We live in interesting times

The financial crisis is just beginning according to some finance insiders, economists and journalists. One of the reasons for this crisis is the high amount of leveraged trading done by banks and other institutions.

Leveraging means using tools to amplify your action. In a physical lever, we need to apply small force at one point to achieve a multiple of that force at some other location by pivoting on a fulcrum point.

Leverage in Physics

So to have the effect of X times a force F, you just have to apply a force F at another suitably chosen point. This is a powerful idea but has been around for millenia most notably used by Archimides in many of his inventions. Infact, he is said to have remarked that give me a fulcrum strong enough and I will move the world.

But the downsides of this is that if you make a small change in F, there will be X times the change on the other side. So a small error propogates multiplicatively in leveraged scenario.

Though this is a crude analogy, but even in finance people started doing something similar. They did leveraged trades so as to need to only invest a small amount but hoping to get a bigger return. They failed to see the downside which is that their risk also balooned and also the fact that if everyone took such extremely leveraged position, the whole system becomes extremely fragile due to a small shock even though the chances of that shock occuring might have reduced.

Many of these financial instruments were results of using complex mathematical tools and methods which were traditionally developed to help in solving scientific and engineering problem. But primitive mathematics like number system and algebra were developed to facilitate trade and commercial activities.

It is funny that first math developed from commerce, then it is used and developed spectacularly well in the field of science and engineering, but then the advanced math when applied back to the field of commerce seems to have backfired.

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