Explanation:
The 90% confidence level implies that we are looking at the worst 10% of the returns. Since there are 30 ordered returns, the tail consists of the worst $30 \times 10% = 3$ returns.
Looking at the lowest returns provided:
1st worst: -18%
2nd worst: -16%
3rd worst: -14%
The Value-at-Risk (VaR) at the 90% confidence level is typically represented by the 3rd worst return, which corresponds to a loss of 14%. Thus, VaR = 14.
Expected Shortfall (ES) is the average of the worst 10% of returns (the tail). So ES = 16.
Option B correctly identifies VaR as 14 and ES as 16.
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Q.58 After using of the historical simulation method, you have been provided with the following 30 ordered percentage returns for an asset:
[-18, -16, -14, -12, -10, -9, -7, -7, -6, -6, -5, -5, -4, -4, -4, -2, -1, 0, 0, 2, 3, 6, 12, 12, 13, 15, 15, 18, 28]
The value-at-risk (VaR) and expected shortfall (ES), at 90% confidence level, respectively, are closest to:
A
Var: 14; ES: 17
B
Var: 14; ES: 16
C
Var: 12; ES: 16
D
Var: 12; ES: 24