Explanation:
The correct answer is B: EUR 22.12 million.
Calculate individual VaR for each asset class using delta-normal VaR at 99% confidence level:
Individual Risk Budgets (VaRᵢ):
Sum of Risk Budgets: 8.62 + 3.33 + 2.96 + 7.21 = 22.12 million EUR
The sum of individual risk budgets (22.12 million) is greater than the portfolio VaR (11.64 million) due to diversification benefits - the negative correlations between assets reduce the overall portfolio risk.
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An investment fund uses risk budgeting as part of its risk management process. Risk is calculated and monitored using delta-normal VaR at the 99% confidence level. The fund's total principal of EUR 100 million is invested across four asset classes comprised of European stocks, non-European stocks, European bonds, and non-European bonds. The total volatility profile of the fund is maintained at 5%. Information on the four asset classes is given below:
| Asset class | Weight | Average return | Volatility | Correlation |
|---|---|---|---|---|
| 1 2 3 4 | ||||
| 1 European stocks | 40% | 12.99% | 9.25% | 1.00 -0.05 -0.07 -0.03 |
| 2 Non-European stocks | 12% | 10.82% | 11.91% | -0.05 1.00 0.02 -0.01 |
| 3 European bonds | 22% | 5.10% | 5.76% | -0.07 0.02 1.00 0.02 |
| 4 Non-European bonds | 26% | 10.53% | 11.94% | -0.03 -0.01 0.02 1.00 |
What is the sum of the risk budgets that should be allocated to the four asset classes?
A
EUR 11.64 million
B
EUR 22.12 million
C
EUR 38.86 million
D
EUR 100.0 million