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Pairs Trading: Algorithmic Trading

In this weeks article we bring you a new financial concept of Pairs trading. Pairs trading is a concept which if implemented with the help of a computer algorithm would give huge benefits to the investor.

Pairs trading refers to opposite positions in two different stocks or indices, that is, a long (bullish) position in one stock and another short (bearish) position in another stock. The objective is to make money on the relative price movements between them. The two stocks might both go up, but the stock you are long will go up more and faster than the stock you are short. Or, the two stocks might both go down, but the stock you are short will drop more and faster than the stock you are long. One half of the pairs trade may be profitable, and the other half of the pairs trade may lose money, but the goal is for the profits to exceed the losses.

Pairs trading can be simple in concept, but can be one of the most complex types of trading in practice. This article will outline the basic approach of pairs trading, and some ideas of how to apply the strategy.

What you do in a pairs trade is try to profit from a situation where one stock looks cheap or expensive relative to another. You buy the stock that is relatively cheap and sell the stock that is relatively expensive, speculating that the long position will rise relative to the short position. To make the trade more intuitive, I look at the price of one stock minus the price of another. I then try to see whether that

difference is historically high or low, or if I expect it to move in one direction or another given stronger performance in one stock over another. Generally, I look at the historical spread between the two stocks to see if there is any consistent relationship. That is, does the spread fluctuate back and forth around an average number (revert to a mean), or does it seem to trend up or down? If there is an average or mean spread price over a particular period of time, I can judge whether I should sell one stock and buy the other based on whether the current spread price is higher or lower than the average. For example, if the average difference between daily closing prices of stock A and stock B (stock A minus stock B) is $1.00, and if the current price of stock A is $53 and stock B is $49, then the current difference is $4.00. That $4.00

is 3.00 points higher than the average difference. So, expecting that the difference will revert back to the mean of $1.00, a trader could infer that either stock A is overpriced at $53 or stock B is under-priced at $49. Either way, the idea would be to sell stock A and buy stock B. If the spread comes back to its average of $1.00, there is the possibility of making $3.00 on that pairs trade. Alternatively, if I expected that stock A would continue to outperform stock B, I would buy stock A and sell stock B. The stocks or indices that make good candidates for the pairs trade should have some measurable relationship.

Ideally, the stocks or indices in the pairs trade should have a positive correlation and betas that are stable over time. Correlation is a statistical coefficient that measures the strength, within a range of +1 to -1, of the relationship between two variables. In this case, the variables are stocks or indices. The idea of correlation as it relates to trading is best described by an example.  If stock A and stock B both move up and down at the same time, then stock A and B have a high positive correlation (close to +1). If stock A moves up and stock B moves down at the same time, then stock A and B have a high negative correlation (close to -1). If stock A and B move up and down completely randomly, then stock A and B have zero correlation. Correlation is calculated by dividing the covariance of the percentage changes of each stock or index divided by the product of the standard deviations for the two stocks. Covariance is a measure of the tendency of the two stocks or indices to move together, and dividing the covariance by the standard deviations sets the correlation between +1 and -1. Many trading software packages include correlations between stocks, but you can use a spreadsheet function to perform the calculation using historical stock and index data. The correlation will indicate the strength of the relationship between the changes of the two stocks for the time covered by the data.