Explanation:
To evaluate the portfolio, we use the Z-score for a 95% confidence interval, which is approximately 1.645.
1. Marginal VaR of Asset X: The Marginal VaR (MVaR) is calculated as: MVaR_X = Z × Beta_X × Sigma_Portfolio MVaR_X = 1.645 × 1.4583 × 0.125 = 0.29986 ≈ 0.2999
2. Percent Contribution of Asset Y VaR to Portfolio VaR: Component VaR (CVaR) of Y = Weight_Y × MVaR_Y MVaR_Y = Z × Beta_Y × Sigma_Portfolio CVaR_Y = Weight_Y × (Z × Beta_Y × Sigma_Portfolio)
The Portfolio VaR is: Portfolio VaR = Total Value × Z × Sigma_Portfolio
Percent Contribution of Y = CVaR_Y / Portfolio VaR = [Weight_Y × Z × Beta_Y × Sigma_Portfolio] / [Total Value × Z × Sigma_Portfolio] = (Weight_Y × Beta_Y) / Total Value = (260 × 0.625) / 500 = 162.5 / 500 = 0.325 = 32.5%
3. Portfolio Diversification Benefit: First, we find the Undiversified VaR by summing the individual VaRs of X and Y: Individual VaR_X = Value_X × Z × Sigma_X = 240 × 1.645 × 0.180 = 71.064 GBP million Individual VaR_Y = Value_Y × Z × Sigma_Y = 260 × 1.645 × 0.100 = 42.770 GBP million Sum of Individual VaRs = 71.064 + 42.770 = 113.834 GBP million
Next, we calculate the Diversified Portfolio VaR: Portfolio VaR = 500 × 1.645 × 0.125 = 102.8125 GBP million
Diversification Benefit = Sum of Individual VaRs - Portfolio VaR Diversification Benefit = 113.834 - 102.8125 = 11.0215 GBP million = GBP 11,021,500.
Option C correctly lists all three values.
Ultimate access to all questions.
No comments yet.
Q.13 A portfolio manager at an investment bank is evaluating a two-asset portfolio. The following table gives risk and return data on the assets and the portfolio:
| Asset | Position value (GBP million) | Return Standard deviation(%) | Beta |
|---|---|---|---|
| X | 240 | 18.0 | 1.4583 |
| Y | 260 | 10.0 | 0.625 |
| Portfolio | 500 | 12.5 | 1.1 |
Determine the marginal VaR of asset X, the percent contribution of asset Y VaR to portfolio VaR, and the portfolio’s estimated diversification benefit at a 95% confidence interval.
A
Marginal VaR of X = 0.2999; percent contribution of asset Y VaR = 78%; portfolio diversification benefit = GBP 113,834,000
B
Marginal VaR of X = 0.4284; percent contribution of asset Y VaR = 50%; portfolio diversification benefit = GBP 102,812,500
C
Marginal VaR of X = 0.2999; percent contribution of asset Y VaR = 32.5%; portfolio diversification benefit = GBP 11,021,500
D
Marginal VaR of X = 0.4284; percent contribution of asset Y VaR = 72%; portfolio diversification benefit = GBP 113,834,000