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Explanation:
B is correct.
The component VaR for stock T (CVaRₜ) can be presented as:
CVaRₜ = VaRₜ * ρₜ,ₚ,
where
VaRₜ = VaR of stock T
ρₜ,ₚ = correlation coefficient between stock T and the portfolio.
Let:
wₜ represent the value of stock T,
σₜ represent the standard deviation of stock T returns, and
α(95%) represent the 95% confidence factor for the VaR estimate, which is 1.645.
Hence,
VaRₜ = wₜ * σₜ * α(95%) = CAD 15 million × 0.13 × 1.645 = CAD 3.208 million.
Therefore,
CVaRₜ = ρₜ,ₚ * VaRₜ = 0.45 × 3.208 = CAD 1.444 million.
A is incorrect. 0.096 is the marginal VaR of stock T, calculated as follows: (0.45 × 0.13 / 0.16) × 1.645 × 0.16. Marginal VaR measure is unitless.
C is incorrect. CAD 2.041 million is the component VaR of stock T if the manager incorrectly uses the 99% VaR, i.e., 15 × 0.13 × 2.326 × 0.45.
D is incorrect. CAD 3.948 million is the incremental VaR of stock T (assuming that the volatility of the portfolio without stock T remains 16% and the correlation of...
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A
CAD 0.096 million
B
CAD 1.444 million
C
CAD 2.041 million
D
CAD 3.948 million