Given two random variables x and y:

(a) Calculate the mean and variance of each of these variables, and the covariance between them.
(b) Suppose x and y represent the returns from two assets. Calculate the mean and variance for the following portfolios:

(c) Find the portfolio that has the minimum variance.
(d) Let portfolio A have 75% in x and portfolio B have 25% in x. Calculate the covariance between the two portfolios.
(e) Calculate the covariance between the minimum variance portfolio and portfolio A, and the covariance between the minimum variance portfolio and portfolio B.
(f) What is the covariance between the minimum variance portfolio and any other portfolio along the efficient set?
(g) What is the relationship between the covariance of the minimum variance portfolio with other efficient portfolios, and the variance of the minimum variance portfolio?

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Probability of State State of of Nature Nature Variablex Variable y 18 15 12 12 IV %inx 125 100 75 50 25 0-25 %inv-25 025 50 75 100 125