Question

Consider the following scenario analysis:

		Rate of Return
Scenario	Probability	Stocks		Bonds
Recession	0.2	-4	%	15	%
Normal economy	0.7	16		11
Boom	0.1	25		3

Assume a portfolio with weights of 0.60 in stocks and 0.40 in bonds.

a. What is the rate of return on the portfolio in each scenario? (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? (Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

a

Recession

Weight of Stocks = 0.6

Weight of Bonds = 0.4

Expected return of Portfolio = Weight of Stocks*Expected return of Stocks+Weight of Bonds*Expected return of Bonds

Expected return of Portfolio = -4*0.6+15*0.4

Expected return of Portfolio = 3.6

Normal

Weight of Stocks = 0.6

Weight of Bonds = 0.4

Expected return of Portfolio = Weight of Stocks*Expected return of Stocks+Weight of Bonds*Expected return of Bonds

Expected return of Portfolio = 16*0.6+11*0.4

Expected return of Portfolio = 14

Boom

Weight of Stocks = 0.6

Weight of Bonds = 0.4

Expected return of Portfolio = Weight of Stocks*Expected return of Stocks+Weight of Bonds*Expected return of Bonds

Expected return of Portfolio = 25*0.6+3*0.4

Expected return of Portfolio = 16.2

b

Stock
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Recession	0.2	-4	-0.8	-16.9	0.0057122
Normal	0.7	16	11.2	3.1	0.0006727
Boom	0.1	25	2.5	12.1	0.0014641
	Expected return %=	sum of weighted return =	12.9	Sum=Variance Stock=	0.00785
			Standard deviation of Stock%	=(Variance)^(1/2)	8.86
Debt
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Recession	0.2	15	3	4	0.00032
Normal	0.7	11	7.7	0	0
Boom	0.1	3	0.3	-8	0.00064
	Expected return %=	sum of weighted return =	11	Sum=Variance Debt=	0.00096
			Standard deviation of Debt%	=(Variance)^(1/2)	3.1
Covariance Stock Debt:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Recession	0.2	-16.9	4	-0.001352
Normal	0.7	3.1	0	0
Boom	0.1	12.1	-8	-0.000968
			Covariance=sum=	-0.00232
		Correlation A&B=	Covariance/(std devA*std devB)=	-0.845172201
	Expected return%=	Wt Stock*Return Stock+Wt Debt*Return Debt
	Expected return%=	0.6*12.9+0.4*11
	Expected return%=	12.14
	Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
	Variance	=0.6^2*0.08859^2+0.4^2*0.03098^2+2*0.6*0.4*0.08859*0.03098*-0.84517
	Variance	0.00187
	Standard deviation=	(variance)^0.5
	Standard deviation=	4.32%