Tuesday, 1 March 2011

The Shark Tank

Some papers feel like they were written over drinks at the pub one night. So it is for a recent Nature paper co-authored by an Oxford ecologist and a Bank of England economist (doi:10.1038/nature09659). What these two were doing at the same pub remains unclear, but the result is an interesting analysis of the banking system's inherent fragility using established food web models.

Increased globalization of the banking system in recent decades has resulted in significant interdependency. As much as two-thirds of the growth in banks' balance sheets is accounted for by banks lending to banks and to other financial institutions. The collapse of Lehman Brothers in the autumn of 2008 caused a global financial crisis as waves of banks, each dependent on banks in the preceeding wave, found themselves in financial trouble.

Interdependency is a common theme in ecology. Species interactions range from relationships which benefit both species (mutualistic interactions) to those in which one species eats the other (predatory interactions), but all depend on the population dynamics of interacting species. Predator and prey population sizes depend on each other. If rabbit food is scarce, rabbit populations decrease, and fox populations follow closely behind. Similarly, if bank #1 fails, then bank #2 which lent bank #1 money now has debts that won't be repaid, and if bank #2 fails then bank #3 which lent money to bank #2 now has the same problem. These "financial ecosystems" can be modelled with banks replacing species in standard food web interaction models. In this model each bank has assets (interbank loans and external assets such as mortgages or bonds) and liabilities (interbank borrowing and deposits from customers). The difference between these two must be positive or the bank fails. Each bank must also keep a fraction of its money as a reserve. This reserve insulates banks from shocks. If the bank's customers decide they want to take their money out, the bank has a reserve of money so that the customers can be paid immediately. If those reserves aren't big enough the bank then has to find money in other ways, either through selling off its assets or by borrowing money from another bank. If a fraction of the bank's assets are wiped out by a shock, the bank fails if it does not have sufficient capital reserves. This paper looks at how an initial failure is propagated through the financial ecosystem, and how the size of the reserve affects this propagation.

Three types of shocks were examined, and each had a different outcome. When a single shock hits a single bank, all other banks are affected only by their interbank loans. Increased connectivity attenuates risk. Fewer banks fail in the second wave. In a second situation, a generalized decrease in market prices causes bank #1 to fail. In this situation, bank #2 now has two problems: a generalized decrease in market prices and outstanding loans to bank #1 which won't be repaid. The shock amplifies as more and more banks fail, and connectivity propagates risk. The third situation attempts to describe the most recent financial crisis; intrabank loans decrease following an initial shock, and affected banks follow suit. This liquidity-hoarding shock does not attenuate as the second and third generation of banks are affected.

Some interesting observations emerge. If all banks do the same thing and hold a similar mix of assets, each bank individually is less likely to fail if the value of one of those assets decreases. The system as a whole, however, is much more volatile, since it behaves like a single bank. One big shock could wipe out the whole banking system. If regulators want to decrease systemic risk, they should encourage diversification. They should also encourage modularity, so that failures from one type of financial activity do not contaminate banks engaged in unrelated activities. The United States has already proposed the Volcker rule to do precisely that.

As the authors point out, the banking system is not quite as simple as the model they used. One major difference is that in reality there tends to be a few large, well-connected banks and many more smaller banks. The smaller banks are especially well-connected to the big banks, since the big banks have a proportionally big share of the banking market. The spread of infections uses a model similar to food webs. In the epidemiology of infectious diseases, people with lots of interpersonal connections (ie big banks) are known as "super-spreaders", and a web with super-spreaders maximizes the number of infected individuals. Regulations aimed at reducing systemic risk, as opposed to bank-by-bank risk, should require super-spreader banks to have larger reserves than other banks.

This is not the first time the financial world has turned to science to find answers. The Black-Scholes model used for pricing derivatives is, at its core, a heat dispersion equation. Perhaps interbanking webs will be better than these much-scapegoated derivatives at identifying and reducing systemic risk.