Question

Tyler Trucks stock has an annual return mean and standard deviation of 14.0 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? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Round the z-score value to 3 decimal places when calculating your answer. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

Portfolio's Return = [Weight(i) * Return(i)]

= [0.5 * 14%] + [0.5 * 11.2%] = 7% + 5.6% = 12.6%

Portfolio's Standard Deviation = [{w(TT)² * (TT)²} + {w(MMM)² * (MMM)²} + {2 * w(TT) * w(MMM) * (TT) * (MMM) * Correlation(TT,MMM)}]^1/2

= [{(0.5)² * (0.37)²} + {(0.5)² * (0.55)²} + {2 * 0.5 * 0.5 * 0.37 * 0.55 * (-0.5)}]^1/2

= [0.034225 + 0.075625 - 0.050875]^1/2 = [0.058975]^1/2 = 0.2428, or 24.28%

Prob[R<={Mean - (Z * Standard Deviation)}] = 1%

Prob[R<={(0.126/12) - (2.326 * 0.2428 * (1/12)^1/2)}] = 1%

Prob[R<={0.0105 - 0.1631}] = 1%

Prob[R<=-0.1526] = 1%

So, Smallest Expected Loss = -15.26%