Consider the following information: Rate of Return If State Occurs State of Prob

Question

Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom .15 .38 .48 .28 Good .45 .22 .19 .15 Poor .30 .04 .09 .06 Bust .10 .16 .34 .11 a. Your portfolio is invested 24 percent each in A and C, and 52 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculaitons. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return 10.02 % 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.) Variance 3.57 b-2 What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation 19.52 %

im not sure if i solved for B right the varience

Explanation / Answer

Expected return of portfolio in Boom = 0.24*0.38 + 0.52*0.48 + 0.24*0.28 = 0.4080

Expected return of portfolio in Good = 0.24*0.22 + 0.52*0.19 + 0.24*0.15 = 0.1876

Expected return of portfolio in Poor = 0.24*-0.04 + 0.52*-0.09 + 0.24*-0.06 = -0.0708

Expected return of portfolio in Bust = 0.24*-0.16 + 0.52*-0.34 + 0.24*-0.11 = -0.2416

Expected return is the weighted average of individual returns in each state of economy.

Expected return of portfolio = 0.15*0.4080 + 0.45*0.1876 + 0.3*-0.0708 + 0.1*-0.2416 = 0.1002 = 10.02%

Variance is the sum of squared deviations from the mean times the probability.

Variance = 0.15*(0.4080-0.1002)^2 + 0.45*(0.1876-0.1002)^2 + 0.3*(-0.0708-0.1002)^2 + 0.1*(-0.2416-0.1002)^2 = 0.0381036

Standard deviation = sqrt(Variance) = sqrt(0.0381036) = 0.1952 = 19.52%

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