Tyler Trucks stock has an annual return mean and standard deviation of 16 percen

Question

Tyler Trucks stock has an annual return mean and standard deviation of 16 percent and 49 percent, respectively. Michael Moped Manufacturing stock has an annual return mean and standard deviation of 12.6 percent and 49 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 5.0 percent?

Explanation / Answer

Expected Return on the portfolio = 0.5 * 16% + 0.5 * 12.6% = 8% + 6.3% = 14.3%

Expected Monthly Return = 14.3/12 = 1.192%

Variance of portfolio = wA2SDA2 + wB2SDB2 + 2wAwBSDASDBcor(A,B)

                                = 0.52 * 0.492 + 0.52 * 0.492 + 2 * 0.5 * 0.5 * 0.49 *0.49 *0.5 = 0.180075

Standard Deviation of portfolio = 0.1800750.5 = 42.435%

Expected Monthly Standard Deviation = 42.435% * (1/12)0.5 = 12.25%%

Using the z table, 5% probability is 1.6448 standard deviations below the mean:

Probaility that returns over next month will be less than 0.01192 – 1.6448 x 0.1225 = 5%

Thus, probability of returns < - 0.1896 = 5%

Thus, the smallest expected loss in the coming month with a probability of 5 percent is 18.96%.

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