Projection
Charge-off rate on credit card loans, all commercial banks, annualized. Fitted values dashed; the 9 projected quarters sit on the paper tint with the selected scenario's P10 to P90 and P25 to P75 bands.
- Actual
- Fitted
- Baseline
- Severely adverse
- 2008 replay
- Custom
- P10 to P90
What the scenario applies
Unemployment is the scenario's input. The model reads it as a four-quarter change, together with house price growth chained from today's level.
- Baseline4.6% peak
- Severely adverse10.0% peak
- 2008 replay9.9% peak
- Custom8.0% peak
- Baseline0.3 pp peak
- Severely adverse4.7 pp peak
- 2008 replay4.0 pp peak
- Custom3.4 pp peak
- Baseline0.2% trough
- Severely adverse-18.7% trough
- 2008 replay-7.2% trough
- Custom-11.8% trough
Estimates
Coefficients, their standard errors, and what they mean for the credit card book.
log COt = 0.245 + 0.841 · log COt−1 + 0.0323 · ΔUR₄ − 0.0018 · HPI − 0.207 · pandemic + ε
Ordinary least squares with Newey–West standard errors at four lags. 165 quarters, 1985 Q2 to 2026 Q2.
| Term | Estimate | Std. error | t | 95% interval |
|---|---|---|---|---|
| Intercept | 0.2446 | 0.0562 | 4.35 | |
| Lagged log charge-off (persistence)per log point | 0.8411 | 0.0358 | 23.48 | |
| Δ Unemployment, 4 quarters (pp)per point | 0.0323 | 0.0108 | 2.98 | |
| House price growth, YoY (%)per percent | -0.0018 | 0.0027 | -0.67 | |
| Pandemic stimulus indicator (2020Q2–2021Q4)indicator | -0.2071 | 0.0510 | -4.06 |
- Adjusted R²in sample, log scale
- 0.929
- Root mean square errorin sample, in levels
- 0.41 pp
- Durbin–Watson2.0 means no leftover autocorrelation
- 2.13
- Half-life of a loss shockfrom the persistence term
- 4.0 quarters
- One point of ΔUR₄, on impactlift in the loss rate
- +3.3%
- One point of ΔUR₄, sustainedlong-run lift in the loss rate
- +22.5%
Persistence carries most of the fit. With ρ near 0.84, a shock to losses fades by half in about 4 quarters, which is roughly what delinquency roll rates imply. The labor term does the economic work: each point that unemployment has risen over the past year lifts losses 3.3% on impact and 23% if it stays there. House prices have the sign I expected and a t-statistic of -0.67 for this book. I kept the term because it belongs in the story and because the severely adverse scenario moves it a long way.
Checks
How the model would have done, and what I rejected to arrive at it.
Two recessions, run blind
I re-estimated the model on data ending the quarter before each recession, then ran it forward for twelve quarters on the unemployment and house price path that actually happened. Scenario error is removed, so what remains is the model's own.
- Model peak
- 9.34%
- Actual peak
- 10.54%
- RMSE
- 1.51 pp
- Model peak
- 5.54%
- Actual peak
- 7.65%
- RMSE
- 0.96 pp
It follows the shape of both episodes and undershoots both peaks, by 1.2 points in 2009. I left that in. Loss models with this structure tend to undershoot at the top, which is why banks pair them with documented overlays, and a version tuned until it hit 2009 would say less about the next recession.
What was rejected
Six specifications on the same sample, each given the same two tests. I chose on the 2008 result rather than on fit. The unemployment-level variant fits almost as well in sample and misses the 2009 peak by more than five points, which is the difference between a model and a curve.
| Specification | Adj. R² | RMSE | DW | 2009 peak error | 2001 peak error |
|---|---|---|---|---|---|
| AR(1) + ΔUR₄ + HPI + pandemicchosen | 0.929 | 0.41 pp | 2.13 | −1.20 pp | −2.11 pp |
| Drop pandemic indicator | 0.916 | 0.44 pp | 1.83 | −1.20 pp | −2.11 pp |
| Add real GDP growth | 0.929 | 0.41 pp | 2.11 | −1.25 pp | −2.21 pp |
| Unemployment level instead of change | 0.915 | 0.47 pp | 1.89 | −5.62 pp | −3.34 pp |
| Same spec, fit in levels (not logs) | 0.918 | 0.44 pp | 1.95 | −3.68 pp | −3.20 pp |
| Static: no lag, UR level + HPI | 0.359 | 1.24 pp | 0.14 | −6.64 pp | −3.85 pp |
Peak error is the predicted peak minus the actual peak in the blind run, in percentage points. Negative means the model came in low.
Documentation
Written in the order SR 11-7 reviewers read it. The download carries the full estimation, validation, and projection tables, generated from the same model file as the charts above.
The model projects the quarterly, annualized net charge-off rate on credit card loans at U.S. commercial banks over a 9-quarter horizon, given a macro scenario. I built it to show the modeling and documentation practice behind CCAR and DFAST loss forecasting on public industry aggregates.
It is meant for comparing scenarios and reading sensitivities. It is calibrated to no institution and should carry no capital, reserving, or pricing decision.