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Saturday, January 25, 2014

116. Econophysics



A financial market is a complex system in which a large number of traders interact with one another, and also react to information, and determine the ‘best’ price for a given item. The time evolution of the price and the number of transactions of a traded item is generally unpredictable.



The time series indicating the price variation of an item is found to be essentially indistinguishable from a stochastic or random process. Like other complex systems, financial markets are open systems with many interacting subunits, and the subunits interact nonlinearly.


In the study of stock markets, the so-called efficient-market hypothesis serves as a useful benchmark. An efficient market is defined as one in which all the available information is processed instantly when it reaches the market, and in which this fact is immediately reflected in new values of prices of the traded assets. The efficient-market hypothesis (EMH) makes the idealized stipulation that any market is highly efficient in determining the most rational price of a traded item or asset. It was originally formulated in the 1960s. There are two assumptions involved here:
(i) the market is efficient; and
(ii) the behaviour of traders is strictly rational.
As we shall see below, this is only an idealization.

Why does the time series of returns appear to be random? This is because it carries so much information that there are no readily discernible regularities in it. It is, by and large, a 'non-redundant' time series, meaning that the information it carries is almost irreducible, or algorithmically incompressible, for most practical purposes (cf. Part 23). The EMH requires that the concerned time series for market prices has a 'dense' amount of non-redundant information. Since there are limits on the speed and capacity of our computers, a time series carrying this information is almost indistinguishable from a totally random time series. Of course, analysis of the deviation from a totally random time series is a good way of testing the degree of validity of the EMH in a given situation.


Suppose there is good demand for a commodity because of its attractive existing price. Naturally, the price will increase. This will then reduce the demand. And a reduced demand will entail a lowering of the price, and so on, till the demand and the price have reached a state of equilibrium. Thus negative feedbacks tend to stabilize an economy, as per conventional economic theory. This law of diminishing returns implies a single equilibrium point for an economy, and such situations are amenable to analytical control.



By and large, resource-based economic activities (e.g. agriculture and mining) tend to follow the law of diminishing returns. By contrast, knowledge-based parts of an economy are generally governed by the law of increasing returns or positive feedback.


As demonstrated by the pioneering studies of Brian Arthur during the 1990s, positive feedbacks often occur in an economy, with the resultant multiple equilibrium points. Small shifts in the economy can get amplified, rather than smothered out. The economy evolves like any open, nonlinear complex system. There can be multiple bifurcations in phase space, and it is difficult to predict which bifurcation branch will be chosen by the market forces. What is more, once the random events select a particular branch or path in phase space, the choice tends to get locked-in, regardless of the advantages of the alternatives.

An example is the history of the VCR industry. The market started out with two competing formats, VHS and Beta, selling at about the same price. (It appears, in hindsight, that Beta was technically superior.) In the beginning there were increasing returns for each format, as their market shares increased. For example, a large number of VHS recorders in the hands of consumers motivated the vendors to stock more prerecorded tapes in the VHS format. This encouraged more people to buy VHS recorders. The same law of increasing returns operated for the Beta format also. In the beginning there were fluctuations in the fortunes of the two competing brands, attributable to factors such as external circumstances, ‘luck’, and corporate manoeuvring. Then, perhaps by chance, increasing returns on early gains by VHS (reduced production costs per unit on increased volumes of production) tilted the game in favour of VHS, driving the other technology out of the market. This is something which could not have been predicted in the beginning.

The law of increasing returns can go beyond the product with which a company started (Arthur 1990): ‘Not only do the costs of producing high-technology products fall as a company makes more of them, but the benefits of using them increase. Many items such as computers or telecommunications equipment work in networks that require compatibility. When one brand gains a significant market share, people have a strong incentive to buy more of the same product so as to be able to exchange information with those using it already.’



Path dependence

In a positive-feedback economy, although the individual transactions are small and essentially random events, they can accumulate by the positive (nonlinear) feedbacks. A number of characteristics or historical antecedents of positive-feedback economies can be listed:

1. In a particular industry, there is often a clustering of firms in a specific geographical location. A different location would have been better, but there is a kind of freezing of historical accidents in what has actually happened. Why? The first firm chooses a location for some logical (or even illogical) reason. The choice of the second firm depends not only on the (real or perceived) merits of that region, but also on the fact that it is profitable to be near the first firm. There is a cascading effect because the third firm may be influenced more by the presence of the first two firms in that region, than by the absolute merit of that region; and so on.

2. Railroad gauges are what they are at present because, once a particular choice was made (even arbitrarily), it was economical to stick to that choice everywhere in that region. There is a self-enforcement effect operating here.

3. The initial advantage possessed by a country or a multinational corporation can snowball into total dominance at the global level, until a better or cheaper product overcomes the monopoly. This highlights the importance of industrial research in any knowledge-based economy. Another important factor is the timing of release of a product.

In the language of evolution of the phase-space trajectory, what we are seeing here are random bifurcations in phase space (cf. Part 30). Once a branch of a bifurcation gets selected for further time-evolution, there is no going back; there is only a locked-in trajectory along a particular path in phase space. Thus the evolution of a positive-feedback economy has a strong path dependence. This can cause even hitherto successful economies to become locked into inferior paths of development. There is always a danger that a sound technology, with good long-term potential, may get rejected just because it has a long gestation period and slow initial growth. Similarly, when two new technologies compete, the one with a better initial acceptance by people may oust the other from the market, even when the other technology is inherently better (as shown by later events). Early superiority or ‘selectional advantage’ is no guarantee of long-term fitness. Arthur (1990) cites the example of how the U.S. nuclear-power programme got ‘phase-locked’ into the light-water-cooled reactors option, even though the high-temperature, gas-cooled, reactor designs may be inherently superior.

The bottom line is that, unlike negative-feedback economies, positive feedback economies do not head for a unique equilibrium; their phase-space trajectory is not path-independent. Like in a chaotic system, even identical-looking initial conditions can lead to divergence in trajectories, simply because even small events or errors may get hugely amplified as time passes. Long-term accurate forecasting then becomes difficult, if not impossible.

Kurzweil (2005) has made an interesting point about the long-term predictability of stocks of companies dealing with information technologies. Such technologies are highly influential in just about every industry now. 'With the full realization of the GNR revolutions in a few decades, every area of human endeavour will essentially comprise information technologies and thus will directly benefit from the law of increasing returns'. [Here GNR stands for Genetics-Nanotechnology-Robotics.] This should mean that it makes sense to make long-term investments in the stocks of companies dealing with such technologies (provided the companies are managed well !).


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The emergence of humans has sharply accelerated the rise of the overall complexity of our Earth. This has happened, and is still happening at an ever-increasing pace, because of the evolution of cultural complexity. A major reason for this is the very high level of intelligence possessed by humans. I shall discuss the nature of intelligence in the next few posts. That will be the final topic in this series of blog posts under the label 'Understanding Natural Phenomena'.