Question

Consider the following information:

  

		Rate of Return if State Occurs
State of Economy	Probability of State of Economy	Stock A	Stock B	Stock C
Boom	0.64	0.21	0.25	0.25
Bust	0.36	0.07	0.11	0.01

  

Requirement 1:

What is the expected return on an equally weighted portfolio of these three stocks? (Do not round your intermediate calculations.)

A) 17.43% B) 19.93% C) 29.46% D) 32.23% E) 11.70%

  

Requirement 2:

What is the variance of a portfolio invested 30 percent each in A and B and 40 percent in C? (Do not round your intermediate calculations.)

A) 0.012965 B) 0.010965 C) 0.007465 D) 0.015465 E) 0.015165

Answer 1

1.

Stock A
Scenario	Probability	Return%	=rate of return% * probability
Boom	0.64	21	13.44
Bust	0.36	7	2.52
	Expected return %=	sum of weighted return =	15.96
Stock B
Scenario	Probability	Return%	=rate of return% * probability
Boom	0.64	25	16
Bust	0.36	11	3.96
	Expected return %=	sum of weighted return =	19.96
Stock C
Scenario	Probability	Return%	=rate of return% * probability
Boom	0.64	25	16
Bust	0.36	1	0.36
	Expected return %=	sum of weighted return =	16.36

Expected return%=	Wt A*Return A+Wt B*Return B+Wt C*Return C
Expected return%=	0.333333333333333*15.96+0.333333333333333*19.96+0.333333333333333*16.36
Expected return%=	17.43

2

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%
Boom	0.64	21	13.44	5.04
Bust	0.36	7	2.52	-8.96
	Expected return %=	sum of weighted return =	15.96	Sum=Variance Stock A=
			Standard deviation of Stock A%	=(Variance)^(1/2)
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%
Boom	0.64	25	16	5.04
Bust	0.36	11	3.96	-8.96
	Expected return %=	sum of weighted return =	19.96	Sum=Variance Stock B=
			Standard deviation of Stock B%	=(Variance)^(1/2)
Stock C
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%
Boom	0.64	25	16	8.64
Bust	0.36	1	0.36	-15.36
	Expected return %=	sum of weighted return =	16.36	Sum=Variance Stock C=
			Standard deviation of Stock C%	=(Variance)^(1/2)
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	0.64	5.0400	5.04	0.001625702
Bust	0.36	-8.96	-8.96	0.002890138
			Covariance=sum=	0.00451584
		Correlation A&B=	Covariance/(std devA*std devB)=	1
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	0.64	5.04	8.64	0.002786918
Bust	0.36	-8.96	-15.36	0.004954522
			Covariance=sum=	0.00774144
		Correlation A&C=	Covariance/(std devA*std devC)=	1
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	0.64	5.04	8.64	0.002786918
Bust	0.36	-8.96	-15.36	0.004954522
			Covariance=sum=	0.00774144
		Correlation B&C=	Covariance/(std devB*std devC)=	1
	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=	0.007465