Net the recoveries, use average loans, annualise, then split by segment and set it against the allowance.
A bank's net charge-off ratio is gross charge-offs minus recoveries, annualised, divided by average loans for the period. An illustrative bank that charged off $14.2 million in a quarter and recovered $3.1 million has net charge-offs of $11.1 million; on $7,000 million of average loans that is 0.159 per cent for the quarter, or 0.63 per cent annualised. Its $91.0 million allowance covers 2.05 years of losses at that pace.
Worked in full in Bank Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The net charge-off ratio is the realised credit loss line: what the bank has actually written off, net of what it later collected. Provisions are an estimate and move with the reserve model; charge-offs are the loans that went bad. Analysts read the ratio quarter by quarter, by segment, and against the allowance, and most of the errors come from the denominator and the annualisation.
| Segment | Average loans | Gross charge-offs | Recoveries | Net charge-offs |
|---|---|---|---|---|
| Commercial and industrial | 1,800 | 3.0 | 0.9 | 2.1 |
| Commercial real estate | 2,900 | 2.4 | 0.2 | 2.2 |
| Residential mortgage | 1,500 | 0.3 | 0.2 | 0.1 |
| Consumer and card | 800 | 8.5 | 1.8 | 6.7 |
| Total | 7,000 | 14.2 | 3.1 | 11.1 |
Loans were $6,850 million at the start of the quarter and $7,150 million at the end. The allowance for credit losses opened at $88.0 million and the quarter's provision was $14.1 million.
Net charge-offs = gross charge-offs − recoveries = 14.2 − 3.1 = 11.1
Recoveries are 21.8 per cent of gross charge-offs, a reminder that a charge-off is not the final loss.
Quarterly ratio = 11.1 ÷ 7,000 = 0.159%
Use average loans for the period, ideally the daily average. Here the simple average of opening and closing loans gives the same 7,000.
Annualised ratio = 0.159% × 4 = 0.634%, or 63 basis points
On a day count: 11.1 × 365 ÷ 92 ÷ 7,000 = 0.629%
Excel: =(GrossCO-Recoveries)*4/AvgLoans, or *365/Days for the day-count version.
Both annualisation methods are in use and they differ by about half a basis point here. Quarterly regulatory and peer data are annualised, so a quarterly figure of 0.159 per cent must be multiplied up before it is compared with anyone else's 0.63.
| Segment | Annualised NCOs | NCO ratio | Share of loans | Share of NCOs |
|---|---|---|---|---|
| Commercial and industrial | 8.4 | 0.47% | 25.7% | 18.9% |
| Commercial real estate | 8.8 | 0.30% | 41.4% | 19.8% |
| Residential mortgage | 0.4 | 0.03% | 21.4% | 0.9% |
| Consumer and card | 26.8 | 3.35% | 11.4% | 60.4% |
| Total | 44.4 | 0.63% | 100% | 100% |
The consumer and card book is 11.4 per cent of loans and 60.4 per cent of net charge-offs. The total ratio of 0.63 per cent is therefore mostly a statement about consumer credit, and it is mix-sensitive: if the consumer book's charge-offs doubled, the bank's ratio would rise to 1.02 per cent with no change anywhere else. Card portfolios carry high charge-off rates by design and are priced for them, so the right comparison is segment against segment, not the total against a peer with a different mix.
Allowance roll-forward: 88.0 + provision 14.1 − net charge-offs 11.1 = 91.0
Reserve build = 14.1 − 11.1 = 3.0, provision 1.27 times net charge-offs
Allowance to period-end loans = 91.0 ÷ 7,150 = 1.27%
Years of charge-offs covered = 91.0 ÷ 44.4 = 2.05
A provision above net charge-offs means the bank is building reserves: it expects losses to rise or loans to grow. A provision below them means it is releasing reserves, which flatters earnings for as long as the release lasts. The coverage in years translates the allowance into time: at the current pace of losses, the existing reserve would absorb two years of write-offs with no new provisions.
| NCO ratio | Annual NCOs, $m | Years covered |
|---|---|---|
| 0.63% | 44.4 | 2.05 |
| 1.00% | 70.0 | 1.30 |
| 1.50% | 105.0 | 0.87 |
| 2.00% | 140.0 | 0.65 |
| 3.00% | 210.0 | 0.43 |
At a 1.50 per cent loss rate the allowance covers less than a year, and every further quarter of losses has to be provided for through earnings. That is where charge-offs meet pre-provision earnings: the question is whether the bank's PPNR can fund the provisions without touching capital, which is worked in how to calculate a bank's PPNR. For the stock of problem loans rather than the flow of write-offs, see the Texas ratio.
Net the recoveries, divide by average loans, annualise, and split by segment: here $11.1 million in a quarter is 0.63 per cent a year, 60.4 per cent of it from a consumer book that is 11.4 per cent of loans, against an allowance that covers 2.05 years. The book's own bank, its capital readings and its margin are in the free Bank Management workbooks.
It depends on the loan mix. In the illustrative bank, residential mortgages charge off at 0.03 per cent a year and consumer and card loans at 3.35 per cent, which blend to 0.63 per cent overall. Compare each segment with peers in the same segment, and read the total against the allowance: here the reserve covers 2.05 years of losses at the current pace.
No. Net charge-offs are losses actually written off, net of recoveries; the provision is the expense that sets the allowance for expected losses. In the illustrative quarter the provision was $14.1m against $11.1m of net charge-offs, 1.27 times, so the bank built its allowance by $3.0m to $91.0m.
Multiply the quarterly ratio by four, or use a day count: net charge-offs times 365 divided by days in the quarter, over average loans. With $11.1m of net charge-offs on $7,000m of loans, the first gives 0.634 per cent and the 92-day count gives 0.629 per cent.
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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: regulation, compliance and banking → · All 1682 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.