Skip to content

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

A risk manager uses a kernel-smoothed estimate of the loss distribution. Compared with the plain historical simulation estimate of the 99% VaR from a sample of 250 observations, which feature of the kernel approach is most relevant to the tail?

Because a kernel spreads probability around each observation, the smoothed density places some mass beyond the worst observed loss, whereas plain historical simulation places none there. This gives a more informative tail, though it does not guarantee lower VaR or remove equal weighting.

  1. AThe kernel estimate can assign probability mass to losses larger than the worst observed loss, while historical simulation cannotCorrect
  2. BThe kernel estimate always gives a lower VaR because smoothing removes extreme observations
  3. CThe kernel estimate requires the returns to be independent and normally distributed
  4. DThe kernel estimate eliminates the effect of equal weighting of old observations

Explanation

Each kernel spreads mass around its observation, so some density lies beyond the largest observed loss; historical simulation gives zero probability beyond it. Smoothing does not systematically lower VaR, does not require normality, and does not change the weighting of ages of data.

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