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FRM Part I · FRM Exam Part I · Calculating and Applying VaR

A firm holds a linear portfolio of $10 million in an equity index. Historical simulation uses 200 daily index returns. After applying them to today's value, the sorted P&L shows the worst outcomes: -$600k, -$520k, -$450k, -$400k. Under the convention VaR(97.5%) is the loss at rank equal to 2.5% of 200 = 5th worst, and the 5th-worst return is -3.8%. The firm then uses the 6th-worst return of -3.5% as the 96.9% estimate. A volatility-adjusted version rescales each historical return by (current volatility / volatility on that day). Current daily volatility is 2.0% and the volatility on the day of the 5th-worst return was 1.6%. What is the volatility-adjusted loss for that day on the $10 million portfolio?

The volatility-adjusted loss is $475,000. The historical return of -3.8% is scaled by current volatility over the volatility on that day, 2.0% divided by 1.6%, which is 1.25, giving -4.75%. Applied to a $10 million portfolio this is $475,000.

  1. A$475,000Correct
  2. B$380,000
  3. C$608,000
  4. D$304,000

Explanation

Adjusted return = -3.8% x (2.0/1.6) = -3.8% x 1.25 = -4.75%. Applied to $10m gives a loss of $475,000. $380,000 is the unadjusted loss, $304,000 inverts the ratio (3.8% x 0.8 x $10m), and $608,000 wrongly multiplies by 1.6.

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