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

A bank uses age-weighted (BRW) historical simulation with decay factor λ = 0.98 and 250 observations. The weight on the most recent observation is (1−λ)/(1−λ^250) times λ^0, and weights decline by λ per day of age. Compared with equally weighted historical simulation (weight 0.4% each), what is the approximate weight on the most recent observation, and what is the effect on VaR following a recent large loss?

The newest observation gets about 0.02/(1−0.0064), roughly 2.0%, versus 0.4% under equal weighting. Because recent data carry much more probability mass, a recent large loss pushes the tail and VaR up much faster than in the equally weighted approach.

  1. AAbout 2.0%; VaR rises more quickly because recent losses carry more weightCorrect
  2. BAbout 0.4%; VaR is unchanged because weights sum to one
  3. CAbout 2.0%; VaR falls because older observations are discounted
  4. DAbout 0.98%; VaR rises only after 250 days

Explanation

λ^250 = 0.98^250 ≈ 0.0064, so the weight is 0.02/(1−0.0064) ≈ 2.0%, five times the equal weight of 0.4%. A recent large loss therefore occupies far more probability mass in the tail, lifting VaR faster. The other options misstate the weight or the direction.

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