Consider the following information about three stock:s Rate of Return If State O

Question

Consider the following information about three stock:s Rate of Return If State Occurs State of Economy Boom Normal Bust Probability of State of Economy 0.20 0.40 0.40 Stock A 0.34 0.25 0.03 Stock B 0.46 0.23 -0.25 Stock C 0.50 0.20 -0.42 a-1 if your portfolio is invested 35 percent each in A and B and 30 percent in C, what is the portfolio expected return? (Do not round intermediate calculations. Enter the answer as a percent rounded to 2 decimal places.) Portfolio expected return a-2 What is the variance? (Do not round intermediate calculations. Round the final answer to 5 decimal places.) Variance a-3 What is the standard deviation? (Do not round intermediate calculations. Enter the answer as a percent rounded to 2 decimal places.) Standard deviation b. If the expected T-bill rate is 4.70 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter the answer as a percent rounded to 2 decimal places.) Expected risk premium C-1 If the expected inflation rate is 2.70 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations. Enter the answers as a percent rounded to 2 decimal places.) Approximate expected real return Exact expected real return c-2 What are the approximate and exact expected real risk premiums on the portfolio? (Do not round intermediate calculations. Enter the answers as a percent rounded to 2 decimal places.) Approximate expected real risk premiunm Exact expected real risk premium

Explanation / Answer

Answer a-1.

Expected Return in Boom = 35% * 0.34 + 35% * 0.46 + 30% * 0.50
Expected Return in Boom = 0.43

Expected Return in Normal = 35% * 0.25 + 35% * 0.23 + 30% * 0.20
Expected Return in Normal = 0.228

Expected Return in Bust = 35% * 0.03 + 35% * (-0.25) + 30% * (-0.42)
Expected Return in Bust = -0.203

Expected Return on Portfolio = 0.20 * 0.43 + 0.40 * 0.228 + 0.40 * (-0.203)
Expected Return on Portfolio = 0.096 = 9.60%

Answer a-2.

Variance = 0.20 * (0.43 - 0.096)^2 + 0.40 * (0.228 - 0.096)^2 + 0.40 * (-0.203 - 0.096)^2
Variance = 0.065041

Answer a-3.

Standard Deviation = (0.065041)^(1/2)
Standard Deviation = 0.2550 = 25.50%

Answer b.

Expected Risk Premium on the Portfolio = Expected Return on Portfolio - Expected T-bill Rate
Expected Risk Premium on the Portfolio = 9.60% - 4.70%
Expected Risk Premium on the Portfolio = 4.90%

Answer c-1.

Approximate Expected Real Return = Expected Return on Portfolio - Inflation Rate
Approximate Expected Real Return = 9.60% - 2.70%
Approximate Expected Real Return = 6.90%

Exact Expected Real Rate of Return = (Expected Return on Portfolio - Inflation Rate) / (1 + Inflation Rate)
Exact Expected Real Rate of Return = (9.60% - 2.70%) / (1 + 2.70%)
Exact Expected Real Rate of Return = 6.72%

Answer c-2.

Approximate Expected Real Return = Expected Risk Premium - Inflation Rate
Approximate Expected Real Return = 4.90% - 2.70%
Approximate Expected Real Return = 2.20%

Exact Expected Real Rate of Return = (Expected Risk Premium - Inflation Rate) / (1 + Inflation Rate)
Exact Expected Real Rate of Return = (4.90% - 2.70%) / (1 + 2.70%)
Exact Expected Real Rate of Return = 2.14%

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