Bank runs and liquidity mismatch: why assets and available cash are different

Liquidity concerns meeting payments when they come due

Liquidity asks whether an institution can obtain the cash needed for current obligations on feasible terms. Solvency asks whether assets are sufficient for liabilities under an appropriate valuation. The two can interact: an urgent sale at a low price can impair asset value, while doubts about value can make funding harder to obtain. They remain distinct questions with different time horizons.

The liquidity-mismatch withdrawal game starts with fifty unit deposits, ten units of cash and forty units in a long asset. The long asset returns 1.5 per unit at maturity but only 0.5 if liquidated early. Diamond and Dybvig’s paper supplies the classic bank-run framework. The Modic game isolates cash-flow accounting; it does not solve the full strategic model or forecast the behaviour of any actual bank.

Worked example: the same assets, different withdrawal timing

Every amount below is an invented teaching unit. The exercise contains no deposit insurance, central-bank facility or external funding source; adding one would change the feasible payments.

1. Request ten early withdrawals. The initial cash pays them without liquidating the long asset. Forty late deposits remain, backed by the asset’s maturity value of sixty, or 1.5 per remaining depositor under the board’s payout rule.
2. Reset and request thirty early withdrawals. After the cash pays ten, another twenty units of cash are needed. At a liquidation price of 0.5, obtaining them requires selling all forty units of the long asset.
3. Inspect the remaining claims and maturity assets. Twenty late deposit claims remain while no long asset remains to pay them. If requests exceed available liquidation proceeds, unpaid early claims also remain claims; they do not vanish because the board runs out of cash.

Accounting reveals a mechanism, not a failure probability

The exercise lets you select withdrawal demand directly. It does not model why depositors withdraw, what they know or which equilibrium they expect others to select. Those are central questions in a strategic run model. Treating a selected high-withdrawal scenario as a measured chance of a real run would confuse a stress case with an estimated probability.

An actual institution also has many asset maturities, funding sources, collateral arrangements and legal rules. The point of the small model is to make the missing questions concrete: how quickly can assets be converted, at what prices, with which obligations ahead of others? A claim that everything is fine because final asset value is high skips timing. A claim that every cash shortage proves insolvency skips valuation and available funding.

Insurance compares a different distribution of outcomes

The insurance-deductible simulation asks how a stated loss probability, premium loading and deductible change wealth in loss and no-loss states. Its displayed certainty equivalent uses logarithmic utility. OpenStax’s insurance chapter provides context about insurance and imperfect information. The selected utility function makes the preference calculation explicit instead of claiming to measure your own risk tolerance.

Under fair full coverage in the toy example, a forty-unit loss with probability one-quarter costs an expected premium of ten, leaving ninety in either state from initial wealth one hundred. With a loading or deductible, the outcome distribution changes. This is an expected-utility exercise about one specified loss; it does not price every risk, model claim denial or show that a particular real policy is appropriate.

Questions to ask about a risk claim

Use these to turn a reassuring or alarming headline into a request for information. They identify what the claim would need to specify before it could support a conclusion.

• Write a dated list of payments due and assets available. Separate maturity value, current market value and proceeds from an urgent liquidation.
• State which scenario is chosen and which probability, if any, is estimated. A severe selected stress does not itself quantify its likelihood.
• Keep unpaid claims on the ledger. Record priority, legal protection and funding facilities if they matter; do not assume them into or out of a real institution.
• Distinguish a mathematical preference calculation from a personal recommendation. Check the loss definition, coverage exclusions, premium and resources available outside the model.

Drawdown recovery adds the changing-base problem

In the drawdown-recovery experiment, a fifty-percent loss followed by a fifty-percent gain turns one hundred into seventy-five. The percentages use different bases. Returning from seventy-five to one hundred then requires a gain of one-third. The historical maximum drawdown remains fifty percent even though the current shortfall has narrowed to twenty-five percent.

This arithmetic is exact for the selected path, but it does not forecast the next return. Like the withdrawal ledger, it rewards careful attention to what a number measures and when it is measured. Before comparing two risk summaries, check whether they describe current cash, terminal wealth, a historical peak loss or a utility-weighted evaluation. Each may be useful without answering the others.