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 .30 .40 .31 Good .55 .17 .11 .10 Poor .25 .03 .06 .04 Bust .05 .10 .26 .07 a. Your portfolio is invested 26 percent each in A and C, and 48 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).) Expected return 10 % 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 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 %

Explanation / Answer

Given Data:

The expected returns are just the possible returns multiplied by the associated probabilities:

E(RA) = (0.15 x 0.30) +(0.55 x 0.17) + (0.25 x 0.03) + (0.05 x 0.10) = 15%

Similarly, E(RB) =15% and E(Rc) = 12%

VarianceA = 0.15 (0.30 - 0.15)2 + 0.55 (0.17 - 0.15)2 +  0.25 (0.03 - 0.15)2 + 0.05 (0.10 - 0.15)2 = 0.00736

Similarly VarianceB = 0.01288 and VarianceC = 0.00734

Standard Deviation; (Square Root of Variance)

Stock A = 0.08579

Stock B = 0.11349

Stock C = 0.08567

State of Economy Probability Stock A Stock B Stock C BOOM 0.15 0.30 0.40 0.31 GOOD 0.55 0.17 0.11 0.10 POOR 0.25 0.03 0.06 0.04 BUST 0.05 0.10 0.26 0.07

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