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Answer: CAD 523,350
The correct answer is C, CAD 523,350. The explanation for this is as follows: 1. The value of stock XYZ (Vxyz) is CAD 5 million. 2. The standard deviation of returns for stock XYZ (σXYZ) is 15% annually. 3. The 99% confidence factor for the VaR estimate (α(99%)) is 2.326. 4. 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.
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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?
A
CAD 162,972
B
CAD 234,906
C
CAD 523,350
D
CAD 632,152