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Using mean-variance, I estimate a co-variance matrix $\Sigma$ to obtain the best weights in my portfolio.

However, there are other ways to compute the volatility $\sigma$ than historical standard deviation, for instance using Yang and Zhang estimator.

I don't understand however the link between the vol. estimation and the co-variance matrix. I know that on the diagonals you'll find the volatility, but how do you re-calculate the co-variance matrix after you have obtained more efficient volatility estimates?

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  • $\begingroup$ A rough answer: If you know by which sum of squares of one variable you can estimate the variance/volatility, the covariance is a sum of products of two variables. See quant.stackexchange.com/questions/27741/… and the formula for $\sigma^2_{rs}$. $\endgroup$
    – Horst Grünbusch
    Commented May 10, 2017 at 11:12

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