Question

You decide to invest in a portfolio consisting of 19 percent Stock X, 40 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		.78			9.40%			2.80%			11.80%
Boom		.22			16.70%			24.70%			16.20%

7.22%

6.19%

2.45%

1.84%

4.95%

Answer 1

Stock X
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Normal	0.78	9.4	7.332	-1.606	0.00020118
Growth	0.22	16.7	3.674	5.694	0.000713276
	Expected return %=	sum of weighted return =	11.01	Sum=Variance Stock X=	0.00091
			Standard deviation of Stock X%	=(Variance)^(1/2)	3.02
Stock Y
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Normal	0.78	2.8	2.184	-4.818	0.001810624
Growth	0.22	24.7	5.434	17.082	0.006419484
	Expected return %=	sum of weighted return =	7.62	Sum=Variance Stock Y=	0.00823
			Standard deviation of Stock Y%	=(Variance)^(1/2)	9.07
Stock Z
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(C)^2* probability
Normal	0.78	11.8	9.204	-0.968	7.30879E-05
Growth	0.22	16.2	3.564	3.432	0.00025913
	Expected return %=	sum of weighted return =	12.77	Sum=Variance Stock Z=	0.00033
			Standard deviation of Stock Z%	=(Variance)^(1/2)	1.82
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	0.78	-1.6060	-4.818	0.000603541
Growth	0.22	5.694	17.082	0.002139828
			Covariance=sum=	0.002743369
		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	0.78	-1.606	-0.968	0.000121259
Growth	0.22	5.694	3.432	0.00042992
			Covariance=sum=	0.000551179
		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	0.78	-4.818	-0.968	0.000363778
Growth	0.22	17.082	3.432	0.001289759
			Covariance=sum=	0.001653538
		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	=0.19^2*0.03024^2+0.4^2*0.09072^2+0.41^2*0.01823^2+2*(0.19*0.4*0.03024*0.09072*1+0.4*0.41*0.09072*0.01823*1+0.19*0.41*1*0.03024*0.01823)
	Variance	0.002451
	Standard deviation=	(variance)^0.5
	Standard deviation=	4.95%