I've tried the approach described in my second message and I always get the denominator equal to 1. Is this wrong?
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Calculating a correlation formula with matrices
Hello,
I have a formula for intra-portfolio correlation but I think that it would be much easier to compute using matrices. Can someone show me please, how can I compute Q using the intraportfolio correlation formula using matrices? (the formula can be found at: http://en.wikipedia.org/wi
I thought that I would have two vectors: I containing Xi values, J containing Xj and a matrix P containing the correlation coefficients.
So, how can I coupute Q using the I,J vectors and P matrix?
Thanks,
M
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Answers
Hi,
Being X[1... n] the array with the fraction invested in each asset, from a set o n asstes (obviously sum[x1 ... Xn] = 1), the correlation P is given by the following equation:
P = 2 * (xi / (xi + xj)) - 1
Then, the algorithm for calculating Q is:
--------------------------
calculateP(Xi, Xj)
{
P = Xi / (Xi + Xj)
return 2*P - 1
}
--------------------------
calculateQ(n, X[])
{
Q1=0, Q2=0
for (i=1, n)
for (j =1, n)
{
xij = X[i] * X[j]
Q1 += xij * P(X[i], X[j]);
Q2 += xij;
}
return "Q = " Q1/Q2;
}
Jose
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by: mircea_aPosted on 2007-07-01 at 15:56:00ID: 19400383
Correction (and I think I've got it, is this right???): :)
I think that probably I should put all the weights in a signle vector W....
So I think that the numerator would be euqal to something like:
W^T x P x W
and denominator equal to W^T x W
(Where W^T is W transposed)