Do expectations matter or do asset prices fully reflect economic fundamentals? Do hetero geneous beliefs of millions of different investors cancel out on average due to aggregation, or can optimistic or pessimistic views cluster together and cause prices to deviate from underlying economic fundamentals? These questions have been a matter of heavy debate among economists as well as financial practitioners for many decades already. Keynes, for example, argued that stock prices are not governed by an objective view of 'fundamentals', but by 'what average opinion expects average opinion to be'. In Keynes words "Investment based on genuine long term expectation is so difficult as to be scarcely practicable. He who attempts it must surely lead much more laborious days and run greater risks than he who tries to guess better than the crowd how the crowd will behave; and, given equal intelligence, he may make more disastrous mistakes" (Keynes, 1936, p.157).
In contrast, new classical economists have viewed "market psychology", "investors sentiment" and "trend following speculation" as being irrational and therefore inconsistent with the rational expectations hypothesis (REH) and the efficient market hypothesis (EMH). Friedman, for example, argued that irrational speculative traders would be driven out of the market by rational traders, who would trade against them by taking long opposite positions, thus driving prices back to fundamentals. In Friedman's words: "People who argue that speculation is generally destabilizing seldom realize that this is largely equivalent to saying that speculators lose money, since speculation can be destabilizing in general only if speculators on the average sell when the currency is low in price and buy when it is high" [emphasis added] (Friedman, 1953, p.175).
In empirical work much attention has been paid to the closely related question whether asset prices exhibit excess volatility, that is, whether volatility of asset prices is larger than volatility of underlying economic fundamentals. In particular the work by Shiller (1987, 2000) has emphasized the possibility of excess volatility and persistent deviations of asset prices from a fundamental RE benchmark. In behavioral finance, for example, Thaler (1994) has argued that quasi rationality may be a key source of deviations from the RE fundamental benchmark and excess volatility. Quasi rationality means less than fully rational behavior, for example, due to investors sentiment, overconfidence or overreaction. However work by Boldrin and Levine (2001) argues that patterns of returns behavior that look like evidence of "irrationality" or "bounded rationality" may be simply rational reaction of stock markets to earnings profiles generated by technological change. Our paper is focused more on higher frequency fluctuations than Boldrin and Levine (2001), but related arguments must always make one wary of concluding that patterns of booms and crashes in stock market values are evidence of any kind of irrational pricing. See the discussion of Kleidon's work below.
Experimental work has also addressed the question of possible deviations from the bench mark RE fundamental in speculative asset markets. For example, Smith, Suchanek and Williams (1988) showed that speculative bubbles and deviations from a benchmark RE fundamental are frequently observed in experimental asset markets. These temporary bubbles tend to disappear however towards the end of the experimental asset market and also tend to become smaller as traders become more experienced. Kleidon (1994) has written a recent review paper about market "pathologies" such as crashes, blow offs, excess volatility, anomalies, etc.; see also Plott and Sunder (1988) and Camerer (1989). In particular he points out how the experimental literature in an asymmetric information setting has shown that REE is not achieved immediately but tends to be achieved by experienced traders. Kleidon states, "The laboratory results provided insight into when imperfect aggregation is more likely to occur, namely an absence of common information about preferences or beliefs of other traders and a lack of traders experience in the market setting." Kleidon (1994, p. 4, 5) stresses the careful differentiation between modeling "new 'external' information about fundamentals, that is, information about expected future cash flows or discount rates that reaches any trader or investor for the first time" and modeling "rational changes in internal information about fundamentals."
The debate whether expectations affect asset prices and may lead to excess volatility should be viewed in the light of two important developments in the recent literature: bounded rationality and heterogeneous agents systems. Bounded rationality and heterogeneous agents may be viewed as building blocks in behavioral finance, where traders are viewed as boundedly rational agents using simple, habitual rule of thumb rules, see e.g. Shefrin (2000). Although rational expectations remains an important benchmark, work on bounded rationality in the past decade may be viewed as an attempt to explore deviations from this benchmark. General surveys on bounded rationality in expectations and learning are e.g. Sargent (1993), Grandmont (1998) and Evans and Honkapohja (2001). In particular, Sargent (1999) argues that many of the bounded rational expectations equilibria may be viewed as 'approximate' rational expectations equilibria.
Contents
1 Introduction
2 Adaptive Belief Systems
- 2.1 The EMH benchmark with rational agents
2.2 Heterogeneous beliefs
2.3 Evolutionary dynamics
3 Large Type Limits
- 3.1 Evolution for finitely many traders
3.2 The limit evolution
4 Convergence to large type limits
- 4.1 Notation
4.2 The convergence theorem
4.3 Applicability
4.4 Preliminaries
4.5 Uniform law of large numbers
5 Dynamical consequences
- 5.1 Structural stability and persistence
5.2 Application to large type limits
6 Evolutionary dynamics in a simple LTL
7 Concluding Remarks
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Evolutionary dynamics in financial markets with many trader types
