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

A portfolio's loss distribution is approximated by 100 equally likely historical simulation outcomes. The five worst losses (in USD millions) are 14, 12, 11, 10 and 8, and the sixth worst is 6. Using this sample, what is the 95% Expected Shortfall?

The 95% Expected Shortfall is USD 11.0 million. With 100 equally likely outcomes, the worst 5% is five observations, and their average loss is (14+12+11+10+8)/5 = 11. ES averages the tail losses rather than reporting a single quantile.

  1. AUSD 11.0 millionCorrect
  2. BUSD 6.0 million
  3. CUSD 10.0 million
  4. DUSD 11.5 million

Explanation

The 95% ES is the average of the losses in the worst 5% tail, which is 5 observations out of 100. Average = (14+12+11+10+8)/5 = 55/5 = 11.0. Using 6 as the VaR figure would give 6.0, which is only the boundary and ignores tail magnitude.

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