You have a portfolio of two assets, X and Y. The returns of X and Y follow a joint probability function as follows: There is a 25% chance that X will return 16% and
Y will return 10%; there is a 60% chance that X will return 9% and Y will return 7%; and there is a 15% chance that Y will return 15% and X will return 5%. Find the covariance of X and Y.
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A. B. C. D.D
For a joint probability function, the covariance of X and Y is given by the formula: double summation (over all X, and over all Y) of P(X,Y)*[X - E(X)]*[Y - E(Y)]. E(X) will be 25% * 16% + 60% * 9% + 15% * 5% = 4% + 5.4% + 0.75% = 10.15%. Similarly, we will find that E(Y) = 8.95%. Next, we plug these values into our formula and obtain 25% * (16% - 10.15%) *(10% - 8.95%) + 60% (9% - 10.15%) * (7% - 8.95%) + 15% (5% - 10.15%) * (15% - 8.95%) = -1.79%%.