Question

Tyler Trucks stock has an annual return mean and standard deviation of 15 percent and 44 percent, respectively. Michael Moped Manufacturing stock has an annual return mean and standard deviation of 10.2 percent and 50 percent, respectively. Your portfolio allocates equal funds to Tyler Trucks stock and Michael Moped Manufacturing stock. The return correlation between Tyler Trucks and Michael Moped Manufacturing is 0.5. What is the smallest expected loss for your portfolio in the coming month with a probability of 5 percent? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Round the z-score value to 3 decimal places when calculating your answer. Enter your answer as a percent rounded to 2 decimal places.)

Smallest expected loss

%

Answer 1

E(R) = [Ri] / n = (0.15 + 0.102) / 2 = 0.126, or 12.60%

= [(wA² x A²) + (wB² x B²) + (2 x wA x wB x A x B x Correlation_(A,B))]^1/2

= [(0.5² x 0.44²) + (0.5² x 0.50²) + (2 x 0.5 x 0.5 x 0.44 x 0.50 x 0.5)]^1/2

= [0.0484 + 0.0625 + 0.0550]^1/2 = [0.1659]^1/2 = 0.4073, or 40.73%

Prob[R (0.1260 / 12) - {1.645(0.4073)(1 / 12)^1/2}] = 5%

Prob[R {0.0105 - 0.1934}] = 5%

Prob[R -0.1829] = 5%