Your portfolio allocates equal funds to the DW Co. and Woodpecker, Inc. DW Co. s

Question

Your portfolio allocates equal funds to the DW Co. and Woodpecker, Inc. DW Co. stock has an annual return mean and standard deviation of 15 percent and 44 percent, respectively. Woodpecker, Inc., stock has an annual return mean and standard deviation of 11.4 percent and 58 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 16 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Explanation / Answer

Portfolio return Rp= Wa x Ra + Wb x Rb

                                = 0.50 x 15% + 0.50 x 11.40%

                                = 13.20%

Since, correlation is zero, portfolio standard deviation would be the average of their standard deviations:

Portfolio SD = 0.50 x 44% + 0.50 x 58%

                        = 51%

Expected loss = Rp – Z x SD
                                           = 13.20 % - 0.99446 x 51%

                                = -37.52%

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