TOWARD A THEORY OF HETEROGENEOUS MARKETS

At the end of this in-depth review of some of the techniques and models used with high-frequency data, there is clear evidence that price movements of foreign exchange rates and other financial assets for short to medium-term horizons are predictable to some extent. This is substantiated by a positive forecast quality and high real-time trading model returns (e.g. Dacorogna et al, 1992; Pictet et al, 1992; Gencay et al, 2001c, 2002). More generally, financial returns of whatever asset substantially depart from the random walk model and are being predicted with some success by market participants.

Where does this sustained predictability originate? Are the real-time trading models, for instance, successful in capturing the inefficiencies of the foreign exchange (FX) market? Because this market is widely held to be the most efficient of the financial markets, does this success conflict with the theory of efficient markets, which precludes the ability to forecast and denies the existence of profitable trading models? Should we conclude from this evidence that markets are inefficient? We believe that we should rather adapt our theory of the financial market to the reality of the stylized facts and of markets that are very efficient in a newly defined way.

The motivation of this chapter is to explain why and how markets can be at the same time highly efficient and to some extent predictable. There are a number

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of reasons for this that are all associated with market dynamics. We want to put in perspective the current theory of efficiency and suggest to move beyond it. This is one of the big challenges ahead in the theory of finance. Many researchers are working in this special field, such as the whole movement of "behavioral finance" around Robert Shiller,1 or parts of the econophysics group and many others who see the need to find ways of moving from a rather static definition to a more dynamic one.

12.1 DEFINITION OF EFFICIENT MARKETS

In conventional economics, markets are assumed to be efficient if all available information is reflected in current market prices (Fama, 1970, 1991). Economists have embarked on weak, semi-strong, and strong-form efficiency tests. The weak-form tests investigate whether market prices actually reflect all available information. The semi-strong tests are based on so-called event studies, where the degree of market reaction to "news announcements" is analyzed. The strong-form tests, finally, analyze whether specific investors or groups have private information from which to take advantage. By and large, most studies conclude that the major financial markets are efficient and that all information is reflected in current prices. However, the conclusions of such studies have been bogged down by methodological questions: in particular, whether any observed departures from market efficiency are due to any genuine market inefficiency or whether a deficiency of the market pricing model is being used as a yardstick to compare actual with theoretical prices.

The inference that in an efficient market no excess return can be generated with trading models is based on the assumption that all investors act according to the rational expectation model (Shiller, 1989; Fama, 1970). If this assumption is wrong, the conclusion that forecasting is impossible is also questionable. The assumption of rational expectations has been called into question on various platforms and the idea of heterogeneous expectations has become of increasing interest to specialists. Shiller (1989), for example, argues that most participants in the stock market are not "smart investors" (following the rational expectation model) but rather follow trends and fashions. The modeling of "noise trader" has become a central subject of research in market microstructure models. On the FX market, there is much investigation of "speculative bubbles" and the influence of technical analysis on the dealers strategy (see, for example, Frankel and Froot, 1990). Some attention has also been caught by the possibility of time-varying expectations, which better reflect to our view of the market (Bekaert and Hodrick, 1992). Variation over time in expected returns poses a challenge for asset pricing theory because it requires an explicit dynamic theory in contrast to the traditional static capital asset pricing model (CAPM).

1 See, for instance, Shiller (2000) where the author claims that the market agents are essentially acting irrationally.

In summary, the conclusion that financial asset prices are not predictable is based on three assumptions: market prices reflect all the information available, news and events that hit the market are normally distributed, and the market is composed of homogeneous agents. The two first assumptions are reasonable starting points for the definition. The third assumption poses a real problem. It is clear that all market agents have in fact bounded rationality. They cannot be omniscient and do not all enjoy the same freedom of action and access to the markets. Recent works by Kurz (1994) and Gouree and Hommes (2000) present new theoretical models to tackle this problem. Introducing the heterogeneity of agents can give rise to very interesting nonlinear effects in the models. They show that many of the price fluctuations can be explained by endogenous effects. Similar conclusions are reached by Farmer and Lo (1999) in their discussion of market efficiency. They base their analysis on a comparison with the evolution of ecological systems. Farmer (1998) develops a market model inspired by ecological systems that contains agents with various trading strategies.

12.2 DYNAMIC MARKETS AND RELATIVISTIC EFFECTS

We just saw that conventional economics makes its inferences on efficient markets on the basis of a model in which economic agents are entities that act according to the rational expectation strategy. Any differences in planning horizons, frequency of trading, or institutional constraints are neglected. However, there is substantial empirical evidence that investors have heterogeneous expectations, as noted in Muller et al. (1993a) and Muller et al. (1997a). Surveys on the forecasts of participants in the FX market reflect the wide dispersion of expectation at any point in time. The huge volume of FX trading is another indication reinforcing this idea because it takes differences in expectation among market participants to explain why they trade.2 In Chapter 7, we presented the heterogeneous market hypothesis; at the end of this book the need for such a view becomes clear. It is the most elegant way to reconcile market efficiency with the stylized facts. Lux and Marchesi (1999) have developed simulation models of financial markets that include agents with different strategies (fundamentalists and chartists). They were able to show (Lux and Marchesi, 2000) that this model can reproduce most of the empirical regularities (fat tails, long memory, and scaling law) even though they use normally distributed news in their simulations.

The theoretical work on financial markets with heterogeneous agents has also gained momentum in the literature. Among this literature, Brock (1993), Brock and Kleidon (1992), Brock and LeBaron (1996), Brock and Hommes (1997), and Hommes (2000) investigate the underlying source for the structural heterogeneity of financial markets. Brock (1993) studies the interacting particles system theory to build structural asset pricing models. Brock and Hommes (1997) build a general theory of expectation formation, which nests rational expectations in an

2 Over $1500 billion US is traded every day in the different centers like Tokyo, London, and New York according to a survey taken every 3 years by the Bank for International Settlements (1999).