Answer-first summary for fast verification
Answer: CAD 1.444 million
## Explanation 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 **Given:** - wT = CAD 15 million (value of stock T) - σT = 13% = 0.13 (standard deviation of stock T returns) - α(95%) = 1.645 (95% confidence factor for VaR) - ρT,p = 0.45 (correlation coefficient) **Calculation:** 1. **VaRT** = wT × σT × α(95%) = CAD 15 million × 0.13 × 1.645 = CAD 3.208 million 2. **CVaRT** = ρT,p × VaRT = 0.45 × 3.208 = CAD 1.444 million **Why other options are incorrect:** - **A (CAD 0.096 million)**: This is the marginal VaR of stock T, which is unitless - **C (CAD 2.041 million)**: This would be the component VaR if using 99% VaR (2.326 instead of 1.645) - **D (CAD 3.948 million)**: This is the incremental VaR of stock T, calculated as (15/248) × (248 × 0.16 × 1.645)
Author: LeetQuiz .
Ultimate access to all questions.
A risk manager is evaluating the risks of a portfolio of stocks. Currently, the portfolio is valued at CAD 248 million and contains CAD 15 million in stock T. The annualized standard deviations of returns of the overall portfolio and of stock T are 16% and 13%, respectively. The correlation of returns between the portfolio and stock T is 0.45. Assuming the risk analyst uses a 1-year 95% VaR and the returns are normally distributed, what is the component VaR of stock T?
A
CAD 0.096 million
B
CAD 1.444 million
C
CAD 2.041 million
D
CAD 3.948 million
No comments yet.