Aug 08

How to get portfolio variance from covariance matrix – 10 min screencast

by David Harper, CFA, FRM, CIPM

I am still screencasting VaR mapping topics, but I realized the VaR mapping presumes matrix math. Here I illustrate (using Jorion’s example in Chapter 7) how we get to portfolio VaR/variance using the covariance-variance matrix. The example assumes:

We have $300 million U.S. dollars invested in two currencies: $200 MM in Canadian dollars (CAD) and the other $100 in Euros (EUR).
Given a correlation between CAD and EUR, we can populate the covariance matrix. An FRM candidate must know how to do this: covariance(EUR,CAD) = correlation(EUR,CAD)*volatility(EUR)*volatility(CAD)

The covariance-variance matrix is the capital sigma. To get portfolio variance, we post-multiply the vector of positions (x) by the covariance matrix, then pre-multiply the transposed vector (x’)