Answer: ES with the updated models will be larger than the old estimate.

## Explanation When a volatility smile slopes downward to the right (also known as a **reverse skew**), it indicates that: - **Out-of-the-money (OTM) put options** (which protect against downside risk) have **higher implied volatility** than at-the-money (ATM) or out-of-the-money call options. - This pattern is common in equity markets where investors are willing to pay more for downside protection, leading to higher implied volatility for OTM puts. ### Key Points: 1. **Long position in DAX**: The firm is exposed to downside risk (market declines). 2. **Volatility smile sloping downward to the right**: Higher implied volatility for OTM puts suggests the market expects larger tail losses than a normal distribution would imply. 3. **Change in methodology**: Using the distribution of returns implied by market prices (rather than historical or normal distributions) will incorporate this market-implied tail risk. ### Impact on Expected Shortfall (ES): - **Expected Shortfall (ES)** measures the average loss in the worst-case scenarios (beyond VaR). - When using market-implied distributions that account for higher tail risk (due to the volatility smile), the estimated ES will **increase** because: - The distribution has fatter tails (higher probability of extreme losses). - The average loss in the worst cases will be larger. Therefore, **ES with the updated models will be larger than the old estimate**. **Correct Answer: A**

Author: LeetQuiz .