Tyler Trucks stock has an annual return mean and standard deviation of 8 percent
ID: 2716557 • Letter: T
Question
Tyler Trucks stock has an annual return mean and standard deviation of 8 percent and 27 percent, respectively. Michael Moped Manufacturing stock has an annual return mean and standard deviation of 19.0 percent and 63 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 8 percent and 27 percent, respectively. Michael Moped Manufacturing stock has an annual return mean and standard deviation of 19.0 percent and 63 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
Tyler Trucks stock
Annual Return = 8%
Annual Standard Deviation = 27%
Michael Moped Manufacturing stock
Annual Return = 19%
Annual Standard Deviation = 63%
Tyler Trucks stock = 50%
Michael Moped Manufacturing stock's Weight = 50%
correlation = .5
Probability = 1%
Annual Portfolio return = (8% + 19%)/2 = 13.5%
Monthly Portfolio return = 13.5%/12 = 1.125%
Annual Portfolio Standard Deviation =
Portfolio Standard Deviation = Sqrt(0.50^2 x 0.27^2 + 0.50^2 + 0.63^2 + 2 x 0.50 x 0.50 x 0.27 x0.63 x.5) = 40%
Portfolio Standard Deviation = 40%
Monthly Portfolio Standard Deviation = 40%/ sqrt(12) = 11.55%
Prob[RP,T 1.125% - 2.326 x 11.55% = 1%
Prob[RP,T -25.74%
The smallest expected loss for your portfolio in the coming month with a probability of 1.0 percent = -25.74%
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