FRM Part I · FRM Exam Part I · Measures of Financial Risk
Daily portfolio returns are normally distributed with mean zero and a standard deviation of 1.5%. The portfolio value is USD 80 million. Using z = 2.326 at 99% and the normal expected shortfall factor φ(2.326)/0.01 = 2.665, what is the 99% one-day expected shortfall?
The 99% one-day expected shortfall is about USD 3.20 million. Dollar volatility is 1.5% of USD 80 million, or USD 1.2 million, and multiplying by the normal ES factor of 2.665 gives 3.198 million. The 2.79 million figure is VaR, not ES.
- AUSD 2.79 million
- BUSD 3.20 million
- CUSD 4.26 millionCorrect
- DUSD 5.59 million
Explanation
Daily sigma in dollars = 0.015 × 80 = USD 1.2 million. ES = 2.665 × 1.2 = USD 3.198 million, about 3.20 million. VaR would be 2.326 × 1.2 = 2.79 million, which is a distractor. Using 4.26 is wrong, so check: the correct figure is 3.20.
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