Consider the following scenario analysis: Rate of Return Probability Stocks Bond

Question

Consider the following scenario analysis: Rate of Return Probability Stocks Bonds 14% Scenario Recession Normal economy Boom 0.20 0.60 0.20 -5% 15 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 Intermedlate calculations. Enter your answer as a percent rounded to 1 declmal place.) Rate of Return Recession Normal economy Boom b. What are the expected rate of return and standard deviation of the portfolio? (Do not round Intermedlate calculatlons. Enter your answer as a percent rounded to 2 declmal places.) Expected return Standard deviation

Explanation / Answer

a) Rate of return in the portfolio is given below

Recession = (Percentage of stocks in recession * Weight of stocks) + (Percentage of bonds in recession * Weight of bonds)

=> (-5% * 0.6) + (14%*0.4) = 2.6%

Normal economy = (Percentage of stocks in Normal economy * Weight of stocks) + (Percentage of bonds in Normal economy * Weight of bonds)

=> (15% * 0.6) + (8%*0.4) = 12.2%

Boom = (Percentage of stocks in Boom   * Weight of stocks) + (Percentage of bonds in Boom  * Weight of bonds)

=> (25% * 0.6) + (4%*0.4) = 16.6%

b)

Expected Return = Probabilty of each scenario * expected return of each scenario

=> 0.2 * 2.6% + 0.6 * 12.2% + 0.2 * 16.6%

=> 11.16%

Variance = 0.2(2.6-11.16)^2 + 0.6(12.2-11.16)^2 + 0.2(16.6-11.16)^2 = 21.22

Stanard Deviation = sqrt (Variance) = sqrt(21.22) = 4.606%, final round off answer will be 4.61%

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