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 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.)

Answer 1

		Rate of Return if State Occurs
State of	Probability of
Economy	State of Economy (p)	Stock A (rA )	Bond B (rB)	Expected return of each state of economy rE (= rA*60% + rB*40%)	Expected return of each state of economy * p	(rE-rp)	(rE-rp)^2	Variance calculation = p*(rE-rp)^2
Recession	0.2	-5.00%	14.00%	2.6%	0.52%	-8.56%	0.73%	0.15%
Normal Economy	0.6	15.00%	8.00%	12.2%	7.32%	1.04%	0.01%	0.01%
Boom	0.2	25.00%	4.00%	16.6%	3.32%	5.44%	0.30%	0.06%
Weight of stocks in portfolio		0.60	0.40
Expected return of portfolio (Sum) rp					11.16%
Variance of portfolio (sum)								0.21%
Standard Deviation of portfolio = (variance)^(1/2)								4.61%

a. What is the rate of return on the portfolio in each scenario?

Recession	2.6%
Normal Economy	12.2%
Boom	16.6%

b. What are the expected rate of return and standard deviation of the portfolio?

Expected return of portfolio = 11.16%                                   

Standard Deviation of portfolio = 4.61%

Formulas used in excel: