Question

Your portfolio allocates equal funds to DW Co. and Woodpecker, Inc. DW Co. stock has an annual return mean and standard deviation of 14 percent and 43 percent, respectively. Woodpecker, Inc., stock has an annual return mean and standard deviation of 11.2 percent and 57 percent, respectively. The return correlation between DW Co. and Woodpecker, Inc., is zero. What is the smallest expected loss for your portfolio in the coming month with a probability of 5 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

E(rP) = [w(DW) * r(DW)] + [w(WPI) * r(WPI)]

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

P = [{w(DW) * (DW)}² + {w(WPI) * (WPI)}² + {2 * w(DW) * w(DWI) * (DW) * (WPI) * Correlation(DW<WPI)}]^1/2

= [{0.5 * 0.43}² + {0.5 * 0.57}² + {2 * 0.5 * 0.5 * 0.43 * 0.57 * 0}]^1/2

= [0.046225 + 0.081225 + 0]^1/2

= [0.12745]^1/2

= 0.3570. or 35.70%

Prob(R <= (Monthly Avg. AR) – [Mini expect. * SD * (monthly average)^1/2] = Probability
So, putting in the values,

Prob(R<= (0.126/12) - [1.645 * 0.357 * (1/12)^0.5] )= 5%

Prob(R<= 0.0105 - 0.1695 ) = 5%

Prob(R<= -0.1590) = 5%

So, smallest expected loss over the next year with prob. of 5% = 15.90%