The function we need to minimise is $$ \text{Var}(A - \alpha B) = \text{E} \left[ (A - \alpha B)^2 \right] - \text{E} \left[ A - \alpha B \right]^2. $$ Since it isn't specified in the question, we can assume that the means of $A$ and $B$, $\mu_A$ and $\mu_B$ are both zero. So, we have $$ \text{E}[A] = 0 $$ $$ \text{E}[B] = 0 $$ $$ \text{E} \left[ A - \alpha B \right] = 0. $$ So, we need to solve $$ \text{Var}(A - \alpha B) = \text{E} \left[ (A - \alpha B)^2 \right]. $$ Expanding the expectation gives $$ \text{Var}(A - \alpha B) = \text{E} \left[ A^2 \right] + \alpha^2 \text{E} \left[ B^2 \right] - 2\alpha \text{E}[AB]. $$ Since the means of $A$ and $B$ are zero, we have $$ \text{E}[A^2] = \text{Var}(A) = \sigma_A^2, $$ $$ \text{E}[B^2] = \text{Var}(B) = \sigma_B^2. $$ We can use the correlation between $A$ and $B$ to obtain $\text{E}[AB]$. Recall the definition of the correlation coefficient, $$ \rho_{AB} = \frac{\text{E}[(A - \mu_A)(B - \mu_B)]}{\sigma_A \sigma_B}. $$ Given that we know that $\mu_A = \mu_B = 0$, we are left with $$ \sigma_A \sigma_B \rho_{AB} = \text{E}[AB] = 0.008. $$ Plugging everything back into our equation gives $$ \text{E}\left[ (A - \alpha B)^2 \right] = \sigma_A^2 + \alpha^2 \sigma_B^2 -2 \alpha \sigma_A \sigma_B \rho_{AB}. $$ To minimise this function with respect to $\alpha$, we simply need to take the derivative and set it to zero. $$ \frac{\partial}{\partial A} \text{E}\left[ (A - \alpha B)^2 \right] = 2 \alpha \sigma_B^2 - 2 \sigma_A \sigma_B \rho_{AB} = 0. $$ Solving this equation gives $$ \alpha = \frac{\sigma_A \rho_{AB}}{\sigma_B} = 0.05. $$