FRM Part II · FRM Exam Part II · VaR Mapping
A portfolio worth $10 million has a beta of 1.2 relative to a market index. The index has a daily return volatility of 1.0%. Using beta mapping and a normal distribution, what is the one-day 95% VaR (z = 1.645) due to market risk?
The beta-mapped exposure is 1.2 times $10 million, or $12 million. Multiplying by the index daily volatility of 1% and the 95% normal multiplier of 1.645 gives a one-day VaR of $197,400. Omitting the beta would understate the risk.
- A$197,400Correct
- B$164,500
- C$137,083
- D$279,120
Explanation
Index exposure = 1.2 × $10m = $12m. VaR = 12m × 1.645 × 0.01 = $197,400. Ignoring beta gives $164,500; dividing by beta gives $137,083; using 99% z (2.326) gives $279,120.
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