# Problem Set 7 helpful hints

1. The least risky combination of Security A and Security B in Problem 1 is found by calculating ${w_A} = \displaystyle\frac{{\sigma _B^2 - {\sigma _{AB}}}}{{\sigma _A^2 + \sigma _B^2 - 2{\sigma _{AB}}}}$ and ${w_B} = 1 - {w_A}$.
2. It will always be the case for 2 security portfolios that by following the minimum variance portfolio weighting scheme in the previous bullet point, such a portfolio must have zero variance if ${\rho _{AB}} = 1$ or -1.
3. In part B of Problem 2, the Sharpe Ratio for security j is $\displaystyle\frac{{E({r_j}) - {r_f}}}{{{\sigma _j}}}$.