Question

Assume that the % expected return for security A and the market M for a good, normal and bad economy (probabilities .3,.4,.3) are 20, 16, and 10 for A and 8, 4, and 12 for M. Also assume that you invest 40% in A and 60% in M. Compute the covariance between A and M.

Answer 1

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Good	0.3	20	6	4.6	0.0006348
Normal	0.4	16	6.4	0.6	0.0000144
Bad	0.3	10	3	-5.4	0.0008748
	Expected return %=	sum of weighted return =	15.4	Sum=Variance Stock A=	0.00152
			Standard deviation of Stock A%	=(Variance)^(1/2)	3.9
Stock M
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Good	0.3	8	2.4	0.4	4.8E-06
Normal	0.4	4	1.6	-3.6	0.0005184
Bad	0.3	12	3.6	4.4	0.0005808
	Expected return %=	sum of weighted return =	7.6	Sum=Variance Stock M=	0.0011
			Standard deviation of Stock M%	=(Variance)^(1/2)	3.32
Covariance Stock A Stock M:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Good	0.3	4.6	0.4	0.0000552
Normal	0.4	0.6	-3.6	-8.64E-05
Bad	0.3	-5.4	4.4	-0.0007128
			Covariance=sum=	-0.000744