Rate of Return Scenario Probability Stocks Bonds Recession .20 6 % +17 % Normal

Question

Rate of Return Scenario

Probability Stocks Bonds

Recession .20 6 % +17 %

Normal economy .50 +20 +8

Boom .30 +29 +6

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 Bonds Stocks

Explanation / Answer

A)Recession = (- 6 *.6)+(17*.4)

                     = -3.6+ 6.8 = 3.2%

Normal = (20*.6)+(8 *.4) = 12+ 3.2 = 15.2%

Boom = (29*.6)+(6*.4) = 17.4+ 2.4= 19.8%

b)Expected return = (3.2 *.2)+(15.2* .5)+(19.8*.30)

                      = .64+ 7.6+ 5.94

                       = 14.18%

Variance = (3.2-14.8)^2 + (15.2-14.8)^2 + (19.8-14.18)^2

          = (-11.6)^2 + (.4)^2 + (5.62)^2

          = 134.56+ .16+ 31.5844

          = 166.3044

Standard deviation = Square root of 166.3044

                             = 12.90%

c) Investment in stock is better as expected return in stock is higher than expected return in bond .

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