Bank A
| Assets | Liabilities + equity | ||
|---|---|---|---|
| reserves | 100 | deposits | 300 |
| loans | 200 | borrowing | 0 |
| bonds | 40 | equity | 40 |
| Total | 340 | Total | 340 |
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Monetary systems · Lesson 6
Why banks cannot lend without limit
Separate profitability, capital, liquidity, and confidence.
By the end: Diagnose whether a bank needs funding, loss absorption, or both.
Capital is loss-absorbing funding
A bank's equity is the difference between asset values and liabilities. If it has assets 100 and liabilities 92, it has equity 8. A previously unrecognized loss of 10 makes equity negative 2 at those valuations. Borrowing another 10 adds assets and liabilities equally. It supplies liquidity but does not repair the negative equity. New share capital or a credible restructuring changes the loss-absorbing position.
Regulators impose capital requirements, including ratios to risk-weighted assets and leverage measures. Risk weights attempt to distinguish exposures, while leverage limits also constrain size without relying on those weights. Reported regulatory capital is not identical to simple book equity. Our arithmetic uses a hypothetical equity-to-assets rule to isolate the mechanism; it is not a Basel rule or a real bank's requirement.
Calculate capacity to absorb losses before lending
Capital describes claims that can absorb losses under the relevant rules. In our simple books, equity is assets minus liabilities. Imagine an additional paper bank with assets 500, deposit liabilities 430, borrowing 30, and equity 40. Deposits and borrowing sum to 460. If asset values fall by 25 while those obligations remain unchanged, assets become 475 and equity becomes 15. The shareholders' residual shrinks first in this accounting example. The bank has not paid depositors 25, and their claims have not disappeared. The question is how much value remains after honoring the obligations.
Borrowing 25 afterward does not restore the lost equity. If the loan arrives as reserves, assets rise from 475 to 500 and borrowing rises from 30 to 55. Total liabilities become 485, leaving equity 15. Issuing new shares for 25 has a different counterpart. Assets rise to 500 but liabilities stay 460, so equity becomes 40. The new shareholders have supplied loss-absorbing funding instead of creating another fixed debt claim. The bank's owners and lenders have different rights, and the accounting must reflect which contract was issued.
The hypothetical rule displayed below requires equity equal to at least 10% of total assets. This means one unit of equity for every ten units of assets. Consider a separate bank with assets 150 and equity 18. Ten percent of 150 is 15, so it currently exceeds the requirement by 3. If new loans create deposits without changing equity, maximum assets under this one rule are 180. Lending 30 would bring assets to 180 and equity would remain 18. The initial excess equity of 3 supports 30 of expansion under this assumed ratio, not 3.
Now let that bank recognize a fresh loss of 4 before lending. Assets fall to 146 and equity to 14. The required equity on assets 146 is 14.6, so the bank is below the hypothetical minimum despite positive equity. Positive equity and compliance with a capital requirement are therefore different tests. The institution can have assets worth more than its liabilities yet still lack the margin required for continued operations under the rule. A regulator's response requires institutional details; the arithmetic alone does not say that a particular remedy is available or sufficient.
Actual regulatory capital is more complicated than this book-equity fraction. Some instruments qualify under specified conditions, some reported assets or gains receive adjustments, and exposures can include commitments not represented in this small balance sheet. Risk-weighted measures give different exposures different weights; leverage measures constrain size without that same weighting. Consequently, our calculation explains why expansion can use capital capacity but cannot certify a real bank's compliance. A reserve balance is an asset inside the denominator, not a substitute name for equity in the numerator. More settlement assets do not automatically mean more loss absorption.
Liquidity is the ability to pay on time
A bank often funds long-lived loans with deposits withdrawable on demand. This maturity mismatch makes a solvent institution vulnerable to a run. Depositors may demand payment before loan repayments arrive. Selling assets quickly can realize losses, turning a liquidity problem into a solvency problem. Fear of later losses can itself motivate withdrawal.
Deposit insurance protects eligible balances under jurisdiction-specific limits and conditions. It can reduce incentives to run, but neither covers every creditor nor makes every bank asset safe. Central-bank liquidity can support eligible institutions against collateral. Supervision, capital, and resolution rules address risks that liquidity alone cannot fix. Moral hazard arises if protection encourages risks whose losses someone else expects to bear.
Match due payments to available assets
Liquidity concerns amounts and dates. Suppose a bank has reserves 15, loans worth 90, deposits 95, and equity 10. Its assets exceed liabilities by 10. If customers request an external transfer of 25 today, however, the bank lacks 10 of reserves under a rule requiring settlement without an overdraft. Expected loan receipts next month do not settle an obligation due now. A complete liquidity assessment asks when cash arrives, which obligations can be demanded early, and which assets can be converted into the required payment instrument before the deadline.
Maturity is the date an obligation falls due. A five-year loan and a demand deposit can have the same face amount but very different maturity terms. The depositor may request payment today while the bank cannot demand immediate repayment of a performing five-year loan. That mismatch is not the same as an accounting imbalance. Both sides can be recorded correctly and still expose the bank to withdrawal pressure. The bank may plan to use reserve buffers, ordinary incoming payments, asset sales, or eligible borrowing, but those sources have prices and conditions.
A forced sale can connect liquidity pressure to losses. In a separate paper example, a bank records a bond at 50 but can sell it immediately for only 43. Selling provides 43 of liquid assets and removes a bond recorded at 50. The difference of 7 reduces equity if it was not already recognized. A bank with equity 6 before this unrecognized loss would have negative equity of 1 afterward. The sale can make today's payment possible while exposing a pre-existing valuation problem. Calling the sale a liquidity operation does not remove the loss.
Borrowing against the bond can avoid selling at that moment, but does not guarantee full funding. If the lender assesses collateral value at 43 and applies a 20% haircut, it advances 80% of 43, which is 34.4. A need for 40 would remain partly unmet. The lender also needs the legal right to take collateral and rules for valuation and repayment. A bank cannot assume that every asset listed at 50 supports a loan of 50. Changes in market value or facility eligibility can reduce borrowing capacity precisely when funding is under pressure.
Deposit insurance and central-bank facilities change some incentives and payment options, but they are institutional arrangements rather than balance-sheet identities. Insurance may protect eligible depositors up to specified limits while excluding other creditors or balances. Its payout arrangements and timing matter to someone needing funds now. Central-bank access may require approved counterparties, acceptable collateral, and solvency conditions. A statement that a bank has valuable long-term assets therefore does not prove it can borrow whatever amount it needs, and a statement that support exists does not establish that every depositor or creditor is protected.
Work through the accounts and assumptions
A hypothetical capital constraint
This teaching rule uses book equity and total assets. It is not a real regulatory capital requirement.
Inspect both banks' books
Currency units. Both banks remain visible. Δ means change from the opening snapshot. Choose a named experiment; changing it resets playback and all balances.
Opening balance sheets
Bank B
| Assets | Liabilities + equity | ||
|---|---|---|---|
| reserves | 100 | deposits | 300 |
| loans | 200 | borrowing | 0 |
| bonds | 40 | equity | 40 |
| Total | 340 | Total | 340 |
System deposits: 600. System reserves: 200.
Each bank has 340 assets, 300 deposit liabilities, and 40 equity. No cash or other banks are included.
Step 0 / 4
All stages and totals
| Stage | Deposits | Reserves | A equity |
|---|---|---|---|
| Opening balance sheets | 600 | 200 | 40 |
| Customers move 80 deposits to B | 600 | 200 | 40 |
| A further 40 payment cannot settle yet | 600 | 200 | 40 |
| An assumed eligible central-bank loan adds 40 | 600 | 240 | 40 |
| The delayed 40 payment settles | 600 | 240 | 40 |
Opening balance sheets. Each bank has 340 assets, 300 deposit liabilities, and 40 equity. No cash or other banks are included.
Customers move 80 deposits to B. A now has 20 reserves. Total reserves remain 200. A has positive equity but less payment capacity.
A further 40 payment cannot settle yet. The lab blocks the payment: A has only 20 reserves. No entries are posted. Other sources of liquidity are not automatic.
An assumed eligible central-bank loan adds 40. A gains reserves and borrowing of 40. The central bank, not shown, gains a loan asset and reserve liabilities of 40. Eligibility and adequate collateral are assumed, not tested.
The delayed 40 payment settles. A can now transfer 40 reserves to B. Equity remains 40. The banking system has 240 reserves and owes the central bank 40.
| Problem | Immediate symptom | What changes the relevant constraint? |
|---|---|---|
| Liquidity shortage | Cannot settle today | Eligible funding or liquid-asset sale |
| Asset losses | Equity falls | New equity, earnings, or restructuring |
| Unprofitable lending | Expected returns too low | Different pricing, costs, or risks |
Read the funding operation without treating it as capital
Withdrawal pressure is the initial experiment on this page. Both banks begin with assets 340, deposits 300, and equity 40. A's first transfer of 80 reduces its reserves from 100 to 20 and deposits from 300 to 220. Assets are 20 plus 200 plus 40, totaling 260. Liabilities plus equity are 220 plus 40, also 260. The equity amount is unchanged. A has fewer immediately usable settlement assets, even though its equity is a larger fraction of its smaller asset total. A capital ratio can improve while payment capacity becomes more constrained.
The next requested payment is 40, but A has only 20 of reserves. The model displays a blocked stage without posting entries. A's assumed central-bank loan then adds 40 of reserves and borrowing. Assets rise to 300, matched by deposits 220, borrowing 40, and equity 40. After the delayed payment settles, reserves return to 20, deposits fall to 180, and borrowing remains 40. Assets are 260 again. A owes fewer deposits but now owes the central bank. The funding has changed its liquidity and the composition of its liabilities without changing equity.
B receives both customer transfers and ends with reserves 220 and deposits 420, with its other opening categories unchanged. System reserves rise from 200 to 240 because the central bank supplied 40, not because either customer transfer created them. System deposits remain 600. A's remaining reserves of 20 cannot repay borrowing of 40 immediately without another source of liquidity. The sequence does not model repayment of that funding, collateral returns, interest charges, or future loan receipts. It demonstrates completion of the delayed transfer under an assumed facility, not a complete recovery plan.
Select Loan loss for the contrasting capital case. It begins from the opening balances, not from the funded state just examined. A loses 60 of loan value and equity falls from 40 to negative 20, while reserves remain 100. A can have more reserves than in the withdrawal example yet a worse loss-absorbing position. Choosing experiments resets balances and playback; Reset returns the selected experiment to its opening snapshot. The controls do not permit adding central-bank borrowing to the loss scenario. For that combination, use a separate paper calculation rather than assuming the interface has tested eligibility.
On paper, start from that loss state with assets 280, deposits 300, and equity negative 20. A further reserve loan of 30 would raise assets to 310 and add borrowing of 30. Liabilities would be 330 and equity would remain negative 20. Nothing in the balanced entries says that a central bank would lend in those circumstances. Conversely, a share contribution of 30 in settlement assets would raise assets to 310 while leaving liabilities 300, producing equity 10. Even that positive equity does not demonstrate compliance with every requirement or eliminate upcoming payment obligations.
The lending decision has several constraints
A bank compares expected interest and fees with funding costs, operating costs, expected losses, and the cost of required capital. It also needs willing, creditworthy borrowers and a plan for payment outflows. Extra reserves can help with liquidity without making a bad borrower safe or supplying equity. Extra equity can absorb losses without guaranteeing that the bank has the right settlement asset today.
Borrowing against collateral also has limits. If collateral worth 100 has a 20% haircut, the maximum advance under that rule is 80. Whether a bank can access such credit, and whether the collateral remains worth 100 during stress, are separate questions. Stress tests vary these assumptions rather than treating one good-looking ratio as proof of safety.
Combine profitability, capital, and liquidity constraints
A lending decision needs an expected income calculation as well as balance-sheet capacity. Consider an additional one-year paper loan of 100 charging interest of 7. Assume funding costs attributable to the loan are 3, operating costs are 1, and expected credit losses are 2. Subtracting those amounts from interest leaves 1 before tax and any further required return on shareholders' funds. The contractual interest rate is 7%, but expected net income is not 7. If expected credit losses rise to 4 while the other assumptions remain fixed, the expected result becomes a loss of 1.
An expected credit loss is an average under specified risk assumptions, not a claim that the bank will collect exactly 98 on every loan of 100. One illustrative portfolio could contain 100 equal loans with a complete loss of principal on two and full principal recovery on the other 98, ignoring timing and recoveries. That produces an average principal loss of 2 per 100 lent across that constructed portfolio. A different concentration of losses can threaten the bank even with the same average. Capital provides protection against adverse outcomes; calculating an expected profit does not make losses impossible.
Funding cost and deposit creation are consistent with each other. A can create a deposit when granting a loan without first transferring an existing customer's money. If the borrower then pays someone at B, A must fund the settlement outflow. It may use reserves that have an alternative return, borrow, attract deposits, or sell assets. Those choices have costs and risks. Origination accounting therefore does not imply costless lending. Nor does a bank's ability to obtain funding prove that the borrower's project generates enough income to service its debt.
Separate constraints can bind at different stages. Suppose a bank can fund a proposed 50 payment outflow but is already at its hypothetical capital limit. More borrowing can improve available reserves while leaving the capital constraint unsolved, and can expand total assets while funds remain unspent. Another bank may have ample equity but insufficient eligible collateral for today's funding need. A third may have both capacity measures but reject the loan because its expected return is negative. These are distinct reasons for refusing credit, even when each refusal appears to the customer simply as a rejected application.
A useful paper stress comparison changes one assumption at a time. Start with assets 300, liabilities 270, and equity 30, including reserves 20. A loss of 12 leaves assets 288 and equity 18 without increasing reserves. A transfer of 15 instead leaves reserves 5, assets 285, liabilities 255, and equity 30. The loss damages the residual; the transfer reduces a liquid asset and a deposit obligation together. Applying both leaves reserves 5, assets 273, liabilities 255, and equity 18. These calculations identify the separate shortfalls. They do not prescribe a rescue, establish legal access to funding, or predict how depositors will behave.
Exercises
A simple lending ceiling
A bank has assets 200 and equity 20. A hypothetical rule requires equity of at least 10% of assets. New loans create matching deposits and no immediate profit or loss. How much extra lending fits the rule? What if shareholders first contribute 10 in cash?
Hint
Equity issuance increases both equity and assets before new lending.
Worked answer
| Position | Equity | Assets | Maximum assets at 10% |
|---|---|---|---|
| Initial | 20 | 200 | 200 |
| After contribution | 30 | 210 | 300 |
| After 90 lending | 30 | 300 | 300 |
Initially it has no room: 20 is exactly 10% of 200. After the contribution, assets are 210 and equity 30. The rule permits assets up to 300, leaving room for 90 of additional lending. Real requirements include other constraints, so this is only the stated simplified limit.
A loan is not a recapitalization
A bank has assets 98 and liabilities 100. A central bank lends it 15. Has the loan restored positive equity?
Hint
Add the reserve asset and borrowing liability together.
Worked answer
| Before | After liquidity loan | |
|---|---|---|
| Assets | 98 | 113 |
| Liabilities | 100 | 115 |
| Equity | −2 | −2 |
No. Assets become 113 and liabilities 115, leaving equity negative 2. The bank has more liquidity. The example does not establish its eligibility for central-bank credit or justify lending to an insolvent institution.
Sources and further reading
These references support the mechanisms and identify institutional context. They are optional; the explanations and worked answers above stand alone. Numerical examples are teaching cases, not live financial data or personal financial advice.
- Bank of England: What is capital?
Loss absorption and prudential oversight. Our equity-to-assets example is deliberately simpler than regulatory capital rules.
- Bank of England: Money creation in the modern economy, 2014
Bank lending, deposit creation and destruction, constraints, and asset purchases. UK institutional explanation, not a universal timetable or a current rate announcement.