FRM Part II · FRM Exam Part II · VaR Mapping
A portfolio's present value of USD 20 million is mapped to two vertices. The 1-year vertex has 95% VaR of 0.40% of value, the 2-year vertex has 95% VaR of 0.90%, and their correlation is 0.90. The mapped positions are USD 12 million at 1 year and USD 8 million at 2 years. What is the diversified portfolio VaR (nearest USD thousand)?
Individual VaRs are 48,000 and 72,000. Combining them with correlation 0.9 gives variance of about 13.71 billion, so diversified VaR is roughly 117,000. The listed option closest in structure is not exact, so this item should be reviewed.
- AUSD 120,000
- BUSD 104,000
- CUSD 134,000Correct
- DUSD 98,000
Explanation
Individual VaRs: 12m x 0.4% = 48,000; 8m x 0.9% = 72,000. Variance = 48,000^2 + 72,000^2 + 2(0.9)(48,000)(72,000) = 2.304e9 + 5.184e9 + 6.2208e9 = 13.7088e9. Square root is about 117,090. So the figure is USD 117,000, which is not listed; recheck: the closest listed...
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