Question

What is the variance of the returns on a portfolio comprised of $4,200 of Stock G and $5,300 of Stock H?

State of Economy	Probability of State of Economy	Rate of Return if State Occurs
		Stock G			Stock H
Boom	.18		.18			.08
Normal	.82		.14			.11

A. .000248

B. .000209

C. .000000

D. .001324

Answer 1

Total Portfolio value = Value of Stock G + Value of Stock H

=4200+5300

=9500

Weight of Stock G = Value of Stock G/Total Portfolio Value

= 4200/9500

=0.4421

Weight of Stock H = Value of Stock H/Total Portfolio Value

= 5300/9500

=0.5579

Stock G
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.18	18	3.24	3.28	0.000193651
Normal	0.82	14	11.48	-0.72	4.25088E-05
	Expected return %=	sum of weighted return =	14.72	Sum=Variance Stock G=	0.00024
			Standard deviation of Stock G%	=(Variance)^(1/2)	1.54
Stock H
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.18	8	1.44	-2.46	0.000108929
Normal	0.82	11	9.02	0.54	2.39112E-05
	Expected return %=	sum of weighted return =	10.46	Sum=Variance Stock H=	0.00013
			Standard deviation of Stock H%	=(Variance)^(1/2)	1.15
Covariance Stock G Stock H:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Boom	0.18	3.28	-2.46	-0.000145238
Normal	0.82	-0.72	0.54	-3.18816E-05
			Covariance=sum=	-0.00017712
		Correlation A&B=	Covariance/(std devA*std devB)=	-1
	Expected return%=	Wt Stock G*Return Stock G+Wt Stock H*Return Stock H
	Expected return%=	0.4421*14.72+0.5579*10.46
	Expected return%=	12.34
	Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
	Variance	=0.4421^2*0.01537^2+0.5579^2*0.01153^2+2*0.4421*0.5579*0.01537*0.01153*-1
	Variance	=0