FRM Part II · FRM Exam Part II · VaR Mapping
A portfolio manager holds a single equity position worth USD 10 million. Using the single-index (beta) mapping, the stock has a beta of 1.2 relative to the market index. The index's daily volatility is 1.0% and the stock's residual (specific) risk is ignored in the mapped VaR. At a 95% confidence level (z = 1.645), what is the mapped one-day VaR?
The mapped one-day VaR is USD 197,400. The position maps to an index exposure of 1.2 times USD 10 million, or USD 12 million. Multiplying by 1% daily volatility gives USD 120,000, and applying 1.645 gives USD 197,400, ignoring specific risk.
- AUSD 1,645,000
- BUSD 1,974,000
- CUSD 164,500
- DUSD 197,400Correct
Explanation
Index exposure = beta x position = 1.2 x 10,000,000 = 12,000,000. Mapped volatility = 12,000,000 x 1% = 120,000. VaR = 1.645 x 120,000 = 197,400. Ignoring beta gives 164,500; the larger options use 10x or wrong scale.
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