#### [email protected]

##### Active Member

Probably a dumb matrix math/ covariance question on the spreadsheet pack forward tab for diversified VAR:

To calculate portfolio variance, you do the following:

1. calculate the individual volatilities (matrix)

2. multiply 1. by the correlation matrix

3. multiply 2. by 1. again to get the "covariance matrix" (sigma)

4. multiply 3. by the portfolio weightings (PV of cash flows representing the 3 primitives making up the forward) i.e. sigma*x

5. multiply 4. by weights again i.e. x*sigma*x = portfolio variance

I can see diversified portfolio variance = sqrt(x'*sigma*x).

Then, covariance(x,y) = p(x,y)*sigma(x)*sigma(y).

My question is when we multiply matrices 1. and 2. (volatilities * correlation) why is this not sufficient to have the covariance? why the additional step (i.e. step 3.)? Is it because we need 2 volatilities to multiply out of the correlation formula to get covariance?

Thanks