Value at Risk (VaR) Calculator
Parametric VaR plus CVaR (Expected Shortfall) for any return series at any confidence level. Returns skew and kurtosis so you can see when your data violates the normal-distribution assumption.
Results
| Confidence | VaR | CVaR | VaR ($) | CVaR ($) |
|---|---|---|---|---|
| 95% | -1.06% | -1.37% | -$1,057.16 | -$1,369.86 |
| 99% | -1.57% | -1.82% | -$1,569.13 | -$1,821.31 |
With 95% confidence, you should not lose more than 1.06% ($1,057) over a 1-day holding period. On the worst 5% of days, the average loss (CVaR) is 1.37%. Daily volatility is 0.75%; annualized, 11.92%. Caveat: skewness of -0.66 indicates asymmetric distribution. Parametric VaR likely understates true tail risk for this data — actual large-loss days may be more common than the 5% the 95% number implies.
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Frequently asked questions
What VaR really tells you
Value at Risk became the dominant risk metric in the 1990s because it gave a single, digestible number to senior managers and regulators: "your 1-day 99% VaR is $4 million." That clarity was its strength and its weakness. VaR tells you the threshold loss you should not exceed at a chosen confidence level. It does not tell you how bad it gets if you do.
Three ways to compute VaR
- Parametric (this calculator): assume normal returns, compute analytically from the volatility. Fast, clean, used here. Underestimates tail risk for fat-tailed assets.
- Historical simulation: empirically count quantiles of the historical return series — i.e. for 95% VaR, find the 5th-worst day in your sample and use that. Captures actual tail behavior of your data without assuming a distribution.
- Monte Carlo: simulate thousands of paths under a model (could be normal, t-distribution, or more complex) and read off the empirical quantile. Most flexible, most computationally expensive. The QuantOracle API has
/v1/simulate/montecarlofor this.
Why CVaR is increasingly preferred
After 2008, regulators and risk managers shifted attention from VaR to CVaR (Conditional VaR, also called Expected Shortfall). CVaR is the average loss given that you are in the tail beyond VaR. Two portfolios can have identical VaRs but very different CVaRs — one with a smooth tail, one with a few catastrophic outcomes. CVaR distinguishes them; VaR does not. Basel III replaced VaR with CVaR (97.5% confidence) for trading-book regulatory capital in 2019.
Skewness and kurtosis as red flags
Parametric VaR assumes returns are normal. Real returns often are not. Skewness measures asymmetry: most equity strategies have negative skew (big losses more common than big gains). Excess kurtosis above zero means fat tails — rare events of either direction happen more often than the normal distribution predicts. When skewness is meaningfully nonzero or excess kurtosis is meaningfully above zero, parametric VaR is understating real risk. Use historical simulation or Monte Carlo with a fat-tailed distribution instead.
The square-root-of-time scaling
VaR scales with the square root of the holding period: VaR(T-day) = VaR(1-day) × √T. So 10-day VaR is √10 ≈ 3.16x the 1-day VaR, not 10x. This assumes returns are independent across days, which is approximately true for most liquid assets but breaks down during crises (when volatility clusters and serial correlation rises). For autocorrelated return series, the actual scaling is faster than √T.
Related risk metrics
See the Sharpe ratio calculator for the upside-vs-volatility ratio, the Kelly calculator for optimal position sizing given an edge, and the composite /v1/risk/full-analysis endpoint for max drawdown, Sortino, Calmar, and other risk metrics in a single API call.