Monday, December 29, 2008

How the Stock Market Works 2: Some Simple Statistical Arbitrage

So I'm gonna attempt to explain some statistical arbitrage (or stat arb, in the truncated parlance of the street). Depending on your experience level, your reaction to this post should range from "duh" all the way through "well uhh" straight through to the "what the fu..." Its OK, you're gonna make it, I promise. Just stick with it and you will come out a smarter person on the other side.

In finance, there are many assets which seem to be driven by the same process. The fate of a collection of oil companies will rise and fall with the price of oil. A parent company may make record profits only if its partially owned subsidiary company gets a new contract. Or it could be something as simple as company A owns a 20% stake in company B. For whatever reason, there are plenty of examples of how the price of two seemingly different assets are linked together. When an educated investor sees two stocks moving together, he should know that there is an opportunity for profit.

Asset prices that move in concert are known as "cointegrated." Although this term has a technical definition, the intuition is straightforward. If the price of an asset rises, we would expect the price of its cointegrated partners to be rising as well. If prices are not moving together, it is because of some temporary anomaly. Thus an investor can profit by buying one cointegrated asset and selling another.

In particular, suppose we have two related assets- A and B- and we observe A rising and B falling. The arbitrageur can then sell A and buy B. Now he has a "market-neutral" position. Theoretically he does not care what direction the market as a whole takes because he is both long and short.

The investor above is betting only that the spread between the two cointegrated assets will narrow (long and short at the same time is known as a spread) . This will occur if A decreases more than B decreases or if A increases less than B increases.

For example, suppose we're long 100 shares of B and short 100 shares of A. If the market increases, its likely that our two stocks will also increase. We will make profit if the money we make in one side of the spread is more than we're losing on the other. If A rises 2 points and B rises 2.5 points, we will have lost 200 on the short position and made 250 on the long position, netting out to a profit of 50 dollars. Else, if A rose 3 points, we would lose 50 dollars.

It is important to note that a trader can make a spread out of any two assets. You could go long gold and short gasoline for example. But it is the idea of cointegration that makes the above spread so powerful. If two assets are truly related, then the spread will eventually narrow, netting the stat arb a profit.

The risks are twofold. The first is that the spread will increase so much in the short term as to bankrupt the arbitrageur before the relationship returns to normal. This is a very real risk, especially if leverage is involved. The second risk is that the relationship will cease to exist. Perhaps company A dumped its holdings of company B. Maybe company A had a corrupt CEO who embezzled billions and takes the equity to zero overnight. Either way, the fortunes of the two companies could diverge quite strikingly.

On the whole, the cointegration trading described above is useful only for calm and stable markets. But risk profiles can be adjusted for any market. In a benign market, this strategy would seek small but frequent intraday returns. The stat arb would thus make alot of trades to capitalize off of low volatility in the size of the spread itself. In a crazy market like we have now, the number of trades would be cut down dramatically. Spreads have gotten very volatile, and opposing small moves could send one to the poorhouse. Waiting for spreads to widen significantly is the only way to implement this strategy in a high volatility marketplace.
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