Skip to content

FRM Part I · FRM Exam Part I · Stress Testing

A portfolio has a delta-normal sensitivity to a 1 percentage point rise in rates of a loss of USD 4.0 million. A stress scenario assumes a 3 percentage point parallel rise and the manager scales linearly. The bond holdings have positive convexity such that the actual loss for a 3-point rise is USD 11.0 million. What is the main issue illustrated, and the size of the linear-scaling error?

Linear scaling gives 3 × USD 4.0 million = USD 12.0 million, while the true loss is USD 11.0 million. Positive convexity cushions losses for large rate rises, so the linear approach overstates the loss by USD 1.0 million.

  1. ALinear scaling overstates the loss by USD 1.0 million because convexity reduces the lossCorrect
  2. BLinear scaling understates the loss by USD 1.0 million because convexity adds to the loss
  3. CLinear scaling is exact; the difference is due to correlation
  4. DLinear scaling overstates the loss by USD 7.0 million because of the sign of delta

Explanation

Linear estimate is 3 × 4.0 = USD 12.0 million. Actual loss is 11.0 million because positive convexity cushions the loss when rates rise. The linear approach overstates the loss by 12.0 − 11.0 = USD 1.0 million. The option saying it understates has the wrong direction.

Did you get it right without looking?

One question tells you little. A timed set on Stress Testing shows your real accuracy, how long you take and where you lose marks.

Practise Stress TestingFree diagnostic mock

More Stress Testing questions