A supervisor is evaluating the risks associated with a portfolio of stocks. The current value of the portfolio is CNY 124 million, which includes CNY 14 million invested in stock Y. The annual standard deviations of returns for the entire portfolio and stock Y are 16% and 12%, respectively. The correlation coefficient of returns between the portfolio and stock Y is 0.52. Assuming the risk analyst uses a 1-year 95% Value at Risk (VaR) model and that returns are normally distributed, determine the component VaR for stock Y.

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Explanation:

The component Value-at-Risk (VaR) for stock Y is calculated using the formula:

$CVaRy = \rho_{py} \cdot w_y \cdot \sigma_y \cdot \alpha(95\%)$

where:

$\rho_{py}$ is the correlation coefficient between stock Y and the portfolio, which is 0.52.
$w_y$ is the value of stock Y, which is CNY 14 million.
$\sigma_y$ is the standard deviation of stock Y returns, which is 12% or 0.12.
$\alpha(95\%)$ is the 95% confidence factor for the VaR estimate, which is 1.645.

Plugging in the values:

$VaRy = w_y \cdot \sigma_y \cdot \alpha(95\%) = 14,000,000 \cdot 0.12 \cdot 1.645 = 2,763,600$

$CVaRy = 0.52 \cdot 2,763,600 = 1,437,072$

Rounded to the nearest whole number, the component VaR of stock Y is approximately CNY 1.437 million, which corresponds to option B.

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Financial Risk Manager Part 2