Your portfolio is invested 28 percent each in A and C and 44 percent in B. What

Question

Your portfolio is invested 28 percent each in A and C and 44 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

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) = .28(.354) + .44(.454) + .28(.334) = .3924 or 39.24%

            Good:    E(Rp) = .28(.124) + .44(.104) + .28(.174) = .1292 or 12.92%

            Poor: E(Rp) = .28(.014) + .44(.024) + .28(–.054) = –.00064 or –.064%

            Bust:   E(Rp) = .28(–.114) + .44(–.254) + .28(–.094) = –.17or –17.00%

            And the expected return of the portfolio is:

            E(Rp) = .19(.3924) + .41(.1292) + .31(–.00064) + .09(–.17) = .1120 or 11.20%

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 = .19(.3924 – .1120)2 + .41(.1292 – .1120)2 + .31(–.00064 – .1120)2 + .09(–.17 – .1120)2 = .090564

sp = (.090564).5 = .3009 or 30.09%

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