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

A bank applies a kernel estimator to historical returns and compares it with a plain historical simulation at the 99% level. The sample has 250 observations. Which is a correct comparison?

At 99% with 250 observations, plain historical simulation depends on roughly 2.5 tail points, making it unstable. Kernel smoothing uses neighbouring observations to stabilize the quantile, but it creates no new independent data and still assumes the past represents the future.

  1. APlain historical simulation at 99% relies on about 2.5 tail observations, while kernel smoothing uses information from nearby points to stabilize the quantileCorrect
  2. BKernel smoothing increases the number of actual independent observations to above 250
  3. CPlain historical simulation is smooth, whereas the kernel estimate is a step function
  4. DKernel smoothing eliminates dependence on the assumption that past returns represent the future

Explanation

With 250 observations, 1% of the sample is 2.5 points, so the quantile is sensitive to a few values. Kernel smoothing borrows information from neighbouring observations to stabilize it. It does not create new independent data or remove the stationarity assumption.

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