Variance-minimising hedge ratio between two stocks

You are long one share of stock A and short $h$ shares of stock B. What value of $h$ minimises the variance of the combined position's value?

$h=\tfrac{\operatorname{Cov}(A,B)}{\operatorname{Var}(B)}=\rho\tfrac{\sigma_A}{\sigma_B}$. The variance is $\sigma_A^2-2h\operatorname{Cov}(A,B)+h^2\sigma_B^2$, a quadratic in $h$ minimised where its derivative vanishes. This is the regression slope of A on B, and the remaining variance is $\sigma_A^2(1-\rho^2)$.