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P1.T4.30. Expected shortfall (ES)

Suzanne Evans

Well-Known Member
AIMs: Explain and calculate expected shortfall (ES), and compare and contrast VaR and ES.


30.1. You collected your bank's trading book's daily mark-to-market profit & loss (P&L) for the last two years, which is 500 trading days. The ten worst losses were (in millions, losses as positives): 18.0, 15.0, 15.0, 13.0, 9.0, 9.0, 8.0, 7.0, 6.0, 5.0. What is the historical 99.0% confident daily expected shortfall (ES; aka, conditional VaR or expected tail loss)?

a. $9.0 million
b. $10.5 million
c. $14.0 million
d. $16.5 million

30.2. A bond with a face value of $10.0 million has a one-year probability of default (PD) of 1.0% and an expected recovery rate of 35.0%. What is the bond's one-year 99.0% expected shortfall (ES; aka, CVaR)?

a. $3.25 million
b. $6.5 million
c. $9.1 million
d. Not enough information: need the tail distribution

30.3. A portfolio contains two independent (i.i.d.) and very risky bonds, each with identical face values of $15.0 million, one-year default probabilities (EDF) of 10.0% and loss given default (LGD) of 65.0%. What is the two-bond portfolio's one-year 99.0% expected shortfall (ES)?

a. $3.25 million
b. $8.67 million
c. $15.00 million
d. $19.50 million

30.4. Over the next year, a operational process model predicts an 95% probability of no loss occurrence and a 5% probability of a single loss occurrence. If the single loss occurs, the severity is characterized by three possible outcomes: $10.0 million loss with 20% probability, $18.0 million loss with 50% probability, and $25.0 million loss with 30% probability. What is the model's one-year 90% expected shortfall (ES)?

a. $9.25 million
b. $10.00 million
c. $13.88 million
d. $18.50 million