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You decide to invest in a portfolio consisting of 26 percent Stock A, 49 percent Stock B, and the remainder in Stock C. Based on the following information, what is the variance of your portfolio? Probability of State of Economy Return if State Occurs State of Economy Stock A Stock B Stock C - 3.70% Recession -10.30% -12.70% .116 17.10% Normal 9.60% 10.70% .669 21.59% 25.19% 29.89% Вoom .215

Answer 1

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Recession	0.116	-10.3	-1.1948	-20.16945	0.004718958
Normal	0.669	9.6	6.4224	-0.26945	4.85716E-06
Boom	0.215	21.59	4.64185	11.72055	0.002953483
	Expected return %=	sum of weighted return =	9.87	Sum=Variance Stock A=	0.00768
			Standard deviation of Stock A%	=(Variance)^(1/2)	8.76
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Recession	0.116	-3.7	-0.4292	-15.84495	0.002912324
Normal	0.669	10.7	7.1583	-1.44495	0.000139679
Boom	0.215	25.19	5.41585	13.04505	0.003658727
	Expected return %=	sum of weighted return =	12.14	Sum=Variance Stock B=	0.00671
			Standard deviation of Stock B%	=(Variance)^(1/2)	8.19
Stock C
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(C)^2* probability
Recession	0.116	-12.7	-1.4732	-29.09305	0.009818304
Normal	0.669	17.1	11.4399	0.70695	3.34352E-05
Boom	0.215	29.89	6.42635	13.49695	0.003916605
	Expected return %=	sum of weighted return =	16.39	Sum=Variance Stock C=	0.01377
			Standard deviation of Stock C%	=(Variance)^(1/2)	11.73
Covariance Stock A Stock B:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Recession	0.116	-20.1695	-15.84495	0.003707174
Normal	0.669	-0.26945	-1.44495	2.6047E-05
Boom	0.215	11.72	13.04505	0.003287246
			Covariance=sum=	0.007020466
		Correlation A&B=	Covariance/(std devA*std devB)=	0.978085655
Covariance Stock A Stock C:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% for C(C)	(A)*(C)*probability
Recession	0.116	-20.16945	-29.09305	0.006806773
Normal	0.669	-0.26945	0.70695	-1.27436E-05
Boom	0.215	1172.06%	13.49695	0.003401121
			Covariance=sum=	0.010195151
		Correlation A&C=	Covariance/(std devA*std devC)=	0.991627599
Covariance Stock B Stock C:
Scenario	Probability	Actual return% -expected return% For B(B)	Actual return% -expected return% for C(C)	(B)*(C)*probability
Recession	0.116	-15.84495	-29.09305	0.005347344
Normal	0.669	-1.44495	0.70695	-6.83388E-05
Boom	0.215	13.04505	13.49695	0.00378547
			Covariance=sum=	0.009064475
		Correlation B&C=	Covariance/(std devB*std devC)=	0.94301137
	Expected return%=	Wt Stock A*Return Stock A+Wt Stock B*Return Stock B+Wt Stock C*Return Stock C
	Expected return%=	0.26*9.87+0.49*12.14+0.25*16.39
	Expected return%=	12.62
	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	=0.26^2*0.08762^2+0.49^2*0.08192^2+0.25^2*0.11734^2+2*(0.26*0.49*0.08762*0.08192*0.97809+0.49*0.25*0.08192*0.11734*0.94301+0.26*0.25*0.99163*0.08762*0.11734)
	Variance	0.008326