Skip to content

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

An analyst estimates VaR using a kernel density with a Gaussian kernel and a very large bandwidth on a left-skewed, fat-tailed return sample. Relative to the true distribution, what is the most likely result at the 99.9% level?

The estimate becomes oversmoothed and drifts toward a symmetric bell shape, washing out skewness and fat-tail features. This bias typically understates extreme tail losses at 99.9%. Spikes at each observation would arise from a very small bandwidth, not a large one.

  1. AThe estimated tail is too heavy, so VaR is overstated by the discreteness of observations
  2. BThe estimated distribution is oversmoothed and closer to a symmetric bell shape, so extreme losses and skewness are understated in the tailCorrect
  3. CVaR is unchanged because bandwidth only affects the center
  4. DThe estimate collapses to a set of spikes at each observation

Explanation

A very large bandwidth oversmooths, blending observations into a broad symmetric shape. This blurs skewness and fat-tail features, adding bias and typically understating tail severity. Spikes arise from a very small bandwidth, not a large one.

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