Calculator Inputs
Example Data Table
Sample daily returns (percent). Use these to test series mode.
| Date | Return (%) | Cumulative Index |
|---|---|---|
| 2026-02-03 | 0.20 | 100.2000 |
| 2026-02-04 | -0.10 | 100.0998 |
| 2026-02-05 | 0.35 | 100.4501 |
| 2026-02-06 | -0.25 | 100.1990 |
| 2026-02-09 | 0.15 | 100.3493 |
| 2026-02-10 | 0.05 | 100.3995 |
| 2026-02-11 | -0.30 | 100.0983 |
| 2026-02-12 | 0.40 | 100.4987 |
| 2026-02-13 | -0.05 | 100.4484 |
| 2026-02-16 | 0.10 | 100.5489 |
Formula Used
This calculator uses the normal (parametric) approach to estimate a one-tailed loss threshold.
- Z = N^{-1}(confidence)
- mu_h = mu * h (or 0 if drift is excluded)
- sigma_h = sigma * sqrt(h)
- Long: VaR_return = Z * sigma_h - mu_h
- Short: VaR_return = Z * sigma_h + mu_h
- VaR_currency = PortfolioValue * max(0, VaR_return)
How to Use This Calculator
- Enter your portfolio value, confidence level, and horizon.
- Select Long or Short to match your exposure.
- Choose Manual to input mu and sigma directly, or Series to estimate from returns or prices.
- Click Calculate VaR. Your results appear above the form.
- Use Download CSV or Download PDF to export outputs.
Why Parametric VaR Matters in Daily Risk Controls
Parametric Value at Risk (VaR) converts volatility into a practical loss limit in currency terms. Risk teams use it for daily reporting, intraday limit checks, and quick comparisons across desks. Because the method is closed form, it is fast enough for repeated what-if analysis as positions change.
Inputs That Drive the Loss Quantile
The calculator links portfolio value, mean return (mu), volatility (sigma), confidence, horizon, and position direction. Confidence is mapped to a standard normal Z score, such as 1.645 for 95% and 2.326 for 99%. Holding sigma constant, the jump from 95% to 99% raises the threshold about 41%. You may enter mu and sigma directly, or paste a return series to estimate them. Use consistent units: if sigma is daily, set horizon in days; if weekly, use weeks. The tool can accept prices too, converting them into simple returns before estimation. Cleaning outliers and aligning calendars improves stable mu and sigma estimates for each asset and benchmark.
Interpreting VaR Alongside Expected Shortfall
VaR answers: what loss will not be exceeded with this confidence over the horizon? For a long position, VaR = V * (Z * sigma * sqrt(h) - mu * h). Example: V 10,000,000; sigma 1.2% daily; mu 0.03% daily; h 1; confidence 99%. VaR is about 276,000. VaR does not describe the average loss beyond the cutoff, so pair it with Expected Shortfall, stress tests, and scenario shocks.
Horizon Scaling, Aggregation, and Concentration
With independent daily returns, scaling uses sigma * sqrt(h) and mu * h; five trading days multiply sigma by sqrt(5) about 2.236. If returns cluster, this rule can understate risk. When exposures are concentrated, diversification benefits may be overstated, so compute VaR by asset class or factor bucket. Component VaR helps identify positions that dominate the total.
Model Validation and Practical Limitations
Backtesting compares realized P&L with VaR forecasts and counts exceptions. At 99% confidence, about one breach per 100 days is expected; more suggests stale sigma, regime shifts, or non-normal tails. Improve robustness by refreshing sigma with EWMA, adding liquidity buffers, and documenting assumptions for governance and audit.
FAQs
1) What does parametric VaR assume?
It assumes returns follow a normal distribution and that risk is summarized by mu and sigma over the chosen horizon. If tails are fat or volatility shifts quickly, results can understate losses.
2) Should I include mean return (mu) in VaR?
Often, drift is small versus volatility for short horizons, so many teams set mu to zero for conservatism. For longer horizons or stable carry strategies, including mu may be reasonable.
3) Why does VaR scale with the square root of time?
Under independent returns, variances add across periods, so standard deviation scales with sqrt(h). If returns are autocorrelated or volatility clusters, square-root scaling may misestimate risk.
4) How many observations should I paste?
More is usually better, but relevance matters. Many practitioners start with 60 to 250 daily points, then update regularly. Use the estimator option if you want faster adaptation to new volatility.
5) What is an exception in backtesting?
An exception occurs when actual loss exceeds the VaR estimate for that day. At 99% confidence, about 1 exception per 100 days is expected, assuming the model fits well.
6) Is VaR enough for risk management?
No. VaR is a useful summary, but it ignores tail severity beyond the threshold. Combine it with Expected Shortfall, scenario analysis, stress testing, and liquidity-aware limits for stronger controls.