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

A portfolio manager has 250 daily historical returns and applies the age-weighted (BRW) historical simulation with decay factor λ = 0.98. The most recent observation has weight w1 = (1−λ)/(1−λ^250). Compared with the ordinary equal-weighted approach, what is the weight on the observation that is 1 day older than the most recent one relative to the most recent one?

The weight is 0.98 times that of the most recent observation. In age-weighted historical simulation, weights decline geometrically by the decay factor λ for each additional day of age, and normalization only scales all weights so they sum to one.

  1. A0.98 times the weight of the most recent observationCorrect
  2. B0.02 times the weight of the most recent observation
  3. C1.02 times the weight of the most recent observation
  4. DThe same weight, since all observations are normalized to sum to one

Explanation

In BRW, the weight on the observation i days old is λ^(i−1) times the weight on the most recent. So the observation one day older has weight λ = 0.98 times the latest. Option 0.02 confuses λ with 1−λ. Normalization changes the level, not the ratio.

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