Skip to content

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

A risk manager uses age-weighted historical simulation with lambda = 0.90 and a very large sample. The weight on the most recent observation is (1 - lambda)/(1 - lambda^n), approximately 1 - lambda for large n, and each older observation's weight is multiplied by lambda. What is the approximate weight on the observation that is 3 days old (the most recent being age 1)?

The weight is about 0.0810. The age-i weight is lambda raised to (i-1) times (1 - lambda). For age 3 with lambda 0.90, that is 0.81 times 0.10, which equals 0.081, since the first observation has weight 0.10.

  1. A0.0810Correct
  2. B0.0900
  3. C0.1000
  4. D0.0729

Explanation

Weight at age i is lambda^(i-1)(1-lambda). For i = 3: 0.9^2 x 0.10 = 0.81 x 0.10 = 0.0810. Option D (0.0729) uses lambda^3 without scaling by (1-lambda) correctly, i.e. 0.9^3 x 0.10 = 0.0729, which is the weight at age 4. Option C is the weight for age 1.

Did you get it right without looking?

One question tells you little. A timed set on Non-parametric Approaches shows your real accuracy, how long you take and where you lose marks.

Practise Non-parametric ApproachesFree diagnostic mock

More Non-parametric Approaches questions