Question

Consider the following information: State of Probability of Rate of Return If State Occurs Economy State of Economy Stock A Stock B Stock C Boom .15 .350 .450 .330 Good .45 .120 .100 .170 Poor .35 .010 .020 − .050 Bust .05 − .110 − .250 − .090 Your portfolio is invested 30 percent each in A and C and 40 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)What is the standard deviation of this portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.15	35	5.25	24.55	0.009040538
Good	0.45	12	5.4	1.55	0.000108113
Poor	0.35	1	0.35	-9.45	0.003125588
Bust	0.05	-11	-0.55	-21.45	0.002300513
	Expected return %=	sum of weighted return =	10.45	Sum=Variance Stock A=	0.01457
			Standard deviation of Stock A%	=(Variance)^(1/2)	12.07
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.15	45	6.75	34.3	0.01764735
Good	0.45	10	4.5	-0.7	0.00002205
Poor	0.35	2	0.7	-8.7	0.00264915
Bust	0.05	-25	-1.25	-35.7	0.00637245
	Expected return %=	sum of weighted return =	10.7	Sum=Variance Stock B=	0.02669
			Standard deviation of Stock B%	=(Variance)^(1/2)	16.34
Stock C
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(C)^2* probability
Boom	0.15	33	4.95	22.6	0.0076614
Good	0.45	17	7.65	6.6	0.0019602
Poor	0.35	-5	-1.75	-15.4	0.0083006
Bust	0.05	-9	-0.45	-19.4	0.0018818
	Expected return %=	sum of weighted return =	10.4	Sum=Variance Stock C=	0.0198
			Standard deviation of Stock C%	=(Variance)^(1/2)	14.07
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	0.15	24.5500	34.3	0.012630975
Good	0.45	1.55	-0.7	-0.000048825
Poor	0.35	-9.45	-8.7	0.002877525
Bust	0.05	-2145.00%	-35.7	0.003828825
			Covariance=sum=	0.0192885
		Correlation A&B=	Covariance/(std devA*std devB)=	0.977947353
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	0.15	24.55	22.6	0.00832245
Good	0.45	1.55	6.6	0.00046035
Poor	0.35	-945.00%	-15.4	0.00509355
Bust	0.05	-21.45	-19.4	0.00208065
			Covariance=sum=	0.015957
		Correlation A&C=	Covariance/(std devA*std devC)=	0.939234916
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	0.15	34.3	22.6	0.0116277
Good	0.45	-0.7	6.6	-0.0002079
Poor	0.35	-8.7	-15.4	0.0046893
Bust	0.05	-35.7	-19.4	0.0034629
			Covariance=sum=	0.019572
		Correlation B&C=	Covariance/(std devB*std devC)=	0.851287636
	Expected return%=	Wt Stock A*Return Stock A+Wt Stock B*Return Stock B+Wt Stock C*Return Stock C
	Expected return%=	0.3*10.45+0.4*10.7+0.3*10.4
	Expected return%=	10.54
	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	=0.3^2*0.12073^2+0.4^2*0.16337^2+0.3^2*0.14073^2+2*(0.3*0.4*0.12073*0.16337*0.97795+0.4*0.3*0.16337*0.14073*0.85129+0.3*0.3*0.93923*0.12073*0.14073)
	Variance	0.019563
	Standard deviation=	(variance)^0.5
	Standard deviation=	13.99%