Tyler Trucks stock has an annual return mean and standard deviation of 14 percen

Question

Tyler Trucks stock has an annual return mean and standard deviation of 14 percent and 37 percent, respectively. Michael Moped Manufacturing stock has an annual return mean and standard deviation of 11.2 percent and 55 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 1.0 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Tyler Trucks stock has an annual return mean and standard deviation of 14 percent and 37 percent, respectively. Michael Moped Manufacturing stock has an annual return mean and standard deviation of 11.2 percent and 55 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 1.0 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Explanation / Answer

E(R) = (0.14 + 0.112) / 2 = 0.126
We convert it to monthly statistics=> 0.126/12 = 0.0105

= [(.5^2)(37^2) + (.5^2)(55^2) + 2(.5)(.5)(37)(55)(.5)] = 1607.25
=> (1607.25/12)^1/2 = 11.5731

The 1% loss level is 2.326 standard deviation below the mean.

So, the smallest expected loss:

Prob[Rp< 0.0105 - 2.326 x 11.5731] = 0.01
Prob[Rp< -26.9085] = 0.01

So, the smallest expected loss is 26.91% in the coming month

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