Free tool
CVaR calculator — expected shortfall from any return series.
Paste periodic returns and get historical VaR and CVaR at 95% and 99% — the same historical method documented in our methodology. Everything runs in your browser; nothing is uploaded.
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The formula, in plain terms
Sort the return series ascending. VaR at confidence α is the empirical (1 − α) quantile — the cut-off return. CVaR at α is the mean of all observations at or below that cut-off:
CVaR_α = mean( r : r ≤ VaR_α )
The full definition, coherence properties and a worked example live in the glossary entry: CVaR (Conditional Value at Risk). For the conceptual difference with VaR — and why risk desks prefer the tail average — read CVaR vs VaR.
Frequently asked questions
- What is CVaR (Conditional Value at Risk)?
- CVaR — also called expected shortfall — answers the question VaR leaves open: when the loss exceeds the VaR threshold, how much do you lose on average? Where VaR is a cut-off (a quantile), CVaR is the average of everything beyond it. It is a coherent risk measure: diversification can never make CVaR worse, which is why Basel III and institutional risk desks use it as the internal standard.
- How does this calculator compute CVaR?
- Historical method: your pasted returns are sorted ascending; VaR at 95% is the empirical 5% tail cut-off, and CVaR at 95% is the simple average of the observations at or beyond that cut-off. No distributional assumption is made. The computation runs entirely in your browser — nothing you paste is uploaded or stored.
- How many observations do I need?
- The calculator requires at least 20, but tail estimates are noisy on small samples: at 99% confidence with 100 observations, CVaR is the mean of just one point. For decisions that matter, use multi-year daily series — the MEDGE Portfolio Analyzer computes CVaR 95 and 99 on full price history for any portfolio of tickers and weights.
- Is CVaR better than VaR?
- They answer different questions. VaR gives a threshold ("you will not lose more than X on 95% of days"); CVaR describes the bad 5% ("when you do, you lose Y on average"). VaR can be gamed by piling risk beyond the threshold; CVaR cannot, because it averages the tail. Our CVaR vs VaR article walks through a worked example of the difference.
- Is this financial advice?
- No. The calculator is an educational tool: it computes descriptive statistics of the sample you paste, nothing more. Outputs are illustrative and are not a recommendation to buy or sell anything. For personalized advice, consult a licensed financial advisor.
Related
CVaR on your actual portfolio, not a pasted sample.
The MEDGE Portfolio Analyzer computes CVaR 95/99, Monte Carlo fans and crisis backtests on live weights. Free tier, no brokerage connection.
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