WHEN Hurricane Andrew scythed through Florida and Louisiana in 1992, it left
behind a cruel trail of destruction. But people living along the storm track
were not the only ones to take a beating. The financial waves triggered by this
most costly hurricane ever spread around the world, battering many insurance
companies and sinking others.
Now, given that seers, soothsayers and scientists have all failed to find a
reliable way to forecast truly devastating storms, a prudent insurance company
chief might at least hope for some idea of how to offset the firm鈥檚 risk against
such disasters. And a company with a more aggressive style might even want to
know what impact another costly storm would have on its rivals, and be ready to
exploit any business opportunities that might arise.
Today, such business decisions are based largely on rules of thumb gained
from long experience. But company chiefs long to do better. They hunger for some
way to replace hunches and experience with a systematic approach to making
decisions. They want to be able to develop theories about how their business
works which they can put to the test in rigorous, repeatable experiments. In
short, they want business to become a science.
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As recently as the early 1980s, the idea of subjecting social and behavioural
systems to scientific study was shunned because humans were thought to be 鈥渢oo
complex鈥� and 鈥渦npredictable鈥�. But, in reality, these have never been the main
barriers. The real problem has been the lack of laboratories in which to conduct
experiments.
Today, we have these laboratories. They come in the form of powerful
computers running simulations of real-life behaviour. And, while these
simulations are still in their infancy, their promise is hard to miss. Already,
people from such diverse fields as stock market trading, supermarket design and
the insurance business are starting to explore their money-making
possibilities.
In the autumn of 1987, W. Brian Arthur, an economist from Stanford
University, California, and John Holland, a computer scientist from the
University of Michigan, shared a house while they visited the Santa Fe Institute
in New Mexico. During hours of evening conversations over numerous beers, Arthur
and Holland hit upon the idea of creating a virtual stock market inside a
computer鈥攐ne that could be used to answer questions that people in finance
have pondered for decades.
Economists, for example, refer to a quantity called the fundamental value of
a share. This is simply the sum of all the dividends that a person can expect to
receive by holding on to the share indefinitely鈥攂ut adjusted, or
鈥渄iscounted鈥�, to take account of factors such as inflation which make a dollar
today worth more than a dollar in future. Arthur and Holland wanted to know if
the average price of a share settles down to its fundamental value. This
conjecture forms the basis of one of the most cherished tenets of finance
theory, which academics use to understand market behaviour.
Another common question is whether a market eventually settles into a fixed
pattern of buying and selling, or whether a rich 鈥渆cology鈥� of trading rules
emerges instead. But how should Arthur and Holland go about creating a model
exchange capable of giving answers that are relevant to real life?
Finance theory was one option open to them. Its virtue is that it provides a
set of rules on which deductions can be based. Take the prediction of the price
of a share. Conventional wisdom has it that tomorrow鈥檚 share price is simply the
discounted expectation of today鈥檚 price plus a factor taking into account one
day鈥檚 worth of the share鈥檚 dividend.
This calculation assumes that other factors, such as how fast the share is
trading and economic indicators such as the interest rate remain the same. But
in real life, of course, they don鈥檛. So there may actually be many perfectly
reasonable ways to predict tomorrow鈥檚 price, based on different ways of
combining all or some of these variables. For example, we could say that
tomorrow鈥檚 price will equal today鈥檚 price. Or we might predict that the new
price will be today鈥檚 price divided by the dividend rate. And so on. Finance
theory really doesn鈥檛 give any help in choosing which to use.
The simple observation that there is no single, best way to process
information sets deductive logic on a slippery slope. In the real world, a
trader has not only to decide which forecasting method to use, but must also
make assumptions about how other investors are going to make the same decision.
Ultimately the reasoning chases its own tail. If I am a trader, I have to base
my decisions partly on what I think other traders will do, knowing that they are
basing their decisions on what they think I will do.
All this led Arthur and Holland to the not very surprising conclusion that
deductive methods based on grand laws are, at best, an oversimplified academic
fiction. Instead, they decided to build their model stock market from the bottom
up, starting with individual traders. Their model includes 60 software 鈥渁gents鈥�
representing the traders. Each one is assumed to summarise recent market
activity by a collection of descriptors (labelled A, B, C and so on), which are
statements about the state of the market, such as 鈥渢he price has gone up every
day for the past week,鈥� or 鈥渢he price is higher than the fundamental value鈥�, or
鈥渢he trading volume is high鈥�.
The traders then decide whether to buy or sell by invoking rules of the form:
鈥淚f the market fulfils conditions A, B, and C, then buy, but if conditions D, G,
S, and K are fulfilled, then hold.鈥� Each trader has a collection of such rules,
but uses only one of them at a time. This rule is the one the trader views as
its current, most accurate rule.
As buying and selling proceeds, traders can re-evaluate their rules and bring
another into play if it has proved profitable in the past. Suppose I鈥檓 an agent
using one rule, but I know that another is useful when the inflation rate rises.
When inflation does goes up, I will abandon the existing rule in favour of the
other.
Traders can also recombine successful rules to form new ones that they can
then test in the market. This is carried out using what is called a genetic
algorithm, an invention of Holland鈥檚 that mimics the way the genes of two
parents are mixed in a fertilised egg. The genetic algorithm generates new rules
by combining elements from two 鈥減arent鈥� rules.
This simulated market, which trades just one company鈥檚 shares, runs on a
desktop computer. Before trading begins, the traders are fed a particular
history of stock prices, interest rates and dividends, and are assigned a set of
rules. The traders then randomly choose one of their rules and use it to start
buying and selling.
Adapting to the market
After the first round of trading, each agent assesses how good its current
rule is by comparing it with the way all its other rules would have performed.
It then generates a new rule, and chooses the best rule for the next round of
trading. And so the process goes, period after period, buying, selling, placing
money in bonds, modifying and generating rules, estimating how good the rules
are, and, in general, acting in the same way that traders act in real financial
markets.
A frozen moment in this artificial market is displayed in the
Diagram.
It shows the time history of the share price and the fundamental value of the
stock, where the price of the share is the white line and the top of the red
region is the fundamental value. The black region, where the white line is
higher than the top of the red region, represents a speculative bubble in which
investors are willing to pay more for the share than it is truly worth (as
measured by the fundamental value). In the pink region, where the white line
sinks far below the top of the red, the market has crashed.
So did this simulated market answer any of Arthur and Holland鈥檚 questions?
After many periods of trading and modification of trading rules, what emerges is
a kind of ecology of predictors, with different traders employing different
rules to make their decisions. Furthermore, the price of the share always
settles down to a random fluctuation about its fundamental value. However,
within these fluctuations a very rich behaviour is seen: market moods,
overreactions to price movements and all the other things associated with real
speculative markets.
Indeed, the model appears to be very realistic. The bubbles and crashes
resemble closely those seen in real life. And variants of the model are now
being tested by both investment houses and finance theorists to study the
dynamics of price movements, and to look at how traders move from one rule to
another in the face of what their colleagues are doing.
Arthur and Holland鈥檚 agent-based approach can be used for simulating more
than just the stock market. If you picture the agents on the virtual trading
floor sporting sharp clothes and cell phones, the agents in another simulation,
called SimStore, would have shopping trolleys and wire baskets. SimStore is a
model of a real British supermarket鈥攖he Sainsbury鈥檚 store at South Ruislip
in West London. It is the result of a collaboration between Ugur Bilge of
SimWorld, which is based in London, Mark Venables of Sainsbury鈥檚 and me.
The agents in SimStore are software shoppers, armed with shopping lists. They
make their way round the silicon store, picking goods off the shelves according
to rules such as the nearest neighbour principle: 鈥淲herever you are now, go to
the location of the nearest item on your shopping list.鈥� Using these rules,
SimStore generates the paths taken by customers, from which it can calculate
customer densities at each location. The
diagram shows customer densities
around the store with blue as the highest density and white the lowest.
It is also possible to link all points visited by, say, at least 30 per cent
of customers to form a most popular path. A genetic algorithm can then change
where in the supermarket different goods are stacked and so minimise, or
maximise, the length of the average shopping path. Shoppers, of course, don鈥檛
want to waste time, so they want the shortest path. But the store manager would
like to have them pass by almost every shelf, to encourage impulse buying. So
there is a dynamic tension between the minimal and maximal shopping paths that
needs further exploration. Among other uses, this model is aimed at helping
Sainsbury鈥檚 to redesign its stores so as to generate greater customer
throughput, reduce inventories and shorten the time that products are on the
shelves.
In both stock market and supermarket, the agents represent individual people.
A quite different type of business simulation emerges when the agents are
companies and the model is one of an entire industry鈥攚hich brings us back
to insurance. Over the past couple of years, I and colleagues at the Santa Fe
Institute and Complexica, also in Santa Fe, have designed an agent-based model
of the world鈥檚 catastrophe insurance industry.
As a crude first cut, the insurance industry can be regarded as an interplay
between three components: firms which offer insurance, clients who buy it, and
events which determine the outcomes of the 鈥渂ets鈥� placed between the insurers
and their clients. In 鈥淚nsurance World鈥�, the agents are primary insurers and
reinsurers, the firms that insure the insurers, so to speak. This world can be
perturbed by natural events, such as hurricanes and earthquakes, as well as
factors such as changes in government regulations, which alter the ground rules
of the insurance game, and global capital markets, which govern the availability
of funds.
So what is Insurance World good for? Insurers and reinsurers talk incessantly
about getting a better handle on uncertainty, so they can assess their risk more
accurately and price their products more profitably. Yet it鈥檚 self-evident that
if everyone had perfect foreknowledge of natural hazards, this would spell the
end of the insurance industry. On the other hand, complete ignorance of hazards
is also pretty bad news, since it means there is no way to weight the bets the
firms make and price their product. This suggests that there is some optimal
level of uncertainty at which the insurance companies (though perhaps not their
clients) can operate in the most profitable and efficient fashion. With
Insurance World, we hope to be able to find this optimal level, and whether it
varies between firms. Does it, for example, vary between reinsurers, primary
insurers and/or customers?
Another question to ask is which of the standard metaphors used to
characterise organisations鈥攁 machine, a brain or an organism, for
example鈥攎ost accurately represents the insurance industry. And how is
this picture of the organisation shaped by the 鈥渞ules鈥� used in the boardrooms of
the companies that make up the industry? Understanding which metaphor works best
should help to uncover good rules for operating those firms.
The simulator calls for the decision makers of each firm to set a variety of
parameters, such as their desired market share in certain geographical and/or
commercial sectors and the level of risk they want to take on. They also have to
estimate economic parameters such as future interest and inflation rates, and
assess the likelihood of hurricanes and earthquakes. The simulation then runs
for 10 years in steps of three months, at which time a variety of outputs can be
examined.
For instance, the
Diagram shows how the market for hurricane insurance
around the Gulf of Mexico is split between five primary insurers in this toy
world. The initial market shares were almost identical鈥攂ut not quite. In
this experiment, firm 4 has a slightly larger initial market share than any of
the others, an advantage that it uses to squeeze out the other firms. This is
not a result of a better premium-setting strategy or any other business tactic,
but is solely down to the 鈥渂rand effect鈥�, in which buyers tend to purchase
insurance from companies they know about.
Large-scale, agent-based simulations like the three described here are in
their infancy. But they clearly show how computers can create laboratories for
doing experiments that have never been possible before. These experiments are
exactly the sort called for by the scientific method: they are controlled and
repeatable. So, for the first time in history, we have the opportunity to create
a true science of human affairs. The consequence could be studies of, say, the
mechanisms underlying revolution or how racism takes hold of an institution. If
I were placing bets on the matter, I鈥檇 guess that the world of business and
commerce will lead the charge into this entirely new science.