Does anyone know how to calculate the correlation of two portfolios directly from the covariance matrix?i.e. if I have a CAPM model r(i) = B(i)*mkt+e(i) which gives me cov matrix C when B(i) and sigma(i) are known or estimatedhow would I calculate the correlation between two portfolios with weight vectors a nd b that each sum to one?I can see that Var(a) = a'BB'a + a'Va where V is diagonal and V(i,i) = sigma(i)^2 but cant get a grip on Corr(a,b)many thanks....

QuoteOriginally posted by: aptenodyteDoes anyone know how to calculate the correlation of two portfolios directly from the covariance matrix?i.e. if I have a CAPM model r(i) = B(i)*mkt+e(i) which gives me cov matrix C when B(i) and sigma(i) are known or estimatedhow would I calculate the correlation between two portfolios with weight vectors a nd b that each sum to one?I can see that Var(a) = a'BB'a + a'Va where V is diagonal and V(i,i) = sigma(i)^2 but cant get a grip on Corr(a,b)many thanks....Ifr_a = a*c+e_a=Sum(a(i)*c(i))+e_ar_b = b*c+e_b=Sum(b(i)*c(i))+e_bthenVar(a) = a'cc'a=a'Ca +e_a^2Cov(a,b)=a*b=a'Cb The possible problem: if you have constraints like a(i)>0; b(i)>0; then the residuals are not orthogonal in general

If a and b are portfolio weight vectors with the market covariance matrix being then the covariace between a and b is . (Simply write out the double sum.) So now you substitute the assumed covariance under CAP-M (in your notation, BB' + V, I think), and off you go. The usual correlation from covariance and standard deviations formula applies.This formula works with any of the MPT models I guess.