Simply Complexity by Johnson Neil

Author:Johnson, Neil [Johnson, Neil]
Language: eng
Format: epub, mobi, pdf
Publisher: Oneworld Publications (academic)
Published: 2009-09-30T22:00:00+00:00

6.2 The problem with finance theory as it stands – or walks

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 ta where a = 0.5. This is the square root of t. The square root can also be written as √t, and so t0.5 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 90.5 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.

It turns out that this random walk represents the standard model of how financial markets move. And so it is this model which most finance professionals use to try to work magic with our savings. Most importantly, we can see that the main assumption underlying this random walk model of the markets is that the next price movement is best described by the toss of a coin. Heads gives an up movement of the price by a certain amount and tails gives a corresponding down movement.

But that immediately sets off alarm bells in our heads, based on what we have seen in this book. A financial market is a Complex System, and the output of a Complex System will not generally be a random walk. In particular, we discussed in chapter 3 that one of the emergent phenomena in real-world Complex Systems is that they tend to be characterized by a walk that is neither too disordered nor too ordered – more specifically, the patterns that are observed tend to have values of the parameter a which are not equal to the random walk value of 0.5.

We are right to be worried. There is now a significant body of research which confirms that the price-series produced by real-world financial markets are characterized by values of a which differ significantly from 0.5. And here comes the big shock. Not only does the a value differ from 0.5 for any particular market, but the way in which it differs from 0.

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