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

A risk committee is reviewing 99% one-day VaR from historical simulation using a 1,000-day window. The window contains a calm period only, with a maximum single-day loss of 3% for the portfolio. Management argues the VaR is reliable because it uses actual data and no model. Which critique is most valid?

The main critique is that historical simulation can only reflect outcomes seen in its window. A calm sample omits stress events, and the 99% tail rests on very few observations, so the estimate is imprecise and likely too low. It requires no normality assumption or correlation matrix.

  1. AThe estimate is limited to the experience in the window, so it cannot reflect stress events not in the sample and has poor precision in the extreme tailCorrect
  2. BThe method assumes returns are normally distributed, which understates risk in calm periods
  3. CThe method requires the correlation matrix to be estimated, which is unreliable in calm periods
  4. DThe estimate is biased upward because the sample contains too many observations

Explanation

Non-parametric VaR depends entirely on the sample; a calm window contains no crisis outcomes, so VaR will be too low, and extreme quantiles rest on very few observations (at 99% with 1,000 days, about 10 tail points). The method does not assume normality or need a correlation matrix, and more observations do not bias upward.

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