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	0.15	0.05	0.23
Bust	0.36	0.07	0.07	-0.09

  

Requirement 1:

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

(Click to select)9.77%12.27%21.80%24.57%4.04%

  

Requirement 2:

What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C? (Do not round your intermediate calculations.)

Answer 1

1

Stock A
Scenario	Probability	Return%	=rate of return% * probability
Boom	0.64	15	9.6
Bust	0.34	7	2.38
	Expected return %=	sum of weighted return =	11.98
Share B
Scenario	Probability	Return%	=rate of return% * probability
Boom	0.64	5	3.2
Bust	0.34	7	2.38
	Expected return %=	sum of weighted return =	5.58
Share C
Scenario	Probability	Return%	=rate of return% * probability
Boom	0.64	23	14.72
Bust	0.34	-9	-3.06
	Expected return %=	sum of weighted return =	11.66

Expected return%=	Wt Stock A*Return Stock A+Wt Share B*Return Share B+Wt Share C*Return Share C
Expected return%=	0.3333*11.98+0.3333*5.58+0.3333*11.66
Expected return%=	9.77

2

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.64	15	9.6	3.02	0.000583706
Bust	0.34	7	2.38	-4.98	0.000843214
	Expected return %=	sum of weighted return =	11.98	Sum=Variance Stock A=	0.00143
			Standard deviation of Stock A%	=(Variance)^(1/2)	3.78
Share B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.64	5	3.2	-0.58	2.15296E-05
Bust	0.34	7	2.38	1.42	6.85576E-05
	Expected return %=	sum of weighted return =	5.58	Sum=Variance Share B=	0.00009
			Standard deviation of Share B%	=(Variance)^(1/2)	0.95
Share C
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(C)^2* probability
Boom	0.64	23	14.72	11.34	0.008230118
Bust	0.34	-9	-3.06	-20.66	0.01451241
	Expected return %=	sum of weighted return =	11.66	Sum=Variance Share C=	0.02274
			Standard deviation of Share C%	=(Variance)^(1/2)	15.08
Covariance Stock A Share B:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Boom	0.64	3.0200	-0.58	-0.000112102
Bust	0.34	-4.98	1.42	-0.000240434
			Covariance=sum=	-0.000352537
		Correlation A&B=	Covariance/(std devA*std devB)=	-0.983270983
Covariance Stock A Share C:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% for C(C)	(A)*(C)*probability
Boom	0.64	3.02	11.34	0.002191795
Bust	0.34	-4.98	-20.66	0.003498151
			Covariance=sum=	0.005689946
		Correlation A&C=	Covariance/(std devA*std devC)=	0.998824319
Covariance Share B Share C:
Scenario	Probability	Actual return% -expected return% For B(B)	Actual return% -expected return% for C(C)	(B)*(C)*probability
Boom	0.64	-0.58	11.34	-0.000420941
Bust	0.34	1.42	-20.66	-0.000997465
			Covariance=sum=	-0.001418406
		Correlation B&C=	Covariance/(std devB*std devC)=	-0.990944921
	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	=0.2^2*0.03777^2+0.2^2*0.00949^2+0.6^2*0.15081^2+2*(0.2*0.2*0.03777*0.00949*-0.98327+0.2*0.6*0.00949*0.15081*-0.99094+0.2*0.6*0.99882*0.03777*0.15081)
	Variance	0.009245