Question

(13-3) You want to assess the expected return and risk of your portfolio, which contains three stocks. You are basing your assessment on a simple forward-looking model based on three states of the world. The weights in your portfolio are 25% in Stock A, 45% in Stock B and 30% in Stock C. Your assessment of the probable returns of these three stocks in the states of the world are given in the table below. Prob Stock B Stock C Stock A 0.03 Вoom 0.20 0.12 0.18 0.60 0.07 Normal 0.05 0.06 -0.11 0.02 Bust 0.20 -0.06 Calculate the expected return and standard deviation of your portfolio based on these assumptions.

Answer 1

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.2	12	2.4	7.8	0.0012168
Normal	0.6	5	3	0.8	0.0000384
Bust	0.2	-6	-1.2	-10.2	0.0020808
	Expected return %=	sum of weighted return =	4.2	Sum=Variance Stock A=	0.00334
			Standard deviation of Stock A%	=(Variance)^(1/2)	5.78
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.2	18	3.6	13	0.00338
Normal	0.6	6	3.6	1	6E-05
Bust	0.2	-11	-2.2	-16	0.00512
	Expected return %=	sum of weighted return =	5	Sum=Variance Stock B=	0.00856
			Standard deviation of Stock B%	=(Variance)^(1/2)	9.25
Stock C
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(C)^2* probability
Boom	0.2	3	0.6	-2.2	9.68E-05
Normal	0.6	7	4.2	1.8	0.0001944
Bust	0.2	2	0.4	-3.2	0.0002048
	Expected return %=	sum of weighted return =	5.2	Sum=Variance Stock C=	0.0005
			Standard deviation of Stock C%	=(Variance)^(1/2)	2.23
Covariance Stock A Stock B:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Boom	0.2	7.8000	13	0.002028
Normal	0.6	0.8	1	0.000048
Bust	0.2	-10.20	-16	0.003264
			Covariance=sum=	0.00534
		Correlation A&B=	Covariance/(std devA*std devB)=	0.999289568
Covariance Stock A Stock C:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% for C(C)	(A)*(C)*probability
Boom	0.2	7.8	-2.2	-0.0003432
Normal	0.6	0.8	1.8	0.0000864
Bust	0.2	-1020.00%	-3.2	0.0006528
			Covariance=sum=	0.000396
		Correlation A&C=	Covariance/(std devA*std devC)=	0.307851537
Covariance Stock B Stock C:
Scenario	Probability	Actual return% -expected return% For B(B)	Actual return% -expected return% for C(C)	(B)*(C)*probability
Boom	0.2	13	-2.2	-0.000572
Normal	0.6	1	1.8	0.000108
Bust	0.2	-16	-3.2	0.001024
			Covariance=sum=	0.00056
		Correlation B&C=	Covariance/(std devB*std devC)=	0.271775502
	Expected return%=	Wt Stock A*Return Stock A+Wt Stock B*Return Stock B+Wt Stock C*Return Stock C
	Expected return%=	0.25*4.2+0.45*5+0.3*5.2
	Expected return%=	4.86
	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	=0.25^2*0.05776^2+0.45^2*0.09252^2+0.3^2*0.02227^2+2*(0.25*0.45*0.05776*0.09252*0.99929+0.45*0.3*0.09252*0.02227*0.27178+0.25*0.3*0.30785*0.05776*0.02227)
	Variance	0.003399
	Standard deviation=	(variance)^0.5
	Standard deviation=	5.83%