# Correlation and cointegration

### j3

#### 25/09/2015

1

In this post, I want to create a strategy that is able to choose assets that make it look like an index Yt. Then, take the ones most correlated to it.

Take a look at the chart below: We can see here that the Xt and the Xt+c series have exactly the same correlation with Yt.

From this graph, we might prefer Xt+c. For the purpose of this write-up, however, I’m trying to be very similar to Yt. We can clearly see that here, Xt+c have a large deviation.

## Cointegration?

If two or more series are individually integrated (in the time series sense) but some linear combination of them has a lower order of integration, then the series are said to be cointegrated. Beta is such a constant that the difference is a series of order zero. In other words, stationary.
The next 4 time series have a correlation with Yt higher than 0.9, and are cointegrated. Below, I calculate the Beta coefficient for each. The red result has the closest value to 1 and, visually, it bears the closest resemblance to the black one.

## Ok, that makes sense but you told me that you wanted a strategy…

Since I want to be like S&P 500 and I have a diverse decision universe with 150 ETFs, I’m going to define my Asset Allocation every day. My strategies are threefold. I’m looking at the series that has, in the last 100 days:

Strategy 1: The highest correlation.
Strategy 2: The lowest tracking error.
Strategy 3: The Beta coefficient closest to one. The green result is closest to the S&P, and also has the lowest spread. The question I leave you with this is: If I take the cointegrated series with the highest correlation and the highest beta, will that make an S&P with greater returns?

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