Question

Consider the following information: State of Probability of State Rate of Return if State Occurs Economy of Economy Stock A Stock B Stock C Boom .70 .08 .02 .28 Bust .17 -.08 .30 23 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return 0 % b. What is the variance of a portfolio invested 25 percent each in A and B and 50 percent in C? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) Variance of a portfolio

Answer 1

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.7	8	5.6	-2.7	0.0005103
Bust	0.3	17	5.1	6.3	0.0011907
	Expected return %=	sum of weighted return =	10.7	Sum=Variance Stock A=	0.0017
			Standard deviation of Stock A%	=(Variance)^(1/2)	4.12
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.7	2	1.4	-6.3	0.0027783
Bust	0.3	23	6.9	14.7	0.0064827
	Expected return %=	sum of weighted return =	8.3	Sum=Variance Stock B=	0.00926
			Standard deviation of Stock B%	=(Variance)^(1/2)	9.62
Stock C
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(C)^2* probability
Boom	0.7	28	19.6	10.8	0.0081648
Bust	0.3	-8	-2.4	-25.2	0.0190512
	Expected return %=	sum of weighted return =	17.2	Sum=Variance Stock C=	0.02722
			Standard deviation of Stock C%	=(Variance)^(1/2)	16.5
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	0.7	-2.7000	-6.3	0.0011907
Bust	0.3	6.3	14.7	0.0027783
			Covariance=sum=	0.003969
		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	0.7	-2.7	10.8	-0.0020412
Bust	0.3	6.3	-25.2	-0.0047628
			Covariance=sum=	-0.006804
		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	0.7	-6.3	10.8	-0.0047628
Bust	0.3	14.7	-25.2	-0.0111132
			Covariance=sum=	-0.015876
		Correlation B&C=	Covariance/(std devB*std devC)=	-1
	a.Expected return%=	Wt Stock A*Return Stock A+Wt Stock B*Return Stock B+Wt Stock C*Return Stock C
	Expected return%=	0.3333*10.7+0.3333*8.3+0.3333*17.2
	Expected return%=	12.07
	b.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	=0.3333^2*0.04124^2+0.3333^2*0.09623^2+0.3333^2*0.16497^2+2*(0.3333*0.3333*0.04124*0.09623*1+0.3333*0.3333*0.09623*0.16497*-1+0.3333*0.3333*-1*0.04124*0.16497)
	Variance	0.00008