Consider the following scenario analysis: Assume a portfolio with weights of .60

Question

Consider the following scenario analysis:

Assume a portfolio with weights of .60 in stocks and .40 in bonds.

a. What is the rate of return on the portfolio in each scenario? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.)

b. What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Rate of Return Scenario Probability Stocks Bonds Recession 0.20 -5 % 14 % Normal economy 0.60 15 8 Boom 0.20 25 4

Assume a portfolio with weights of .60 in stocks and .40 in bonds.

a. What is the rate of return on the portfolio in each scenario? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.)

b. What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Explanation / Answer

Answer a.

Weight of Stocks in portfolio is 0.60 and weight of bonds in portfolio is 0.40

Recession:

Rate of Return = 0.60 * -5% + 0.40 * 14%
Rate of Return = 2.6%

Normal Economy:

Rate of Return = 0.60 * 15% + 0.40 * 8%
Rate of Return = 12.2%

Boom:

Rate of Return = 0.60 * 25% + 0.40 * 4%
Rate of Return = 16.6%

Answer b.

Expected Rate of Return = 0.20 * 2.6% + 0.60 * 12.2% + 0.20 * 16.6%
Expected Rate of Return = 11.16%

Variance = 0.20 * (0.026 - 0.1116)^2 + 0.60 * (0.122 - 0.1116)^2 + 0.20 * (0.166 - 0.1116)^2
Variance = 0.002122

Standard Deviation = (0.002122)^(1/2)
Standard Deviation = 0.0461
Standard Deviation = 4.61%

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