Problem 11-10 Returns and Standard Deviations [LO 1, 2] Your portfolio is invest

Question

Problem 11-10 Returns and Standard Deviations [LO 1, 2]

Your portfolio is invested 30 percent each in A and C and 40 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

What is the variance of this portfolio? (Do not round intermediate calculations. Round your answer to 5 decimal places (e.g., 32.16161).)

What is the standard deviation of this portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Explanation / Answer

Expected return of the portfolio =

                        Boom:    E(Rp) = .30(.355) + .40(.455) + .30(.335) = 0.389 = 38.90%

                        Good:    E(Rp) = .30(.125) + .40(0.105) + .30(0.175) =0.132 or 13.20%

                        Poor:    E(Rp) = .30(0.15)+ .40(0.025) + .30(–.055) = -0.002 or -0.20%

                         Bust: E(Rp) = .30(-0.115) + .40(-0.255) + .30(-0.095) = -0.165 or -16.50%

And the expected return of the portfolio is:

                        E(Rp) = .2(.3890) + .4(.1320) + .3(–.0020) + .1(–.165) =0.1135 = 11.35%

What is the variance of this portfolio?

To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared

deviations from the expected return. We then multiply each possible squared deviation by its probability, and then sum.

The result is the variance. So, the variance and standard deviation of the portfolio is:

               sp2 = .2(.3890 – .1135)2 + .4(.1320 – .1135)2 + .3(–.0020 – .1135)2 + .1(–.0165 – .1135)2 = .027075

What is the standard deviation of this portfolio?

               sp = (.02546).5 = .164546 or 16.45%

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