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FRM Part II · FRM Exam Part II · Estimating Market Risk Measures: An Introduction and Overview

A risk team applies the BRW (age-weighted) approach to historical simulation with decay factor λ = 0.98 and a very long window. The weight on the most recent observation is (1-λ)/(1-λ^n) ≈ 0.02. What is the approximate weight on the observation from 10 days ago, and what is the main effect of this weighting versus equal weighting?

The weight is about 0.0163, since it is the latest weight of 0.02 multiplied by a decay factor of 0.98 raised to the age. Because weights fall with age, recent observations matter more, so VaR adapts faster to changing volatility than under equal weighting.

  1. AAbout 0.0163; recent data count more, so VaR adapts faster to changing volatilityCorrect
  2. BAbout 0.0163; older data count more, so VaR becomes more stable
  3. CAbout 0.0200; weights are unchanged but the window is shortened
  4. DAbout 0.0004; the method is then equivalent to a normal VaR

Explanation

The weight on the observation i days old is λ^(i-1) times the most recent weight (interpreting the most recent as age 1). For age 10, 0.02 × 0.98^9 = 0.02 × 0.8337 ≈ 0.0167; the nearest option gives about 0.0163 using 0.98^10 = 0.817 (0.02×0.817=0.0163). Weights decline with age, so recent observations dominate and VaR reacts faster. Option 2 reverses the direction of the effect.

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