Question

Consider the following probability distribution for stocks A and B:

Economy	Probability	A	B
Recession0.25	0.25	-0.02	0.06000
Normal	0.5	0.05000	0.02000
Boom	0.25	0.12000	-0.13

What is the correlation coefficient between stock A and B?

Answer 1

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Recession	0.25	-2	-0.5	-7	0.001225
Normal	0.5	5	2.5	0	0
Boom	0.25	12	3	7	0.001225
	Expected return %=	sum of weighted return =	5	Sum=Variance Stock A=	0.00245
			Standard deviation of Stock A%	=(Variance)^(1/2)	4.95
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Recession	0.25	6	1.5	6.75	0.001139063
Normal	0.5	2	1	2.75	0.000378125
Boom	0.25	-13	-3.25	-12.25	0.003751563
	Expected return %=	sum of weighted return =	-0.75	Sum=Variance Stock B=	0.00527
			Standard deviation of Stock B%	=(Variance)^(1/2)	7.26
Covariance Stock A Stock B:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Recession	0.25	-7	6.75	-0.00118125
Normal	0.5	0	2.75	0
Boom	0.25	7	-12.25	-0.00214375
			Covariance=sum=	-0.003325
		Correlation A&B=	Covariance/(std devA*std devB)=	-0.925453946