School Launch

Run a Bank

Build a bank’s balance sheet, set the rate on every line, and read its profit, margin and cushion of equity the way an examiner would. Then stress it: raise interest rates and watch long fixed-rate bonds lose value, or send depositors to the door and see how far the bank’s cash and bonds will stretch.

Banking Lessons 1.3, 2.1, 2.2, 2.3, 2.4, 2.5, 3.3 and 9.4 · about 25 minutes

Net interest income
Net interest margin
Net income
Return on assets (ROA)
Return on equity (ROE)
Equity-to-assets

Income statement for one year

NIM = net interest income ÷ earning assets. Efficiency ratio = operating expenses ÷ (net interest income + fees); lower is leaner. ROE = ROA × assets ÷ equity, which is why a thin cushion magnifies both good years and bad ones.

Rate shock

The 1980s lesson: savings and loans had funded 30-year fixed-rate mortgages with short-term deposits, so when rates soared they paid more for deposits than their old mortgages earned, and hundreds failed.

Bank run

What the bank owns (assets)

Amounts in millions of dollars; rates are yearly.

$ millionrate %
%

Where the money came from

$ millionrate % Equity (the plug)

Equity = assets − deposits − borrowings, so the two sides always balance.

Fees, costs and taxes

Stress tests

points
% of deposits

Try an example

Banks from the course’s worked examples, with rates and costs made up for the example.

Reading a bank

Every balance sheet obeys assets = liabilities + equity. Your deposit is your asset but the bank’s liability, because the bank owes it to you. The loans the bank makes are its assets, because borrowers owe the bank. Equity is what is left over: the owners’ money at risk, and the cushion that absorbs losses before any depositor is touched.

How a bank earns

The bank earns interest on loans and securities and pays interest on deposits and borrowings. The difference is net interest income; divided by the earning assets it is the net interest margin, a few percent at most banks. Add fees, subtract operating costs and a provision for loan losses (money set aside for loans that will not be repaid), then taxes, and what remains is net income.

ROA = net income / assets     ROE = net income / equity

A healthy bank’s ROA is often about 1%. Because each dollar of equity carries many dollars of assets, ROE is much larger, and a loss of a few percent of assets can wipe out a large share of the owners’ money.

Borrowing short, lending long

Deposits can leave any day and their rate can change any month, but a 10-year bond or a fixed-rate mortgage keeps its rate for years. When rates rise, the bank must pay more to keep depositors while old fixed-rate assets keep paying the old rate, and an old bond is worth less, because a buyer can get a new one paying more. The page values the bonds at the new rate with

price = c(1 − (1 + y)−n) / y + (1 + y)−n,

per dollar of face value, where c is the bond’s own rate, y the new market rate and n the years left.

What the model assumes

In the rate shock, deposits, borrowings and the adjustable share of loans reprice by the full amount at once; cash, bonds and fixed-rate loans keep their rates. (Real deposit rates usually lag, so the hit to income is often slower.) Only the bonds are marked to market; fixed-rate loans also lose value, but it shows up here as lower income. In a run, the bank pays first from cash and then sells bonds at today’s price, which turns a paper loss into a real one.

Check yourself

  1. A bank has cash and reserves of $15 million, securities of $20 million and loans of $250 million. It owes depositors $250 million and has other borrowings of $7 million. What is its equity, and its equity-to-assets ratio?
    Answer

    Assets: $285 million; liabilities: $257 million; equity $28 million. Equity-to-assets: 28 ÷ 285 = 9.82%, about $10.18 of assets for each dollar of equity. Load the community bank to see it.

  2. In the community bank example, find the net interest income and the net interest margin.
    Answer

    Interest earned: $20M × 4% + $250M × 6.5% = $0.8M + $16.25M = $17.05M. Interest paid: $250M × 2% + $7M × 5% = $5.35M. Net interest income: $11.7 million. Earning assets are $270 million, so NIM = 11.7 ÷ 270 = 4.33%.

  3. Load the 1980 thrift. What happens to its net interest income when deposit rates go from 4% to 9%, and about how long does its equity last?
    Answer

    Before: $6M − $3.8M = $2.2 million. After: $6M − $8.55M = −$2.55 million a year, because the mortgages still earn 6%. The $5 million of equity lasts about 5 ÷ 2.55 ≈ 2.0 years.

  4. Load the bond-heavy bank. Its $50 million of 10-year bonds pay 3%, and rates rise 2 points. How much do the bonds lose, and what is left of the $8 million of equity?
    Answer

    Each $1,000 bond is now worth $845.57 (=PV(5%, 10, 30, 1000) gives −845.57), a 15.44% drop. On $50 million that is about $7.72 million, leaving only about $0.28 million of equity at market value. If a run forces the bank to sell, the loss becomes real.

  5. Load the rumor run. The bank keeps $3.2 million of cash against $32 million of deposits, and depositors ask for 15%. What must it raise?
    Answer

    Withdrawals: 15% × $32M = $4.8M. Cash covers $3.2M, so the bank must raise $1.6 million by selling assets or borrowing. With no bonds to sell, it must borrow or sell loans, often at a discount.

A bit of history: Deposit insurance began in 1934, after waves of runs in the early 1930s. Since then, according to the FDIC, no depositor has lost a penny of insured funds, and runs by insured depositors have become rare. Uninsured depositors are still the first to leave when worry spreads.

“The prudent man foreseeth the evil, and hideth himself.” — Proverbs 22:3