Overview
Cointegrated Pairs Trading is a trading model based on the assumption that the prices of two assets are Cointegrated.
More specifically, given prices {% p_a %}, {% p_b %} for assets {% a %} and {% b %}, it is assumed that there is a linear combination of the logarithms of the prices that is stationary That is, there is a {% \gamma %} and {% \mu %} such that, {% \epsilon_t %} defined by
{% log(p_{at}) - \gamma log(p_{bt}) - \mu = \epsilon_t %}
is stationary.
The hypothesis can be tested by running a standard OLS Regression on the above equation, and then testing the residuals for stationarity.
Selecting Pairs
It is unlikely that any pair of stocks will be formally co-integrated, however, it may be approximately true, especially in short time periods. Only stocks that are similar (for instance, belonging to the same sector or industry) could be co-integrated.
Many traders would trade large lot sizes, will identify pairs of stocks that are highly correlated. Then, if they need to trade a large block of one, they can try to hedge the execution of the theirs trades with similar trades in the other stock. This makes the correlation between the two somewhat of a self fulfulling prophecy.
Trade Strategy
Once the relationship between the stocks has been established with the regression, the resulting equation can be used to trade the pair.
Restating the equation as
{% \epsilon_t = log(p_{at}) - \gamma log(p_{bt}) - \mu %}
the pairs trader will measure the current value of {% \epsilon %} and place a bet that it will revert back towards zero.