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FRM Part I · FRM Exam Part I · Stress Testing

A trading desk holds a position whose P&L is approximated by delta-gamma: delta = 2.0 million USD per 1% rise in the index, gamma = -0.10 million USD per (1%)^2 in the sense that the second-order term is 0.5 x gamma x (move)^2. Under a stress scenario the index falls 10%. What is the estimated P&L using the delta-gamma approximation?

The estimated P&L is -25.0 million USD. The delta effect is 2.0 x -10 = -20 million, and the gamma effect is 0.5 x -0.10 x 100 = -5 million. Negative gamma worsens losses in a large move, so ignoring it understates the stress loss.

  1. A-20.5 million USD
  2. B-25.0 million USDCorrect
  3. C-15.0 million USD
  4. D-20.0 million USD

Explanation

Delta term = 2.0 x (-10) = -20.0 million. Gamma term = 0.5 x (-0.10) x (-10)^2 = -0.05 x 100 = -5.0 million. Total = -25.0 million. Using delta alone gives -20.0 million, which misses the negative convexity; -15.0 results from adding the gamma term with the wrong sign.

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