Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard deviation of 17%. B has an expected rate of return of 9% and a standard deviation of 14%. The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.
A) 9.5%
B) 10.4%
C) 10.9%
D) 9.9%

Question

Quizplus · Accepted Answer

The risk-free portfolio's rate of return can be calculated using the formula for the expected return of a portfolio consisting of two perfectly negatively correlated assets, A and B: $E(R_p) = \frac{\sigma_B - \sigma_A}{\sigma_B + \sigma_A}E(R_A) + \frac{\sigma_A - \sigma_B}{\sigma_A + \sigma_B}E(R_B)$. Plugging in the given values: $E(R_p) = \frac{14 - 17}{14 + 17} * 12\% + \frac{17 - 14}{17 + 14} * 9\% = \frac{-3}{31} * 12\% + \frac{3}{31} * 9\% = -0.116\% + 0.871\% = 10.4\%$.

Consider Two Perfectly Negatively Correlated Risky Securities a and B