Optimal hedge ratio

You've just invested in stock $A$ and want to protect yourself from potential losses by shorting stock $B$. You're wondering how much of $B$ you should short to reduce the risk of your overall investment. Assume that stock $A$'s return variance is $\sigma_A^2$, stock $B$'s is $\sigma_B^2$, and the correlation coefficient between their returns is $\rho$. For each dollar invested in $A$, how many dollars of $B$ (the hedge ratio $h$) should you short to minimize the variance of your hedged position? Compute $h$ for $\rho = 0.1$, $\sigma_A = 0.2$, $\sigma_B = 0.4$.