Tyler Trucks stock has an annual return mean and standard deviation of 12.0 perc
ID: 2710347 • Letter: T
Question
Tyler Trucks stock has an annual return mean and standard deviation of 12.0 percent and 41 percent, respectively. Michael Moped Manufacturing stock has an annual return mean and standard deviation of 23.0 percent and 67 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?
Explanation / Answer
Answer:
Tyler Trucks
Michael Moped
Annual Return
12%
23%
Standard Deviation
41%
67%
Weight in portfolio
0.5
0.5
Therefore, Expected return on portfolio = E(RP) =
E(RP) = 0.5 x 0.12 + 0.5 x 0.23 = 0.06 + 0.115 = 0.175 = 17.5%
sP = [(0.41x 0.5)2 + (0.67x 0.5)2+ 2 x 0.5 x 0.5 x 0.41 x 0.67 x -0.50]1/2
= [0.042025 + 0.112225 - 0.068675]1/2
= 0.2925
Now we will we convert to monthly statistics:
E(RP) = 0.175 x 1/12 = 0.01458
sP = 0.2925 x (1/12)1/2= 0.0844
As the 1% loss level is 2.576
standard deviations below the mean: Pr[RP<0.175 – 2.576 x 0.0844] = 0.01
which simplifies toPr[RP<-0.0424] = 0.05
We can expect a loss of 4.24 percent or worse over the next month with a 1 percent.
Tyler Trucks
Michael Moped
Annual Return
12%
23%
Standard Deviation
41%
67%
Weight in portfolio
0.5
0.5
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.