Two subtractions and a division. The ratio is lower than CET1 for two reasons, the denominator and the unrealised losses, and it falls further still if the held-to-maturity book is marked.
The tangible common equity ratio is common equity minus goodwill and other intangibles, divided by total assets minus the same intangibles. An illustrative bank with 533,765 of book equity, 48,000 of goodwill and 7,873,765 of assets has TCE of 485,765 and a TCE ratio of 6.21 per cent, while it reports a CET1 ratio of 11.40 per cent. Add the after-tax loss on its held-to-maturity securities and the ratio is 2.09 per cent.
Worked in full in Bank Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
TCE is the measure the market turns to when it stops trusting the regulatory one. It strips out assets that cannot absorb a loss, uses no risk weights and does not filter unrealised losses. That makes it simple to compute and easy to compute in more than one way, so the version matters.
Sagebrook National Bank, the fictional bank of the case, at the end of a year in which market rates rose 425 basis points. Thousands of dollars. Securities are marked with duration and convexity, net of 25 per cent tax. The bank has elected to keep unrealised gains and losses on available-for-sale securities out of CET1, as US banks outside the largest categories may under current rules.
| Input | Value |
|---|---|
| Book common equity, after the AFS loss in AOCI | 533,765 |
| Goodwill (the only intangible) | 48,000 |
| Total assets | 7,873,765 |
| Available-for-sale securities, after-tax mark | −153,835 |
| Held-to-maturity securities, 1,640,000 at cost: after-tax mark | −328,875 |
| Risk-weighted assets | 5,610,000 |
| Published CET1 | 639,600 |
TCE = common equity − goodwill − other intangibles
Tangible assets = total assets − goodwill − other intangibles
TCE ratio = TCE ÷ tangible assets
Common equity excludes preferred stock. Intangibles include core deposit and other acquired intangibles; mortgage servicing rights are usually left in. In Excel: =(Equity-Goodwill-Intang)/(Assets-Goodwill-Intang).
Step 1: TCE. 533,765 − 48,000 = 485,765. The book equity already carries the 153,835 after-tax loss on the available-for-sale book through accumulated other comprehensive income.
Step 2: tangible assets. 7,873,765 − 48,000 = 7,825,765.
Step 3: divide. 485,765 / 7,825,765 = 6.207 per cent, 6.21 rounded.
Step 4: the held-to-maturity mark. The 1,640,000 held-to-maturity book has a duration of 7.8 and loses 26.74 per cent of its value in the shock, 438,500 gross and 328,875 after tax. None of it is in book equity. Take it off both the numerator and the denominator: 156,890 / 7,496,890 = 2.09 per cent.
| Measure | Numerator | Denominator | Ratio |
|---|---|---|---|
| CET1, as published | 639,600 | 5,610,000 | 11.40% |
| TCE ratio | 485,765 | 7,825,765 | 6.21% |
| TCE ratio, HTM marked | 156,890 | 7,496,890 | 2.09% |
The 5.19 point gap between CET1 and TCE has two sources. The numerator differs by exactly the filtered available-for-sale loss, 153,835. The denominator differs because risk-weighted assets are 71.7 per cent of tangible assets: CET1 over tangible assets would be only 8.17 per cent. The held-to-maturity mark then takes another 4.11 points off. What is left, 156,890, is 24.5 per cent of the published capital.
TCE is also the numerator of tangible book value per share, the base on which bank shares are usually priced. An investor paying 1.2 times tangible book for this bank is paying 1.2 times 485,765, not 1.2 times the 639,600 of regulatory capital, and a fall in TCE from unrealised losses feeds straight into the valuation even when CET1 has not moved.
None of the three is wrong. CET1 is the number the supervisor enforces, TCE is what a shareholder owns after writing off goodwill, and the third is what a buyer would see before valuing the deposits. The full purchase-price reading, with the loan mark and the deposit franchise, is worked in what a buyer actually pays for a bank.
| Rise, bp | Retained earnings | AFS mark, net | HTM mark, net | CET1 | TCE ratio | TCE, HTM marked |
|---|---|---|---|---|---|---|
| 0 | 40,901 | 0 | 0 | 11.96% | 8.37% | 8.37% |
| 100 | 33,536 | −39,648 | −91,574 | 11.83% | 7.83% | 6.76% |
| 200 | 26,171 | −77,172 | −174,414 | 11.70% | 7.31% | 5.22% |
| 300 | 18,806 | −112,572 | −248,521 | 11.57% | 6.81% | 3.77% |
| 425 | 9,600 | −153,835 | −328,875 | 11.40% | 6.21% | 2.09% |
CET1 moves only through retained earnings, 56 basis points across the whole range. TCE moves with the available-for-sale mark, and the held-to-maturity version collapses from 8.37 to 2.09. On this balance sheet, the held-to-maturity book is the larger and longer of the two, so the measure that excludes it misses most of the damage.
Subtract intangibles from both sides and divide: 6.21 per cent for a bank that publishes 11.40, and 2.09 once its held-to-maturity securities are marked. Print all three side by side, as the case does. Bank Management reads one balance sheet four defensible ways, and the free workbook for this case returns every reading at once from your own balance sheet, with the bridge between them closing to the dollar. The rate risk behind the marks is measured in EVE sensitivity for a bank.
CET1 is a regulatory numerator over risk-weighted assets; TCE is an accounting numerator over tangible assets, with no risk weights and no filter for unrealised losses on available-for-sale securities. On an illustrative bank CET1 of 639,600 over 5,610,000 of risk-weighted assets is 11.40 per cent, while TCE of 485,765 over 7,825,765 of tangible assets is 6.21 per cent.
Not as usually reported, because held-to-maturity securities are carried at amortised cost. Analysts often add the after-tax mark. On an illustrative bank after a 425 basis point rise, the held-to-maturity book loses 328,875 after tax, and TCE falls from 485,765 to 156,890, a ratio of 2.09 per cent instead of 6.21.
There is no regulatory minimum; it is a market and rating-agency measure. As an illustration, a bank holding 485,765 of TCE against 7,825,765 of tangible assets is at 6.21 per cent, and the same bank before the rate rise was at 8.37. The figure is best read beside CET1 and beside the held-to-maturity mark rather than against a single threshold.
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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