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

A risk analyst estimates the density of daily portfolio returns from 500 historical observations. She replaces the usual histogram with a kernel density estimator using a smooth kernel. Which statement best describes the main advantage of this change for VaR estimation?

The kernel approach yields a smooth, continuous density, so VaR quantiles can be read at any confidence level instead of being restricted to the discrete historical observations. It still needs a bandwidth choice and remains dependent on the sample period.

  1. AIt produces a smooth density from which quantiles can be read off without being limited to the discrete observed returnsCorrect
  2. BIt guarantees the estimated VaR equals the parametric normal VaR
  3. CIt removes the need to choose any smoothing parameter
  4. DIt makes the estimate immune to changes in the sample period

Explanation

A kernel estimator spreads each observation into a smooth local bump, giving a continuous density. Quantiles can then be interpolated rather than restricted to observed points. It still requires a bandwidth choice and still depends on the sample, so the other options are wrong.

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