Nassim Taleb and Charles Tapiero has penned down a new technical article "Too Big to Fail, Too Big to Bear". I am reproducing the article here:
Electronic copy available at: http://ssrn.com/abstract=1497973
Center for Risk Engineering, New York University Polytechnic Institute Page 1
Too Big to Fail, Too Big to Bear,
and Risk Externalities
Nassim N. Taleb*
Charles S. Tapiero*
Abstract
This paper examines the risk externalities stemming from the size of institutions. The problem of
excessive risk taking and their potential external consequences are taken as a case example. Assuming
(conservatively) that a firm risk exposure is limited to its capital while its external (and random) losses
are unbounded we establish a condition for a firm to be too big to fail. In particular, expected risk
externalities’ losses conditions for positive first and second derivatives with respect to the firm capital are
derived. Examples and analytical results are obtained based on firms’ random effects on their external
losses (their risk externalities) and policy implications are drawn that assess both the effects of “too big to
fail firms” and their regulation.
Key words: Risk, Externalities, Economies of Scale
• Department of Finance and Risk Engineering, New York University Polytechnic Institute, The
Research Center for Risk Engineering, New York and Brooklyn.
Electronic copy available at: http://ssrn.com/abstract=1497973
Center for Risk Engineering, New York University Polytechnic Institute Page 2
1. Introduction
“Too Big to Fail” is a dilemma that has plagued economists, policy makers and the public at large. The
lure for “size” embedded in “economies of scale” and Adam Smith factories have important risk
consequences that have not always been assessed or properly defined. Economies of scales underlie the
growth of industrial and financial firms ([6]) to sizes that may be both too large to manage and losses too
large to bear. This is the case for industrial giants such as GM that have grown into a complex and
diversified global enterprise with extremely large failure risk externalities. This is also the case for large
banks that bear risks with systemic consequences that are often ignored and too big to bear. Banks, unlike
industrial firms, draw their legal rights from a common trust, to manage the supply and the management
of money for their own and the common good. Their failure, overflowing into the “Commons”, may thus
far outstrip their internal and direct losses. The losses borne by the “Commons” can be an appreciable
risk externality that banks do not assume. Further, when banks are perceived too big to fail, they may
have a propensity to assume excessive risks to profit in the short term; they may seek to exercise unduly
their market power; rule the “Commons” and price their services unrelated to their costs or quality.
Size may lead such firms to assume leverage risks that are unsustainable. This is the case when banks’
bonuses are indexed to short term performance, at the expense of sustainable performance hard to
quantify risk externalities. Externality is then an expression of market failure. For banks that are too big
to fail, these risk externalities are acute. For example, Frank Rich (The New York Times, Goldman Can
Spare You a Dime, October 18, 2009) has called attention to the fact that “Wall Street, not Main Street,
still rules Washington”. Similarly, Rolfe Winkler (Reuters) pointed out that “Main Street still owns much
of the risk while Wall Street gets all the profits”. Further, a recent study by the National Academy of
Sciences has pointed out to extremely large hidden costs to the energy industry—costs that are not
accounted for by the energy industry, but assumed by the public at large.
Banks and Central Banks rather than Governments, are entrusted to manage responsibly the monetary
policy—not to be used for their own and selfish needs, not to rule the “Commons”, but to the betterment
of society and the supply of the credit needed for a proper functioning of financial markets. A violation
of this trust has contributed to a financial meltdown and to the large consequences borne by the public at
large. In this case, “too big to fail banks” have contributed to an immense negative externality—costs
experienced by the public at large. In this sense, markets with appreciable negative externalities are no
longer efficient, even if we have perfect competition (i.e. complete financial markets). If a firm’s
negative externalities are not compensated by their positive externalities or appropriately regulated, then
their social risks can be substantial. In a recent New York Times article (Sunday Business, section,
October 4, 2009), Gretchen Morgension, referring to a research paper of Dean Baker and Travis
McArthur, indicated the effects of selective failures, letting selected banks grow larger and “subsidized”
at a cost of over 34 Billion dollars yearly over an appreciable amount of time.
Size is no cure to the failure of firms. For example, Fujiara [4], using an exhaustive list of Japanese
bankruptcy data in 1997 (see [2],[3],[5],[8],[10]) has pointed out to firms failure regardless of their size.
Further, since the growth of firms has been fed by debt, the risk borne by large firms seems to have
increased significantly—threatening both the creditor and the borrower. In fact, the growth of size
through a growth of indebtedness combined with “too big to fail” risk attitudes has ushered, has
contributed to a moral hazard risk, with firms assuming non-sustainable growth strategies on the one hand
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and important risk externalities on the other. Furthermore, when size is based on intensely networked
firm (such as large “supply chains”) supply chain risks (see also [15], [16] and [7]) may contribute as well
to the costs of maintaining such industrial and financial organizations. Saito [11] for example, while
examining inter-firm networks noted that larger firms tend to have more inter-firms relationships than
smaller ones and are therefore more dependent, augmenting their risks. In particular, they point out that
Toyota purchases intermediate products and raw materials from a large number of firms; maintaining
close relationships with numerous commercial and investment banks; with a concurrent organization
based on a large number of affiliated firms. Such networks have augmented both dependence and supply
chains risks. Such dependence is particularly acute when one supplier may control a critical part needed
for the proper function of the whole firm. For example, a small plant in Normandie (France) with no
more than a hundred employees could strike out the whole Renault complex. By the same token, a small
number of traders at AIG could bring such a “too big to fail” firm to a bankrupt state. This networking
growth is thus both a result and a condition for the growth to sizeable firms of scale free characteristic
(see also [3],[5]). Simulation experiments to that effect were conducted by Alexsiejuk and Holyst [1]
while constructing a simple model of bank bankruptcies using percolation theory on a network of
cooperating banks (see also [12] on percolation theory). Their simulation have shown that sudden
withdrawals from a bank can have dramatic effects on the bank stability and may force a bank into
bankruptcy in a short time if it does not receive assistance from other banks.
More importantly however, the bankruptcy of a simple bank can start a contagious failure of banks
concluded by a systemic financial failure. As a result, too big to fail and its many associated moral
hazard and risk externalities is a presumption that while driving current financial policy and protecting
some financial and industrial conglomerates (with other entities facing the test of the market on their own
and subsidizing such a policy), can be extremely risky for the public at large.
Size for such large entities thus matters as it provides a safety net and a guarantee by public authorities
that whatever their policy, their survivability is assured at the expense of public funding. The strategic
pursuit of economies of scales can therefore be misleading, based on fallacies that negate the risks of size,
do not account for latent and dependent risks, their moral hazard and significant risk externalities.
The essential question is therefore can economies of scale savings compensate their risks. Such an issue
has been implicitly recognized by Obama’s administration proposals in Congressional committees
calling for banks to hold more capital with which to absorb losses. The bigger the bank, the higher the
capital requirement should be (New York Times, July, 27, 2009, Editorial). However such regulation
does not protect the “commons” from the risk externalities that banks create and the common sustains.
To assess the effects of size and their risk externalities, this paper considers a particular and simple case
based on a firm risk exposure which can lead to a firm’s demise (its capital) and unbounded external
losses for which they assume no consequence. An example is used to demonstrate that such risk exposure
underlying excessive risk taking (motivated by the lure for short term profits) can have accelerating losses
the larger the bank.
Center for Risk Engineering, New York University Polytechnic Institute Page 4
2. Too Big Too Fail and Its Risk Externality.
Given the nature of a speculative position, we assume that the positions has a potential loss probability
distribution bounded above by the firm aggregate capital (its size, consisting of its equity and debt
holdings) or . In some cases, the speculative exposure of trades may be larger
than a firm’s capital. Further, a bank’s loss can have a repercussion on other external losses—the larger
the bank’s loss, the larger the potential external loss. Given a firm’s loss, we let its total loss, including
external losses be given by . As a result, the joint probability distribution of
global financial and firm losses is . A loss resulting
from a firm random exposure of its capital W has thus probability and cumulative distributions:
The effects of size on the aggregate loss are thus a compounded function of the probabilities of losses of
the firm and their external costs. If a firm has a loss whose external consequences (the loss y are
extremely large), then they may be deemed to be “too big to fail” as the negative externalities of its failure
may be too big to bear. In this context, the risks of “too big to fail” firms are similar to “polluters”, the
the greater their risk externalities, the greater their pollution.
The example we consider below assumes a Pareto probability distribution ([9]) for losses conditional on
the bank’s loss. Conditional external losses are bounded below by the bank loss (its capital) and
unbounded above. While, aggregate losses are a mixture probability distribution of the aggregate external
losses. These assumptions result in a fractional hazard rate model bounded by the bank’s capital.
Internal risk exposure (the banks’ capital at risk) is assumed to have an extreme truncated probability to
account for its finite capital at risk. In particular we use a truncated Weibull probability distribution.
Our approach differs from the Copula approach that models co-dependence of losses by the marginal
distribution of each distribution. It also differs from a generalization of the Pareto distribution (or other
probability distributions) that accounts for a potential correlation between the firm and its external losses.
Both such approaches are not be applicable in our case as external losses depend necessarily on the firm
losses but not vice versa. In other words, we assume that external losses are not causal to a bank’s loss
but a bank’s loss is causal to external losses borne by the public at large.
Further, while an inter-temporal framework based on Levy-Wiener processes and fractal diffusion models
can be considered as well, its use is not essential to prove the essential results of this paper. Such an
extension will be considered in a subsequent paper however. The case considered is thus selected for
simplicity and to highlight the effects of a bank’s potential capital loss on its external losses.
Explicitly, let the conditional loss Pareto distribution be:
The loss distribution parameter may be interpreted as the expected loss multiplier “odds” effect for a
given (risk exposure) loss by the bank. The expected external loss is thus . The larger the
“odds” the larger its the risk externalities. For example if a firm loss of 7 Billion dollars has an external
loss of 65 Billion dollars, its parameter is or and .
By the same token since,
Center for Risk Engineering, New York University Polytechnic Institute Page 5
The expected externality multiplier odds effect odds can be further scored and assessed by a logit
distribution. Explicitly, say that:
Then: and with a score defined as a function of both the loss and
economic environmental conditions. A bank whose internal loss is its capital, contribute then to an
expected loss of:
Where is a “Too Big To Bear” index, the larger the index, the larger the external losses and the more
a bank is “too big to fail”. In other words, letting a total capital loss of of 50 Billion dollars, the failure of
the bank’s loss is
Billion dollars.
The unconditional loss probability distribution is then:
The probability of a loss greater than Y and its hazard rate are therefore,
and
If a firm’s expected external loss is then and if it is too big to fail
then . In this case, the external risks of “size” are nonlinear, growing infinitely as the
bank’s size increases.
For demonstration purposes, say that the probability distribution is a constrained extreme
(Weibull) distribution defined by,
The loss probability distribution and its cumulative distribution function are then:
With expected losses:
Center for Risk Engineering, New York University Polytechnic Institute Page 6
The effects of the firm capital size on the expected losses are thus:
The second derivative leads to:
or
Since
The condition for a positive second derivative is:
These conditions establish therefore the conditions for an accelerating loss the larger the firm—a loss that
may be far larger than the firm capital loss.
Center for Risk Engineering, New York University Polytechnic Institute Page 7
Conclusion
The purpose of this paper is to indicate that size matters and its risk externalities may be too big to bear—
in which case firm may be too big to fail. Such firms are “polluters” either by design when they overleverage
their financial bets or speculative positions and are struck by a Black Swan [13], [14]. While
capital set aside (such as VaR—V alue at Risk) may be used to protect their internal losses, such
approaches are oblivious to the far morte important risk extrnalities. For this reason, such firms require
far greater attention and far more regulation. Internalizing risk externalities by ever larger firms is in such
cases inappropriate since the moral hazard and the market power resulting from such sizes will be too
great. Similarly, total controls, total regulation, taxation, nationalization etc. are also a poor answer to
deal with risk externalities. Such actions may stifle financial innovation and technology and create
disincentives to an efficicent allocation of money. Coase observed that a key feature of externalities are
not simply the result of one CEO or Bank, but the result of combined actions of two or more parties. In
the financial sector, there are two predominant parties, Banks that are “too big to fail” and the
Government—a stand in for the public. Banks are entrusted rights granted by the Government and
therefore any violation of the trust (and not only a loss by the bank) would justify either the removal of
this trust or a takeover of the bank. A bargaining over externalities would, economically lead to Pareto
efficient solutions provided that banking and public rights are fully transparent. However, the nontransparent
bonuses that CEOs of large banks apply to themselves while not a factor in banks failure is a
violation of the trust signaled by the incentives that banks have created to maintain the payments they
distribute to themselves. For these reasons, too big too fail banks may entail too large too bear risk
externalities. The result we have obtained indicate that this is a fact when banks internal risks have an
extreme probability distribution (as this is often the case in VaR studies) and when external risks are an
unbounded Pareto distribution.
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