Question

What is the variance of the returns on a portfolio that is invested 40 percent in Stock S and 60 percent in Stock T?

State of Economy	Probability of State of Economy	Rate of Return if State Occurs
		Stock S			Stock T
Boom	.06		.22			.18
Normal	.92		.15			.14
Bust	.02		−.26			.09

.00091

.00136

.00107

.00118

Please show work

Answer 1

Stock S
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.06	22	1.32	7.4	0.00032856
Normal	0.92	15	13.8	0.4	1.472E-05
Bust	0.02	-26	-0.52	-40.6	0.00329672
	Expected return %=	sum of weighted return =	14.6	Sum=Variance Stock S=	0.00364
			Standard deviation of Stock S%	=(Variance)^(1/2)	6.03
Stock T
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.06	18	1.08	3.86	8.93976E-05
Normal	0.92	14	12.88	-0.14	1.8032E-06
Bust	0.02	9	0.18	-5.14	5.28392E-05
	Expected return %=	sum of weighted return =	14.14	Sum=Variance Stock T=	0.00014
			Standard deviation of Stock T%	=(Variance)^(1/2)	1.2
Covariance Stock S Stock T:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Boom	0.06	7.4	3.86	0.000171384
Normal	0.92	0.4	-0.14	-0.000005152
Bust	0.02	-40.6	-5.14	0.000417368
			Covariance=sum=	0.0005836
		Correlation A&B=	Covariance/(std devA*std devB)=	0.805977717
	Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
	Variance	=0.4^2*0.06033^2+0.6^2*0.012^2+2*0.4*0.6*0.06033*0.012*0.80598
	Variance	0.00091