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Answer: CAD 1.444 million
The correct answer is B: CAD 1.444 million. The component Value at Risk (VaR) for stock T (CVaRt) is calculated using the formula: \[ CVaRT = VaRT \times \rho_{T,P} \] where: - \( VaRT \) is the VaR of stock T. - \( \rho_{T,P} \) is the correlation coefficient between stock T and the portfolio. Given: - The value of stock T (\( W_t \)) is CAD 15 million. - The standard deviation of stock T returns (\( \sigma_t \)) is 13% or 0.13. - The 95% confidence factor for the VaR estimate (\( \alpha(95\%) \)) is 1.645. The VaR of stock T (\( VaRT \)) is calculated as: \[ VaRT = W_t \times \sigma_t \times \alpha(95\%) = 15 \times 0.13 \times 1.645 = 3.208 \text{ million} \] Now, using the correlation coefficient (\( \rho_{T,P} = 0.45 \)) between stock T and the portfolio, the component VaR for stock T is: \[ CVaRT = 0.45 \times 3.208 = 1.444 \text{ million} \] This calculation shows that the component VaR of stock T is CAD 1.444 million, which corresponds to option B.
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A risk analyst is evaluating the potential risks of a stock portfolio that has a total value of CAD 248 million. Within this portfolio, there is an allocation of CAD 15 million to stock T. The portfolio's annualized standard deviation of returns is 16%, while stock T has an annualized standard deviation of 13%. Additionally, the correlation coefficient between the portfolio's returns and the returns of stock T is 0.45. The risk manager wants to determine the component Value at Risk (VaR) for stock T, assuming a 1-year time horizon, a 95% confidence level, and normally distributed returns. What is the component VaR for stock T?
A
CAD0.096million
B
CAD 1.444 million
C
CAD 2.041 million
D
CAD 3.948 million