Financial Risk Manager Part 2

Financial Risk Manager Part 2

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  1. 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:

CVaRt=VaRt×ρT,P\text{CVaRt} = \text{VaRt} \times \rho_{T,P}

where:

  • CVaRt\text{CVaRt} is the component VaR for stock T.
  • VaRt\text{VaRt} is the VaR of stock T.
  • ρT,P\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 (VaRt\text{VaRt}) using its weight in the portfolio (wTw_T), its standard deviation (σT\sigma_T), and the 95% confidence factor:

VaRt=wT×σT×α(95%)\text{VaRt} = w_T \times \sigma_T \times \alpha(95\%)

VaRt=14124×0.12×1.645\text{VaRt} = \frac{14}{124} \times 0.12 \times 1.645

VaRt=0.1136×0.12×1.645\text{VaRt} = 0.1136 \times 0.12 \times 1.645

VaRt=0.103 million CNY\text{VaRt} = 0.103 \text{ million CNY}

Then, calculate the component VaR of stock Y:

CVaRt=0.52×0.103\text{CVaRt} = 0.52 \times 0.103

CVaRt=0.05352 million CNY\text{CVaRt} = 0.05352 \text{ million CNY}

However, the provided explanation in the file content has a discrepancy in the calculation of VaRt\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:

VaRt=14124×0.12×1.645\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.

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