The premise of statistical arbitrage, stat arb for short, is cointegration test pairs trading forex there is a statistical mispricing between a set of securities which we look to exploit. Typically a strategy requires going long a set of stocks and short another. What type of stocks make good pairs? What is the mathematical definition of a good pair?

Upon coming up with a good fundamental stock pairing you next need to have a mathematical test for determining if it’s a good pair. What is the difference between correlation and cointegration? When talking about statisitical arbitrage many people often get confused between correlation and cointegration. A man leaves a pub to go home with his dog, the man is drunk and goes on a random walk, the dog also goes on a random walk.

They approach a busy road and the man puts his dog on a lead, the man and the dog are now cointegrated. Hence is stationary assuming that the hedge ratio, , remains constant! I find your blog very interesting. The spread plots clearly illustrate the merits of co-integration over correlation for a mean-reverting strategy. Truly looking forward to more posts related to statistical arbitrage. Thanks, in this post I showed the mathematics that should create a stationary signal. The next post will detail how we test that assumption.

Hopefully i’ll have written it by Sunday evening. Trading systems come in two flavors: model-based and data-mining. This article deals with model based strategies. A significant market inefficiency gives a system only a relatively small edge. Any little mistake can turn a winning strategy into a losing one.

Developing a model-based strategy begins with the market inefficiency that you want to exploit. The inefficiency produces a price anomaly or price pattern that you can describe with a qualitative or quantitative model. The higher the predictive f term in relation to the nonpredictive ε term, the better is the strategy. Trading by throwing a coin loses the transaction costs. Not all price anomalies can be exploited.

16 fractions of a dollar is clearly an inefficiency, but it’s probably difficult to use it for prediction or make money from it. The working model-based strategies that I know, either from theory or because we’ve been contracted to code some of them, can be classified in several categories. Trend Momentum in the price curve is probably the most significant and most exploited anomaly. No need to elaborate here, as trend following was the topic of a whole article series on this blog. There are many methods of trend following, the classic being a moving average crossover. The problem: momentum does not exist in all markets all the time.

Any asset can have long non-trending periods. A random walk curve can go up and down and still has zero momentum. Therefore, some good filter that detects the real market regime is essential for trend following systems. Traders buy when the actual price is cheaper than it ought to be in their opinion, and sell when it is more expensive. This causes the price curve to revert back to the mean more often than in a random walk. The higher the half-life factor, the weaker is the mean reversion. The half-life of mean reversion in price series ist normally in the range of 50-200 bars.