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Explanation:
The total VaR budget will be = Z × σ × V
Total VaR budget = 2.33 × 0.10 × 20
= $4.66 million
For the three asset classes, the VaR will be:
US Stocks = 2.33 × 0.12 × 0.3 × 20 = $1.68 million
US Bonds = 2.33 × 0.05 × 0.4 × 20 = $0.93 million
Non-US Stocks = 2.33 × 0.18 × 0.3 × 20 = $2.52 million
Total undiversified VaR = $5.13 million
Undiversified VaR is the sum of individual VaRs, or the portfolio VaR when there is no short position.
Q.2762 A pension fund needs to allocate $20 million to three different asset classes. The details of the asset classes are shown in the following table:
| Asset class | Volatility |
|---|---|
| US stocks | 12% |
| US bonds | 5% |
| Non-US stocks | 18% |
The total volatility profile for the fund has been decided to be 10%. If the optimal asset allocation between the three classes is 30%, 40% and 30% respectively, what will be the total VaR budget for the fund and the undiversified VaR at a 99% confidence level?
A
Total VaR: $3.30 million; Undiversified VaR: $6.20 million
B
Total VaR: $4.6 million; Undiversified VaR: $6.20 million
C
Total VaR: $4.66 million; Undiversified VaR: $5.13 million
D
Total VaR: $3.30 million; Undiversified VaR: $5.13 million
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