Question

You decide to invest in a portfolio consisting of 17 percent Stock X, 38 percent Stock Y, and the remainder in Stock Z. Based on the following information, what is the standard deviation of your portfolio?

State of Economy	Probability of State			Return if State Occurs
	of Economy
				Stock X			Stock Y			Stock Z
Normal		.75			9.20%			2.60%			11.60%
Boom		.25			16.50%			24.50%			16.00%

Answer 1

Stock X
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Normal	0.75	9.2	6.9	-1.825	0.000249797
Boom	0.25	16.5	4.125	5.475	0.000749391
	Expected return %=	sum of weighted return =	11.03	Sum=Variance Stock X=	0.001
			Standard deviation of Stock X%	=(Variance)^(1/2)	3.16
Stock Y
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Normal	0.75	2.6	1.95	-5.475	0.002248172
Boom	0.25	24.5	6.125	16.425	0.006744516
	Expected return %=	sum of weighted return =	8.08	Sum=Variance Stock Y=	0.00899
			Standard deviation of Stock Y%	=(Variance)^(1/2)	9.48
Stock Z
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(C)^2* probability
Normal	0.75	11.6	8.7	-1.1	0.00009075
Boom	0.25	16	4	3.3	0.00027225
	Expected return %=	sum of weighted return =	12.7	Sum=Variance Stock Z=	0.00036
			Standard deviation of Stock Z%	=(Variance)^(1/2)	1.91
Covariance Stock X Stock Y:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Normal	0.75	-1.8250	-5.475	0.000749391
Boom	0.25	5.475	16.425	0.002248172
			Covariance=sum=	0.002997563
		Correlation A&B=	Covariance/(std devA*std devB)=	1
Covariance Stock X Stock Z:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% for C(C)	(A)*(C)*probability
Normal	0.75	-1.825	-1.1	0.000150563
Boom	0.25	5.475	3.3	0.000451688
			Covariance=sum=	0.00060225
		Correlation A&C=	Covariance/(std devA*std devC)=	1
Covariance Stock Y Stock Z:
Scenario	Probability	Actual return% -expected return% For B(B)	Actual return% -expected return% for C(C)	(B)*(C)*probability
Normal	0.75	-5.475	-1.1	0.000451688
Boom	0.25	16.425	3.3	0.001355063
			Covariance=sum=	0.00180675
		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	=0.17^2*0.03161^2+0.38^2*0.09483^2+0.45^2*0.01905^2+2*(0.17*0.38*0.03161*0.09483*1+0.38*0.45*0.09483*0.01905*1+0.17*0.45*1*0.03161*0.01905)
	Variance	0.002498
	Standard deviation=	(variance)^0.5
	Standard deviation=	5.00%