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 gives 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 elementary monetary misery, and the way central banks can intervene to stabilize the system.
A superb 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 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 finest 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 essentially unstable and offers rise to financial institution runs.
It additionally exhibits 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 higher liquidity disaster and financial institution failures that occurred in the course of the Nice Monetary Disaster. Furthermore, the mannequin prescribes how such occasions could be prevented.
Easy Diamond-Dybvig Mannequin
One of many key features of banks within the economic system is the transformation of illiquid asset into liquid legal responsibility. This sensible feat of monetary engineering provides a whole lot of worth to the economic system however exposes banks to liquidity danger 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 could possibly both be liquidated at t=1 for $1.00 or held till t=2 for a $2.00 payoff.
Every investor on this economic 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 offered on this economic 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 can 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 traders and invests within the first illiquid asset and guarantees to pay $1.28 at t=1 for individuals who withdraw at t=1 and $1.81 to those that withdraw at t=2.
At t=1, the financial institution’s portfolio is simply value $100. If 25 traders withdraw as anticipated, then 32% of the portfolio should be liquidated to pay the traders (25*($1.28) = $32). The remaining 68% of portfolio worth is value $68. At t=2, the remaining 75% of the traders 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 danger pooling and sharing and liquidity transformation is without doubt one of the most necessary features a financial institution can carry out. It’s a formidable feat of monetary engineering that provides a whole lot of worth to the economic system.
Unstable Equilibrium
However this monetary alchemy isn’t with out its prices. Within the above instance, 25 of the 100 traders 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 doable equilibrium. What if a future Sort 2 investor didn’t know what number of traders had been Sort 1 at t=0 and expects a better share of withdrawals at t=1? If, for instance, 79 of the 100 traders withdraw at t=1, the financial institution’s portfolio is value at most $100. If 79 of the traders obtain 1.28%, then the financial institution is predicted to fail (79*$1.28=$101.12 > $100).
Given this new expectation, a rational response can 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 traders’ expectations can change based mostly on no elementary adjustments within the stability sheet.
Purposes
The Diamond-Dybvig Mannequin of liquidity is powerful sufficient for analyzing all sorts of “runs” {that a} advanced supplier 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 traders searching for liquidity on the similar time impose severe harm to the economic system as a result of they power liquidation of productive longer-term investments and interrupt financing of the present productive tasks.
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 type 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 provide 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 traders 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 crucial 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 occasions of uncertainty, notion can form actuality, and stabilizing expectations is simply as necessary as stabilizing stability sheets.
[1] This writer 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.
