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%