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Answer: EUR 2.066 million
## Explanation To calculate the component VaR of stock A, we need to follow these steps: ### Step 1: Calculate the marginal VaR (MVaR) The marginal VaR measures the change in portfolio VaR for a small change in the position of stock A. **Formula:** MVaR = Z-score × σ_portfolio × β_A Where: - Z-score for 99% VaR = 2.326 (from standard normal distribution) - σ_portfolio = 21% = 0.21 - β_A = correlation × (σ_A / σ_portfolio) = 0.37 × (0.16 / 0.21) = 0.37 × 0.7619 = 0.2819 MVaR = 2.326 × 0.21 × 0.2819 = 2.326 × 0.0592 = 0.1377 (or 13.77%) ### Step 2: Calculate component VaR **Formula:** Component VaR = Position value × MVaR Position value of stock A = EUR 15 million Component VaR = 15,000,000 × 0.1377 = EUR 2,065,500 ≈ EUR 2.066 million ### Alternative approach using covariance: Component VaR = Z-score × (covariance between stock A and portfolio / σ_portfolio) × position value Covariance = correlation × σ_A × σ_portfolio = 0.37 × 0.16 × 0.21 = 0.012432 Component VaR = 2.326 × (0.012432 / 0.21) × 15,000,000 = 2.326 × 0.0592 × 15,000,000 = EUR 2.066 million **Therefore, the correct answer is EUR 2.066 million (Option A).**
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A risk analyst is evaluating the risks of a portfolio of stocks. Currently, the portfolio is valued at EUR 200 million and contains EUR 15 million in stock A. The standard deviation of returns of stock A is 16% annually and that of the overall portfolio is 21% annually. The correlation of returns between stock A and the portfolio is 0.37. Assuming the risk analyst uses a 1-year 99% VaR and that returns are normally distributed, how much is the component VaR of stock A?
A
EUR 2.066 million
B
EUR 2.326 million
C
EUR 5.582 million
D
EUR 7.327 million
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