Find portfolio variance You invest $6,000 in the stock and $4,000 in the bond outcome P Rs Rb recession 30% -11% 16% normal 40% 13% 6% boom 30% 27% -4%

outcome	P	Rs	Rb
recession	30%	-11%	16%
normal	40%	13%	6%
boom	30%	27%	-4%

4.4 Ratings (944 Votes)

Stock
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%
Recession	0.3	-11	-3.3	-21
Normal	0.4	13	5.2	3
Boom	0.3	27	8.1	17

	Expected return %=	sum of weighted return =	10	Sum=Variance Stock=
			Standard deviation of Stock%	=(Variance)^(1/2)

Bond
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%
Recession	0.3	16	4.8	10
Normal	0.4	6	2.4	0
Boom	0.3	-4	-1.2	-10

	Expected return %=	sum of weighted return =	6	Sum=Variance Bond=
			Standard deviation of Bond%	=(Variance)^(1/2)

Covariance Stock Bond:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)(B)probability
Recession	0.3	-21	10	-0.0063
Normal	0.4	3	0	0
Boom	0.3	17	-10	-0.0051

			Covariance=sum=	-0.0114
		Correlation A&B=	Covariance/(std devA*std devB)=	-0.98643085

	Expected return%=	Wt StockReturn Stock+Wt BondReturn Bond
	Expected return%=	0.610+0.46
	Expected return%=	8.4
	Variance	=( w2A?2(RA) + w2B?2(RB) + 2(wA)(wB)Cor(RA, RB)?(RA)*?(RB))
	Variance	=0.6^20.1492^2+0.4^20.07746^2+20.60.40.14920.07746*-0.98643
	Variance	0.0035

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