Question

QUESTION 2 Assume that you formed a portfolio by investing $10,000 in AT&T and $15,000 in GE Below is information on three "states of nature and the return that you would see over the next year from each security in each state of nature. What will be the variance of returns for your portfolio? Probability of "state" 1/3 AT&T .13 GE 05 .12 19 1/3 2.0.0058 b. 0.0047 0.0071 d. 0.0028 0.0035

Answer 1

AT&T
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
1	0.3333	13	4.3329	4.0009	0.00053352
2	0.3333	-8	-2.6664	-16.9991	0.00963135
3	0.3333	22	7.3326	13.0009	0.00563355
	Expected return %=	sum of weighted return =	9	Sum=Variance AT&T=	0.0158
			Standard deviation of AT&T%	=(Variance)^(1/2)	12.57
GE
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
1	0.3333	5	1.6665	-6.9988	0.00163261
2	0.3333	12	3.9996	0.0012	4.79952E-11
3	0.3333	19	6.3327	7.0012	0.00163373
	Expected return %=	sum of weighted return =	12	Sum=Variance GE=	0.00327
			Standard deviation of GE%	=(Variance)^(1/2)	5.72
Covariance AT&T GE:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
1	0.3333	4.0009	-6.9988	-0.00093329
2	0.3333	-16.9991	0.0012	-6.79896E-07
3	0.3333	13.0009	7.0012	0.00303376
			Covariance=sum=	0.00209979
		Correlation A&B=	Covariance/(std devA*std devB)=	0.292306419
	Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
	Variance	=0.4^2*0.12569^2+0.6^2*0.05715^2+2*0.4*0.6*0.12569*0.05715*0.29231
	Variance	0.0047