Skip to content

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

A risk manager uses a kernel density estimator on 1,000 daily P&L observations and finds the estimated left tail is very jagged with several spurious bumps. Which adjustment is most appropriate?

Increase the bandwidth. A jagged density with spurious bumps signals undersmoothing, where variance is too high. A wider bandwidth smooths the estimate and lowers variance, though it adds some bias by blurring genuine features of the distribution.

  1. ADecrease the bandwidth to follow the data more closely
  2. BIncrease the bandwidth to smooth the estimate, accepting more biasCorrect
  3. CSwitch to a lower confidence level so the tail is ignored
  4. DRemove all observations beyond the 99th percentile

Explanation

A jagged estimate indicates undersmoothing, meaning the bandwidth is too small and variance is high. Increasing it reduces variance and smooths the bumps, at the cost of added bias. Decreasing the bandwidth would make the jaggedness worse.

Did you get it right without looking?

One question tells you little. A timed set on Non-parametric Approaches shows your real accuracy, how long you take and where you lose marks.

Practise Non-parametric ApproachesFree diagnostic mock

More Non-parametric Approaches questions