
Answer-first summary for fast verification
Answer: CNY 1.437 million
The correct answer is B, which stands for CNY 1.437 million. The component Value-at-Risk (VaR) of stock Y can be calculated using the formula: \[ \text{CVaRt} = \text{VaRt} \times \rho_{T,P} \] where: - \( \text{CVaRt} \) is the component VaR for stock T. - \( \text{VaRt} \) is the VaR of stock T. - \( \rho_{T,P} \) is the correlation coefficient between stock T and the portfolio. Given: - The portfolio's annualized standard deviation of returns is 16%. - The stock Y's annualized standard deviation of returns is 12%. - The correlation of returns between the portfolio and stock Y is 0.52. - The 95% confidence factor for the VaR estimate (α) is 1.645. First, calculate the VaR of stock Y (\( \text{VaRt} \)) using its weight in the portfolio (\( w_T \)), its standard deviation (\( \sigma_T \)), and the 95% confidence factor: \[ \text{VaRt} = w_T \times \sigma_T \times \alpha(95\%) \] \[ \text{VaRt} = \frac{14}{124} \times 0.12 \times 1.645 \] \[ \text{VaRt} = 0.1136 \times 0.12 \times 1.645 \] \[ \text{VaRt} = 0.103 \text{ million CNY} \] Then, calculate the component VaR of stock Y: \[ \text{CVaRt} = 0.52 \times 0.103 \] \[ \text{CVaRt} = 0.05352 \text{ million CNY} \] However, the provided explanation in the file content has a discrepancy in the calculation of \( \text{VaRt} \). It incorrectly uses CAD 15 million as the weight of stock T and a standard deviation of 0.13, which are not provided in the question. The correct calculation should be based on the information given in the question: \[ \text{VaRt} = \frac{14}{124} \times 0.12 \times 1.645 \] After correcting the calculation, we find that the component VaR of stock Y is approximately CNY 0.103 million, which corresponds to option A, not B. Therefore, the correct answer provided in the file content is incorrect based on the given information and calculations.
Author: LeetQuiz Editorial Team
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A
CNY 0.103 million
B
CNY 1.437 million
C
CNY 2.032 million
D
CNY 3.685 million
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