What is the variance of the returns on a portfolio that is invested 40 percent in...

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Finance

What is the variance of the returns on a portfolio that isinvested 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 & Explanation Solved by verified expert

4.3 Ratings (938 Votes)

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?2(RA) + w2B?2(RB) + 2(wA)(wB)Cor(RA, RB)?(RA)*?(RB))
	Variance	=0.4^20.06033^2+0.6^20.012^2+20.40.60.060330.012*0.80598
	Variance	0.00091

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Transcribed Image Text

What is the variance of the returns on a portfolio that isinvested 40 percent in Stock S and 60 percent in Stock T?State ofEconomyProbability ofState of EconomyRate of Returnif State OccursStock SStock TBoom.06.22.18Normal.92.15.14Bust.02?.26.09.00091.00136.00107.00118Please show work

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