TradingCalcVaR / CVaR Calculator
RISK/STATS · VALUE AT RISK · STANDARD
Parametric Value at Risk (VaR) and Conditional VaR (Expected Shortfall), the variance-covariance method. Enter a return series or mean/stdev directly, pick a confidence level.
Input mode
Comma, space, or newline separated. No thousand separators (write 43250.50, not 43,250.50).
Parametric (variance-covariance) method: assumes returns are normally distributed. VaR and CVaR are reported at the same periodicity as the input: a daily return series gives a daily VaR/CVaR, not an annualized one.
The formula
Parametric (variance-covariance) VaR/CVaR assumes returns are normally distributed:
- z = the confidence level's standard-normal quantile (e.g. 1.645 at 95%)
- VaR = −mean + z × stdev
- CVaR = −mean + stdev × normPdf(z) / (1 − confidence)
Worked example
Mean 0, standard deviation 1, 95% confidence:
- z = 1.6449
- VaR = 1.6449 (the textbook 1.645σ result)
- CVaR = 2.0627 (always ≥ VaR)
Modified (Cornish-Fisher) VaR
When you enter a return series (not a bare mean/stdev), this page also computes Modified VaR: a skew/kurtosis-aware correction to the parametric estimate above (the Boudt/Peterson/Croux convention), instead of assuming a normal distribution:
- VaR_modified = VaR − stdev × [(z²-1)/6·S − (z³-3z)/24·K + (2z³-5z)/36·S²]
S = sample skewness, K = sample excess kurtosis (kurtosis − 3). Reduces to the plain parametric VaR exactly when S=0 and K=0.
Where to go next
VaR/CVaR is a single-period risk snapshot, using the series' own historical standard deviation. For a fuller picture across a whole return history, see the portfolio tearsheet (Sharpe, Sortino, drawdown, and more in one call), check whether the same series is trending or mean-reverting with the Hurst exponent calculator, or get a forward-looking volatility estimate instead of a flat historical one with the GARCH volatility calculator. For risk of ruin over many repeated bets/trades instead of a single period, see the Kelly growth-security frontier calculator. This parametric method assumes a normal distribution; for a tail-risk estimate that doesn't make that assumption, see the EVT tail risk calculator.
Use via API or MCP
This calculation is available as a deterministic API call for bots and AI agents.
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What assumptions and edge cases does this calculator use?
Returns are decimals per period (0.02 is 2%), not prices. Give either a return series of at least 2 values or a mean and a standard deviation; the confidence level must be strictly between 0 and 1 (default 95 percent). Modified VaR needs at least 3 returns. A flat series has zero standard deviation and gives an error. Results stay in the period of the input (a daily series gives a daily VaR). Not covered: historical or Monte Carlo VaR, tails beyond the Cornish-Fisher correction, and scaling to another horizon.
What is Value at Risk (VaR)?
The loss magnitude that, at a given confidence level (e.g. 95%), a portfolio or position is not expected to exceed in a typical period. A 95% daily VaR of 3% means losses beyond 3% are expected on roughly 5% of days.
What is CVaR (Expected Shortfall), and why does it differ from VaR?
CVaR is the average loss on exactly those periods where VaR is breached: it answers "how bad is bad," not just "how often is bad." CVaR is always greater than or equal to VaR, since it's conditioned on being in the worse tail beyond the VaR threshold.
What does "parametric" mean here?
This calculator uses the variance-covariance method: it assumes returns are normally distributed and computes VaR/CVaR from the mean and standard deviation alone. It does not use historical simulation (resampling actual past returns) or Monte Carlo simulation. Those are different, separate methods with different assumptions.
Is the output annualized?
No. VaR and CVaR come out at the same periodicity as the input: a daily return series gives a daily VaR/CVaR, a monthly series gives a monthly figure. Annualizing VaR isn't a simple square-root-of-time scaling in general (unlike volatility) unless the mean return is exactly zero.
Why would I supply a return series instead of mean/stdev directly?
If you already know your mean and standard deviation, entering them directly is faster. If you only have raw returns, the calculator computes the sample mean and standard deviation (with Bessel's correction, n-1) for you - and only a return series lets it also compute Modified VaR, since that needs the distribution's actual skewness and kurtosis, not just its first two moments.
What is Modified (Cornish-Fisher) VaR, and why does it differ from parametric VaR?
Parametric VaR assumes returns are normally distributed. Real return series are often skewed and fat-tailed (crashes are more common and more severe than a normal distribution predicts). Modified VaR corrects the parametric estimate for the series' own sample skewness and kurtosis via a Cornish-Fisher expansion, so a negatively-skewed, fat-tailed series gets a higher (more conservative) VaR than the normal-distribution assumption alone would suggest.