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.)

a. Rate of Return on the portfolio in each scenario:

Scenario Analysis:

Rate of Return

Scenario                Probability    Stocks     Bonds      Return of Return

Recession                  0.20         -5 %           14 %

= 0.20((-5% x 60%) + (14% x 40%)) = 0.0052 =               0.5%

Normal economy      0.60         15                8

= 0.60((15% x 60%) + (8% x 40%)) =  0.0732 =                7.3%              

Boom                         0.20        25               4

= 0.20((25% x 60%) + (4% x 40%) = 0.0332 =                 3.3%

Weights                     1.00          0.60          0.40

b. Expected rate of return =

Recession =                      0.0052

Normal economy =           0.0732

Boom =                             0.0332

Total expected returns = 0.1116 = 11.2%

Mean = 3.72% (11.2%/3)

Variance = 0.001168

Standard Deviation = 0.034 = 0.03

Explanation:

a) Data:

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

Weights                     1.00          0.60          0.40

b) The rate of return for each portfolio is derived by weighing the securities, adding the resultant figures and applying the scenario probability.  The expected rate of return is the addition of the returns of all the portfolio under the three scenarios.  The step for obtaining the standard deviation is to calculate the mean, the variance, and getting the square root of the variance.

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