Question

Consider the following information:

		Rate of return if state occurs
State of economy	Probability of state of economy	Stock A	Stock B
Boom	0.2	24%	45%
Good	0.35	9%	10%
Poor	0.3	3%	-10%
Bust	??	-5%	-25%

You have $2,000 invested in stock A and $3,000 invested in stock B. Compute the expected return and total risk of this portfolio.

Answer 1

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

=2000+3000

=5000

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

= 2000/5000

=0.4

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

= 3000/5000

=0.6

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.2	24	4.8	15.9	0.0050562
Good	0.35	9	3.15	0.9	2.835E-05
Poor	0.3	3	0.9	-5.1	0.0007803
Bust	0.15	-5	-0.75	-13.1	0.00257415
	Expected return %=	sum of weighted return =	8.1	Sum=Variance Stock A=	0.00844
			Standard deviation of Stock A%	=(Variance)^(1/2)	9.19
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.2	45	9	39.25	0.03081125
Good	0.35	10	3.5	4.25	0.000632188
Poor	0.3	-10	-3	-15.75	0.007441875
Bust	0.15	-25	-3.75	-30.75	0.014183438
	Expected return %=	sum of weighted return =	5.75	Sum=Variance Stock B=	0.05307
			Standard deviation of Stock B%	=(Variance)^(1/2)	23.04
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	15.9	39.25	0.0124815
Good	0.35	0.9	4.25	0.000133875
Poor	0.3	-5.1	-15.75	0.00240975
Bust	0.15	-13.1	-30.75	0.006042375
			Covariance=sum=	0.0210675
		Correlation A&B=	Covariance/(std devA*std devB)=	0.995515623
	Expected return%=	Wt Stock A*Return Stock A+Wt Stock B*Return Stock B
	Expected return%=	0.4*8.1+0.6*5.75
	Expected return%=	6.69
	Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
	Variance	=0.4^2*0.09186^2+0.6^2*0.23037^2+2*0.4*0.6*0.09186*0.23037*0.99552
	Variance	0.03057
	Standard deviation=	(variance)^0.5
	Standard deviation=	17.48% = risk