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from Neil Pearson's Risk Budgeting p.155

Hi guys, Is it possible to get the covariance between the individual return and portfolio return given the correlation matrix, volatility matrix, weights matrix and return matrix? I know how to get the covariance matrix for all securities using the volatility matrix and correlation matrix, but I'm not sure how to get the covariance between individual security with the portfolio. Is it simply to multiply the weight of the security and covariance matrix, then adding all the elements in the matrix into a single number? Thanks in advance!

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  • $\begingroup$ The easiest way is probably to just do it directly. Assuming you have all your inputs in matrix form, you would simply calculate portfolio returns by crossing the weights matrix with the returns matrix, and then taking the covariance of the resulting array (portfolio return) with the individual return matrix(ces). $\endgroup$
    – Chris
    Aug 16, 2020 at 8:58
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    $\begingroup$ The numerator in (10.3) is THE ITH ROW OF THE COVARIANCE MATRIX (not the whole matrix) scaled by multiplyng by the single number $w_i$ and then the $N$ products are added into a single number (of course the $w_i$ can also be moved out of the summation, reducing the number of multiplications needed to 1) $\endgroup$
    – nbbo2
    Aug 16, 2020 at 9:20
  • $\begingroup$ @noob2 Thanks for explaining the notation! You're a life saver! $\endgroup$
    – ensabahnur
    Aug 16, 2020 at 9:35

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