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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?

Update

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.

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1 Answer 1

It is unclear to me what you ask. You have the covariance matrix and today's weights - then you get an ex-ante TE. Why do you need ex-ante correlation? Ex-ante means that weights are fixed and you take an estimator of the future covariance matrix. What you get is an ex-ante TE (if you scale by $\sqrt{T}$ and you have $T$ periods in a year). If weights change tomorrow then you have and new ex-ante TE.

If you observe the funds for a while and you calculate the TE between the two funds NAVs then you get the ex-post (i.e. realized) TE.

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