Bank Run — The Diamond-Dybvig Model

What a bank run actually is

A bank run is not, in the technical sense of the Diamond-Dybvig model, a verdict on the bank. It is a verdict on what depositors believe other depositors are about to do. A bank may be perfectly solvent — its long-dated loans worth more than its deposit liabilities at maturity — yet still go down in an afternoon because too many people want their money on the same day. The Diamond-Dybvig contribution was to show that this can happen as an equilibrium phenomenon, not just an accident, and that the very feature of banks that makes them useful — funding illiquid loans with liquid deposits — is the same feature that makes them runnable.

Strip the model to the bone and there are three actors: a bank, a large set of identical depositors, and a long-term productive technology that pays a high return at maturity but can only be partially salvaged if liquidated early. Depositors are uncertain whether they will need their money tomorrow (type 1: impatient) or in two periods (type 2: patient). The bank pools their deposits, invests in the long technology, and offers a deposit contract: any depositor showing up at date 1 gets a fixed amount r₁; any waiting until date 2 shares the proceeds of the long investment.

The clever insight is that this contract beats both pure autarky (each depositor invests alone) and a pure storage technology (everyone holds cash). Banks provide liquidity insurance: each individual depositor doesn't know if they'll need cash at date 1, but the bank knows the fraction of the population that will need it, and can plan accordingly. The bank's liabilities are more liquid than its assets — and that is the social purpose of banking.

Maturity transformation, the engine and the vulnerability

The bank's balance sheet is the source of both its productivity and its fragility:

• Liabilities (right side): demand deposits, redeemable on request at par. Short. Liquid.
• Assets (left side): mortgages, business loans, long-dated bonds. Long. Illiquid.

The bank borrows short and lends long. The spread between long rates and short rates is the bank's gross profit margin — call it the term premium that compensates patient capital. But the asymmetry is dangerous. If every depositor simultaneously demands par, the bank has to sell mortgages and bonds into a thin market, accept fire-sale haircuts, and may end up unable to pay everyone. The very liquidity it offers depositors does not exist on the asset side of its balance sheet.

This is what economists mean by maturity transformation: a structural mismatch in which the term of the liabilities is shorter than the term of the assets. In normal times it is invisible — the law of large numbers ensures that only a predictable fraction of depositors withdraw on any given day. In a panic, the law of large numbers fails because withdrawals are correlated.

Two equilibria, one balance sheet

Consider what a single rational depositor should do, taking other depositors' behaviour as given. There are two cases.

Belief about others	Best response	Payoff to me	Equilibrium
Only true liquidity-needers withdraw at date 1	Stay if I'm patient	r₂ > r₁ (long return)	Good equilibrium — bank operates, everyone gets the promised payoff
Everyone will withdraw at date 1	Withdraw immediately	r₁ if I get there in time; 0 if not	Run equilibrium — bank liquidates at a loss, late arrivals are wiped out

Both responses are individually rational. Both beliefs are self-confirming. Which one plays out depends on what economists call a sunspot — a public signal with no fundamental content, but enough common-knowledge salience to coordinate beliefs. A rumour. A news story. A bank's stock price falling. A tweet. The thing that distinguishes the run from the good equilibrium is not the bank's books but the depositors' beliefs about each other's beliefs.

This is the model's intellectually radical claim: a run does not require any underlying fundamental cause. The bank can be perfectly solvent, the assets perfectly safe, and the run still happens because each depositor's optimal action depends on what they think everyone else will do.

Why the deposit contract creates the second equilibrium

The contract is "first-come, first-served": depositors arriving at date 1 receive r₁ until the bank's resources are exhausted, at which point further requests get nothing. This sequential service constraint is essential. If the bank instead paid everyone a pro-rata share of whatever it could salvage, the incentive to race for the exit would disappear — but so would the liquidity insurance benefit (the patient depositors would be partly punished for the impatient).

The Diamond-Dybvig contract is therefore caught in a tradeoff: the very promise that makes the bank useful — pay r₁ on demand, no questions asked, sequentially served — is what creates the run equilibrium. There is no contract within the simple model that achieves the same liquidity insurance without the bad equilibrium. That is what makes external institutional support necessary.

Three remedies that work, and one that doesn't

The model gives us three robust ways to eliminate the run equilibrium without sacrificing the good one — and a clear example of what doesn't help.

1. Deposit insurance

If the depositor knows their balance is insured regardless of whether they withdraw first or last, their incentive to race vanishes. The dominant action becomes "stay until you actually need the money", because withdrawing early costs you the higher long-term return without any safety upside. The run equilibrium ceases to exist.

The US Federal Deposit Insurance Corporation was created on January 1, 1934, after the wave of 1930-33 runs that closed nearly 9,000 banks. The insurance cap began at $2,500 in 1934, was raised to $5,000 later that year, and has been increased a dozen times to its current level of $250,000 per depositor per bank. Bank runs on insured deposits in the US effectively ended with FDIC — every major bank failure since 1934 has been resolved at the supervisor's pace, not the depositor's. The SVB episode in 2023, importantly, was a run on uninsured deposits (more than 90% of SVB's deposit base was over the $250k cap), confirming the model's prediction at the boundary.

2. Suspension of convertibility

If the bank reserves the right to stop honouring withdrawals for a defined period whenever requests exceed a threshold, the late-arriving depositor's payoff is no longer zero — they still get paid, just later. Diamond and Dybvig themselves show this is an equilibrium-eliminating mechanism in a simpler version of their model. Historical examples: the US 1907 panic ended when the New York Clearing House Association issued substitute "clearing-house certificates" and suspended cash payments. Argentina's 2001 corralito froze withdrawals at $250/week and prevented complete collapse of the system, at heavy cost in legitimacy.

Suspension works in theory because it neutralises the sequential-service incentive. It is unpopular in practice because it imposes a real cost on the liquidity-constrained, and signals weakness at exactly the moment confidence is fragile.

3. Lender of last resort (Bagehot)

Walter Bagehot's Lombard Street (1873) gave the central bank's run-stopping playbook in three rules: in a panic, (1) lend freely, (2) at a penalty rate, (3) against good collateral. "Freely" stops the run by reassuring depositors the bank can pay. "Penalty rate" prevents the facility from subsidising bad behaviour in normal times. "Good collateral" protects the central bank's balance sheet. The Federal Reserve's discount window, the ECB's marginal lending facility, the BoE's various liquidity insurance schemes, and the BoJ's Article 38 loans all descend from Bagehot's rule.

Bagehot is what was missing in the 1930-33 US collapse — the Fed, then five years old, declined to act as lender of last resort to most failing banks. Friedman and Schwartz's Monetary History (1963) made the influential case that this was the proximate cause of the depth and length of the Depression. Ben Bernanke, who shared the 2022 Nobel with Diamond and Dybvig precisely for documenting this mechanism, ensured that the Fed did not repeat the error in 2008.

What doesn't work alone

Sheer balance-sheet strength. A higher capital ratio reduces fundamental insolvency risk but does not eliminate the run equilibrium, because the run does not require insolvency. SVB had a capital ratio well above regulatory minima the week it failed. Markets and depositors had simply repriced its mark-to-market hole in long-dated treasuries, and the coordination failure did the rest. Capital is necessary but not sufficient.

Bagehot's rule in arithmetic

Why does lending freely at a penalty rate work? Take a bank with $100 of deposits, $5 of cash reserves, $95 of long-term loans worth $95 at maturity but only $75 if liquidated today. It is solvent (assets > liabilities at maturity) but illiquid (cash < on-demand liabilities at any given moment).

Scenario	Depositors withdraw	Bank can pay	Outcome
Normal day	$3 (3% routine)	$5 (from cash)	No problem
Bad day, no LOLR	$50 (run)	$5 cash + $59 from fire-sale of $75 worth of loans = $64	Insolvent at fire-sale prices, fails
Bad day, with Bagehot LOLR	$50 (run)	$5 cash + $45 borrowed from central bank against $50 of loans at penalty rate	Bank survives, repays LOLR loan when calm returns

The central bank takes no credit risk in the third row because the loans, valued at maturity, exceed the borrowed amount. The penalty rate ensures the bank pays for the privilege and does not seek the facility routinely. The "freely" provision means the bank is never short of cash for legitimate redemptions. The run dies because depositors observe the bank meeting every withdrawal request without strain, and the coordination motive to race evaporates.

A short history of runs

Year	Episode	Region	Notes
1797	Bank Restriction Act	UK	Bank of England suspends gold convertibility during Napoleonic Wars; restoration takes 24 years.
1857	Panic of 1857	US	Run on New York banks after failure of Ohio Life Insurance & Trust.
1866	Overend, Gurney & Co.	UK	Last major UK bank run before Bagehot codified LOLR — and the empirical exhibit that motivated Lombard Street.
1873	Panic of 1873	US	Triggered by Jay Cooke failure; led to a six-year depression.
1907	Knickerbocker crisis	US	Ended when J.P. Morgan personally orchestrated private liquidity support; led directly to creation of the Federal Reserve in 1913.
1930-33	Great Depression banking panics	US	Four waves of runs closed ~9,000 banks. Led to FDIC (1933) and Glass-Steagall (1933).
2007	Northern Rock	UK	First UK retail run since 1866. Customers queued at branches after BoC liquidity request leaked. Nationalised Feb 2008.
2008	Wholesale runs	Global	Bear Stearns (Mar), Lehman (Sep), AIG (Sep), money-market funds (Sep) — runs through repo and commercial paper, not retail deposits.
2013	Cyprus deposit haircut	EU	Insured deposits initially threatened with a levy; revised plan haircut uninsured depositors of two failing banks ~40-60%.
2022	Terra/Luna, FTX	Crypto	Terra: ~$40B market cap evaporates in 4 days when algorithmic peg breaks. FTX: FTT-backed run after CoinDesk reveals Alameda balance sheet.
2023	Silicon Valley Bank	US	$42B withdrawn March 9; further $100B queued for March 10 before regulators closed. Largest US bank failure since 2008; first mobile-app-driven run.

Northern Rock — the first 21st-century run

Northern Rock was a UK building society turned mortgage lender. By 2007 it funded roughly 75% of its loan book through wholesale markets — short-term repo and securitisation — rather than retail deposits. When the asset-backed commercial paper market seized up in August 2007, Northern Rock could not roll its funding. On September 13, the BBC reported that the bank had requested emergency liquidity from the Bank of England. The next morning, queues formed outside branches. About £1 billion (~5% of retail deposits) was withdrawn in the next three days. The UK government extended a blanket guarantee to all Northern Rock depositors on September 17, halting the run. The bank was nationalised in February 2008 and broken up in 2010.

What is striking is that Northern Rock had already lost its wholesale funding — the retail run was the slower, more visible echo of a wholesale run that had already happened. The Diamond-Dybvig framework now had to be extended to the entire short-term funding architecture of modern finance: when repo lenders refuse to roll, the institution faces the same coordination failure even if no retail depositor knows their account is at risk.

SVB 2023 — the run at the speed of a group chat

Silicon Valley Bank served roughly half of US venture-backed startups. Its deposit base was concentrated (a few thousand institutional depositors, ~90% above the $250k FDIC cap), connected (founders and CFOs in the same Slack channels and venture-firm WhatsApp groups), and uninsured.

On March 8, 2023, SVB announced a $1.8 billion realised loss on a $21 billion bond sale and a planned $2.25 billion capital raise. The bond hole was an accounting consequence of the Fed's rate hikes: SVB had bought long-dated treasuries at low yields, and now had to mark them down. The bank was, on a hold-to-maturity basis, still solvent — the bonds would have paid out at par. On a mark-to-market basis, the hole was significant but bridgeable with the capital raise.

The coordination failure happened anyway. On March 9, founders and VCs began texting one another to withdraw. Peter Thiel's Founders Fund advised portfolio companies to pull funds. Y Combinator's group emailed founders. By close of business on March 9, depositors had requested $42 billion in withdrawals — about a quarter of SVB's deposit base in a single day. The bank entered the night with negative cash; an additional $100 billion of withdrawals was queued for the morning of March 10. The FDIC closed SVB at noon Pacific time on March 10.

The federal response was decisive: on March 12 the Treasury invoked a "systemic risk exception" to guarantee all SVB deposits (including the uninsured portion above $250k), and the Fed launched the Bank Term Funding Program offering one-year loans against treasuries at par (not mark-to-market). Both moves were textbook Diamond-Dybvig: deposit insurance plus a Bagehot-rule lender of last resort. The run on First Republic Bank that immediately followed was slower but ended the same way — JPMorgan acquired its remains on May 1, 2023.

The lasting lesson: depositor coordination now happens at the speed of a group chat. Northern Rock's 2007 run took five days to remove 5% of deposits. SVB's 2023 run took one day to remove 25%. The Diamond-Dybvig dynamic is the same; the time constant has collapsed by an order of magnitude.

Shadow banking — same physics, no FDIC

The 2008 crisis was, in large part, a run on shadow banking. Institutions that performed maturity and liquidity transformation outside the regulated banking system — money-market mutual funds, repo lenders, asset-backed commercial paper conduits, securities lenders — had no deposit insurance and no formal Fed access. When the value of their long-term assets (subprime mortgage securities, in particular) was suddenly in doubt, their short-term lenders refused to roll, and a classic Diamond-Dybvig run ensued.

• Bear Stearns (March 2008). Lost $17B of liquidity in three days as repo lenders cut counterparty exposure. JPMorgan acquired at $2/share (later $10/share) with Fed backstopping $30B of dubious assets.
• Money-market funds (September 2008). The Reserve Primary Fund "broke the buck" (NAV < $1) after Lehman exposure; investors pulled $290B from prime funds in three days. The Treasury issued a temporary fund guarantee on September 19 to halt the run.
• Lehman Brothers (September 2008). Filed for bankruptcy after repo and tri-party clearing counterparties withdrew. Allowed to fail without LOLR support — widely viewed as the worst Bagehot-rule failure of the modern era.
• AIG (September 2008). Run on AIG's securities-lending operation and collateral calls on its credit-default-swap book. Federal Reserve extended an $85B credit line on September 16, eventually expanded to $182B.

Post-2008 regulation extended FDIC-style protection imperfectly into the shadow system: the Dodd-Frank Title II resolution authority, the Liquidity Coverage Ratio for prime money-market funds, central clearing for derivatives. The architecture is still incomplete, and 2020 (Treasury market dislocation, money-market fund stress at the start of the COVID shock) showed that runs can still happen in corners the regulators have not yet reached.

Crypto bank runs — institutional learning at high cost

Crypto exchanges and stablecoins have reproduced the Diamond-Dybvig dynamic in a system explicitly built without FDIC or LOLR.

• Terra/Luna (May 2022). Algorithmic stablecoin UST was backed by reflexive minting/burning of the LUNA token. When confidence wavered, holders rushed to redeem UST. The mint-burn mechanism collapsed under volume, and the entire ~$40B ecosystem evaporated over four days. A pure self-fulfilling collapse.
• FTX (November 2022). Functioned as a bank by re-using customer deposits to fund related-party Alameda trading. A CoinDesk article on November 2 revealed the FTT-token concentration; rival exchange Binance announced on November 6 it would liquidate its FTT holdings. Withdrawals overwhelmed the exchange within 48 hours. Classic Diamond-Dybvig with a fraud overlay.
• USDC depeg (March 2023). Circle, USDC's issuer, held ~$3.3B of reserves at SVB. When SVB failed, USDC's $1 peg cracked to ~$0.87 over a weekend before Treasury's SVB rescue restored par. Even a fully-collateralised stablecoin proved runnable because the reserves themselves were exposed to maturity transformation upstream.

The Diamond-Dybvig framework is institutionally portable: any entity offering on-demand redemption against illiquid backing is potentially runnable, regardless of legal form. The presence or absence of deposit insurance and a lender of last resort is what determines the equilibrium structure, not whether the institution calls itself a bank.

Extensions and variants

• Information-based runs (Jacklin-Bhattacharya 1988; Chari-Jagannathan 1988). Drop the sunspot. Depositors update their beliefs about fundamentals from a noisy public signal. Some run because of fundamentals; others run because they fear the fundamentals-driven runs. Hybrid models that match more of the empirical evidence on actual runs.
• Global games (Morris-Shin 1998, 2000). Introduce small heterogeneity in depositors' private information about the bank's fundamentals. The two-equilibria multiplicity is replaced by a unique threshold equilibrium: the bank runs iff fundamentals are worse than a critical level that depends on the contract. The framework is now standard for modeling runs and currency crises empirically.
• Wholesale and repo runs (Gorton-Metrick 2012). Apply Diamond-Dybvig to repo financing. Lenders refuse to roll when haircuts spike; institutions face the same coordination failure as retail depositors. The empirical framework for understanding 2008.
• Sovereign debt as Diamond-Dybvig (Cole-Kehoe 2000). Self-fulfilling crises in sovereign borrowing: investors don't roll because they fear others won't roll. Used to interpret the 2010-12 euro periphery crisis.
• Diamond-Rajan (2001) liquidity-creation theory. Diamond's later work argues that the run-prone deposit contract is socially valuable precisely because it disciplines bank managers: only a bank whose loans are worth more than its deposits can safely promise on-demand par redemption. The fragility is the commitment device.

Common pitfalls

• Treating runs as a verdict on solvency. The model's central insight is that runs can happen on solvent banks. Inferring fundamental weakness from the existence of a run is the same fallacy as inferring that a stock-market crash proves underlying productivity declined.
• Confusing deposit insurance with bank bailouts. Insurance pays depositors and is funded by bank-paid premiums; it does not protect shareholders, bondholders, or management. The SVB resolution wiped out equity entirely while protecting depositors above the cap — closer to enhanced insurance than a bailout in the colloquial sense.
• Assuming a high capital ratio prevents runs. Capital protects against insolvency, not illiquidity. SVB's CET1 ratio at the time of failure was around 12% — well above regulatory minimums. Capital and liquidity are independent failure modes.
• Reading Bagehot as "bail out everyone." Bagehot's rule lends to solvent-but-illiquid institutions against good collateral at a penalty rate. It does not subsidise insolvency. Modern central banks have arguably stretched the rule in 2008-09 and 2020 by accepting weaker collateral and offering below-market rates, blurring the bright line Bagehot intended.
• Ignoring uninsured wholesale liabilities. Modern banks fund themselves with much more than retail deposits — repo, commercial paper, securities lending, brokered deposits. These are the runnable parts of the modern balance sheet. Looking only at retail deposits is looking only at where the lights are best.
• Forgetting that the contract is the problem. The Diamond-Dybvig contract creates both equilibria. Designing a contract that gives liquidity insurance without the run option is the central open problem of banking system design.