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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

A desk's daily P&L is normally distributed with mean zero and standard deviation $2 million, and daily P&Ls are independent and identically distributed. Using the one-tailed 99% normal quantile of 2.326, what is the 10-day 99% VaR? (√10 = 3.1623)

The 10-day 99% VaR is about $14.71 million. The one-day VaR is 2.326 times $2 million, or $4.652 million. Because daily P&Ls are independent with zero mean, the volatility scales with the square root of time, so multiplying by √10 gives $14.71 million.

  1. A$4.65 million
  2. B$10.40 million
  3. C$14.71 millionCorrect
  4. D$46.52 million

Explanation

The one-day 99% VaR is 2.326 × 2 = $4.652 million. With zero mean and independent days, it scales by √10: 4.652 × 3.1623 = $14.71 million. The $4.65 million option is the one-day figure, $46.52 million scales by 10 rather than √10, and $10.40 million uses the 95% quantile 1.645.

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