Value at Risk (VaR) tells you the threshold of bad days, but it ignores what happens beyond that threshold. Expected Shortfall (ES), also called Conditional Value at Risk (CVaR), fixes this critical flaw. It tells you the average loss when things go really wrong - exactly when you need to know most.
The Problem with VaR
VaR answers: "What is the minimum loss I will experience in the worst 5% of days?" But it does not tell you HOW BAD those worst days could be.
Two Portfolios, Same VaR
Both portfolios have 1-day 95% VaR of $10,000:
- Portfolio A: In the worst 5% of days, losses range from $10,000 to $12,000
- Portfolio B: In the worst 5% of days, losses range from $10,000 to $100,000
VaR says they have the same risk. They clearly do not.
What is Expected Shortfall?
Expected Shortfall (ES) is the average loss in the worst cases - specifically, the average of all losses beyond the VaR threshold.
ES Definition: Expected Shortfall at 95% confidence is the average of the worst 5% of losses.
If your 95% VaR is $10,000, ES tells you the average loss on those 5% of really bad days.
Calculating Expected Shortfall
The historical method is straightforward:
- Collect your daily returns (e.g., 100 days)
- Sort from worst to best
- For 95% ES: Take the worst 5 days
- Calculate the average of those 5 worst days
ES Calculation Example
100 days of returns. Worst 5 days (for 95% ES):
- Day 1: -$15,000
- Day 2: -$12,000
- Day 3: -$11,000
- Day 4: -$10,500
- Day 5: -$10,000
95% VaR = $10,000 (the 5th worst day)
95% ES = Average = ($15,000 + $12,000 + $11,000 + $10,500 + $10,000) / 5 = $11,700
On bad days beyond VaR, you lose an average of $11,700.
ES vs VaR: Key Differences
- VaR: Minimum loss in worst X% of cases (a threshold)
- ES: Average loss in worst X% of cases (what actually happens)
- VaR: Ignores tail severity
- ES: Captures tail severity
- VaR: Can be gamed by hiding risk in tails
- ES: Cannot be gamed - all tail losses count
Why ES is Mathematically Superior
ES has a property called "coherence" that VaR lacks:
Subadditivity
For a coherent risk measure, combining portfolios should not increase risk:
- Risk(A + B) should be less than or equal to Risk(A) + Risk(B)
- Diversification should reduce risk, not increase it
VaR can violate this. ES never does. This is why regulators and academics prefer ES.
Using ES in Trading
Position Sizing with ES
Use ES instead of VaR for more conservative sizing:
- Set maximum 1-day 95% ES (e.g., 3% of account)
- Size positions to stay within ES limits
- This accounts for how bad "bad days" really get
ES-Based Position Limit
Account: $100,000. Maximum 1-day 95% ES: 3% = $3,000
Your current ES is $4,500. You need to reduce positions until ES drops to $3,000.
Comparing Strategies
ES reveals hidden risk differences:
- Strategy A: VaR = $5,000, ES = $6,000 (tails are mild)
- Strategy B: VaR = $5,000, ES = $12,000 (tails are severe)
Strategy B has twice the tail risk despite identical VaR.
Risk Budgeting
Allocate ES across strategies:
- Total ES budget: $5,000
- Core strategy: $3,000 ES allocation
- Speculative strategy: $2,000 ES allocation
ES for Options Traders
ES is especially important for options strategies with asymmetric payoffs:
Short Put Example
Selling puts has limited upside (premium) and large downside (assignment at lower price).
- VaR might show moderate risk (most days are small gains)
- ES captures the severe loss when assigned during a crash
ES reveals the true risk of tail events in premium-selling strategies.
Practical ES Calculation
For individual traders, here is a simple approach:
Quick ES Method
- Export daily P&L for last 100 trading days
- Sort from worst to best
- Take the worst 5 days (for 95% ES)
- Calculate the average
Worst 5 days: -3.2%, -2.8%, -2.5%, -2.3%, -2.1%
Average = -2.58%
Your 95% ES is approximately 2.58% of portfolio
ES and Tail Risk Protection
ES helps you size tail hedges appropriately:
- Calculate your unhedged ES
- Determine your maximum acceptable ES
- Buy enough puts/VIX calls to bridge the gap
Hedging Example
- Portfolio: $500,000
- Unhedged 95% ES: 4% = $20,000
- Target ES: 2.5% = $12,500
- Need hedges to reduce tail losses by ~$7,500
Calculate put payoffs in tail scenarios and size accordingly.
Limitations of ES
ES is better than VaR but not perfect:
- Data hungry: Needs many observations to estimate tails accurately
- Still uses historical data: Future tails may be worse than past
- Assumes past represents future: Regime changes can invalidate estimates
- More complex to calculate: Harder to explain to non-quants
Track Your Risk Metrics
Pro Trader Dashboard records your daily P&L history, giving you the data needed to calculate both VaR and Expected Shortfall. Understand your true risk exposure.
ES in Industry and Regulation
Expected Shortfall is increasingly replacing VaR:
- Basel III banking regulations now require ES
- Many hedge funds use ES internally
- Academic research favors ES for its mathematical properties
Combining ES with Other Metrics
For complete risk management, use multiple measures:
- VaR: Quick threshold measure, good for daily monitoring
- ES: Average tail loss, better for risk limits
- Maximum Drawdown: Worst historical peak-to-trough
- Stress Tests: What-if scenarios for extreme events
Summary
Expected Shortfall addresses VaR's biggest weakness: ignoring what happens in the tails. By measuring the average loss in worst-case scenarios, ES gives you a more honest picture of your risk. Use ES for position sizing, risk budgeting, and understanding the true danger in your portfolio - especially for strategies with asymmetric payoffs like options selling.
Learn more about Value at Risk basics or explore tail risk management strategies to protect your portfolio.