What is Expected Shortfall (ES)?

Expected Shortfall (ES) is a way to measure the risk of an investment portfolio focusing on how bad things can get in the worst-case scenarios. It’s also known as Conditional Value at Risk (CVaR), Average Value at Risk (AVaR), Expected Tail Loss (ETL) and Superquantile. In general if an investment has demonstrated stability over time, using Value at Risk (VaR) may be adequate for managing risk in a portfolio containing that investment. However for less stable investments VaR might not provide a complete picture of the risks, as it does not account for losses beyond its threshold. Conditional Value at Risk (CVaR) addresses the limitations of the VaR model. VaR is a statistical method used to measure the level of financial risk within a firm or investment portfolio over a specific period. VaR indicates the maximum expected loss with a given probability and time horizon. In contrast, CVaR represents the expected loss if the VaR threshold is exceeded.  

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Key Points to Understand Conditional Value at Risk (CVaR)

1. Risk Measurement: ES helps investors understand potential losses by focusing on the most extreme, but possible, negative outcomes. 2. q% Level: When we talk about the “expected shortfall at q% level,” we’re looking at the worst q% of scenarios. For example, if q is 5%, ES considers the worst 5% of potential outcomes. 3. Focus on Extreme Losses: Unlike other measures that might only consider the single worst outcome, ES looks at the average of the worst outcomes within that q%.

Why is Expected Shortfall used?

1. Conservativeness: ES is a conservative risk measure because it focuses on the less profitable, riskier outcomes, helping investors prepare for bad scenarios. 2. Ignoring Extreme Profits: For high values of q (like 5%), ES ignores the best-case scenarios that are unlikely to happen. 3. More Useful than VaR: Value at Risk (VaR) tells you the maximum loss you might face within a certain confidence level (like 95%), but it doesn’t tell you how bad things can get beyond that threshold. ES, on the other hand, gives you the average loss in the worst-case scenarios, providing a clearer picture of potential risks. Example to Illustrate Imagine you have a portfolio of investments. You’re concerned about what might happen in the worst 5% of cases (q = 5%).

• Value at Risk (VaR): Suppose VaR tells you that in 95% of cases you won’t lose more than $10,000.
• Expected Shortfall (ES): Now ES looks at that remaining 5% of cases. It calculates the average loss in those worst 5% scenarios. Let us say ES is $15,000. This means that in the worst 5% of cases you can expect to lose on average $15,000.

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In conclusion

• ES is a risk measure that focuses on the worst-case scenarios for your portfolio.
• It considers the average loss in the worst q% of cases, giving you a more detailed understanding of potential risks.
• By using ES, investors can better prepare for extreme losses, making it a useful tool for risk management.

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