Question

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%

Answer 1

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 Stock*Return Stock+Wt Bond*Return Bond
	Expected return%=	0.6*10+0.4*6
	Expected return%=	8.4
	Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
	Variance	=0.6^2*0.1492^2+0.4^2*0.07746^2+2*0.6*0.4*0.1492*0.07746*-0.98643
	Variance	0.0035