Answer-first summary for fast verification
Answer: −15.49%
## Explanation For a uniform distribution between -16% and 18%, the total range is 34%. **Step 1: Calculate 97% VaR** - The left 3% tail covers: x / 34% = 3% - x = 3% × 34% = 1.02% - 97% VaR = -16% + 1.02% = -14.98% **Step 2: Calculate 97% Expected Shortfall (ES)** - ES is the average of all losses beyond the VaR level - For uniform distribution, ES is the midpoint between VaR and the minimum return - ES = (-14.98% + (-16%)) / 2 = -15.49% **Why other options are incorrect:** - **B (-15.15%)**: This is the 95% ES - **C (-14.98%)**: This is the 97% VaR, not ES - **D (-14.30%)**: This is the 95% VaR **Verification:** - 95% VaR: -16% + (5% × 34%) = -14.30% - 95% ES: (-14.30% + (-16%)) / 2 = -15.15%
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A risk analyst at a wealth management company is calculating the ES of a portfolio. The portfolio's returns are expected to follow a uniform distribution, with all returns between 18% and −16% being equally likely. What is the 97% ES of the portfolio?
A
−15.49%
B
−15.15%
C
−14.98%
D
−14.30%