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FRM Part II · FRM Exam Part II · Validating Bank Holding Companies' Value-at-Risk Models for Market Risk

A bank's VaR uses a 250-day historical window with equal weights. After a volatile period ended 200 days ago, recent markets are calm. A validator compares it with an exponentially weighted alternative with decay factor 0.97. Which conclusion is most appropriate?

The equally weighted VaR will likely be higher. It gives the old volatile observations full weight, whereas the EWMA with decay 0.97 almost ignores observations 200 days old, so it reflects the current calm and produces a lower VaR.

  1. AThe equally weighted VaR will likely be higher than the EWMA VaR because it retains the old volatile observations at full weightCorrect
  2. BThe equally weighted VaR will be lower because older data reduces dispersion
  3. CBoth VaR measures will be identical because the same data are used
  4. DThe EWMA VaR will be higher because it weights older observations more heavily

Explanation

With decay 0.97, an observation 200 days old has weight about 0.97^200, roughly 0.002 relative to the latest, so it is almost ignored. The equal-weight window still counts the volatile period fully. Thus the equal-weight VaR is higher in calm markets, though slower to react when volatility rises.

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