Expected Shortfall (CVaR) Calculator
Category: Risk ManagementCalculate Expected Shortfall (Conditional Value at Risk) to better understand and manage extreme market risks beyond traditional VaR measures
Portfolio Parameters
Risk Parameters
Distribution Parameters
Risk Metrics Results
Return Distribution & Risk Measures
Expected Shortfall by Confidence Level
Risk Measure Comparison
| Confidence Level | Value at Risk (VaR) | Expected Shortfall (ES) | ES/VaR Ratio | Risk Level |
|---|
Stress Test Scenarios
Market Crash Scenario
Based on historical market crash patterns (2008 Financial Crisis), this scenario simulates a severe market downturn with increased volatility and correlation.
Volatility Spike Scenario
This scenario models a sudden spike in market volatility (similar to the 2020 COVID crash) with 2x the normal volatility but without sustained directional movement.
Liquidity Crisis Scenario
Models the impact of a liquidity crisis where market depth decreases significantly and slippage increases, causing more severe losses than normal market conditions would suggest.
Risk Management Recommendations
Portfolio Allocation
Your Expected Shortfall is 8.75% of portfolio value, which is moderately high. Consider reducing exposure to more volatile assets or implementing tighter stop-loss levels.
Tail Risk Management
With an ES/VaR ratio of 1.35, your portfolio shows significant tail risk. Consider tail risk hedging strategies like out-of-the-money put options or volatility instruments.
Diversification Strategy
Based on your risk profile, consider adding negatively correlated assets to reduce overall portfolio risk without necessarily sacrificing return potential.
Risk Monitoring
Monitor ES/VaR ratio regularly. If it exceeds 1.5, it indicates that tail risk is increasing, which may require adjusting your portfolio allocation or hedging strategies.
Understanding Expected Shortfall (CVaR)
Expected Shortfall (ES), also known as Conditional Value at Risk (CVaR), measures the average loss in the worst cases of a distribution beyond the Value at Risk (VaR) threshold. While VaR tells you the maximum loss with a given confidence level, ES tells you how bad that loss could be when VaR is exceeded.
Expected Shortfall vs. VaR
- Value at Risk (VaR): Maximum loss at a given confidence level (e.g., 95% VaR is the loss that won't be exceeded 95% of the time)
- Expected Shortfall (ES): Average loss in the worst cases beyond the VaR threshold (e.g., 95% ES is the average loss in the worst 5% of cases)
- Key Difference: ES accounts for the severity of the worst losses, not just their probability
- Coherent Risk Measure: Unlike VaR, ES is a coherent risk measure that satisfies mathematical properties important for risk management
Interpreting ES/VaR Ratio
- Ratio ≈ 1.2-1.3: Normal distribution with typical tail behavior
- Ratio ≈ 1.3-1.5: Moderate tail risk, slightly heavier tails than normal
- Ratio ≈ 1.5-2.0: Significant tail risk, fat-tailed distribution
- Ratio > 2.0: Extreme tail risk, very fat-tailed distribution with potential for severe losses
- Higher ratios indicate that when losses exceed VaR, they tend to be much larger than expected
Mathematical Definition
Expected Shortfall (ES) at confidence level α is defined as:
Where E[X | X > VaRα] denotes the expected value of the loss X, given that X exceeds the VaR at confidence level α.
Applications in Trading and Risk Management
Position Sizing
Use ES to determine conservative position sizes that account for tail risk. Positions can be sized inversely to ES to maintain consistent risk exposure.
Risk Budgeting
Allocate risk across different strategies or assets based on their contribution to total ES, rather than just using standard deviation or VaR.
Stress Testing
ES provides a natural framework for stress testing by focusing on the severity of tail events rather than just their probability.
Regulatory Compliance
Banking regulations like Basel III have shifted from VaR to ES as the primary risk measure for determining capital requirements.
Risk Management Tools:
What this calculates
The average loss on the days that breach VaR — the tail VaR ignores.
- Formula
CVaR = mean of all losses worse than the VaR threshold- Worked example
- If the worst 5% of days average a 32,000 HKD loss while VaR is 19,740, CVaR is 32,000 — the number that matters when things go wrong.
- When to use it
- Alongside VaR, to see how bad the bad days actually are.
- Common mistake
- CVaR needs enough tail observations to mean anything. Computed off a short history it is an estimate of an estimate.