How to use VaR Backtest — Kupiec & Christoffersen
Paste a P&L series and a VaR series. The page runs Kupiec POF, Christoffersen independence, and joint conditional-coverage tests with likelihood-ratio chi-squared p-values — the standard regulatory diagnostics for VaR model adequacy.
What It Does
Use the calculator with intent
Paste a P&L series and a VaR series. The page runs Kupiec POF, Christoffersen independence, and joint conditional-coverage tests with likelihood-ratio chi-squared p-values — the standard regulatory diagnostics for VaR model adequacy.
Risk teams running VaR models who need to demonstrate regulatory adequacy — and self-funded risk-managers who want a real bar, not a vibe.
Interpreting Results
Kupiec POF tests breach frequency; Christoffersen tests breach clustering; the joint test combines both. Failure on any of the three at 5% significance is a flag that the VaR model is misspecified.
Input Steps
Field by field
- 1
Upload data
Upload your VaR forecasts and realized returns (daily granularity is standard).
- 2
Set parameters
Set the confidence level (95% or 99%) and the test window length (≥ 250 days for Basel-style validation).
- 3
Run calculation
Run Kupiec's POF test for unconditional coverage. Reject = wrong number of violations.
- 4
Run calculation
Run Christoffersen's independence test for conditional coverage. Reject = violations cluster (model fails during volatile regimes).
- 5
Read outputs
Read the green/yellow/red Basel zone classification. Yellow zone triggers capital multiplier increases; red rejects the model.
Common Scenarios
Use realistic starting points
Conservative VaR (over-estimates risk)
VaR percentile
99%
Observed breaches
low
POF fails on the low side — too few breaches. Model is too conservative; capital is over-reserved.
Optimistic VaR (under-estimates risk)
VaR percentile
99%
Observed breaches
high
POF fails on the high side; Christoffersen may flag clustering — breaches cluster in stress periods. Model misses tail-risk.
Try These Tools
Run the numbers next
Returns Distribution Analyzer
Paste a returns CSV. Histogram, normal-overlay, QQ plot, skewness, excess kurtosis, Jarque-Bera test, tail-weight index. See why Sharpe alone misleads.
Risk-Adjusted Returns Calculator
Paste a returns CSV. Sharpe, Sortino, Calmar, Omega, alpha, beta, tracking error, information ratio, max drawdown, and tail moments — plus.
FAQ
Questions people ask next
The short answers readers usually want after the first pass.
Related Content
Keep the topic connected
Value at Risk (VaR)
Value at Risk: the loss threshold you'll exceed with probability α. Why historical VaR is brittle and what it doesn't tell you about the tail.
Expected Shortfall (CVaR)
Expected shortfall: the average loss given a VaR breach. Why regulators are migrating from VaR and what ES catches that VaR misses.
Volatility
Volatility as the standard deviation of returns: realized vs implied, the annualization gotcha, and why volatility-of-volatility matters.