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 !).
***
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'.
