Explanation:
Marginal VaR of X: Using the formula MVaR_X = z × σ_p × Beta_X Assuming a 95% confidence interval (z ≈ 1.645): MVaR_X = 1.645 × 0.125 × 1.4583 = 0.29986 ≈ 0.2999
Percent contribution of asset Y to portfolio VaR: MVaR_Y = z × σ_p × Beta_Y = 1.645 × 0.125 × 0.625 = 0.128515 Component VaR (CVaR) of Y = Position_Y × MVaR_Y = 260 × 0.128515 = 33.414 million Portfolio VaR = Position_p × z × σ_p = 500 × 1.645 × 0.125 = 102.8125 million Percent Contribution of Y = CVaR_Y / Portfolio VaR = 33.414 / 102.8125 = 32.5%
Portfolio Diversification Benefit: Individual VaR of X = 240 × 1.645 × 0.18 = 71.064 million Individual VaR of Y = 260 × 1.645 × 0.10 = 42.770 million Undiversified VaR = 71.064 + 42.770 = 113.834 million Diversified Portfolio VaR = 102.8125 million Diversification Benefit = Undiversified VaR - Portfolio VaR = 113.834 - 102.8125 = 11.0215 million = GBP 11,021,500.
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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
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