Question

Given the returns and probabilities for the three possible states listed here, calculate the covariance between the returns of Stock A and Stock B. For convenience, assume that the expected returns of Stock A and Stock B are 0.09 and 0.16, respectively. (Round your answer to 4 decimal places. For example .1244)

	Probability	Return(A)	Return(B)
Good	0.35	0.30	0.50
OK	0.50	0.10	0.10
Poor	0.15	-0.25	-0.30

Answer 1

Covariance = Sum [Prob * (X-AvgX)(Y-AvgY) ]
Scenario	Prob	Ret (X)	(X-AvgX)	Ret (Y)	(Y-AvgY)	(X-AVgX)(Y-AvgY)	Prob* (X-AVgX)(Y-AvgY)
1	0.3500	0.30	0.21	0.50	0.34	0.0714	0.02499
2	0.5000	0.10	0.01	0.10	-0.06	-0.0006	-0.00030
3	0.1500	-0.25	-0.34	-0.30	-0.46	0.1564	0.02346
Covariance = Sum [Prob * (X-AvgX)(Y-AvgY) ]	0.04815

Avg X = 0.09

Avg Y = 0.16

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