10.00 points State of Probability of of .37 21 -.05 -.15 .25 Good 18 .08 -,33 .1

Question

10.00 points State of Probability of of .37 21 -.05 -.15 .25 Good 18 .08 -,33 .12 -.05 .10 Bust a. Your portfolio is invested 25 percent each in A and C, and 50 percent in B. What is the return of the portfolio? (Do not round intermediate calculaitons. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16) b-1 What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g, 32.16161.) ance percent rounded to 2 decimal places,e.g..32.16.) Standard deviation

Explanation / Answer

Expected return is the weighted average of individual returns

Expected return in each state:

Boom = 0.25*0.37 + 0.5*0.47 + 0.25*0.27 = 0.3950

Good = 0.25*0.21 + 0.5*0.18 + 0.25*0.12 = 0.1725

Poor = 0.25*-0.05 + 0.5*-0.08 + 0.25*-0.05 = -0.065

Bust = 0.25*-0.15 + 0.5*-0.33 + 0.25*-0.1 = -0.2275

Expected return = 0.25*0.395 + 0.5*0.1725 + 0.2*-0.065 + 0.05*-0.2275 = 0.1606 = 16.06%

Variance:

Variance is sum of squared deviations from the mean multiplied by the probability

Variance = 0.25*(0.3950-0.1606)^2 + 0.5*(0.1725-0.1606)^2 + 0.2*(-0.065-0.1606)^2 + 0.05*(-0.2275-0.1606)^2 = 0.03152

Std dev = sqrt(Variance) = sqrt(0.03152) = 0.1775 = 17.75%

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