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Answer: CAD 523,350
The correct answer is C, CAD 523,350. To calculate the component Value-at-Risk (VaR) of stock XYZ, we first determine the individual VaR of stock XYZ using the given parameters: 1. The value of stock XYZ (Vxyz) is CAD 5 million. 2. The standard deviation of returns of stock XYZ (oxyz) is 15% annually. 3. The 99% confidence factor for VaR (α(99%)) is 2.326. The individual VaR of stock XYZ is calculated as: \[ VaRxyz = Vxyz \times oxyz \times \alpha(99\%) = CAD 5,000,000 \times 0.15 \times 2.326 = CAD 1,744,500 \] Next, we use the correlation of returns between stock XYZ and the portfolio (p), which is 0.3, to find the component VaR: \[ Component\ VaRxyz = p \times VaRxyz = 0.30 \times CAD 1,744,500 = CAD 523,350 \] This component VaR represents the estimated risk of stock XYZ contributing to the overall portfolio's risk, given the specified conditions and assumptions.
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To determine the calculated component Value at Risk (VaR) for stock XYZ within a CAD 20 million portfolio, consider the following details: The portfolio comprises CAD 5 million allocated to stock XYZ, which has an annual standard deviation of returns at 15%. The overall portfolio exhibits an annual standard deviation of 12%, and the returns of stock XYZ have a correlation coefficient of 0.3 with the overall portfolio returns. The portfolio manager is assessing a 1-year 99% VaR under the assumption of normally distributed returns. What is the component VaR for stock XYZ?
A
CAD 162,972
B
CAD 234,906
C
CAD 523,350
D
CAD 632,152
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