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Answer: 14
The correct answer is **C** (14). ### Explanation: The covariance between the returns of two random variables, R_X and R_Y, is calculated using the formula: Cov(R_X, R_Y) = ΣΣ P(R_X,i, R_Y,j) * (R_X,i - E[R_X]) * (R_Y,j - E[R_Y]) Given the joint probability function and expected returns: - E[R_X] = 14% - E[R_Y] = 9% The calculations are as follows: 1. For R_X = 20% and R_Y = 15%: 0.2 * (20 - 14) * (15 - 9) = 0.2 * 6 * 6 = 7.2 2. For R_X = 15% and R_Y = 10%: 0.4 * (15 - 14) * (10 - 9) = 0.4 * 1 * 1 = 0.4 3. For R_X = 10% and R_Y = 5%: 0.4 * (10 - 14) * (5 - 9) = 0.4 * (-4) * (-4) = 6.4 Adding these results together: 7.2 + 0.4 + 6.4 = 14 Thus, the covariance is **14** percent squared.
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An analyst develops the following joint probability function for the returns of two companies, X and Y:
| Return of Y \ Return of X | 20% | 15% | 10% |
|---|---|---|---|
| 15% | 0.2 | 0 | 0 |
| 10% | 0 | 0.4 | 0 |
| 5% | 0 | 0 | 0.4 |
The expected returns for companies X and Y are 14% and 9%, respectively. The covariance of returns between X and Y (in percent squared) is closest to:
A
0
B
5
C
14