Question

Rate of Return If State Occurs State of Economy Boom Normal Bust Probability of State of Economy .20 .50 .30 Stock B .38 Stock A .26 .10 .01 Stock C .50 .08 .06 -.20 -.40 a-1If your portfolio is invested 30 percent each in A and B and 40 percent in C, what is the portfolio expected return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Portfolio expected return % a-2 What is the variance? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) Variance = a-3 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 % b.If the expected T-bill rate is 3.00 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected risk premium C-1If the expected inflation rate is 2.60 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) % Approximate expected real return Exact expected real return C-What are the approximate and exact expected real risk premiums on the portfolio? (Do not 2 round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Approximate expected real risk premium Exact expected real risk premium

Answer 1

C Stock A Probability 0.2 0.5 0.3 D Stock B 0.26 0.1 0.01 0.38 0.08 -0.2 E Stock C 0.5 0.06 -0.4 0.4 0.3 0.105 8.67% 5.23% 0.3 0.056 20.23% 0.01 31.58% 1 State of economy 2 Boom 3 Normal 4. Bust 5 6 7 % Invested 8 expected return 9 standard deviation 10 a-1 portfolio expected return 11 12 Covariance 13 a-2 variance 14 a-3 standard deviation 15 16 b) 17 expected T-bill rate 18 expected risk premium 19 20 C-1 21 expected inflation rate A&B B&C A&C 0.02675 0.06384 0.01728 0.04517 21.25% 3.00% 2.23% 2.60% 22 2.63% 2.56% 23 approx real return 24 exact expected real return 25 26 C-2 27 approximate real risk premium 28 Exact expected real risk premium 29 2.23% 2.17% 30

1 State of economy 2 Boom 3 Normal 4 Bust Probability 0.2 0.5 0.3 Stock A 0.26 0.1 0.01 Stock B 0.38 0.08 -0.2 Stock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nvested 8 expected return 9 standard deviation 10 a-1 portfolio expected return 11 12 Covariance 13 a-2 variance 14 a-3 standard deviation 15 16 b) 17 expected T-bill rate 18 expected risk premium 19 20 C-1 21 expected inflation rate A&C =($B$2*(E2-D8)*(C2-B8))+($B$3*(E3-D8)*(C3-B8))+($B$4* (E4-D8)*(C4-B8)) 0.03 =B10-B17 0.026 22 23 approx real return 24 exact expected real return =B10-B21 = (1+B10)/(1+B21))-1 25 26 C-2 27 approximate real risk premium 28 Exact expected real risk premium 29 =B18 =B27/(1+B21)