Return on assets measures how well a bank earns on its balance sheet; return on equity multiplies it by leverage, which is why the two have to be read together.
A bank's return on assets is net income divided by average total assets, and its return on equity is net income divided by average common equity. An illustrative bank earning 72,000 on 8,000,000 of average assets and 667,000 of average equity has an ROA of 0.90 per cent and an ROE of 10.79 per cent. The bridge between them is leverage: ROE = ROA × average assets / average equity, and here the multiplier is 11.99.
Worked in full in Bank Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Return on assets measures how much a bank earns on its balance sheet, whatever funds it. Return on equity measures what shareholders earn, and it rises with leverage as much as with performance. A bank can lift its ROE by holding less capital, without lending better or running cheaper. That is why bank analysts start with ROA, decompose it line by line against assets, and only then multiply by leverage.
| Input | Value |
|---|---|
| Total assets, opening and closing | 7,900,000 / 8,100,000 |
| Common equity, opening | 640,000 |
| Net interest income | 229,000 |
| Fee and other income | 41,000 |
| Operating expenses | 148,000 |
| Provision for credit losses | 26,000 |
| Tax rate | 25% |
| Dividends paid | 18,000 |
| Goodwill | 48,000 |
All figures are fictional and chosen to show the mechanism. Net income here is entirely attributable to common shareholders; where a bank has preferred stock, deduct the preferred dividends from net income before computing ROE, but not before computing ROA, which measures the return on the whole balance sheet whoever funds it.
1. Pre-tax income = 229,000 + 41,000 − 148,000 − 26,000 = 96,000; tax 24,000; net income 72,000.
2. Closing equity = 640,000 + 72,000 − 18,000 = 694,000. Average equity = (640,000 + 694,000) / 2 = 667,000.
3. Average assets = (7,900,000 + 8,100,000) / 2 = 8,000,000.
4. ROA = 72,000 / 8,000,000 = 0.90%.
5. ROE = 72,000 / 667,000 = 10.79%.
6. Check: equity multiplier = 8,000,000 / 667,000 = 11.99, and 0.90% × 11.99 = 10.79%.
In Excel: =NI/AVERAGE(Assets_open,Assets_close) and =NI/AVERAGE(Equity_open,Equity_close).
Dividing every line of the income statement by average assets turns the ROA into a sum anyone can compare across banks of different sizes.
| Line | % of assets |
|---|---|
| Net interest income | 2.8625 |
| Fee and other income | 0.5125 |
| Operating expenses | −1.8500 |
| Provision for credit losses | −0.3250 |
| Pre-tax ROA | 1.20 |
| Tax | −0.30 |
| ROA | 0.90 |
Read this way, the bank's ROA is a margin business with a cost base that absorbs almost two-thirds of the margin: its efficiency ratio is 148,000 / 270,000 = 54.81 per cent, as worked in how to calculate a bank's efficiency ratio. Doubling the provision to 52,000 cuts net income to 52,500, the ROA to 0.66 per cent and, with average equity held at 667,000, the ROE to 7.87. Because the multiplier is 11.99, every basis point of ROA is worth 0.120 points of ROE.
| ROA | Equity 7.0% of assets | 8.34% (this bank) | 10.0% |
|---|---|---|---|
| 0.70% | 10.00% | 8.40% | 7.00% |
| 0.90% | 12.86% | 10.79% | 9.00% |
| 1.10% | 15.71% | 13.19% | 11.00% |
The same 0.90 per cent ROA produces an ROE from 9.00 to 12.86 per cent depending only on capital. A peer earning 0.75 per cent on assets with equity of 6.0 per cent, a multiplier of 16.67, reports an ROE of 12.50 per cent and looks better than this bank on the measure shareholders quote most. It is less profitable per dollar of assets and has less capital to absorb a loss.
ROE also sets how fast the bank can grow without new capital. It retains 54,000 of the 72,000, a payout of 25.0 per cent, so equity grows 8.44 per cent on its opening level. Assets growing faster than that dilute the capital ratio. Excluding goodwill, average tangible equity is 619,000 and the return on it is 11.63 per cent before the amortisation add-back; how that return becomes a valuation multiple is in what price to tangible book a bank should trade at.
The income statement behind these lines, with the margin and the deposit beta, is in the free workbooks for this case.
Analysts often treat a return on assets around 1 per cent as the mark of a solidly profitable commercial bank, but the level depends on the business mix and the rate cycle. The illustrative bank earns 0.90 per cent: 2.8625 per cent of net interest income on assets, plus 0.5125 of fees, less 1.85 of costs and 0.325 of provisions, before 0.30 of tax.
Because ROE is ROA times leverage. A peer earning 0.75 per cent on assets with equity of 6.0 per cent of assets has an ROE of 12.50 per cent, above the illustrative bank's 10.79 on a 0.90 ROA, simply because it holds less capital against each dollar of assets. The higher ROE carries a thinner cushion against loss.
Average balances, because net income is earned over the whole year. On year-end equity of 694,000 the illustrative bank's ROE reads 10.37 per cent; on opening equity it reads 11.25; on the average of the two, the consistent measure, it is 10.79.
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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