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 important financial worth, it additionally depends closely on depositor confidence.
If expectations shift — whether or not as a result 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.
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 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 (reminiscent of enterprise loans) makes them essentially unstable and provides rise to financial institution runs.
It additionally exhibits why banks may have a authorities security web 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 will 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 good feat of monetary engineering provides lots 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 immediately. You may make investments on this asset at t=0 for $1.00. It may possibly 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 are able to 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 perform 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 obtainable 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 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 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 traders withdraw as anticipated, then 32% of the portfolio have to 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 perform, and the proportion of investor sorts.
This threat pooling and sharing and liquidity transformation is without doubt one of the most vital capabilities a financial institution can carry out. It’s a formidable feat of monetary engineering that provides lots of worth to the financial system.
Unstable Equilibrium
However this monetary alchemy is just not 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 potential equilibrium. What if a future Kind 2 investor didn’t know what number of traders have been Kind 1 at t=0 and expects the next proportion 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 anticipated to fail (79*$1.28=$101.12 > $100).
Given this new expectation, a rational response can 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 traders’ expectations can change primarily based on no basic modifications within the stability sheet.
Purposes
The Diamond-Dybvig Mannequin of liquidity is powerful sufficient for analyzing all sorts of “runs” {that a} complicated seller financial institution can face — flight of short-term financing, flight of prime brokerage purchasers, 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 in search of liquidity on the similar time impose critical injury to the financial system as a result of they drive 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 drive 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 provide assurances.
The Diamond-Dybvig Mannequin illustrates a basic reality about trendy banking: confidence is the glue that holds the system collectively. When depositors, counterparties, or traders concern a liquidity crunch, their rush to withdraw funds can create the very disaster they concern; that’s, forcing untimely liquidation of long-term property and disrupting financial stability.
Efficient coverage responses, reminiscent of 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 vital as stabilizing stability 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 Economic system, June 1983.
