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	0.72	0.29	0.31	0.15
Bust	0.28	0.11	0.11	-0.07

a) What is the expected return on an equally weighted portfolio of these three stocks?

b) What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C?

Answer 1

a

Stock A
Scenario	Probability	Return%	=rate of return% * probability
Boom	0.72	29	20.88
Bust	0.28	11	3.08
	Expected return %=	sum of weighted return =	23.96
			Standard deviation of Stock A%
Stock B
Scenario	Probability	Return%	=rate of return% * probability
Boom	0.72	31	22.32
Bust	0.28	11	3.08
	Expected return %=	sum of weighted return =	25.4
			Standard deviation of Stock B%
Stock C
Scenario	Probability	Return%	=rate of return% * probability
Boom	0.72	15	10.8
Bust	0.28	-7	-1.96
	Expected return %=	sum of weighted return =	8.84

Expected return%=	Wt Stock A*Return Stock A+Wt Stock B*Return Stock B+Wt Stock C*Return Stock C
Expected return%=	0.3333*23.96+0.3333*25.4+0.3333*8.84
Expected return%=	19.4

b

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.72	29	20.88	5.04	0.001828915
Bust	0.28	11	3.08	-12.96	0.004702925
	Expected return %=	sum of weighted return =	23.96	Sum=Variance Stock A=	0.00653
			Standard deviation of Stock A%	=(Variance)^(1/2)	8.08
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.72	31	22.32	5.6	0.00225792
Bust	0.28	11	3.08	-14.4	0.00580608
	Expected return %=	sum of weighted return =	25.4	Sum=Variance Stock B=	0.00806
			Standard deviation of Stock B%	=(Variance)^(1/2)	8.98
Stock C
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(C)^2* probability
Boom	0.72	15	10.8	6.16	0.002732083
Bust	0.28	-7	-1.96	-15.84	0.007025357
	Expected return %=	sum of weighted return =	8.84	Sum=Variance Stock C=	0.00976
			Standard deviation of Stock C%	=(Variance)^(1/2)	9.88
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	0.72	5.0400	5.6	0.002032128
Bust	0.28	-12.96	-14.4	0.005225472
			Covariance=sum=	0.0072576
		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	0.72	5.04	6.16	0.002235341
Bust	0.28	-12.96	-15.84	0.005748019
			Covariance=sum=	0.00798336
		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	0.72	5.6	6.16	0.002483712
Bust	0.28	-14.4	-15.84	0.006386688
			Covariance=sum=	0.0088704
		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	=0.2^2*0.08082^2+0.2^2*0.0898^2+0.6^2*0.09878^2+2*(0.2*0.2*0.08082*0.0898*1+0.2*0.6*0.0898*0.09878*1+0.2*0.6*1*0.08082*0.09878)
Variance	0.008722