A theoretical study published in May 2026 finds that expanding an interbank network can raise banks’ risk-adjusted expected profits at first, but the advantage can reverse as institutions hold fewer reserves and depend more heavily on their partners.
The result comes from “Interbank network and market efficiency,” a peer-reviewed paper by Tongkui Yu, Xue-Zhong (Tony) He and Na Zhang in the journal Risk Sciences.
The paper does not show that any particular banking system has too many connections. Nor does it calculate an ideal network size for the United States, Europe or China. It identifies a mechanism that regulators have good reason to watch: the same connections that help banks share liquidity risk can also weaken their incentive to keep enough liquidity of their own.
Why banks need one another
Banks regularly send money to other institutions to settle payments, finance transactions and cover short-term funding needs. These arrangements allow a bank with a temporary shortage of cash to obtain funds from another institution that has money available.
This matters because banks face a trade-off. Cash and other liquid assets help them meet withdrawals and payments at short notice. However, money held in reserve is generally less profitable than money used for lending or investment.
The scale of institutional money movement is enormous. The Federal Reserve’s Fedwire Funds Service processed 217.3 million transfers in 2025, with an average daily value of about $4.59 trillion. Fedwire is a real-time payment and settlement system, not a measure of interbank lending, but the figures show how much money routinely moves between participating financial institutions.
An interbank credit network can act as a buffer when liquidity needs do not strike every member at the same time. If one bank faces unusually heavy withdrawals while another has spare funds, a transfer between them can prevent a temporary shortage from becoming a larger problem.
Risk-sharing changes banks’ incentives
Yu, He and Zhang’s model gives banks two broad concerns. Each institution wants to earn a return, but it also wants to survive a liquidity shock. It must decide how much to keep in reserve and whether joining a credit network makes it better off than remaining independent.
At first, adding banks to the network improves risk-sharing. There are more potential sources of liquidity, so the group can absorb shocks more efficiently.
Then behavior begins to change. A bank that expects help from its partners has an incentive to reduce its own reserves and put more money into profit-generating assets. The researchers describe this as free-riding because the bank relies partly on liquidity maintained elsewhere in the network.
That decision can make sense for one institution. If many banks make it at the same time, the network may contain less spare liquidity than its members expect.
In the model’s Nash equilibrium, no individual bank can improve its position by changing its own strategy while every other bank’s choice remains fixed. As the network grows, risk-sharing initially dominates and expected profits rise. Beyond a certain point, free-riding becomes more influential and expected profits fall.
The result is a hump-shaped relationship rather than a straight line. Under the model’s assumptions, the best collective outcome occurs in a relatively small network. Economists call this Pareto optimal when no participant can be made better off without making at least one other participant worse off.
A connection can transmit help or trouble
The finding fits a wider problem in financial regulation. Connections can distribute a local shock across institutions capable of absorbing it. They can also provide routes through which losses and funding pressure spread.
Former Federal Reserve Chair Janet Yellen described this tension in a 2013 speech on interconnectedness and systemic risk. She noted that additional links can improve diversification under some conditions, while allowing distress to move through the system under others.
This is why regulators look beyond whether a bank is simply large. A deeply connected institution may be difficult to close because its failure would affect payment systems, funding markets and counterparties far beyond its own balance sheet. That concern is often described as “too interconnected to fail.”
Real banking networks also tend to be uneven. Large institutions often sit near the center, while smaller banks have fewer or weaker links. The study examines banks of different sizes and finds that their incentives depend partly on their relative deposits and the return available after allowing for liquidity risk. Under some conditions, a smaller bank can benefit by holding fewer reserves and relying more heavily on a larger partner.
Liquidity rules limit the private calculation
Banks do not choose their liquidity positions without regulatory constraints. The Basel III Liquidity Coverage Ratio, for example, requires banks within its scope to maintain enough unencumbered high-quality liquid assets to cover net cash outflows during a 30-day stress period.
A liquidity requirement is different from a capital requirement. Liquidity rules address whether a bank can meet payments when they fall due. Capital rules require a bank to maintain a financial cushion capable of absorbing losses. The supplied paper is mainly concerned with banks’ reserve and liquidity decisions, so describing its regulatory discussion as a capital requirement would blur two separate protections.
The model indicates that a reserve requirement set near its socially preferred level can curb free-riding in a large network. That does not mean it identifies the correct regulatory ratio for a real bank. Actual institutions face credit limits, collateral rules, different business models and changing assessments of counterparty risk. Central banks can also provide emergency liquidity when private markets stop functioning.
The study explains a mechanism, not a universal limit
The paper’s larger-network analysis uses deliberately strong assumptions, including fully connected banks and full commitments to peers. These assumptions allow the researchers to isolate the contest between risk-sharing and free-riding, but they do not describe the full structure of a modern banking system.
Regulators therefore cannot take the model and conclude that a network should contain a fixed maximum number of banks. They would also need to know the size and direction of exposures, how much liquidity each institution holds, which banks occupy central positions and how quickly confidence could disappear during stress.
Even so, the model corrects a tempting assumption. More funding relationships can provide banks with additional protection, but they also affect how much protection each bank chooses to provide for itself. A network’s resilience depends on both parts of that equation.
