Tyler Trucks stock has an annual return mean and standard deviation of 11 percen

Question

Tyler Trucks stock has an annual return mean and standard deviation of 11 percent and 46 percent, respectively. Michael Moped Manufacturing stock has an annual return mean and standard deviation of 10.6 percent and 52 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 .5. What is the smallest expected loss for your portfolio in the coming month with a probability of 16 percent? (Negative amounts should be indicated by a minus sign. Omit the "%" sign in your response. Round your answer to 2 decimal places.)

Incorrect Answers previously provided (-0.34, -34.49%)

Explanation / Answer

The expected return of the portfolio = (11 + 10.6)/2 = 10.8%

Standard deviation of the portfolio = (0.5^2*0.46^2+0.5^2*.52^2+2*.0.5*0.5*0.46*0.52*0.5)^1/2 = 42.46%

from the table for normal distribution 16% of the area occurs for Z value of -2.95

(X - 10.8)/42.46 = -2.95; X - 10.8 = -125.257; X = -114.47

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