Consider the following scenario analysis: Rate of Return Scenario Probability St

Question

Consider the following scenario analysis: 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

(a)

(b) The Expected Return of the Portfolio:

E (R) = .2 * .026 + .6 * .122 + .2 * .166 = 11.16 %

To find the Standard Deviation of the Portfolio follow the following steps:

Variance:

2 = .2*.7327% + .6*.0108% + .2*.2959% = 0.2122%

Standard Deviation:

2 = 0.2122% = 0.0461 = 4.61 %

Scenario Return on Stocks Return on Bonds Probability Portfolio Return Recession -5% 14% 0.20 (-.05*.6+.14*.4=) 2.6% Normal Economy 15% 8% 0.60 (.15*.6+.08*.4=) 12.2% Boom 25% 4% 0.20 (.25*.6+.04*.4=) 16.6%

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