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Expected Shortfall (CVaR) Calculator

Calculate Expected Shortfall (CVaR): the average loss on the days that are worse than your Value at Risk.

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Method
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Results
95% Expected Shortfall$2,425.262.43% of portfolio · z = 1.645, 1-day horizon
Value at Risk$1,923.82the threshold ES averages beyond
Tail probability5%≈ 1 in 20 days
ES ÷ VaR1.26×tail severity
When losses do breach the 95% VaR of $1,923.82, they average $2,425.26. ES captures tail severity, which is why regulators and risk desks increasingly prefer it to VaR.
Parametric VaR assumes normally distributed returns. Real returns have fatter tails, so extreme losses happen more often than the model implies.
Return distribution and loss threshold

Not financial advice. Results are estimates based on the values you enter and simplified assumptions; real trades are affected by fees, slippage, gaps and other factors. Trading involves substantial risk of loss. Read the full disclaimer.

How to calculate Expected Shortfall

Parametric ES (loss) = σ√h × φ(z) ÷ (1 − α) − μh φ = standard normal density, z = normal quantile at confidence α Historical ES = −average of returns at or below the VaR quantile

Worked example

  1. Portfolio $100,000, mean daily return 0.05%, daily volatility 1.2%, 95% confidence.
  2. φ(1.645) = 0.1031, so ES = 1.2% × 0.1031 ÷ 0.05 − 0.05% = 2.425%.
  3. In money: $2,425 — the average loss on the worst 5% of days, versus a VaR of $1,924.

How to interpret Expected Shortfall

ES answers the question VaR avoids: “when it goes badly, how badly?”. For normally distributed returns, 95% ES is about 1.25× VaR; a much larger ratio in historical data signals fat tails. Compare both on the VaR calculator.

Limitations and common mistakes

  • Historical ES at 99% needs a lot of data — with 250 daily returns, only 2–3 observations sit in the tail.
  • ES is always larger than VaR at the same confidence level.
Risk Metrics

Value at Risk (VaR) Calculator

Estimate the loss threshold you should only exceed on a small share of days — parametric or historical.

$100k · σ 1.2% · 95% → VaR $1,924
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Volatility Calculator

Calculate the standard deviation of returns from prices or returns and annualise it for any data frequency.

Monthly returns → σ per month & annualised
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Maximum Drawdown Calculator

Find the largest peak-to-trough decline in an equity curve, its duration and the gain needed to recover.

$12,000 → $9,000 → −25% (needs +33.3%)

Expected Shortfall calculator FAQ

Is Expected Shortfall the same as CVaR?

Yes. Expected Shortfall, Conditional VaR (CVaR) and Expected Tail Loss all describe the average loss beyond VaR.

Why do regulators prefer ES?

ES captures tail severity and adds up sensibly across portfolios, while VaR can miss large tail losses entirely.