Example Data Table
| Day | Return | Position Value | Loss if Return Happens |
|---|---|---|---|
| 1 | 0.80% | 100,000 | -800 |
| 2 | -1.10% | 100,000 | 1,100 |
| 3 | 0.35% | 100,000 | -350 |
| 4 | -2.40% | 100,000 | 2,400 |
| 5 | 1.05% | 100,000 | -1,050 |
Formula Used
Value at Risk estimates a loss threshold that should not be exceeded with a chosen confidence level over a given horizon.
- Parametric (Normal): VaR = V × ( z × σh − μh ), where μh = μ × h and σh = σ × √h.
- Historical simulation: compute rolling horizon returns from observed data, convert to losses, then take the empirical quantile at the confidence level.
- Monte Carlo: simulate many horizon returns (Normal here), convert to losses, then take the simulated quantile at the confidence level.
How to Use This Calculator
- Select a method that matches your data and modeling needs.
- Set confidence level and horizon days for your risk window.
- Enter position value and daily mean and volatility assumptions.
- For historical simulation, paste daily returns and choose their format.
- Press Calculate VaR to view results above the form.
- Use the download buttons to export CSV or PDF for reporting.
Confidence Level and Tail Probability
At 95% confidence, VaR targets the loss exceeded about 1 day in 20; at 99%, about 1 day in 100. Increasing confidence raises the threshold and makes estimates more sensitive to tail behavior. For historical results, the effective tail sample equals roughly (1−c)×N, so 99% VaR with 250 observations relies on about 2 to 3 worst outcomes. Smaller samples amplify noise. Choose confidence to match your risk policy and market.
Horizon Scaling and Liquidity Considerations
VaR is horizon-specific. Under a stable return process, mean scales with h and volatility scales with √h, so a 10‑day horizon can materially increase risk even if daily VaR looks modest. However, horizon scaling is an approximation; gaps, illiquidity, and position changes can break it. If trading is infrequent, treat the horizon as a liquidation window and prefer methods based on actual holding-period returns rather than pure scaling assumptions.
Method Selection and Data Quality
Parametric VaR is fast and transparent for teams, but it assumes a normal loss shape and can understate heavy tails. Historical simulation reflects observed patterns, yet it depends on clean, representative data and can miss regimes not in the sample. Monte Carlo adds flexibility and stress capability, but results vary with model choices and simulation count. As a practical check, compare methods under the same inputs and investigate large divergences before acting.
Interpreting VaR and Expected Shortfall
VaR is not the maximum loss; it is a quantile threshold. Two portfolios can share the same VaR while having very different tail losses. Expected Shortfall, also called CVaR, averages losses beyond the VaR cutoff and better captures tail severity. When VaR seems stable but CVaR rises, it can signal increasing tail risk even if typical volatility is unchanged. Use both for balanced decisions. It supports better limits and tail-aware allocation.
Reporting, Governance, and Backtesting Signals
Operationally, record inputs, method, horizon, and confidence so results are reproducible for reviews. Set limits in both amount and percent of position to handle growth in exposure. Monitor exceptions: the number of days losses exceed VaR should be close to 1−confidence over time. Persistent exceedances may indicate model drift, volatility shifts, or data issues. Pair VaR reports with scenario shocks to inform governance. Automate refreshes and archive exports for audit trails.
FAQs
What does a 95% VaR mean in practice?
With 95% confidence over the chosen horizon, losses should exceed VaR on roughly 5% of periods. It is a threshold, not a guarantee, and exceedances can cluster during stressed markets.
Why can VaR be shown as zero?
If the model implies non‑negative returns at the selected quantile, VaR may compute to zero, especially with high mean assumptions or low volatility. Consider using a higher confidence, longer horizon, or reviewing inputs.
Should I use simple returns or percentages in the returns box?
Either works. Select the input mode that matches your data. Use decimals for 0.01 = 1%, or percentages for 1 = 1%. Keep the format consistent across the entire series.
How many observations are recommended for historical VaR?
More is better, but a practical minimum is 60 daily returns. Around 250 trading days provides a fuller year. For 99% VaR, larger samples are important because the tail relies on very few points.
How does the horizon setting affect the output?
Parametric and simulation methods scale mean by days and volatility by the square root of days. Historical VaR compounds rolling holding‑period returns. Longer horizons generally increase the VaR amount for the same position value.
What is the difference between VaR and Expected Shortfall?
VaR reports a quantile loss threshold. Expected Shortfall averages losses beyond that threshold, capturing tail severity. When tail risk increases, Expected Shortfall often rises even if VaR changes only slightly.