Skip to content

FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A fund has an annualized tracking error of 4% against its benchmark. Assuming active returns are normally distributed with zero mean, what is the approximate 95% one-year relative VaR (use 1.645) and, if the manager reduces active risk by moving to a position with half the active weights while correlations stay unchanged, what is the new relative VaR?

Relative VaR is 1.645 times 4%, or 6.58%. Because tracking error scales linearly with active weights, halving them halves tracking error to 2%, so relative VaR falls to 3.29%. Treating variance scaling as applying to volatility would wrongly give 1.64%.

  1. A6.58% and 3.29%Correct
  2. B6.58% and 1.64%
  3. C3.29% and 1.65%
  4. D6.58% and 4.65%

Explanation

Relative VaR = 1.645 * 4% = 6.58%. Active risk is linear in active weights when all else is constant, so halving active weights halves tracking error to 2%, giving 3.29%. Answering 1.64% wrongly treats risk as scaling with the square of the weights.

Did you get it right without looking?

One question tells you little. A timed set on Portfolio Risk: Analytical Methods shows your real accuracy, how long you take and where you lose marks.

Practise Portfolio Risk: Analytical MethodsFree diagnostic mock

More Portfolio Risk: Analytical Methods questions