# Using Kendall rank correlation to construct a covariance matrix?

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.

• I have the same problem. I wonder if there is anyone to answer this question... – Sara Nov 27 '18 at 17:14

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