| Day | Return (%) | Loss (%) |
|---|---|---|
| 1 | 0.40 | 0.00 |
| 2 | -0.20 | 0.20 |
| 3 | 0.15 | 0.00 |
| 4 | -0.50 | 0.50 |
| 5 | 0.30 | 0.00 |
| 6 | 0.10 | 0.00 |
| 7 | -0.15 | 0.15 |
| 8 | 0.05 | 0.00 |
| 9 | -0.35 | 0.35 |
| 10 | 0.20 | 0.00 |
- σh = σann × √(h / T)
- μh = μann × (h / T)
- VaR% = max(0, z × σh − μh)
- VaR = Portfolio Value × VaR%
- ES% = max(0, σh × φ(z) / (1 − CL) − μh)
- ES = Portfolio Value × ES%
- Select a method: Parametric for volatility-based estimates, or Historical for return-series estimates.
- Enter portfolio value, confidence level, and holding period in days.
- For Parametric, provide annual volatility and optional mean return.
- For Historical, paste daily returns as percentages, one per line.
- Click Calculate VaR. Results appear above the form.
- Use Download CSV or PDF to archive inputs and outcomes.
Value at Risk in Equity Portfolios
Equity Value at Risk (VaR) summarizes potential downside over a chosen horizon at a chosen confidence. If a USD 100,000 portfolio has a 1‑day 95% VaR of 2.10%, the implied loss threshold is USD 2,100. VaR supports limit setting, capital planning, and communication, but it is a probabilistic estimate, not a worst‑case bound.
Many firms quote both percentage and currency VaR to match reporting needs. When positions are leveraged, compute VaR on total exposure, not cash invested. For multi‑stock portfolios, volatility should reflect diversification, so use portfolio variance from weights, volatilities, and correlations when available.
Choosing Confidence and Horizon
Confidence controls tail strictness: 90% is looser, 99% is stricter. Horizon scales risk through time; under common assumptions, volatility grows with the square root of days. For example, moving from 1 to 10 days increases the scale by √10 ≈ 3.16, so a 1‑day 2% VaR could map to about 6.3% before drift adjustments.
Parametric Inputs and Assumptions
The parametric method assumes returns are approximately Normal. You provide annual volatility and optional annual mean, then convert to the holding period using trading days. The calculator uses z‑scores for the selected confidence, producing VaR% = max(0, z·σh − μh). This approach is fast and stable, but it can understate extreme moves when returns are skewed or fat‑tailed.
Historical Returns and Data Quality
Historical VaR uses your observed daily returns, compounds them into rolling holding‑period returns, and takes the empirical loss percentile. Results depend heavily on sample length and regime relevance. Short datasets can miss crises; very long datasets may mix structural changes. Clean inputs by removing obvious data errors, aligning calendars, and using total‑return series where dividends matter.
Using VaR with Expected Shortfall
Expected Shortfall (ES) complements VaR by averaging losses beyond the VaR threshold. Two portfolios can share the same VaR yet have very different tail severity; ES reveals that difference. In reporting, present VaR and ES together, document method and lookback, and backtest exceedances. Use stress tests and scenario analysis alongside VaR for robust equity risk governance. Regulators and internal audit often require documented assumptions, data sources, and model validation schedules for transparency.
FAQs
This calculator uses one-tailed VaR focused on downside losses. The confidence level represents the probability that losses stay below the VaR threshold over the holding period.
Use portfolio volatility when you have multiple equities. Portfolio volatility accounts for weights and correlations, often producing lower risk than a simple average of individual volatilities.
More is usually better. Aim for at least several months of daily data, and preferably one to three years, while ensuring the period is relevant to current market conditions.
A positive mean return can offset short-horizon risk in the formula. This tool floors VaR and ES at zero to keep results interpretable as non-negative loss thresholds.
VaR gives a cutoff loss level, but it ignores how bad losses can get beyond that cutoff. Expected Shortfall estimates the average loss in the tail, improving tail-risk visibility.
Yes, but interpret carefully. Parametric scaling often follows √time, while historical results reflect actual compounded paths. Keep the same method, confidence, and data regime for a fair comparison.