Bank runs are among the most destabilizing events in financial markets, capable of turning liquidity fears into full-blown crises. At the heart of this phenomenon is the Diamond-Dybvig Model, a foundational framework that explains how banks’ role in transforming illiquid assets into liquid liabilities makes them inherently vulnerable. While this role provides significant economic value, it also relies heavily on depositor confidence.
If expectations shift — whether due to real or perceived risks — a self-fulfilling crisis can emerge. This blog explores the mechanics of bank runs — why they happen even in the absence of fundamental financial distress, and how central banks can intervene to stabilize the system.
A good starting point is to look to the research of Douglas Diamond, the Merton H. Miller Distinguished Service Professor of Finance at the University of Chicago, who was awarded the Nobel Prize in Economic Sciences in 2022.[1] Diamond is primarily known for his research into financial intermediaries, financial crises, and liquidity, and his research agenda has been dedicated to explaining what banks do, why they do it, and the consequences of these arrangements.
He is perhaps best known for the Diamond-Dybvig Model[2], which precisely explains how the role of banks in creating liquid liabilities (deposits) to fund illiquid assets (such as business loans) makes them fundamentally unstable and gives rise to bank runs.
It also shows why banks may need a government safety net more than they need other borrowers. Diamond-Dybvig Model is elegant in its simplicity and intuitiveness; it precisely describes how bank failures like Silicon Valley Bank (SVB) in 2023 can happen and, indeed, even the greater liquidity crisis and bank failures that occurred during the Great Financial Crisis. Moreover, the model prescribes how such events can be avoided.
Simple Diamond-Dybvig Model
One of the key functions of banks in the economy is the transformation of illiquid asset into liquid liability. This brilliant feat of financial engineering adds a lot of value to the economy but exposes banks to liquidity risk of their own and makes them inherently unstable.
Assume that there exists an illiquid asset that an investor can hold directly. You can invest in this asset at t=0 for $1.00. It can either be liquidated at t=1 for $1.00 or held until t=2 for a $2.00 payoff.
Each investor in this economy faces uncertain future liquidity needs. Each knows that he or she will need cash either at t=1 (Type 1) or at t=2 (Type 2), but without certainty when at t=0. To be more precise, we can assume that each individual investor has a 25% probability of cash need at t=1 and a 75% probability of cash need at t=2.
Each investor has a simple risk-averse consumption utility function U(C)=110-(100/C). The Type 1 investor consumes $1.00 at t=1 and the Type 2 investor consumes $2.00 at t=2. Each investor’s expected utility at t=0 is 0.25*U(1) + 0.75*U(2)=47.50.
What if a more liquid asset is available in this economy? Instead of $1.00 at t=1 and $2.00 at t=2, the more liquid asset pays off $1.28 at t=1 and $1.81 at t=2. Then the investor’s expected utility at t=0 would be 0.25*U(1.28) + 0.75*U(1.81)=49.11.
This second, more liquid asset does not yet exist. But can a bank create one? Suppose a bank collects $1.00 from 100 investors and invests in the first illiquid asset and promises to pay $1.28 at t=1 for those who withdraw at t=1 and $1.81 to those who withdraw at t=2.
At t=1, the bank’s portfolio is only worth $100. If 25 investors withdraw as expected, then 32% of the portfolio must be liquidated to pay the investors (25*($1.28) = $32). The remaining 68% of portfolio value is worth $68. At t=2, the remaining 75% of the investors can now receive $1.81 ($68*$2.00)/75.
If fraction c receives a at t=1, then each of the remaining can receive (1-c*a)*$2.00/(1-c). This is the optimal contract a bank can write given the payoff structure of the illiquid asset, the investor’s utility function, and the proportion of investor types.
This risk pooling and sharing and liquidity transformation is one of the most important functions a bank can perform. It is an impressive feat of financial engineering that adds a lot of value to the economy.
Unstable Equilibrium
But this financial alchemy is not without its costs. In the above example, 25 of the 100 investors withdraw at t=1 and 75 withdraw at t=2. This is the equilibrium given everyone’s expectation at t=0.
But this is not the only possible equilibrium. What if a future Type 2 investor did not know how many investors were Type 1 at t=0 and expects a higher percentage of withdrawals at t=1? If, for example, 79 of the 100 investors withdraw at t=1, the bank’s portfolio is worth at most $100. If 79 of the investors receive 1.28%, then the bank is expected to fail (79*$1.28=$101.12 > $100).
Given this new expectation, a rational response would be for the Type 2 investor to withdraw at t=1 to get something as opposed to nothing. In other words, an expectation of 100% at t=1 is as self-fulfilling as an expectation of 25% at t=1 and 75% at t=2. The bottom line is that the anticipation of liquidity problems (real or perceived) lead to current real liquidity problems, and investors’ expectations can change based on no fundamental changes in the balance sheet.
Applications
The Diamond-Dybvig Model of liquidity is robust enough for analyzing all types of “runs” that a complex dealer bank can face — flight of short-term financing, flight of prime brokerage clients, flight of derivative counterparties, loss of cash settlement privileges, among others.
It also serves as a useful framework for analyzing the economic consequences of a liquidity crisis and policy responses. Panicked investors seeking liquidity at the same time impose serious damage to the economy because they force liquidation of productive longer-term investments and interrupt financing of the current productive projects.
Financing by central banks as lender of last resort might be needed in this case. To force the optimal solution as the dominant strategy, you need some kind of insurance from a credible provider (deposit insurance, Fed line of credit, or other third-party guarantees), and if the clamor for liquidity is systemic, only the central bank can credibly offer assurances.
The Diamond-Dybvig Model illustrates a fundamental truth about modern banking: confidence is the glue that holds the system together. When depositors, counterparties, or investors fear a liquidity crunch, their rush to withdraw funds can create the very crisis they fear; that is, forcing premature liquidation of long-term assets and disrupting economic stability.
Effective policy responses, such as deposit insurance and central bank intervention, are critical to breaking the cycle of self-fulfilling expectations. Whether analyzing classic bank runs or modern financial contagion, the lessons of liquidity management remain clear: in times of uncertainty, perception can shape reality, and stabilizing expectations is just as important as stabilizing balance sheets.
[1] This author was a graduate student at the University Chicago Booth School in the late 90’s and was one of his students.
[2] Douglas Diamond, Phillip Dybvig, “Bank Runs, Deposit Insurance, and Liquidity,” Journal of Political Economy, June 1983.
#Bank #Runs #Liquidity #Crises #Insights #DiamondDybvig #Model