My task:

I have an (n,n) correlation matrix. I want to add another variable (which is a combination of two existing variables) and end up with an (n+1,n+1) matrix.

I have estimates of all expected returns and variances.

However, I do not know how to calculate correlation coefficients or covariances for the new variable (or if this is possible).

I am not working from a sample. These figures are estimates of long-term asset returns. The new variable could be thought of as a portfolio containing x% of asset i and (100-x)% of asset j - so I have already calculated it's expected return and variance.

Any help would be much appreciated.