Your portfolio is invested 31 percent each in A and C and 38 percent in B. What

Question

Your portfolio is invested 31 percent each in A and C and 38 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

Answer: Requirement 1:

Calculation of the Expected return of the portfolio:

This portfolio does not have an equal weight in each asset. We first need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get:

                        Boom: E(Rp) = .31(.361) + .38(.461) + .31(.341) = .28709 or 28.71%

                        Good:    E(Rp) = .31(.131) + .38(.111) + .31(.181) = .1389 or 13.89%

                        Poor:    E(Rp) = .31(.021) + .38(.031) + .31(–.067) = –.00249 or –0.249%

                        Bust:    E(Rp) = .31(–.121) + .38(–.261) + .31(–.101) = –.168 or –16.8%

                        And the expected return of the portfolio is:

                        E(Rp) = .20(.2871) + .40(.1389) + .30(–.00249) + .10(–.168) = .095433 or 9.54%

Answer:Requirement 2:

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 = .20(.2871 – .0954)2 + .40(.1389 – .0954)2 + .30(–.00249 – .0954)2 + .10(–.168 – .0954)2 = .017919

               sp = (.017919).5 = .13386 or 13.39%

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