Answer-first summary for fast verification
Answer: 0.0176
A is correct. Explanation: Let \( J = \text{return on stock J} \) and \( K = \text{return on stock K} \). Note that \( \text{Corr}(J,K) = \rho_{J,K} = \frac{\text{Cov}(J,K)}{\sigma_J \cdot \sigma_K} \), which means that: \[ \text{Cov}(J,K) = \rho_{J,K} \cdot \sigma_J \cdot \sigma_K \] Given: \[ \text{Cov}(J,K) = 0.0054 \] \[ \sigma_K = 0.11 \] \[ \rho_{J,K} = 0.37 \] Plugging in the values: \[ 0.0054 = 0.37 \cdot \sigma_J \cdot 0.11 \] Solving for \( \sigma_J \) (standard deviation of stock J): \[ \sigma_J = \frac{0.0054}{0.37 \cdot 0.11} \approx 0.1327 \] The variance of stock J, \( \sigma_J^2 \), is obtained by squaring the standard deviation of stock J: \[ \sigma_J^2 = 0.1327^2 \approx 0.017609 \text{ or } 0.0176 \]
Author: LeetQuiz Editorial Team
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A fund manager who follows a value-oriented investment strategy aims to identify stocks that are undervalued. Currently, the manager is evaluating the returns of two technology sector stocks, referred to as stock J and stock K. Through the assessment, the manager has determined the correlation coefficient between the returns of stock J and stock K to be 0.37, and the covariance of their returns to be 0.0054. Knowing that the standard deviation of the returns for stock K is 0.11, calculate the variance of the returns for stock J.
A
0.0176
B
0.0407
C
0.0735
D
0.1327
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