9 – M4 L2A 09 Variance Of 2 Stocks Part 2 V4

Let’s clean up the formulas a bit. We can move the constant factor exposures outside of the covariance operators. Also, the covariance of a factor with itself is also called the variance of that factor. So, the expressions now look like this. So, to summarize, we can express the pairwise covariance of two stocks as a sum of four terms, written in terms of the two factors. Now we have the variance of the first stock, the variance of the second stock, and their covariances written in terms of the two factors. So, that’s pretty great, because we actually have the pieces we need to fill in a covariance matrix of assets. Recall that another way to get these four values is to use a time series of the stocks to calculate the variances and covariances. But as we mentioned earlier, this approach doesn’t scale well when handling thousands of stocks. So, instead, we have modeled the covariance matrix of assets in terms of the common risk factors. We can plug the formulas for the variances and covariances into the four elements of this covariance matrix of assets. It becomes a bit hard to read. So, let’s use these images of ice cream to help us keep track of the different pieces.

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