Estimate tail losses beyond your chosen confidence level. Compare historical, parametric, and simulation approaches quickly. Export results, audit inputs, and strengthen risk decisions today.
Sample daily returns you can paste into the Historical field.
| Day | Return | Notes |
|---|---|---|
| 1 | 0.0040 | Small gain |
| 2 | -0.0065 | Moderate loss |
| 3 | 0.0022 | Rebound |
| 4 | -0.0120 | Tail event |
| 5 | 0.0015 | Stabilization |
Conditional VaR (CVaR), called Expected Shortfall, estimates the average loss once portfolio losses exceed the VaR cutoff. It complements VaR by capturing tail severity rather than only a single quantile. Risk teams use CVaR to compare strategies with similar volatility but different downside profiles, and to set limits that reflect extreme-loss behavior. In reporting, CVaR is typically expressed in currency, aligning with budgeted loss capacity.
The confidence level α controls how much data falls into the tail: tail probability equals (1−α). For α=0.95, roughly 5% of scenarios define the tail mean; for α=0.99, about 1% do. Higher α generally increases VaR and CVaR, but CVaR can grow faster because it averages the worst outcomes. A practical check is tail count: too few tail points makes CVaR noisy and sensitive to single shocks.
Parametric estimation assumes returns follow a normal distribution with mean μ and volatility σ, producing a closed-form VaR and CVaR. Historical estimation uses observed returns directly, ranking the implied losses and averaging those beyond the VaR threshold. Monte Carlo simulates many return scenarios from μ and σ, then computes an empirical tail; more simulations improve stability but cost time. Method choice should reflect data quality and tail realism.
This calculator converts returns to losses using L = −V·R, where V is portfolio value and R is the horizon return. Under standard scaling, expected return grows with the number of days h, while volatility grows with √h. If your returns are already horizon-aligned, keep h=1 to avoid double scaling. For multi-asset portfolios, V should reflect valuation and include any relevant leverage or notional adjustments.
VaR is the loss threshold exceeded with probability (1−α); CVaR is the expected loss given that threshold is breached. If CVaR is much larger than VaR, the tail is heavy, implying larger conditional losses during stress. Review worst-loss and average-loss diagnostics to detect outliers or regime shifts. Use CVaR alongside stress tests, concentration checks, and model validation before setting limits, capital buffers, or escalation triggers.
VaR is a loss cutoff at confidence α. Conditional VaR is the average loss of outcomes that are worse than VaR, so it reflects tail severity rather than only a threshold.
Use parametric for fast, stable estimates when returns are near-symmetric. Use historical when you trust your return history and want empirical tails. Use Monte Carlo when you need scenario volume and controlled assumptions.
At least 30 observations are required here, but 250+ daily points is better. Higher confidence levels need more data, because the tail contains fewer points and the tail mean becomes unstable.
VaR selects one quantile. Conditional VaR averages losses beyond that quantile. If the tail is heavy, the worst losses rise quickly, pushing the conditional average up more than the cutoff.
With standard scaling, expected return scales with h and volatility with √h. Larger horizons usually increase both VaR and Conditional VaR in currency terms, especially when volatility dominates the drift term.
Yes. After running a calculation, use the CSV and PDF buttons in the results card. Exports include method, inputs, VaR, Conditional VaR, and a scenario-loss preview for traceability.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.