Enter portfolio assumptions and historical returns
Paste daily returns as percentages or decimals. The tool sorts observations, finds the empirical tail cutoff, then converts it into a loss estimate.
Sample historical return set
You can test the calculator with the example series below. Values are shown as daily percentage returns.
| Day | Return | Day | Return | Day | Return |
|---|---|---|---|---|---|
| 1 | -1.25% | 2 | 0.42% | 3 | -0.67% |
| 4 | 1.14% | 5 | -2.10% | 6 | 0.35% |
| 7 | -0.48% | 8 | 0.91% | 9 | -1.73% |
| 10 | 0.28% | 11 | -0.15% | 12 | 1.32% |
| 13 | -0.84% | 14 | 0.57% | 15 | -1.46% |
Historical VaR method
Historical VaR does not assume a normal distribution. It uses actual historical returns and selects the loss threshold from the empirical tail.
Step 1: Convert each historical return into an effective portfolio return.
effective return = raw return for a long portfolio.
effective return = -raw return for a short portfolio.
Step 2: Sort effective returns from worst to best.
Step 3: Find the empirical tail cutoff at alpha = 1 - confidence.
cutoff return = empirical quantile of sorted returns
Step 4: Convert the cutoff into value at risk.
one-day VaR % = max(0, -cutoff return)
one-day VaR amount = portfolio value × one-day VaR %
holding-period VaR ≈ one-day VaR × √days when scaling is enabled.
Expected shortfall is also reported. It averages all tail losses at or beyond the VaR cutoff, giving a deeper view of severe downside scenarios.
Steps for accurate estimates
- Enter the current portfolio value you want to stress-test.
- Select the confidence level, such as 95% or 99%.
- Choose the holding period and decide whether to scale it.
- Select long or short, depending on how losses arise.
- Paste historical returns as percentages or decimal values.
- Press the calculate button to generate the summary, chart, and scenario table.
- Export results as CSV or PDF for reporting, review, or documentation.
Frequently asked questions
1. What does Historical VaR measure?
Historical VaR estimates a potential portfolio loss using actual past returns. It identifies the loss threshold that should only be exceeded at the chosen tail probability.
2. Why use historical returns instead of a normal model?
Historical returns preserve observed skewness, jumps, and fat tails. That makes the estimate more grounded when recent market behavior is not well described by a smooth distribution.
3. What confidence level should I choose?
95% is common for routine monitoring, while 99% is stricter for capital and stress work. Higher confidence usually produces a larger VaR number.
4. How many observations are enough?
More observations generally improve stability. Short histories can create jumpy percentile cutoffs, especially when you select very high confidence levels like 99%.
5. What is the difference between VaR and expected shortfall?
VaR gives the cutoff loss. Expected shortfall averages losses beyond that cutoff, so it provides more information about how severe the worst tail outcomes may be.
6. Should I use holding-period scaling?
Scaling is a practical approximation, not a full historical revaluation. It can be helpful for quick estimates, but direct multi-day historical windows are more rigorous.
7. Can this calculator handle short portfolios?
Yes. The short option flips the return direction so gains and losses are evaluated from the short position’s perspective before VaR is calculated.
8. Does Historical VaR predict the future?
No. It uses past return patterns to estimate potential risk. Regime changes, liquidity shocks, and structural breaks can make future losses differ sharply.