FRM Part II · FRM Exam Part II · VaR Mapping
A bond portfolio has a market value of USD 50 million and a modified duration of 4. Using the duration (delta-normal) approach, the daily yield volatility is 0.05 percentage points (5 basis points) and the 95% z-value is 1.645. What is the 1-day 95% VaR?
The 1-day 95% VaR is USD 164,500. Daily price volatility is modified duration 4 times 5 basis points, or 0.20%, which is USD 100,000 on USD 50 million; multiplying by 1.645 gives USD 164,500.
- AUSD 82,250
- BUSD 164,500Correct
- CUSD 411,250
- DUSD 1,645,000
Explanation
Price change volatility = 4 x 0.0005 = 0.2% of value, or USD 50m x 0.002 = USD 100,000. VaR = 1.645 x 100,000 = USD 164,500. The USD 82,250 option uses half the duration; USD 1,645,000 mistakes 5 bp for 50 bp.
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