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FRM Part I · FRM Exam Part I · Calculating and Applying VaR

A portfolio manager estimates 1-day VaR using historical simulation with 1,000 equally weighted daily observations. Next, she switches to the age-weighted (BRW) approach with decay factor lambda = 0.98. Compared with equal weighting, which result is most likely if a very large loss occurred 900 days ago and recent markets are calm?

VaR will tend to fall. Age-weighting with lambda 0.98 gives recent observations much more weight and almost none to a loss from 900 days ago. Because recent markets are calm, the tail is determined by smaller recent losses, so the estimate drops relative to equal weighting.

  1. AThe estimated VaR will tend to fall, because the old loss receives a much lower weightCorrect
  2. BThe estimated VaR will rise, because older observations receive higher weights
  3. CThe estimated VaR will be unchanged, because weights only affect the mean
  4. DThe estimated VaR will rise, because the number of observations is effectively increased

Explanation

With lambda = 0.98, the weight on an observation 900 days old is about 0.98^900, which is nearly zero. The large old loss therefore barely contributes to the tail, while recent calm observations dominate, so VaR tends to fall. Weights affect the ranking cumulative probabilities, not just the mean.

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