# What are the applications of cointegration?

We have had several posts on cointegration, and I must admit that I have only seen them mentioned here and there but I have no real experience using this concept.

My question is pretty simple: how do you use cointegration to create strategies?

In other words, in what fields are you using this concept?

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Be careful: even if you have two processes $A_t$ and $B_t$ that you find to be cointegrated (ie as explained upper you have a linear combination of $A$ and $B$ that is iid), it does not mean that you can trade it.

It means that if you identified two parameters $\theta_A$ and $\theta_B$ such that $$C_t:=\theta_A A_t + \theta_B B_t \sim {\cal N}(0,v)$$

you can buy the residuals ($\epsilon_t = \theta_A A_t + \theta_B B_t - C_t$) of the regression against $C_t$ when they are cheap and sell them high, but only if you can trade it.

For instance, if $A$ is a stock or a future and $B$ is a macroeconomic indicator, you will not be able to buy and sell $B$. Some people nevertheless try to trade the cointegration just using $A$, because $C_t$ is cheap means cheap with respect to current economic conditions and because the macro variables are changing slower than stock prices, but they are exposed to macro trends or jumps.

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If you fit a VAR(p) model to two or more securities in levels, then it will incorporate the cointegration effects. If you project this to the horizon and convert back into security prices, then you will be able to calculate the distribution of profits at the horizon. In this sense you could then perform a traditional optimization. This is useful in the case where one of the variables in the VAR(p) model is not traded. In this case, when the variable is cheap, you would only purchase it if it has favorable properties from perspective of the whole portfolio, rather than just individually.

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