Given two random variables x and y

State of Nature Probability variable x variable y

I 0.2 18 0

II 0. 2 5 -3

III 0.2 12 15

IV 0.2 4 12

V 0.2 6 1

(i) Calculate the mean and variance of each of these variables and the covariance between them

(ii) Suppose x and y represent the returns from two assets. Calculate the mean and variance for the following part folios.

% in x 125 100 75 50 25 0 -25

% in y -25 0 25 50 75 100 125

(iii)Find the portfolio that has the minimum variance.

(iv)Let portfolio A have 75% in x and portfolio B has 25% in x. Calculate the covariance between the two portfolios.

(v) Calculate the covariance between the minimum variance portfolio and portfolio A.