Scenario Probability Stocks Bonds Recession .20 ?5 % +19% Normal economy .70 +20

Question

Scenario Probability Stocks Bonds Recession .20 ?5 % +19% Normal economy .70 +20 +10 Boom .10 +32 +9 ________________________________________ Consider a portfolio with weights of .6 in stocks and .4 in bonds. a. What is the rate of return on the portfolio in each scenario? (Do not round intermediate calculations. Round your answers to 1 decimal place.) Scenario Rate of Return Recession _________% Normal economy _________% Boom _________% b. What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected rate of return _________% Standard deviation __________% c. Which investment would you prefer? Portfolio, or Bonds, or Stocks

Explanation / Answer

a. Rate of Return Recession = .6*(-5%) + .4*19% =4.60% Rate of Return Normal = .6*(20%) + .4*10% =16.00% Rate of Return Boom = .6*32% + .4*9% =22.80% b. expected rate of return of portfolio = .2*4.6% + .7*16% + .1*22.8% =14.40% standard deviation of the portfolio = sqrt(2*(4.6%- 14.40%)^2+ .7*(16%-14.40%)^2 + .1*(22.8%-14.40%)^2 ) =14.17% c. expected rate of return of stock = .2*(-5%) + .7*20% + .1*32% =16.20% expected rate of return of bond = .2*(19%) + .7*10% + .1*9% =11.70% I would prefer portfolio because it has less variability

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