12.2 DYNAMIC MARKETS AND RELATIVISTIC EFFECTS

econometrically tractable system. Brock and Kleidon (1992) show how bid-ask spreads fluctuate over the day by firm size categories as a measure of "thickness" of the market. Brock and LeBaron (1996) stress not only the standard asymmetric information theory in matching key stylized facts, but also the importance of the role of multiple time scales. Hommes (2000) provides a review of recent work on heterogeneous agent financial theory.

There are many ways to describe heterogeneous expectations. We believe that the most promising approach is to differentiate the expectations according to their time dimension because we consider the different time scales of the market participants the key characteristic of the market. Some are short-term traders, others have long-term horizons with market makers at the short-term end of the scale and central banks at the long-term end. Contrary to the usual assumption, there is no privileged time scale in the market. The interaction of components with different time scales gives rise to characteristically relativistic effects3 such as certain properties of volatility clusters, trend persistence, lag between interest rate adjustment, and FX rate adjustment. The latter is a good example of what conventional theory considers an inefficiency whereas we see it as an effect arising from the different time scales involved in the market. To take advantage of the lag in adjustment between interest rate and exchange rate moves, an investor needs to tie up his/her money for months or even years. This is a very long time for an FX trader. Some investors will thus tend to ignore these profit opportunities whereas others invest in them, as is testified by the development of managed currency funds based on this property. The combination of all of these effects ultimately enables the construction of successful forecasting and trading models.

In long time intervals, market price changes are "flatter" and have fewer relevant movements (trend changes) than in short-term intervals. The higher the resolution and the smaller the intervals, the larger the number of relevant price movements. The long and the short-term traders thus have different trading opportunities: the shorter the trading horizon, the greater the opportunity set. A market participants response to outside events should always be viewed as relative to ones intrinsic opportunity set. A short-term trader does not react in the same way as a long-term trader. Economic decision makers, such as traders, treasurers, and central bankers, interpret the same information differently. The variation in perspective has the effect that specific price movements cannot lead to a uniform reaction; rather, they result in individual reactions of different components. In turn, these reactions give rise to secondary reactions, with the different components reacting to their respective initial response. Watching the intraday price movements, one clearly sees the sequences of secondary reactions triggered by the initial events. See, for example, Goodhart and Curcio (1991); Almeida et al. (1998) on news effect on the FX market or Franke and Hess (1997) on the

3 We use here the term "relativistic" to express the dynamic interaction between different market components relative to each other rather than relative to the news that has impacted the market. These effects are sometimes called endogenous effects in the literature, Kurz (1994).

Deutsche Termin-Borse. The existence of different trading strategies in the market was also put forward in Chapter 7 to explain the HARCH effect of asymmetry in the information flow at different frequencies. LeBaron (2000) shows that introducing agents with different time horizons in his market model gives rise to heteroskedasticity effects in the resulting price volatility.

The delay with which the secondary reactions unfold is called the relaxation time. If diverse components with different time scales interact in the market, there is typically a mixture of long and short relaxation times following the impact of outside events. If different relaxation times are combined, the resulting autocorrelation decays hyperbolically or almost hyperbolically. This is a natural explanation of the long memory effects detected in financial markets. Dacorogna et al. (1993) studied the autocorrelation function for short-term absolute returns, confirmed the hyperbolic decay, and revealed that volatility clusters tend to have a longer memory than assumed by other studies of the subject. We saw in Chapter 7 that many studies confirm this effect.

There is yet another phenomenon, which originates from the fact that financial markets are spread worldwide. Economic and political news and trading activity are not stationary. They have a clear-cut pattern of moving around the world in a 24-hr cycle. The price data of foreign exchange rates reflect this in terms of a 24-hr seasonality in market volatility, Muller et al. (1990). This seasonality can be accounted for by introducing a business time scale such as in Dacorogna et al. (1993). The 24-hr cycle implies that market reactions to an event cannot be simultaneous and that there are distinct relaxation times following the event. Geographical components related to the business hours of the different trading centers must be added to the time components. The interaction of geographical components leads to behaviors such as the "heat wave" effect proposed by Engle etal. (1990).

12.3 IMPACT OF THE NEW TECHNOLOGY

The realization that there is value in the data to define an investment strategy has brought to life many new firms that specialize in modeling financial markets and in providing trading advices on the basis of technical models. The question is, of course, will the impact of the new technology be a passing phenomenon or will it have a long-term effect? As the relativistic phenomenon arises from the interaction of components with different time scales, it will remain appropriate as long as heterogeneous expectations continue to exist in the market. The interaction process may become more complex, but it cannot disappear.

News technologies enable users to identify additional trading opportunities to increase their profits. This quickens their pace of trading and contributes to higher market volume and liquidity. The improved liquidity lowers the spreads between bid and ask prices. Lower spreads imply lower transaction costs, which in turn increase the opportunity horizon for profitable trading. The new technology

12.4 ZERO-SUM GAME OR PERPETUUM MOBILE?

introduces a shift in perspective, with components starting to focus on more numerous short-term time intervals.

As components become increasingly short-term in their focus, the spectrum of short-term components increases. This has the effect that relative differences among components become more significant and the relativistic effects more pronounced. Contrary to accepted notions, which assume that sufficient buying power can "trade away" any phenomenon, the increased buying power will have the overall effect of enhancing the relativistic effects. Thus the very basis of our ability to forecast and build profitable trading models will be enhanced. This statement must be qualified in the sense that the reaction patterns will become increasingly diversified, and therefore more complex, and the speed of adjustment will increase requiring more and more sophisticated models.

12.4 ZERO-SUM GAME OR PERPETUUM MOBILE?

Conventional thought has it that financial markets must be a zero-sum game. This is true if we take a static view. In reality, the financial markets are dynamic and they are highly complex.

Markets are a platform for components to take advantage of the diversity of interests. They are able to match their opposing objectives when one component buys and another component sells. The lower the friction, the easier a counterpart for a particular transaction is found and the larger, therefore, is the particular components opportunity set. By being able to go ahead with a particular transaction, the flexibility of the respective components is increased and their profit potential improved.

The new technology fosters the ability of the market to provide an environment for the generation of wealth. As explained, interaction within the market gives rise to relativistic effects and relaxation times. To the extent that these relativistic effects are understood and incorporated into forecasting and trading model technology, market participants have the opportunity to generate additional profit or limit their losses. In our terminology, the profit that is generated is energy extracted from the market. Improved efficacy of component interaction generates additional energy and reduces the friction associated with buying and selling within the market. The process may be compared to the search for more efficient engines in the automobile industry where everybody gains from it in the long term.

Have we achieved a perpetuum mobile" The answer is clearly no. Like any other technological innovation, the new technology does not generate energy from nothing, but it does take advantage of the energy potential existing in the financial markets. By offering a service to the economic agents, financial markets are not closed systems but do get a permanent input of money. This makes them highly open systems in terms of energy. Besides, a lot of resources have been put into the new technology in the form of extensive research, development work, and hardware to treat the information. Numerous studies have shown that simple trading rules do not work in efficient markets. Only elaborated treatment of the