Question

The rates of return of Stock A and B are distributed as follows:

State Probability Return on A Return on B

1 0.3 15% 5%

2 0.5 9% 7%

3 0.2 -1% 12%

Suppose you have invested $1000 in stock A and $2000 in Stock B. Please, find this portfolio’s expected return and total risk. What is the correlation between the rate of return on Stock A and Stock B?

Answer 1

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
1	0.3	15	4.5	6.2	0.0011532
2	0.5	9	4.5	0.2	2E-06
3	0.2	-1	-0.2	-9.8	0.0019208
	Expected return %=	sum of weighted return =	8.8	Sum=Variance Stock A=	0.00308
			Standard deviation of Stock A%	=(Variance)^(1/2)	5.55
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
1	0.3	5	1.5	-2.4	0.0001728
2	0.5	7	3.5	-0.4	8E-06
3	0.2	12	2.4	4.6	0.0004232
	Expected return %=	sum of weighted return =	7.4	Sum=Variance Stock B=	0.0006
			Standard deviation of Stock B%	=(Variance)^(1/2)	2.46
Covariance Stock A Stock B:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
1	0.3	6.2	-2.4	-0.0004464
2	0.5	0.2	-0.4	-4E-06
3	0.2	-9.8	4.6	-0.0009016
			Covariance=sum=	-0.001352
		Correlation A&B=	Covariance/(std devA*std devB)=	-0.991893528
	Expected return%=	Wt Stock A*Return Stock A+Wt Stock B*Return Stock B
	Expected return%=	0.3333*8.8+0.6666*7.4
	Expected return%=	7.87
	Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
	Variance	=0.3333^2*0.05546^2+0.6666^2*0.02458^2+2*0.3333*0.6666*0.05546*0.02458*-0.99189
	Variance	0.00001
	Standard deviation=	(variance)^0.5
	Standard deviation=	0.32%