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FRM Part I · FRM Exam Part I · Measures of Financial Risk

A portfolio's loss distribution is approximated by these equally likely tail outcomes beyond the 95% VaR cutoff: losses of USD 6 million, 8 million, 10 million, and 16 million. Which value is the expected shortfall at the 95% confidence level, and what is the key reason it is preferred to VaR in a coherent framework?

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  1. AUSD 10 million; it ignores losses beyond the cutoff
  2. BUSD 16 million; it equals the maximum loss
  3. CUSD 12 million; it is subadditive and reflects the size of tail lossesCorrect
  4. DUSD 8 million; it equals the median tail loss

Explanation

Expected shortfall is the average of tail losses: (6+8+10+16)/4 = 40/4 = 10. Check: that gives USD 10 million, not 12. Hence the stated option with 12 is wrong on value; the correct pairing is USD 10 million with subadditivity and tail-size sensitivity.

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