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:
CVaRt=VaRt×ρT,P
where:
- CVaRt is the component VaR for stock T.
- VaRt is the VaR of stock T.
- ρT,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 (VaRt) using its weight in the portfolio (wT), its standard deviation (σT), and the 95% confidence factor:
VaRt=wT×σT×α(95%)
VaRt=12414×0.12×1.645
VaRt=0.1136×0.12×1.645
VaRt=0.103 million CNY
Then, calculate the component VaR of stock Y:
CVaRt=0.52×0.103
CVaRt=0.05352 million CNY
However, the provided explanation in the file content has a discrepancy in the calculation of 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:
VaRt=12414×0.12×1.645
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.