School of Business and Economics

(10 marks)

Q10. Given two random variables, X and Y,

Probability of State of Nature	State of Nature	Variable X	Variable Y
0.2	I	-5	0
0.3	II	5	10
0.5	III	10	20

(a) Calculate the mean E(X), E(Y), variance VAR(X), VAR(Y), and covariance COV(X,Y) between X and Y.

(b) Suppose X and Y represent the returns from two assets. Calculate the mean and variance for the following portfolio 75% in X and 25% in Y.
(10 marks)
Solution

(a) Calculate the mean and variance of each of these variables, and the covariance between them.

=0.2(-5-5.5)(0-13) + 0.3(5-5.5)(10-13) + 0.5(10-5.5)(20-13) = 43.5

(b)

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