Turn each pool's annual loss rate into a lifetime one, adjust the forecast years, and see which inputs move the reserve.
Under the WARM method, a CECL allowance is historical annual loss rate × expected remaining life × amortised cost for each loan pool, plus an adjustment for the reasonable and supportable forecast and a qualitative overlay. On an illustrative $5,000 million loan book with an average remaining life of 4.26 years, that gives $51.58 million from history, $12.26 million for a one-year forecast above historical losses and $2.50 million of overlay: an allowance of $66.34 million, 1.33 per cent of loans.
Worked in full in Bank Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
CECL, the current expected credit loss standard in ASC 326, requires a US bank to hold an allowance for the losses it expects over the whole remaining life of its loans, not only those already incurred. The standard took effect for SEC filers other than smaller reporting companies in 2020 and for other entities in 2023, and it does not prescribe a method: discounted cash flow, vintage, probability-of-default and loss-rate approaches are all used. The weighted average remaining maturity method, WARM, is one acceptable approach among them and one of the simplest, often favoured for less complex pools at smaller banks: it turns a loss rate that is measured per year into one that covers the life of the pool. The arithmetic is short; the judgement sits in the remaining life and in the forecast.
| Pool | Amortised cost | Historical annual loss rate | Expected remaining life, years | Forecast loss rate, next year |
|---|---|---|---|---|
| Commercial and industrial | 1,200 | 0.35% | 2.2 | 0.60% |
| Commercial real estate | 2,000 | 0.20% | 4.5 | 0.45% |
| Residential mortgage | 1,300 | 0.04% | 6.8 | 0.06% |
| Consumer | 500 | 2.60% | 1.6 | 3.40% |
| Total | 5,000 | 4.26 |
The historical rate is the average annual net charge-off rate of each pool over a full cycle, calculated as in how to calculate a bank's net charge-off ratio. The remaining life is the contractual term adjusted for expected prepayments, measured as a weighted average life: the sum of the balances expected to be outstanding each year, divided by today's balance. The bank's supportable forecast runs one year, after which it reverts straight to historical rates. All rates are illustrative.
Lifetime rate = annual loss rate × remaining life
Commercial real estate: 0.20% × 4.5 = 0.90%; consumer: 2.60% × 1.6 = 4.16%
Pool allowance = amortised cost × lifetime rate
Commercial real estate: 2,000 × 0.90% = 18.00; total across pools = 51.58
For the forecast year, replace the historical rate with the forecast rate:
Adjustment = amortised cost × (forecast rate − historical rate) × 1 year
Commercial real estate: 2,000 × (0.45% − 0.20%) = 5.00; total = 12.26
Overlay = 0.05% × 5,000 = 2.50
Allowance = 51.58 + 12.26 + 2.50 = 66.34, or 1.33% of loans
Excel, one row per pool: =Balance*HistRate*Life+Balance*(FcRate-HistRate)*MIN(FcYears,Life), then add the overlay to the sum. The forecast adjustment is applied here to today's balance; a fuller model applies it to the average balance of the forecast year.
| Pool | Lifetime rate | Historical allowance | Forecast adjustment | Pool allowance | % of pool |
|---|---|---|---|---|---|
| Commercial and industrial | 0.77% | 9.24 | 3.00 | 12.24 | 1.02% |
| Commercial real estate | 0.90% | 18.00 | 5.00 | 23.00 | 1.15% |
| Residential mortgage | 0.27% | 3.54 | 0.26 | 3.80 | 0.29% |
| Consumer | 4.16% | 20.80 | 4.00 | 24.80 | 4.96% |
| Qualitative overlay | 2.50 | 0.05% | |||
| Total | 51.58 | 12.26 | 66.34 | 1.33% |
History provides 77.7 per cent of the allowance, the forecast 18.5 per cent and the overlay 3.8 per cent. The consumer pool, a tenth of the loans, carries more than a third of the allowance; the residential book, with the longest life, carries little because its annual loss rate is so low. Life multiplies the rate, so a long-lived pool with a modest rate can need more reserve than its annual losses suggest: commercial real estate loses 4.00 a year at its historical rate but needs 18.00 before any forecast.
| Case | Allowance | Change | % of loans |
|---|---|---|---|
| No forecast adjustment (history only) | 54.08 | −12.26 | 1.08% |
| CRE remaining life 3.5 years | 62.34 | −4.00 | 1.25% |
| Base case | 66.34 | 0.00 | 1.33% |
| CRE remaining life 5.5 years | 70.34 | 4.00 | 1.41% |
| Forecast period two years | 77.00 | 10.66 | 1.54% |
| Consumer loss rates 1.5 times higher | 78.74 | 12.40 | 1.57% |
Each 10 basis points of allowance on this book is $5.0 million of provision expense, charged against earnings in the quarter the assumption changes. Slower prepayments alone, one more year of life on commercial real estate, add $4.00 million without a single loan deteriorating. Whether pre-provision earnings can absorb such a build is the question worked in how to calculate a bank's PPNR.
Multiply each pool's annual loss rate by its expected remaining life, adjust the forecast years to the forecast rate, add a documented overlay: here $66.34 million, 1.33 per cent of $5,000 million of loans. The allowance is most sensitive to the two inputs nobody observes directly, the remaining life and the forecast. How an allowance and its marks feed through to the capital ratios the depositor reads is in the free Bank Management workbooks.
The weighted average remaining maturity method multiplies a pool's historical annual loss rate by the pool's expected remaining life to get a lifetime loss rate, then applies it to amortised cost. In the worked case commercial real estate loses 0.20 per cent a year over 4.5 years, a 0.90 per cent lifetime rate, or $18.00 million on $2,000 million before the forecast adjustment.
For the forecast period, replace the historical rate with the forecast rate and add the difference to the allowance; after it, revert to history. With a one-year forecast the illustrative bank adds $12.26 million, taking the allowance from $54.08 million to $66.34 million. Extending the forecast to two years adds another $10.66 million.
Because it covers losses over the remaining life of the loans, not the next twelve months. The illustrative book loses $21.72 million a year at historical rates, 0.43 per cent of loans, but its lifetime allowance is $66.34 million, 1.33 per cent, because the average loan has 4.26 years to run and the forecast is above history.
This article is one calculation from Bank Management. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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