Tuesday, 21 April 2009

Quant funds and the field approximation

It has come to general attention recently that many quant funds have had a terrible few months: see here for more details. Specifically the momentum following funds have suffered badly from the crap rally of the last little while.

What is going wrong?

One way to see the issue is to consider a technique that sometimes works well in statistical physics. Don't panic, I promise there will be no hard maths. It's like this. Sometimes, you want to know how a given something behaves inside a solid. Let's make the something an atom (although it doesn't have to be). Say this is an atom of impurity in an otherwise pure crystal. How will this impurity affect things?

One could attempt to model the interaction of the atom of impurity with its neighbours, and their neighbours, and so on. If you could do those calculations, the results would be precise. But often you can't, because there are too many effects to consider, and too many other atoms which can exert an effect. So a good short cut is to first calculate the properties of a perfectly pure crystal, and then consider the impurity like a boat in the sea with these properties. You don't model each neighbour separately, in other words: you model the combination of their effects as one thing. This is sometimes called the field approximation, as you are calculating the field of the pure crystal, and then looking about how the impurity behaves in that field.

This works pretty well for one impurity, and it isn't too bad when there are many, providing the percentage of impurity atoms is low enough. But once the percentage of impurities starts rising to the point where one impurity interacts with another, the approximation starts to fail rather badly. Furthermore if the impurities change the way the crystal interacts with itself, then this also means that a new approach is needed.

And so it is with hedge funds. When there were few quant hedge funds interacting with a market that was mostly driven by real money, then the fund's model of market behaviour was reasonable. But as the percentage of trading activity that was hedge fund originated increases, that model becomes less and less tractable. I suspect that phase transitions are possible, whereby the market dynamics suddenly change for only a small increase in the percentage of fund activity. What's happening, then, is that we have too many hedge funds chasing too few arbs. Things won't get better until the capital allocated to quant funds declines significantly.



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