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 percent rounded to 1 decimal 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 intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) 

Answer 1

Solution: Scenario Recession Normal economy Boom Rate of Return 2.60% 12.20% 16.60% Explanation: Recession : (-5% x 0.60) +(14% x 0.40) = 2.60% Normal economy: (15% x 0.60) + (8% 0.40) = 12.20% Boom : (25% x 0.60) + (4% 0.40) = 16.60% Expected return Standard deviation 11.16% 4.61% Explanation: Expected return = (0.20 x 2.60%) + (0.60 x 12.20%) + (0.20 x 16.60%) = 11.16% Variance = [0.2 x 2.6-11.16)^2] + [0.6 x (12.20 - 11.16)^2] + [0.2 x (16.6-11.16)^2) = 21.22 Standard deviation = (Square root of 21.22] = 4.61%

Answer 2

Answer a.

Weight of Stocks in portfolio is 0.60 and weight of bonds in portfolio is 0.40

Recession:

Rate of Return = 0.60 * -5% + 0.40 * 14%
Rate of Return = 2.6%

Normal Economy:

Rate of Return = 0.60 * 15% + 0.40 * 8%
Rate of Return = 12.2%

Boom:

Rate of Return = 0.60 * 25% + 0.40 * 4%
Rate of Return = 16.6%

Answer b.

Expected Rate of Return = 0.20 * 2.6% + 0.60 * 12.2% + 0.20 * 16.6%
Expected Rate of Return = 11.16%

Variance = 0.20 * (0.026 - 0.1116)^2 + 0.60 * (0.122 - 0.1116)^2 + 0.20 * (0.166 - 0.1116)^2
Variance = 0.002122

Standard Deviation = (0.002122)^(1/2)
Standard Deviation = 0.0461
Standard Deviation = 4.61%