Correlation between mean-variance efficient portfolios

If the covariance solution between the returns series of the minimum-variance portfolio ( $ A $ ) and any other portfolio along the efficient frontier ( $ B $ ) is

$$ Cov_{A, B} = \frac{1}{\mathbf{1}^T\mathbf{\Sigma}^{-1}\mathbf{1}} $$ What is the derivation of the closed-form analytical solution for the correlation between those portfolios, $ \rho_{A, B}=? $

Just divide covariance by the square roots of the two variances. In this case you would want $$ \frac{1/a}{\sqrt{\frac{1}{a}\frac{c}{b^2}}}, $$ which takes value $$ \frac{|1^{\top}\Sigma^{-1}\mu|}{\sqrt{(1^{\top}\Sigma^{-1}1)(\mu^{\top}\Sigma^{-1}\mu)}}. $$

引用自：https://quant.stackexchange.com/questions/59450