Question

Consider the following information:

  

				Rate of Return if State Occurs
State of	Probability of
Economy	State of Economy			Stock A			Stock B			Stock C
Boom		.15			.35			.45			.27
Good		.55			.16			.10			.08
Poor		.25		–	.01		–	.06		–	.04
Bust		.05		–	.12		–	.20		–	.09

  

a.	Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected return

%

  

b-1.	What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)

Variance

b-2.	What is the standard deviation? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Standard deviation

%

Answer 1

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.15	35	5.25	21.8	0.0071286
Good	0.55	16	8.8	2.8	0.0004312
Poor	0.25	-1	-0.25	-14.2	0.005041
Bust	0.05	-12	-0.6	-25.2	0.0031752
	Expected return %=	sum of weighted return =	13.2	Sum=Variance Stock A=	0.01578
			Standard deviation of Stock A%	=(Variance)^(1/2)	12.56
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.15	45	6.75	35.25	0.018638438
Good	0.55	10	5.5	0.25	3.4375E-06
Poor	0.25	-6	-1.5	-15.75	0.006201563
Bust	0.05	-20	-1	-29.75	0.004425313
	Expected return %=	sum of weighted return =	9.75	Sum=Variance Stock B=	0.02927
			Standard deviation of Stock B%	=(Variance)^(1/2)	17.11
Stock C
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(C)^2* probability
Boom	0.15	27	4.05	20	0.006
Good	0.55	8	4.4	1	5.5E-05
Poor	0.25	-4	-1	-11	0.003025
Bust	0.05	-9	-0.45	-16	0.00128
	Expected return %=	sum of weighted return =	7	Sum=Variance Stock C=	0.01036
			Standard deviation of Stock C%	=(Variance)^(1/2)	10.18
Covariance Stock A Stock B:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Boom	0.15	21.8000	35.25	0.01152675
Good	0.55	2.8	0.25	0.0000385
Poor	0.25	-14.20	-15.75	0.00559125
Bust	0.05	-2520.00%	-29.75	0.0037485
			Covariance=sum=	0.020905
		Correlation A&B=	Covariance/(std devA*std devB)=	0.972858405
Covariance Stock A Stock C:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% for C(C)	(A)*(C)*probability
Boom	0.15	21.8	20	0.00654
Good	0.55	2.8	1	0.000154
Poor	0.25	-1420.00%	-11	0.003905
Bust	0.05	-25.2	-16	0.002016
			Covariance=sum=	0.012615
		Correlation A&C=	Covariance/(std devA*std devC)=	0.986754074
Covariance Stock B Stock C:
Scenario	Probability	Actual return% -expected return% For B(B)	Actual return% -expected return% for C(C)	(B)*(C)*probability
Boom	0.15	35.25	20	0.010575
Good	0.55	0.25	1	0.00001375
Poor	0.25	-15.75	-11	0.00433125
Bust	0.05	-29.75	-16	0.00238
			Covariance=sum=	0.0173
		Correlation B&C=	Covariance/(std devB*std devC)=	0.993491459
	Expected return%=	Wt Stock A*Return Stock A+Wt Stock B*Return Stock B+Wt Stock C*Return Stock C
	Expected return%=	0.3*13.2+0.4*9.75+0.3*7
	a. Expected return%=	9.96
	Variance	=w2A*σ2(RA) + w2B*σ2(RB) + w2C*σ2(RC)+ 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB) + 2*(wA)*(wC)*Cor(RA, RC)*σ(RA)*σ(RC) + 2*(wC)*(wB)*Cor(RC, RB)*σ(RC)*σ(RB)
	Variance	=0.3^2*0.1256^2+0.4^2*0.17108^2+0.3^2*0.10178^2+2*(0.3*0.4*0.1256*0.17108*0.97286+0.4*0.3*0.17108*0.10178*0.99349+0.3*0.3*0.98675*0.1256*0.10178)
	b. Variance	0.01848
	Standard deviation=	(variance)^0.5
	c. Standard deviation=	13.59%