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FRM Part II · FRM Exam Part II · VaR Mapping

A $10 million equity position has a beta of 1.2 to an index whose daily volatility is 1.0%. The position's residual (specific) daily return volatility is 0.9% of position value and is uncorrelated with the index. Using a normal distribution at 95% confidence (z = 1.645), what is the one-day total VaR including specific risk?

Systematic and specific risks are uncorrelated, so they combine in quadrature: the square root of 1.2% squared plus 0.9% squared is 1.5%. Multiplying $10 million by 1.5% and 1.645 gives a one-day 95% VaR of $246,750.

  1. A$246,750Correct
  2. B$345,450
  3. C$197,400
  4. D$148,050

Explanation

Systematic volatility = 1.2 × 1% = 1.2%. Total volatility = sqrt(1.2² + 0.9²) = sqrt(2.25) = 1.5%. VaR = 10m × 1.5% × 1.645 = $246,750. Adding volatilities linearly (2.1%) gives $345,450, which wrongly assumes perfect correlation.

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