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 belongings into liquid liabilities makes them inherently weak. Whereas this position offers vital financial worth, it additionally depends closely on depositor confidence.

If expectations shift — whether or not because 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 elementary monetary misery, and the way central banks can intervene to stabilize the system.

A great place to begin 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 identified 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 finest identified for the Diamond-Dybvig Mannequin[2], which exactly explains how the position of banks in creating liquid liabilities (deposits) to fund illiquid belongings (corresponding to enterprise loans) makes them basically unstable and provides rise to financial institution runs.

It additionally reveals why banks might 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 higher liquidity disaster and financial institution failures that occurred through the Nice Monetary Disaster. Furthermore, the mannequin prescribes how such occasions may be prevented.

Easy Diamond-Dybvig Mannequin

One of many key capabilities of banks within the financial system is the transformation of illiquid asset into liquid legal responsibility. This sensible feat of economic engineering provides plenty 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 instantly. You possibly can make investments on this asset at t=0 for $1.00. It might 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 (Sort 1) or at t=2 (Sort 2), however with out certainty when at t=0. To be extra exact, we will assume that every particular person investor has a 25% likelihood of money want at t=1 and a 75% likelihood of money want at t=2.  

Every investor has a easy risk-averse consumption utility operate U(C)=110-(100/C). The Sort 1 investor consumes $1.00 at t=1 and the Sort 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 an alternative 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 just value $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 value $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 sorts.

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

Unstable Equilibrium

However this monetary alchemy shouldn’t be 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 attainable equilibrium. What if a future Sort 2 investor didn’t know what number of buyers have been Sort 1 at t=0 and expects the next share of withdrawals at t=1? If, for instance, 79 of the 100 buyers withdraw at t=1, the financial institution’s portfolio is value 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 Sort 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 elementary adjustments within the stability sheet. 

Functions

The Diamond-Dybvig Mannequin of liquidity is powerful sufficient for analyzing all kinds of “runs” {that a} complicated vendor financial institution can face — flight of short-term financing, flight of prime brokerage shoppers, flight of spinoff 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 critical harm to the financial system as a result of they drive liquidation of productive longer-term investments and interrupt financing of the present productive tasks. 

Financing by central banks as lender of final resort is perhaps wanted on this case. To drive the optimum resolution because the dominant technique, you want some form 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 elementary 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 belongings and disrupting financial stability.

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

[1] This writer was a graduate scholar on the College Chicago Sales space College within the late 90’s and was one in all his college students.

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