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	.33
Good		.50		.12	.10	.17
Poor		.25		.01	.02	−.05
Bust		.10		−.11	−.25	−.09

Requirement 1:

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. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Expected return of the portfolio

%

Requirement 2:

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

Variance of the portfolio

(b)	What is the standard deviation of this portfolio? (Do not round intermediate calculations. Enter your answer as a percentage 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	24.6	0.0090774
Good	0.5	12	6	1.6	0.000128
Poor	0.25	1	0.25	-9.4	0.002209
Bust	0.1	-11	-1.1	-21.4	0.0045796
	Expected return %=	sum of weighted return =	10.4	Sum=Variance Stock A=	0.01599
			Standard deviation of Stock A%	=(Variance)^(1/2)	12.65
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.15	45	6.75	33	0.016335
Good	0.5	10	5	-2	0.0002
Poor	0.25	2	0.5	-10	0.0025
Bust	0.1	-2.5	-0.25	-14.5	0.0021025
	Expected return %=	sum of weighted return =	12	Sum=Variance Stock B=	0.02114
			Standard deviation of Stock B%	=(Variance)^(1/2)	14.54
Asset C
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(C)^2* probability
Boom	0.15	33	4.95	21.7	0.00706335
Good	0.5	17	8.5	5.7	0.0016245
Poor	0.25	-5	-1.25	-16.3	0.00664225
Bust	0.1	-9	-0.9	-20.3	0.0041209
	Expected return %=	sum of weighted return =	11.3	Sum=Variance Asset C=	0.01945
			Standard deviation of Asset C%	=(Variance)^(1/2)	13.95
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	24.6000	33	0.012177
Good	0.5	1.6	-2	-0.00016
Poor	0.25	-9.40	-10	0.00235
Bust	0.1	-2140.00%	-14.5	0.003103
			Covariance=sum=	0.01747
		Correlation A&B=	Covariance/(std devA*std devB)=	0.950139884
Covariance Stock A Asset C:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% for C(C)	(A)*(C)*probability
Boom	0.15	24.6	21.7	0.0080073
Good	0.5	1.6	5.7	0.000456
Poor	0.25	-940.00%	-16.3	0.0038305
Bust	0.1	-21.4	-20.3	0.0043442
			Covariance=sum=	0.016638
		Correlation A&C=	Covariance/(std devA*std devC)=	0.94330385
Covariance Stock B Asset C:
Scenario	Probability	Actual return% -expected return% For B(B)	Actual return% -expected return% for C(C)	(B)*(C)*probability
Boom	0.15	33	21.7	0.0107415
Good	0.5	-2	5.7	-0.00057
Poor	0.25	-10	-16.3	0.004075
Bust	0.1	-14.5	-20.3	0.0029435
			Covariance=sum=	0.01719
		Correlation B&C=	Covariance/(std devB*std devC)=	0.847770108
	1)Expected return%=	Wt Stock A*Return Stock A+Wt Stock B*Return Stock B+Wt Asset C*Return Asset C
	Expected return%=	0.3*10.4+0.4*12+0.3*11.3
	Expected return%=	11.31
	2 a)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*0.12647^2+0.4^2*0.14539^2+0.3^2*0.13947^2+2*(0.3*0.4*0.12647*0.14539*0.95014+0.4*0.3*0.14539*0.13947*0.84777+0.3*0.3*0.9433*0.12647*0.13947)
	Variance	0.01789
	2 b) Standard deviation=	(variance)^0.5
	Standard deviation=	13.37%