Financial institution Runs and Liquidity Crises: Insights from the Diamond-Dybvig Mannequin

Financial institution runs are among the many most destabilizing occasions in monetary markets, able to turning liquidity fears into full-blown crises. On the coronary heart of this phenomenon is the Diamond-Dybvig Mannequin, a foundational framework that explains how banks’ position in reworking illiquid property into liquid liabilities makes them inherently susceptible. Whereas this position supplies vital financial worth, it additionally depends closely on depositor confidence.

If expectations shift — whether or not as a consequence of actual or perceived dangers — a self-fulfilling disaster can emerge. This weblog explores the mechanics of financial institution runs — why they occur even within the absence of basic monetary misery, and the way central banks can intervene to stabilize the system.

start line is to look to the analysis of Douglas Diamond, the Merton H. Miller Distinguished Service Professor of Finance on the College of Chicago, who was awarded the Nobel Prize in Financial Sciences in 2022.[1]  Diamond is primarily recognized for his analysis into monetary intermediaries, monetary crises, and liquidity, and his analysis agenda has been devoted to explaining what banks do, why they do it, and the implications of those preparations. 

He’s maybe greatest recognized for the Diamond-Dybvig Mannequin[2], which exactly explains how the position of banks in creating liquid liabilities (deposits) to fund illiquid property (equivalent to enterprise loans) makes them basically unstable and offers rise to financial institution runs.

It additionally reveals why banks may have a authorities security internet greater than they want different debtors. Diamond-Dybvig Mannequin is elegant in its simplicity and intuitiveness; it exactly describes how financial institution failures like Silicon Valley Financial institution (SVB) in 2023 can occur and, certainly, even the better liquidity disaster and financial institution failures that occurred in the course of the Nice Monetary Disaster. Furthermore, the mannequin prescribes how such occasions might be prevented.

Easy Diamond-Dybvig Mannequin

One of many key features of banks within the financial system is the transformation of illiquid asset into liquid legal responsibility. This sensible feat of economic engineering provides a whole lot of worth to the financial system however exposes banks to liquidity threat of their very own and makes them inherently unstable.

Assume that there exists an illiquid asset that an investor can maintain straight. You may make investments on this asset at t=0 for $1.00. It may well both be liquidated at t=1 for $1.00 or held till t=2 for a $2.00 payoff.

Every investor on this financial system faces unsure future liquidity wants. Every is aware of that she or he will want money both at t=1 (Kind 1) or at t=2 (Kind 2), however with out certainty when at t=0. To be extra exact, we will assume that every particular person investor has a 25% chance of money want at t=1 and a 75% chance of money want at t=2.  

Every investor has a easy risk-averse consumption utility operate U(C)=110-(100/C). The Kind 1 investor consumes $1.00 at t=1 and the Kind 2 investor consumes $2.00 at t=2.  Every investor’s anticipated utility at t=0 is 0.25*U(1) + 0.75*U(2)=47.50.

What if a extra liquid asset is on the market on this financial system? As a substitute of $1.00 at t=1 and $2.00 at t=2, the extra liquid asset pays off $1.28 at t=1 and $1.81 at t=2.  Then the investor’s anticipated utility at t=0 could be 0.25*U(1.28) + 0.75*U(1.81)=49.11.

This second, extra liquid asset doesn’t but exist. However can a financial institution create one?  Suppose a financial institution collects $1.00 from 100 buyers and invests within the first illiquid asset and guarantees to pay $1.28 at t=1 for many who withdraw at t=1 and $1.81 to those that withdraw at t=2. 

At t=1, the financial institution’s portfolio is barely price $100. If 25 buyers withdraw as anticipated, then 32% of the portfolio should be liquidated to pay the buyers (25*($1.28) = $32). The remaining 68% of portfolio worth is price $68. At t=2, the remaining 75% of the buyers can now obtain $1.81 ($68*$2.00)/75. 

If fraction c receives a at t=1, then every of the remaining can obtain (1-c*a)*$2.00/(1-c). That is the optimum contract a financial institution can write given the payoff construction of the illiquid asset, the investor’s utility operate, and the proportion of investor varieties.

This threat pooling and sharing and liquidity transformation is without doubt one of the most essential features a financial institution can carry out. It’s a powerful feat of economic engineering that provides a whole lot of worth to the financial system.

Unstable Equilibrium

However this monetary alchemy just isn’t with out its prices. Within the above instance, 25 of the 100 buyers withdraw at t=1 and 75 withdraw at t=2. That is the equilibrium given everybody’s expectation at t=0. 

However this isn’t the one potential equilibrium. What if a future Kind 2 investor didn’t know what number of buyers have been Kind 1 at t=0 and expects the next proportion of withdrawals at t=1? If, for instance, 79 of the 100 buyers withdraw at t=1, the financial institution’s portfolio is price at most $100. If 79 of the buyers obtain 1.28%, then the financial institution is anticipated to fail (79*$1.28=$101.12 > $100).

Given this new expectation, a rational response could be for the Kind 2 investor to withdraw at t=1 to get one thing versus nothing. In different phrases, 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 underside line is that the anticipation of liquidity issues (actual or perceived) result in present actual liquidity issues, and buyers’ expectations can change based mostly on no basic modifications within the steadiness sheet. 

Functions

The Diamond-Dybvig Mannequin of liquidity is powerful sufficient for analyzing all sorts of “runs” {that a} complicated vendor financial institution can face — flight of short-term financing, flight of prime brokerage shoppers, flight of by-product counterparties, lack of money settlement privileges, amongst others.

It additionally serves as a helpful framework for analyzing the financial penalties of a liquidity disaster and coverage responses. Panicked buyers looking for liquidity on the identical time impose severe injury to the financial system as a result of they power liquidation of productive longer-term investments and interrupt financing of the present productive initiatives. 

Financing by central banks as lender of final resort may be wanted on this case. To power the optimum answer because the dominant technique, you want some sort of insurance coverage from a reputable supplier (deposit insurance coverage, Fed line of credit score, or different third-party ensures), and if the clamor for liquidity is systemic, solely the central financial institution can credibly supply assurances. 

The Diamond-Dybvig Mannequin illustrates a basic fact about trendy banking: confidence is the glue that holds the system collectively. When depositors, counterparties, or buyers worry a liquidity crunch, their rush to withdraw funds can create the very disaster they worry; that’s, forcing untimely liquidation of long-term property and disrupting financial stability.

Efficient coverage responses, equivalent to deposit insurance coverage and central financial institution intervention, are important to breaking the cycle of self-fulfilling expectations. Whether or not analyzing traditional financial institution runs or trendy monetary contagion, the teachings of liquidity administration stay clear: in instances of uncertainty, notion can form actuality, and stabilizing expectations is simply as essential as stabilizing steadiness sheets.

[1] This creator was a graduate pupil on the College Chicago Sales space College within the late 90’s and was considered one of his college students.

[2] Douglas Diamond, Phillip Dybvig, “Financial institution Runs, Deposit Insurance coverage, and Liquidity,” Journal of Political Financial system, June 1983.