University of Toronto · FACULTY OF ECONOMICS

ECO349H5 Chap.8 Liquidity Transformation and Bank Runs

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Chapter 8 of 9 · ECO349H5

Liquidity Transformation and Bank Runs

Pooling, liquidation and belief

Banks transform liquid short-term claims into funding for longer-lived assets. Depositors value access before the assets naturally mature, while the asset side may deliver more only if held to completion. The bank therefore keeps reserves for normal early withdrawals and invests the remaining resources.

The arrangement can improve allocation through risk sharing, but it also creates exposure to unusually high withdrawals.

Locate the reserve threshold

Start with resources per unit of deposits. If withdrawals do not exceed reserves, promised early payments can be met without selling long assets. Once withdrawals cross the reserve share, the bank faces a cash gap.

The graph has a kink at that threshold because the marginal source of payment changes from available reserves to premature liquidation.

Liquidation recovery is the cash raised per unit of long asset sold. Divide the cash gap by that recovery rate to find the amount of project value that must be liquidated. Do not confuse cash obtained with assets surrendered.

When recovery is below the asset’s maturity payoff, raising one unit of cash destroys more than one unit of future value.

Separate liquidity from solvency

A bank is illiquid when it cannot meet payments on schedule without a costly sale, even though the maturity value of assets may exceed liabilities. It is insolvent when asset value is insufficient to cover promised liabilities.

Fire sales can turn a liquidity shortage into a solvency problem by destroying value, but the concepts remain distinct. State which balance-sheet test is being applied.

Maturity transformation is not itself evidence of insolvency. Under ordinary withdrawal demand, pooled reserves can serve early consumers while long assets earn their maturity return for patient depositors.

The vulnerability comes from a mismatch between immediate redemption promises and assets that are costly to realize early. More reserves reduce that exposure but also leave fewer resources in the high-return long technology.

Explain strategic withdrawal

Sequential service pays depositors in the order they arrive.

If a patient depositor expects others to wait, leaving funds in the bank can be optimal because the long asset matures. If the same depositor expects many others to withdraw, waiting may mean arriving after liquid resources have been exhausted.

Early withdrawal can then be individually rational even when everyone would prefer the no-run outcome.

This logic creates multiple equilibria under the model’s conditions: a stable outcome supported by confidence and a run supported by pessimistic beliefs. The explanation must contain the feedback loop.

Expected withdrawals lead to actual withdrawals, which force liquidation, shrink resources for those who wait and validate the incentive to withdraw. Simply writing that depositors panic omits the strategic mechanism.

Assess safeguards by channel

Deposit insurance can weaken the reason to run when the promise is credible, but pricing and supervision matter because protection can alter bank incentives.

A lender of last resort can supply temporary liquidity against assets, which addresses a timing problem more directly than an underlying capital shortfall. Reserve requirements provide immediate cash, while capital absorbs losses.

Match each instrument to the failure it is meant to contain.

For revision, draw the reserve kink, calculate a cash gap and liquidation quantity, then write the patient depositor’s choice under optimistic and pessimistic beliefs. Finish by testing a policy: identify whether it changes available cash, losses, depositor incentives or bank risk taking.

This sequence preserves the connection between accounting mechanics and equilibrium beliefs instead of treating bank runs as a purely psychological event.

In this chapter

What this chapter covers

  • 01

    Maturity transformation

  • 02

    Reserve share

  • 03

    Liquidation haircut

  • 04

    Sequential service

  • 05

    Run equilibrium

Worked example · free

Liquidate assets after reserves run out

Q [5 marks]. AskSia assigned five practice marks to this liquidity calculation; they are not an official University marking scheme. Reserves equal thirty percent of deposits, withdrawals reach forty percent and early liquidation recovers fifty percent. Find the long-asset value that must be sold.
Withdrawals up to the reserve share require no project sale; beyond that threshold, liquidation rises with the funding gap.Withdrawals up to the reserve share require no project sale; beyond that threshold, liquidation rises with the funding gap.Withdrawal share fProject liquidation Lreserves absorbforced sale1-x
Withdrawals up to the reserve share require no project sale; beyond that threshold, liquidation rises with the funding gap.
  • 2Subtract available reserves from early withdrawal demand to obtain the cash funding gap.
  • 3Divide the cash gap by the liquidation recovery rate to measure assets surrendered.
Withdrawals exceed reserves by ten percent of deposits. At fifty-percent recovery, the bank must sell project value equal to ten divided by 0.5, or twenty percent of deposits, to raise the needed cash.
Sia tip — Report the cash shortage and the larger amount of long assets liquidated as two different balance-sheet quantities.
Glossary

Key terms

Liquidity Risk
Liquidity Risk is the danger that cash obligations arrive before assets can be realized without loss.
Fire Sale
A Fire Sale is a rapid asset disposal at a depressed recovery value.
FAQ

Liquidity Transformation and Bank Runs FAQ

Why do banks hold reserves?

Reserves meet early withdrawals without destroying long projects. Holding too much sacrifices long returns, while holding too little exposes the institution to costly liquidation under normal demand.

How can a run be self-fulfilling?

Expected withdrawals exhaust reserves and force asset sales, reducing what remains for those who wait. Anticipating that loss gives patient depositors a reason to join the withdrawal surge.

Is illiquidity the same as insolvency?

No. Illiquidity concerns cash timing, while insolvency concerns asset value relative to liabilities. Forced liquidation can connect them, but the initial diagnosis requires the valuation date and recovery assumption.

Study strategy

Exam move

Draw the reserve kink, compute the funding gap, adjust for the haircut and narrate the belief feedback loop.

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