Wednesday, June 20, 2012

Pairs trading and colinearity

We sometimes recognize a couple of assets as being co-related. However, the dependence regime changes over time, making this co-relation non-linear and depending on, let's say, a phase. A more robust concept is multiple co-linearity, which implies that a linear combination of the returns of those assets is linearly related, and has a constant mean and variance.

Let's say that two assets are co-linear and that the returns of one of them have been consistently larger than the other. It makes sense to sell short the asset with larger past returns and buy the asset with smaller past returns. With this, we would have a quantitative model to measure large discrepancies of the return of the linear combination, for example, execute this strategy when the absolute value of the return exceeds twice the standard deviation. This gives a statistical arbitrage oportunity.

One example that I like to use is the pair EURUSD and GC (NYMEX Gold 100oz) and I used that to get a hold on some coins. Another perhaps more interesting application would be corn and wheat. They seem to have periods when one is the loved child of agricultural commodity traders. They are normally worth the around the same, being wheat historically more expensive. Corn catched up and had a period that was more expensive, but wheat had recently a rally and got to be USD100 more expensive per contract. Obviously, the gap close down to a difference of USD20. It then widened and is now sitting around USD40-USD50. This simple model would have yield a potentical change of USD80 per contract.

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