How banks earn, and how loans go bad

A bank is a spread business

A bank gathers deposits at one rate and lends at a higher rate. The gap between the interest it pays and the interest it earns is net interest income, and for most retail banks that gap is the core of profit.

The arrangement works because depositors are happy to keep money liquid while borrowers want to keep a loan for years. The bank promises instant access on one side of the balance sheet and accepts slow repayment on the other.

That mismatch creates the bank's real risk. Loans cannot be called back quickly, so a bank depends on confidence: if every depositor asked for cash on the same day, no bank could pay them all at once.

Net interest margin

A bank holds 8,00,000 in loans earning 9% and funds them with 7,20,000 of deposits costing 4%. Interest income is 72,000 and interest expense is 28,800, so net interest income is 43,200. Against earning assets of 8,00,000 that is a net interest margin of 5.4%.

Subtract operating costs of 20,000 to reach pre-tax profit of 23,200. After tax at 25% the bank keeps 17,400. On assets of 8,00,000 that is a return on assets of about 2.18%; on equity of 80,000 it is a return on equity of 21.75%.

Thin capital, large consequences

Only 80,000 of the 8,00,000 balance sheet is equity; the rest is owed to depositors and other creditors. Equity is therefore 10% of assets, meaning every 1 of capital supports 10 of assets.

Leverage magnifies a small return on assets into a large return on equity, but it magnifies losses in exactly the same way. A loan book that loses 10% of its value can erase all of the equity at once.

This is why banks are regulated on capital rather than on profit. A capital ratio of 10% is a buffer, and the buffer is what stands between a bad year and a failed bank.

Expected credit losses

Lenders price loans for the losses they expect, not just for the ones they fear. Expected loss combines three estimates: how likely a borrower is to default, how much is lost if they do, and how much is owed at that moment.

Across a 10,00,000 portfolio with a 3% probability of default and a 60% loss given default, expected loss is 18,000. The bank must earn more than that from performing loans to make the book worthwhile.

Unexpected loss, the amount beyond the average, is what capital is held against. Provisioning for the average and capitalising the tail is the split that keeps a bank solvent through a bad year.