
Financial Risk Manager Part 2
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- A manager is evaluating the risks linked to a portfolio comprising several stocks. The portfolio currently holds a value of CNY 124 million, with CNY 14 million allocated to stock Y. The annualized standard deviation of returns for the overall portfolio is 16%, while that for stock Y is 12%. The correlation coefficient between the returns of the portfolio and stock Y is 0.52. If a risk analyst employs a 1-year 95% Value at Risk (VaR) methodology, assuming the returns follow a normal distribution, what is the component Value at Risk for stock Y?
- A manager is evaluating the risks linked to a portfolio comprising several stocks. The portfolio currently holds a value of CNY 124 million, with CNY 14 million allocated to stock Y. The annualized standard deviation of returns for the overall portfolio is 16%, while that for stock Y is 12%. The correlation coefficient between the returns of the portfolio and stock Y is 0.52. If a risk analyst employs a 1-year 95% Value at Risk (VaR) methodology, assuming the returns follow a normal distribution, what is the component Value at Risk for stock Y?
Explanation:
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:
where:
- is the component VaR for stock T.
- is the VaR of stock T.
- 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 () using its weight in the portfolio (), its standard deviation (), and the 95% confidence factor:
Then, calculate the component VaR of stock Y:
However, the provided explanation in the file content has a discrepancy in the calculation of . 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:
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.