Herd Behavior Bubbles And Crashes Essay Example

Herd Behavior Bubbles And Crashes Essay Example Herd Behavior Bubbles And Crashes Essay Herd Behavior Bubbles And Crashes Essay Above average returns are reflected in a generally more optimistic attitude that fosters the disposition to overtake others bullish beliefs and viscera. This economic influence makes bubbles transient phenomena and leads to repeated fluctuations around fundamental values. For a long time, the thinking about the functioning of stock markets in the economics profession was dominated by the Efficient Market Hypothesis (MME). Recent empirical investigations as well as factual developments have, however, eroded the trust in a theory which denies the existence of any systemic deviations of stock prices from their fundamental values. From the empirical side, one of the most discussed facts that gives rise to doubts in the verbal efficiency of stock marketers the finding that stock prices exhibit more volatility than fundamentals or expected returns do. The volatility debate has recently been summarized and evaluated by West (iii). He finds evidence in favor of the excess volatility hypothesis to be persuasive and states that it cannot be explained adequately by standard models of expected returns or rational bubbles. Being not compatible with the random walk models suggested by the MME, the finding of excess volatility points to intrinsic dynamic forces of speculative markets not related to fundamental factors. In his conclusion West, therefore,suggests that it might be necessary consider non-standard models focusing on fads and sociological or psychological mechanisms. A related empirical finding is the recent evidence on mean- reversion in asset prices (e. G. Potherb and Summers, 1988, and references therein). Technically, this means that there is positive autocorrelation over short horizons and negative autocorrelation over longer intervals in the data. A possible explanation is speculative overshooting of the price trend which is gradually eliminated beyond some range. Potherb and Summers, too, repose fads models to understand this regularity. The case for behavioral models Of financial markets was already made emphatically by Sheller (iii), where also some hints are given concerning relevant material in other sciences. Another important author to be mentioned here is Kindergarten (1989). Throughout his penetrating book he highlights the importance of psychological factors and * Earlier versions of this paper were presented in seminars at the Universities of Bamberger, Fielded, Cologne and Munich. I would like to thank Carl Carmella, Reins Franken, Max Hobble, Alexander Henderson, Lurch Meyer, Caravans Garnishment, Michael Schmidt, Hans-Werner Sin, Rajah Seth and especially Charles Kindergarten for helpful discussions, comments, and suggestions. The perceptive comments and suggestions of the referees are also gratefully acknowledged. Iii ] 882 THE ECONOMIC JOURNAL irrational factors in explaining historical financial crises. L Following these authors, the aim in this paper is to construct an elementary model of stock market dynamics which explicitly includes contagion of opinion and behavior and to offer a behavioral explanation for the empirical findings discussed above. Of course, the search for a theory which includes some kind Of non-rational behavior has not gone unrecognized by economic and financial theorists and a new paradigm began gradually to arise in the past few years under the heading of noise trader models. This line of research is characterized by the introduction of traders which in some way deviate from a perfectly rational scheme of behavior. These agents appear as naive traders, noise traders or chartists. Some authors (Delano et al. 1990, 1991) assume that noise traders misperceive expected returns, others describe their behavior as following a impel feedback rule and study the resulting dynamics of the market (Day and Hang, 1990; connote and Leland, 1990; Carmella, 1992). The way in which this paper aims at contributing to this body of literature is that the psychological factors which influence the behavior Of unsophisticated traders will be modeled explicitly. This means that a formalism is introduced which describes the formation of expectations by those who are not fully informed about fundamentals. These expectations depend mainly (perhaps among other things) on the behavior and expectations of others. Thus, what will be modeled is the process of mutual mimetic contagion among speculators. The key mechanism is similar to that described in Karmas (1 993) recent formalizations recruitment ant populations, which Karma suggested to be also of relevance for the analysis of social dynamics in speculative markets. The mechanism introduced below seems to be also consistent with Topsoils (I 991) theory of mimetic contagion, where the agents try to trace out information about fundamentals from the bid and ask prices of others (who, however, may be as uninformed as they are themselves). The mechanics Of the contagion process are laid out in Section l. In Section II a more complete description of the market process is developed by adding a fundamentalist group of traders and deriving the dynamics of prices. Conditions are given under which contagion may lead to the existence of (positive or negative) bubbles, I. E. Stationary states where actual prices exceed fundamental values or are below them. Bull and bear markets are, however, not stationary in reality. Bubbles grow up and burst, and periods where assets are undervalued or overvalued do not last forever. So it seems to be more appropriate to model them as transient phenomena. Section Ill, therefore, develops a model where switches been bull and bear markets occur periodically. The reason for this oscillation is that we allow additional econometricians to influence the process of opinion formation. To be precise, a slowly changing optimistic or pessimistic bias is 1 The following quotation from the preface to the second edition seems to be characteristic his position: the dismissal of conventional explanations of historical events with the remark that they violate the assumptions of economic analysis [I. . Full rationality] is infuriating It is time that economics accept reality. Kindergarten, 1989, p. Xiii). K Royal Economic Society 1995 This content downloaded from 122. 170. 126. 130 on Moon, 9 Mar 2015 04:01 :50 1995] BEHAVIOR, BUBBLES AND CRASHES 883 added to the contagion process. This variable for the overall disposition of the market depends on the only hard information available to naive speculators: the development of their actual returns includin g capital gains. Hence, speculators are not simply blind followers of the crowd: they quickly react on others behavior in order not to miss profit opportunities, but they also try to find out whether prevailing optimism or pessimism has a firm grounding in he markets actual development. The consequence is that once the pool of additional buyers in a bull market is exhausted and price increases diminish a gradual erosion of confidence in the validity of bullish beliefs occurs. This ends with a crash, and the game is repeated with reversed signs. Section IV concludes and points to possible extensions of the present approach. AN ELEMENTARY FORMALIZATION OF CONTAGION The present section is mainly concerned with the determination of the behavior of those traders who do not have access to information about fundamental values. In the absence of any piece of such information they serially have to rely on what can be observed on the market as the only base of their actions. Though I do not intend to discuss h ere what kinds of behavior can be designated as rational, should emphasis that following others Opinion is not irrational as long as there is no other source of information (see Orleans (I 989) and Lectures (1 992) for intensive discussion). If we accept this extreme assumption as an accurate description of the information set of a considerable part of traders, then a first conclusion could be that a speculator will be more willing to buy (sell) if he sees most traders eying (selling). The reason is that others behavior may presumably be influenced by better information about future developments of the market and may thus reveal information. As already mentioned such conjectures may be false, but nevertheless may lead to self-reinforcing fluctuations. The underlying process of contagion will be formalized by referring to the concept of synergistic originally developed in elementary particle and laser physics (see e. G. Hake, 983) and applied to various problems from the social sciences by Woodlice and Hag (1983) among others. 3 Synergistic basically insists of a probabilistic, macroscopic approach to the analysis of the dynamics of multi-component systems with interactions among the units constituting the system. Infection of attitudes will now be made explicit: with a high portion of optimistic traders, it would be very probable that the few remaining, pessimistic ones would also change their attitude and buy stocks. The same is to be expected with reversed signs. Hence one may postulate probabilities exist for a pessimistic trader to become optimistic, say p+, and viscera,p,+. With contagion both probabilities should depend on the actual distribution of attitudes captured by the index x or the number n: = p_+(x) = p-+(n/N), p+_ = p+_(x) = p+_(n/N). Note that this formulation implies all other individuals influence one reticular speculator in the same way. This excludes the existence of financial gurus whose statements attract exceptional attention by others. Another simplifying assumption is that every individual may change his opinion only once at any one time. Assuming furthermore that the transition probabilities are the same for all actors and considering a large population of speculators the number of actual transitions from one subgroup to the other (I. E. Teens n+ and n_) can be approximated by the product members of subgroup times probability to change to another subgroup. Thus, the change n the composition of the population of naive speculators can be determined in the following way: those who are pessimistic turn to an optimistic attitude with probability p+,. Consequently, we expect a fraction n_p+- to switch from the n _ to the n+group. Vice versa, with the probability p+ a bullish speculator is infected with a nega tive disposition implying that approximately a fraction n+p+ of this population will change their trading strategy.