I have two portfolio's called Comb & Global. They both have the same investable universe lets says 3000 stocks & are measured against the same benchmark. So it is possible that both funds hold the same stocks. I would like to examine the correlation of the ex-ante between the two funds.
I know I can calculate the ex-ante tracking error as below,
te = sqrt((port_wgt - bm_wgt)' * cov_matrix * (port_wgt - bm_wgt))
I also know the correlation is calculated by
p = cov(x,y) / stdev(x) * stdev(y)
I was wondering the best way to calculate the ex ante correlation between the two funds? Is there a relationship between the two funds weights that I can make use of?
I should have mentioned that the two portfolios are sub portfolios and are combined into one portfolio. So I wanted to see the correlation of the ex ante tracking error between the two sub portfolio's.
I realised I can do the following,
port_wgts - number_of_companies x 2 matrix cov_matrix - number_of_companies x number_of_companies matrix
so the below line will return a 2x2 covariance matrix.
port_wgts' * cov_matrix * prt_wgts
So I have the variances of both sub portfolios - taking the square root of this gives me the tracking error for both.
Convert the 2 X 2 covariance matrix to a correlation matrix by the following
D = Diag(cov_matrix)^(1/2) corr_matrix = D^-1 * cov_matrix * D^-1
So I now have the correlation between the two sub portfolios just using the weights.