How a bank makes money

Pays you 1.5 percent. Lends it at 6. The difference is the business, and it has been the business for about eight hundred years.

Everything else a bank does — the app, the branches, the card, the mortgage adviser — is either a way of collecting deposits or a way of placing loans.

Three transformations

Size. Ten thousand deposits of 3,000 become one loan of 30,000,000. No saver could have made that loan; no borrower could have negotiated with ten thousand savers.

Time. Deposits are repayable today. Loans are repayable over decades. The bank absorbs the difference, which works perfectly until a large number of depositors want their money on the same morning.

Risk. Some borrowers do not repay. The saver is not exposed to any individual borrower; the bank is exposed to all of them, and prices that in.

For those three services it charges the gap between the two rates. Not a fee, a gap — which is why most people never think of themselves as paying a bank anything.

Predict

A bank has 1,000,000 of deposits. It pays 1.5 percent on them and lends at 6 percent. Roughly what does it earn in a year, before costs?

Choose one answer

45,000 — the gap of 4.5 points on the whole millionAbout 36,000, because only part of the deposits are lentAbout 60,000, since the loans are the main assetIt cannot be estimated without knowing the fees

Lock in answer

Run the bank

Below is a bank with a million of deposits. Everything that makes it profitable or not is on screen. The controls start at plausible settings; only the write-off rate moves.

Net interest margin

≈ Hypothetical model, not a forecast

A bank's core economics: pay one rate on deposits, charge another on loans, add fees, subtract losses.

It assumes

• Every deposit pays one rate and every loan charges one rate, forever.
• Fee income and operating costs are both flat shares of the loan book.
• Write-offs arrive smoothly rather than all in one bad year, which is not how they arrive.
• There is no equity, no capital requirement and no tax in this model.

It ignores

• Capital, leverage limits and the equity funding part of the balance sheet
• Rates that move, and the fact that deposit and loan rates move at different speeds
• Duration mismatch, which is how banks actually blow up
• Deposits leaving in a hurry
• Tax, which varies by jurisdiction and is out of scope here

Everything else held still, find the write-off rate at which this bank stops making money altogether. Note how small it is.

Loans written off each year0.5%

Loan book, final year

1,209,815

Interest earned

72,589

Interest paid away

21,350

Net interest income

51,239

Net interest margin

4.235%

Gap between the two rates

4.5%

Fee income

7,259

Operating costs

24,196

Loans written off

6,049

Profit before tax, final year

28,253

Profit before tax over the period

238,321

Costs against income

0.414

• Net interest income
• Operating costs
• Written off
• Profit before tax

◷ Not there yet — keep moving the controls.

Under three percent. A bank lending at 6 against deposits costing 1.5 is wiped out by a write-off rate of about 2.8 percent of its book.

That is the single most important thing to understand about banking, and it explains almost every regulation attached to it. The margin is thin, the leverage is enormous, and a modest deterioration in the quality of the loan book is not a bad year — it is the whole business.

Where the rest of the money comes from

The model has a fee income line at 0.6 percent of the book, which looks like a detail. In a real retail bank it is nothing of the kind — it is often a third or more of the total, and it behaves quite differently from the spread. That is the subject of the next lesson.

There is also a structural point hidden in the controls. Notice what happens when the deposit rate and the loan rate move by the same amount: nothing much. Notice what happens when they move by different amounts, which is what actually occurs — deposit rates tend to follow the market up slowly and come down quickly. Most of the variation in a retail bank's fortunes is in that lag.

Check

Central bank rates rise by two points. What tends to happen to a retail bank's margin in the following year?

Choose one answer

It is unchanged, because both rates rise togetherIt widens, because loan rates reprice faster than deposit ratesIt narrows, because savers demand more immediatelyIt depends entirely on the write-off rate

Check answer

Who pays, who benefits, who carries the risk

Who pays. The borrower pays the visible price, and the depositor pays an invisible one: the difference between what the money could have earned and what it was paid. Both halves of the spread come out of a customer.

Who benefits. The bank, on the gap. And genuinely, both customers — the borrower gets a mortgage no individual saver would have written, the saver gets instant access to money that has been lent for twenty-five years. Neither could have arranged that alone.

Who carries the risk. Mostly the bank, which is why underwriting is the whole job. But not entirely: the depositor carries the risk that the bank fails, which is why deposit protection schemes exist in most countries — and the state, and therefore the taxpayer, carries the tail of it.

Worth remembering

• A bank's core business is the gap between the rate it pays on deposits and the rate it charges on loans.
• It performs three transformations — size, time and risk — and the time one is what makes banks fragile.
• The spread between two rates and the net interest margin are different numbers, because deposits that are not lent still have to be paid for.
• In the worked example, a write-off rate of under three percent of the loan book wipes out the whole profit.
• Rising central bank rates usually widen a retail bank's margin at first, because loan rates reprice faster than deposit rates.