Financial Risk Manager Part 2

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Explanation:

The correct answer is C, CAD 523,350. The explanation for this is as follows:

The value of stock XYZ (Vxyz) is CAD 5 million.
The standard deviation of returns for stock XYZ (σXYZ) is 15% annually.
The 99% confidence factor for the VaR estimate (α(99%)) is 2.326.
The correlation of returns between stock XYZ and the portfolio (p) is 0.3.

To calculate the individual VaR of stock XYZ, we use the formula: $\text{VaRxyz} = Vxyz \times \sigmaXYZ \times \alpha(99\%)$

Plugging in the values, we get: $\text{VaRxyz} = CAD 5,000,000 \times 0.15 \times 2.326 = CAD 1,744,500$

The component VaR of stock XYZ is then calculated by multiplying the individual VaR by the correlation coefficient: $\text{Component VaRxyz} = p \times \text{VaRxyz} = 0.30 \times CAD 1,744,500 = CAD 523,350$

This calculation shows that the estimated component VaR of stock XYZ, considering its correlation with the portfolio and the overall risk profile, is CAD 523,350.

Explanation:

The correct answer is C, CAD 523,350. The explanation for this is as follows:

The value of stock XYZ (Vxyz) is CAD 5 million.
The standard deviation of returns for stock XYZ (σXYZ) is 15% annually.
The 99% confidence factor for the VaR estimate (α(99%)) is 2.326.
The correlation of returns between stock XYZ and the portfolio (p) is 0.3.

To calculate the individual VaR of stock XYZ, we use the formula: $\text{VaRxyz} = Vxyz \times \sigmaXYZ \times \alpha(99\%)$

Plugging in the values, we get: $\text{VaRxyz} = CAD 5,000,000 \times 0.15 \times 2.326 = CAD 1,744,500$

This calculation shows that the estimated component VaR of stock XYZ, considering its correlation with the portfolio and the overall risk profile, is CAD 523,350.

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A portfolio manager is evaluating the risk profile of a CAD 20 million portfolio which includes CAD 5 million invested in stock XYZ. The portfolio has an annual standard deviation of returns of 12%, while stock XYZ has an annual standard deviation of 15%. The returns of stock XYZ are correlated with the portfolio returns at a coefficient of 0.3. Using a 1-year Value at Risk (VaR) at the 99% confidence level under the assumption of normally distributed returns, what is the calculated component VaR for stock XYZ?

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Last updated: January 25, 2026 at 14:03

CAD 162,972

10.3%

CAD 234,906

13.8%

CAD 523,350

72.4%

CAD 632,152

3.4%