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 47 percent, respectively. Michael Moped Manufacturing stock has an annual return mean and standard deviation of 12.2 percent and 47 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 16.0 percent

Explanation / Answer

Answer:

Tyler Trucks

Michael Moped

Annual Return

14%

12.2%

Standard Deviation

47%

47%

Weight in portfolio

0.5

0.5

Therefore, Expected return on portfolio = E(RP) =

E(RP) = 0.5 x 0.14 + 0.5 x 0.122 = 0.07 + 0.061 = 0.131 = 13.1%

sP = [(0.47x 0.5)2 + (0.47x 0.5)2+ 2 x 0.5 x 0.5 x 0.47 x 0.47 x 0.50]1/2

     = [0.055225 + 0.055225 + 0.055225]1/2

     = 0.407

Now we will we convert to monthly statistics:

E(RP) = 0.131 x 1/12 = 0.0109

sP = 0.407 x (1/12)1/2= 0.1175

As the 15% loss level is 1.405

standard deviations below the mean: Pr[RP<0.131 – 1.405 x 0.1175] = 0.16

which simplifies toPr[RP<-0.034] = 0.05

We can expect a loss of 3.4 percent or worse over the next month with a 16 percent.

Tyler Trucks

Michael Moped

Annual Return

14%

12.2%

Standard Deviation

47%

47%

Weight in portfolio

0.5

0.5

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