Question

You have a two stock portfolio with $3,000 in stock A and $7,000 in stock B. You believe the following probability distribution exists for your stocks.

State of the Economy	Probability of State Occurring	Market Rate of Return of Stock A	Market Rate of Return of Stock B	Portfolio Return
Boom	0.3	-25%	25%
Normal	0.5	10%	15%
Recession	0.2	30%	5%

1. Calculate Expected rate of Return, Risk, and CV of Stock A

2. Calculate portfolio expected rate of return, portfolio risk , and portfolio CV. Note: expected rate of Return , risk, and CV of Stock B are 16,7, and 0.44 respectively .

Answer 1

Total Portfolio value = Value of Stock A + Value of Stock B

=3000+7000

=10000

Weight of Stock A = Value of Stock A/Total Portfolio Value

= 3000/10000

=0.3

Weight of Stock B = Value of Stock B/Total Portfolio Value

= 7000/10000

=0.7

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.3	-25	-7.5	-28.5	0.0243675
Normal	0.5	10	5	6.5	0.0021125
Recession	0.2	30	6	26.5	0.014045
	Expected return %=	sum of weighted return =	3.5	Sum=Variance Stock A=	0.04053
			Standard deviation of Stock A%	=(Variance)^(1/2)	20.13
			Coefficient of variation=	Std. dev./return=	5.7514
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.3	25	7.5	9	0.00243
Normal	0.5	15	7.5	-1	0.00005
Recession	0.2	5	1	-11	0.00242
	Expected return %=	sum of weighted return =	16	Sum=Variance Stock B=	0.0049
			Standard deviation of Stock B%	=(Variance)^(1/2)	7
			Coefficient of variation=	Std. dev./return=	0.4375
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	0.3	-28.5	9	-0.007695
Normal	0.5	6.5	-1	-0.000325
Recession	0.2	26.5	-11	-0.00583
			Covariance=sum=	-0.01385
		Correlation A&B=	Covariance/(std devA*std devB)=	-0.982856743
	Expected return%=	Wt Stock A*Return Stock A+Wt Stock B*Return Stock B
	Expected return%=	0.3*3.5+0.7*16
	Expected return%=	12.25
	Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
	Variance	=0.3^2*0.20131^2+0.7^2*0.07^2+2*0.3*0.7*0.20131*0.07*-0.98286
	Variance	0.00023
	Standard deviation=	(variance)^0.5
	Standard deviation=	1.52%