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I am wondering if it's mathematically 'correct' to employ a correlation matrix based on Kendall-correlation when constructing a covariance matrix?

I.e., is it wrong to multiply standard deviations of e.g. returns with the Kendall-correlation-matrix to form a covariance matrix?

That is, I am only changing the correlation estimates to be based on Kendall's tau instead of the standard Pearson linear correlation coefficient when 'constructing' my covariance matrix.

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  • $\begingroup$ I have the same problem. I wonder if there is anyone to answer this question... $\endgroup$
    – Sara
    Commented Nov 27, 2018 at 17:14

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A first hint:

To convert Kendall's $\tau$ to the Pearson correlation coefficient $\rho$, one could use the relationship: $$\rho = \sin\Bigl(\frac{\pi}{2}\tau\Bigr)$$

But keep in mind that this only holds for the bivariate normal copula assumption, I don't know if this also holds to convert "plain vanilla" correlation matrices, see McNeil et al. (2005: Proposition 5.29).

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