Since
the financial crisis of 2008, an explosion of research has aimed to
understand what makes financial markets prone to sporadic crises. The
potential sources of trouble are many, including debt and leverage,
financial concentration and the problem of “too big to fail,” as
well as perverse incentives for bankers to take on large risks.
Markets go wrong in any of a thousand ways, and, unfortunately, it
seems that understanding each one requires intimate familiarity with
the fine details of the financial architecture, contracts, legal
regulations, individual incentives and so on.
Yet
a narrow focus on details can distract attention from profund
similarities. Network scientists know that the topology of a network
– the pattern of links or relationships that hold it together –
can have a decisive influence on its properties. In the context of
financial networks, new
research suggests that subtle changes in network topology may be
the key to understanding a common pathway by which financial markets
become unstable. For all the forbidding complexity of the modern
financial system, they suggest, instability tends to follow from the
emergence of particular cycles or closed circuits of dependence
within the network topology, as these tend to amplify disturbances or
distress.
I'll
explain the basic logic of the work briefly below. It's a theoretical
paper, and not meant as a recipe for detailed practical policy. But
it does help clarify a basic mechanism that drives instability, and
offers broad insights on the kinds of policies that could avoid it.
First,
a little background. Some of the motivation for this work comes from
the history of thinking in ecology. Back in the
1970s, ecologists widely believed that the stability of an ecosystem
would generally be enhanced by increasing complexity, as reflected in
the presence of a large number of interactions between a diverse set
of species. But the theoretical ecologist Robert May overturned this
intuition, at least partly, by showing in simplified network models
of food webs that complexity can in some cases undermine stability.
His analysis indicated that networks with a larger number of
interactions could be less stable, and inspired ecologists to begin
searching for possible new factors that might account for ecosystem
stability – for example, the presence of specific topological
motifs within food webs.
Just
after the financial crisis, May – who was formerly the Chief
Science Advisor to the UK Government – joined with the Bank of
England's Andrew Haldane in
arguing for the relevance of this insight to the stability of
financial
systems
as well. Financial networks have grown enormously more complex in the
past 30 years, and, as May and Haldane noted, the pre-crisis
literature in economics and finance mostly viewed this as a good
thing. Traditional thinking held that more complexity, achieved
through a wider spectrum of financial instruments, greater
diversification and wider spreading of risks, would improve
stability. Yet May and Haldane pointed to a handful of studies,
mostly in the last decade, linking rising complexity with increasing
instability.
Six
years later, this idea that too much complexity can cause trouble is
becoming less “radical,” although the story also remains
unsatisfyingly complicated. Models serving as examples tend to
include fairly
intricate details of how financial institutions interact –
particulars of contracts, for example, or mechanisms for debt default
resolution. Do such details always play a decisive role? Or is there
a simple and general story about how changes in network topology
create instability that stands above the details?
This
is the question asked – and answered, in the affirmative – by
this paper. What Marco
Bardoscia and
colleagues do is to study a class of models of the Interbank network,
and probe the stability of the network as they vary two parameters
characterizing its complexity. These are 1) market integration,
reflecting the number of banks participating in the financial system,
and 2) diversification, referring to the proliferation of financial
contracts. Importantly, the study doesn't test stability in the usual
way of running stress tests and estimating the total losses likely to
amount from some assumed shocks to the system. This approach requires
specific assumptions on the nature of the financial contracts and
mechanisms of distress propagation, making it difficult to draw general conclusions.
Instead,
Bardoscia and colleagues study how gradual changes in the
interconnection pathways in the network can create mechanisms that
tend to amplify small disturbances, rather than dampening them away.
For example, the figure below illustrates how
the network goes from being stable to unstable just due to gradual
diversification, normally thought of as beneficial for risk
management. It shows a network eigenvalue λmax
reflecting whether the propagation dynamics of the network dampen
(λmax
<
1) or amplify (λmax
>
1) small disturbances. The researchers used the
balance sheets of the top 50 listed banks in the European Union as a
starting point, and then simulated a process in which banks gradually
increase the degree of diversifi cation by creating further exposures
towards additional counterparties. They carefully rebalanced the
network at each stage to keep the assets and liabilities consistent
with the original balance sheets
and the interbank leverages of all banks fixed. As the degree of
diversi fication increases, a bank's exposures spread out across ever
more counterparties. Even though the total interbank exposure of each
bank remains constant, the banking system eventually goes unstable,
and it doesn't even take a lot of diversification to make it happen.
As the figure shows, instability first arises when contracts link
together just 3% of all the possible pairs that could in principle be
linked.
This
example illustrates the transition from stability to instability as
complexity increases through diversification. The paper equally
establishes that a simular transition takes place if complexity
rises just through an increase in the number of banks.
The
conclusion is that more complex and highly networked markets should
generically tend toward instability. A financial system can go
unstable as the number of banks increases, or as
the number of contracts among banks increases, even if the individual
leverage of banks does not increase. In either case, instability
appears as a holistic, network effect, even though each bank
individually has an unchanging risk profi le. The implication:
financial policies that seem wise from the point of view of the
risks to individual banks can actually – and counter-intuitively –
increase fi nancial instability to the whole system.
The
paper also goes into some detail on the origin of such instability, which
lies in the fact that in both processes banks get increasingly
involved in multiple cycles (i.e. closed chains) of contracts. This
is an interesting technical detail that I won't get into, although
such factors might well prove useful as targets for monitoring by
authorities. In any event, it's clear that systemic risk cannot be
reduced through measures long thought to reduce risks in standard
economics. Banking proliferation and diversification, if excessive,
can create worse problems than they solve.
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