Simply Complexity (18 page)

So the network representing the correlations between all currency pairs has too much information to be very useful in practice. In addition, currency traders would love to have a simple method for deducing whether certain exchange rates are actually dominating the FX market. This would support the popular notion among traders that certain currencies can be “in play” over a given time period. This is where the technical approach of tree construction which the researchers then adopted, proved itself so powerful. The tree – or rather the so-called minimal tree – approach was originally developed by Rosario Mantegna from the University of Palermo and Gene Stanley of Boston University. The trees are minimal in that between
n
objects, they only contain
n-
1 connections. Hence as shown in
figure 5.2
, the three currency situation which leads to
n
= 6 possible exchange rates, has only
n
-1 = 5 connecting lines between these exchange rates. The tree is constructed as follows: the amount that any two exchange rates are correlated is first represented as a distance, with the most correlated having the shortest distance. Then the most important correlations are picked out so that the network retains its general shape – very much like creating a skeleton structure from a full object. In our three currency example,
figure 5.2
shows that the exchange rates involving the Euro as the base currency (i.e. Euro/£ and Euro/US$) are both clustered together near the center of the tree. Using traders’ terminology, the Euro is therefore in play. As a check that the resulting tree was actually capturing something meaningful about the market, the researchers created a random FX market by shuffling up some of the data randomly, like a pack of cards. The tree resulting from randomizing the data was very different in character from the true tree, justifying the researchers’ claims. Although it is such a simple test – as simple as shuffling a deck of cards – such randomization tests are an extremely valuable tool in the Complexity Science trade, since there is typically very little data available for more conventional tests of statistical significance.

The researchers also looked at how the tree’s structure changed over time – as though it were being blown by the invisible wind that shapes the FX markets as a whole. Part of this wind corresponds to the feedback produced by the traders themselves working in the different currencies at different times; part is produced by the economic climate; and part comes from the demand generated by multinational corporations who need to change large amounts of particular currencies. For example, a large motor company like Ford which has lots of sales in the Far East, will often need to turn this cash back into dollars on the FX market, and might therefore create a bit of a breeze themselves. By contrast, you or I going into our local bank and changing money ready for our overseas vacations has no measurable effect on the tree whatsoever. Indeed, we would be very lucky to rustle a single leaf. The researchers found that even though the FX market does change rapidly enough to identify changes in how different currency-pairs are clustering together on the tree, there are links in the tree which can last for several
years
. This remarkable finding shows that there is a certain robust structure to the FX markets. In particular, they sustain themselves like some kind of autonomous machine – a true Complex System.

Let’s take another look at a collection of decision-making objects competing for a limited resource – but now we add the twist that some of these objects are connected together. For example, two people might exchange information over the telephone. This research idea was originally examined by Sean Gourley and Sehyo Charley Choe of Oxford University in collaboration with Pak Ming Hui of the Chinese University of Hong Kong. In particular, they carried out computer simulations and developed a mathematical theory to explain their observations, using the crowd-anticrowd picture from
chapter 4
. Their original motivation for the study was prompted by all the talk in the popular press about globalization. In particular, they started to ask themselves the following questions: is getting connected a good or bad
thing? How does increased access to both global (i.e. public) information and local (i.e. private) information, affect the success of both the population as a whole and its individual members? Thinking in terms of future technologies, what are the possible benefits and dangers of introducing communication channels between collections of intelligent devices, microsensors, semiautonomous robots, nanocomputers, and even biological microorganisms such as bacteria? These questions will clearly be relevant to a wide range of computational, technological, biological and socio-economic systems over the next hundred years or so.

The researchers’ approach was to generalize the binary-decision game mentioned in
chapter 4
by adding a certain number of local connections between the objects. As before, the objects in question could be biological (e.g. a population of cellular organisms competing for nutrients), computational (e.g. a grid of software modules competing for processing time), mechanical (e.g. a constellation of sensors or devices competing for communications bandwidth or operating power) or social (e.g. a population of companies competing for business). The researchers’ analysis uncovered a rich interplay between the global competition for resources and the local connectivity between objects. For a population with modest resources, they found that adding small amounts of interconnectivity between members of the population
increased
the disparity between successful and unsuccessful people and reduced the mean success rate. By contrast, in a higher resource population they found that low levels of interconnectivity increased the mean success rate and enabled most objects to be successful. At high levels of interconnectivity, the overall population became fairer (i.e. smaller disparity in success rates) but less efficient (i.e. smaller mean success-rate), irrespective of the global resource level.

In other words, they found that the consequences of “wiring up” a competitive population depend quite dramatically on the interplay between the local connectivity and the amount of available global resource. The upshot is that instead of saying glibly that it is good to get connected, we should instead say that “Depending on your priorities regarding fairness and efficiency, it might be good to get connected – as long as you don’t get too
connected”. Admittedly it is not quite as catchy a phrase, but it is certainly more correct.

This brings to a close not only this chapter, but also the first part of this book. We saw that Complexity represents a subtle mix between order and disorder, and that Complex Systems are able to move themselves around between these two extremes without any outside help. Their key ingredient is feedback, which may come in the form of memory from the past or information from other points in space via network connections. We have also seen how we can capture the essence of Complexity using collections of decision-making objects which may, or may not, have network connections between them. With this in mind, we now proceed to look at the applications where Complexity can probably be most useful – and we investigate how we can use the ideas that we have already seen in order to understand the real-world systems of interest. By mixing together elements from our study of collections of objects and of networks, we can then begin to build a coherent, universal picture of a wide range of complex problems.

We’d all like to be able to predict financial market movements. Being able to predict tomorrow’s weather or traffic would be an extremely useful skill, but many people would practically sell their souls in order to have an edge in the markets. And with the purchasing power of the average pension diminishing all the time, maybe second-guessing movements in the stock market is something that we’ll all be forced to do in the future. There is of course one huge problem: financial markets are complicated, dynamical systems which are continually changing in ways that defy most experts. However, the good news is that they are constantly generating huge streams of data which can be used to cross-check your favorite prediction model – should you be lucky enough to have one.

The main reason for believing that some form of market prediction might be possible lies in the fact that each price movement is actually a real-time record of the aggregated actions of the market’s many participants – and each of these participants is effectively trying to win in a vast global market “game”. Indeed in its simplest form, this global market game boils down to a binary-decision game of the kind discussed in
chapters 1
and
4
: should I buy or should I sell? There is therefore reason to believe that prediction models which manage to emulate this underlying multi-trader
decision game – in particular, binary decision models of the type discussed in
chapters 1
and
4
– could indeed prove profitable.

Prediction in financial markets is fundamentally different from predicting the weather, the outcome from a roulette wheel, or the outcome from tossing a coin. In a market, the individual objects (i.e. traders) are each trying to predict price movements in order to decide whether to buy or sell. The net demand to buy or sell then determines the subsequent price movement. This resulting price movement then gets fed back to the traders, who may use it in their next decision of whether to buy or sell. This cyclic process goes on continually, with price movements being fed back to traders who then make decisions whether to buy or sell. And like all humans, traders can’t help but notice what has happened before in the market. They will tend to see patterns – or believe they see patterns – and then react to what they think they see, or what they have heard. In other words, a financial market is riddled with feedback. This feedback leads to new decisions of whether to buy or sell, which leads to a new price, which leads to new feedback, which leads to new decisions, which leads to a new price – and so on.

Such intrinsic feedback does not arise when gambling on a roulette wheel or with the toss of a coin. These objects are made up of molecules – and even though they may appear to behave in a complicated way, they are simply following Newton’s Laws of motion. There is no decision-making going on, and hence – unlike the market – the outcome obtained is in no way linked to the predictions of the people who are actually playing and gambling. Likewise, even if everyone had the perfect prediction model of the weather, the weather would still do what the weather does. All that would happen is that everyone would know exactly what to wear the next day. However, this is not true in the markets. If everyone were to be given the perfect prediction model, it would immediately
stop
being the perfect prediction model because of this strong feedback effect. Everyone would use the prediction model in order to decide their next trade, and this would dramatically distort the market. At this point the prediction model would stop working. For example, if the model predicted that stock should be sold, everyone would then try to sell at the same time and the stock would instantaneously become worthless since no
one would be prepared to act as a buyer. The upshot is that any prediction model which is too widely known or used will actually hurt the value of the stock held by the traders rather than help them make money.

So, in terms of Complexity Science, financial markets are a wonderful system to look at. They consist entirely of collections of decision-making objects with large intrinsic feedback, and therefore satisfy our main criteria for Complexity. Moreover, the abundance of past and present data means that financial markets provide the most well-documented, and longest running, record of a human-based Complex System in the history of the planet. Hence they are set to play an important role as a test case real-world system in the advancement of Complexity Science – quite apart from their obvious intrinsic interest for commercial purposes.

The method that your pension fund manager or stockbroker uses to manage the risk and contents of your portfolio will always have one huge in-built limitation – no matter how clever he or she is. It can only ever be as good as the model he or she employs to describe the underlying market movements. And since these people are playing with our hard-earned cash, and essentially with our future financial security, we’d better understand more about what model they actually use.

In
chapter 3
, we discussed a random walk – otherwise known as a drunkard’s walk – which is generated by flipping a coin and moving forward or backward one step according to whether the outcome is heads or tails. We saw that the approximate distance moved by the drunkard during a time
t
, can be written as
t
^a
where
a
= 0.5. This is the
square root
of
t
. The square root can also be written as √
t
, and so
t
^0.5
is just another way of writing this same square root. This means that if we wait 9 seconds, with each second corresponding to one step, then the approximate distance moved by the drunkard away from his starting point will be 9
^0.5
steps – in other words, √9 steps which is equal to 3. In terms of our earlier filing analogy, the distance moved is equivalent to the
change in the shelf position – and in terms of financial markets, it is equivalent to the change in the price.