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

A bank computes 1-day 99% historical simulation VaR using the last 250 daily returns on a portfolio worth USD 100 million. The three worst returns in the window are -4.0%, -3.2% and -2.6%, and the fourth worst is -2.1%. Using the convention that VaR is the loss at the observation that leaves 1% of observations in the tail (rounded to the nearest whole observation, 2.5 rounded up to 3), what is VaR?

VaR is USD 2.6 million. One percent of 250 observations is 2.5, rounded to 3, so the third worst return, -2.6%, defines the cutoff. Applying 2.6% to the USD 100 million portfolio gives the loss estimate.

  1. AUSD 4.0 million
  2. BUSD 3.2 million
  3. CUSD 2.6 millionCorrect
  4. DUSD 2.1 million

Explanation

1% of 250 is 2.5 observations, rounded up to 3. The third worst return is -2.6%, so VaR = 2.6% x 100 million = USD 2.6 million. Using the worst return (4.0 million) ignores the percentile; 3.2 is the second worst.

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