which regime switches are relatively rare.That is, if Model 1 determines the change in earnings in period t,it is likely that it determines earnings in period t+1 also.The same applies to Model 2.With some small probability,though,the regime changes,and the other model begins generating earnings.For reasons that will become apparent,we often require the regime-switching probabilities to be such that the investor thinks that the world is in the mean-reverting regime of Model 1 more often than he believes it to be in the trending regime of Model 2. The transition probabilities associated with Models 1 and 2 and with the underlying regime-switching process are fixed in the investor's mind.In order to value the security,the investor needs to forecast future earnings.To do this,he uses the earnings stream he has observed to update his beliefs about which regime is generating earnings.Once this is done,he uses the regime-switching model to forecast future earnings.The investor updates in a Bayesian fashion even though his model of earnings is incorrect.For instance,if he observes two consecutive earnings shocks of the same sign,he believes more strongly that he is in the trending earnings regime of Model 2.If the earnings shock this period is of the opposite sign to last period's earnings shock,he puts more weight on Model 1,the mean-reverting regime. Our model differs from more typical models of learning.In our framework, the investor never changes the model he is using to forecast earnings,but rather uses the same regime-switching model,with the same regimes and transition probabilities throughout.Even after observing a very long stream of earnings
of the previous section. Model 1 generates effects identical to those predicted by conservatism. An investor using Model 1 to forecast earnings reacts too little to an individual earnings announcement, as would an investor exhibiting conservatism. From the perspective of Griffin and Tversky (1992), there is insufficient reaction to individual earnings announcements because they are low in strength. In fact, these announcements have extremely high weight when earnings follow a random walk, but investors are insensitive to this aspect of the evidence. In contrast, the investor who believes in Model 2 behaves as if he is subject to the representativeness heuristic. After a string of positive or negative earnings changes, the investor uses Model 2 to forecast future earnings, extrapolating past performance too far into the future. This captures the way that representativeness might lead investors to associate past earnings growth too strongly with future earnings growth. In the language of Griffin and Tversky, investors overreact to the information in a string of positive or negative earnings changes since it is of high strength; they ignore the fact that it has low weight when earnings simply follow a random walk. The investor also believes that there is an underlying regime-switching process that determines which regime the world is in at any time. We specify this underlying process as a Markov process as well, so that whether the current regime is Model 1 or Model 2 depends only on what the regime was last period. We focus attention on cases in which regime switches are relatively rare. That is, if Model 1 determines the change in earnings in period t, it is likely that it determines earnings in period t#1 also. The same applies to Model 2. With some small probability, though, the regime changes, and the other model begins generating earnings. For reasons that will become apparent, we often require the regime-switching probabilities to be such that the investor thinks that the world is in the mean-reverting regime of Model 1 more often than he believes it to be in the trending regime of Model 2. The transition probabilities associated with Models 1 and 2 and with the underlying regime-switching process are fixed in the investor’s mind. In order to value the security, the investor needs to forecast future earnings. To do this, he uses the earnings stream he has observed to update his beliefs about which regime is generating earnings. Once this is done, he uses the regime-switching model to forecast future earnings. The investor updates in a Bayesian fashion even though his model of earnings is incorrect. For instance, if he observes two consecutive earnings shocks of the same sign, he believes more strongly that he is in the trending earnings regime of Model 2. If the earnings shock this period is of the opposite sign to last period’s earnings shock, he puts more weight on Model 1, the mean-reverting regime. Our model differs from more typical models of learning. In our framework, the investor never changes the model he is using to forecast earnings, but rather uses the same regime-switching model, with the same regimes and transition probabilities throughout. Even after observing a very long stream of earnings N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343 319