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)
Where to go next
VaR/CVaR is a single-period risk snapshot. For a fuller picture across a whole return history, see the portfolio tearsheet (Sharpe, Sortino, drawdown, and more in one call), or check whether the same series is trending or mean-reverting with the Hurst exponent calculator.
Use via API or MCP
This calculation is available as a deterministic API call for bots and AI agents.
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.