Question

The probabilities of an economic boom, normal economy, and a recession are 2 percent, 93 percent, and 5 percent, respectively. For these economic states, Stock A has deviations from its expected returns of 0.04, 0.07, and −0.11 for the three economic states respectively. Stock B has deviations from its expected returns of 0.14, 0.08, and −0.22 for the three economic states, respectively. What is the covariance of the two stocks?

Answer 1

Stock A
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Boom	0.02	4	0.08	-2.04	8.3232E-06
Normal	0.93	7	6.51	0.96	8.57088E-05
Recession	0.05	-11	-0.55	-17.04	0.001451808
	Expected return %=	sum of weighted return =	6.04	Sum=Variance Stock A=	0.00155
			Standard deviation of Stock A%	=(Variance)^(1/2)	3.93
Stock B
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Boom	0.02	14	0.28	7.38	0.000108929
Normal	0.93	8	7.44	1.38	0.000177109
Recession	0.05	-22	-1.1	-28.62	0.004095522
	Expected return %=	sum of weighted return =	6.62	Sum=Variance Stock B=	0.00438
			Standard deviation of Stock B%	=(Variance)^(1/2)	6.62
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	0.02	-2.04	7.38	-3.01104E-05
Normal	0.93	0.96	1.38	0.000123206
Recession	0.05	-17.04	-28.62	0.002438424
			Covariance=sum=	0.00253152