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FRM Part II · FRM Exam Part II · Non-parametric Approaches

A bank's market risk team wants to use a non-parametric density estimate of portfolio losses. Which limitation must they still accept after applying kernel smoothing to a 2-year historical sample?

Kernel smoothing does not create new information, so the estimate still depends on the historical sample being representative of future conditions. If the two-year window misses stress regimes, the smoothed density will understate risk, even though expected shortfall and option portfolios can still be handled.

  1. AThe estimate remains dependent on the historical sample being representative of future conditionsCorrect
  2. BThe estimate can no longer produce an expected shortfall
  3. CThe estimate requires specifying a parametric distribution for the tails
  4. DThe estimate cannot be computed for portfolios with options

Explanation

Kernel smoothing improves the shape of the estimated density but does not add information beyond the sample, so it inherits the assumption that history is representative. Expected shortfall can still be computed from the density, no parametric tail is needed, and option portfolios can be revalued under historical scenarios.

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