FRM Part II · FRM Exam Part II · VaR Mapping
A bond portfolio has two mapped positions: 4 million at vertex A with standalone VaR of 120,000 and 6 million at vertex B with standalone VaR of 150,000. The correlation between the two vertices is 0.50. What is the diversified portfolio VaR (to the nearest 1,000)?
Diversified VaR is about 234,000. Combining the two standalone VaRs with correlation 0.5 gives variance of 54.9 billion (14.4bn + 22.5bn + 18.0bn), whose square root is roughly 234,307. The simple sum of 270,000 wrongly assumes perfect correlation.
- A270,000
- B234,000Correct
- C210,000
- D180,000
Explanation
VaR² = 120,000² + 150,000² + 2(0.5)(120,000)(150,000) = 14.4bn + 22.5bn + 18.0bn = 54.9bn. Square root ≈ 234,307, so about 234,000. The undiversified sum of 270,000 assumes correlation 1.
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