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PERSPECTIVE doi:10.1038/nature09659 Systemic risk in banking ecosystems Andrew G. Haldane' & Robert M. May' In the run-up to the recent financial crisis, an increasingly elaborate set of fmancial instruments emerged, intended to optimize returns to individual institutions with seemingly minimal risk. Essentially no attention was given to their possible effects on the stability of the system as a whole. Drawing analogies with the dynamics of ecological food webs and with networks within which infectious diseases spread, we explore the interplay between complexity and stability in deliberately simplified models of financial networks. We suggest some policy lessons that can be drawn from such models, with the explicit aim of minimizing systemic risk. n the 1960s, the notion of the 'balance of nature' played a significant In what follows, we first consider the role of the growth in intrafmancial I part as ecologists sought a conceptual foundation for their subject. In particular, Evelyn Hutchinson', following Elton', suggested that "oscillations observed in arctic and bored fauna may be due in part to system claims in generating bank failure and instability, focusing on the problems inherent in prevailingmethods ofpricing complex derivatives,or arbitrage pricing theory (APT). Second, we sketch various ways in which the communities not being sufficiently complex to damp out oscillations". such an initial bank failure, or 'shock', may propagate to cause cascades of He went on to state, based on a misunderstanding ofMacArthur's' paper, subsequent failure. Third, we outline some tentative policy lessons that that there was now a "formal proof of the increase in stability of a com- might be drawn from these deliberately oversimplified models. Last, we ask munity as the number of links in its food web increases". how we might reshape the financial system to realize the economic benefits To the direct contrary, however, a closer examination of model eco- individual banks can deliver, while at the same time paying deliberate and systems showed that a random assembly ofNspecies, each of which had explicit attention to their system-wide stability. feedback mechanisms that would ensure the population's stability were it alone, showed a sharp transition from overall stability to instability as Potential causes of an initial shock the number and strength of interactions among species increased. More Events external to the banking system, such as recessions, major wars, civil explicitly, for N3, 1 this transition occurs once ma' > 1, where in is the unrest or environmental catastrophes, clearly have the potential to depress average number of links per species, and (±) a their average strengths. the value of a bank's assets so severely that the system fails. Although In ecology this has, since the 1970s, prompted a search for special probably exacerbated by such events, including global imbalances (China food-web structures that may help reconcile complexity with persistence as producer and saver, the United States as consumer and debtor), the or stability`'. Along these lines there is, for example, tentative evidence present crisis seems more akin to self-harm caused by overexuberance for modularity' (particularly in plant-pollinator associations, where within the financial sector itself. Perhaps as much as two-thirds of the linkages tend to be overdispersed or disassociative), and more generally spectacular growth in banks' balance sheet over recent decades reflected for nested hierarchies in food webs". The fact that some features of the increasing claims within the financial system, rather than with non- network structure of interactions (such as predator/prey ratios) inferred financial agents. One key driver of this explosive intrasystem activity from the Burgess Shale communities are similar to those in present day came from the growth in derivative markets. ones" reinforces hopes that this is a meaningful area of research. In 2002, when Warren Buffet first expressed his view that "derivatives are In the wake of the global financial crisis that began in 2007, there is financial weapons of mass destruction"", markets—although booming— increasing recognition of the need to address risk at the systemic level, as seemed remarkably stable. Their subsequent growth, illustrated in Fig. 1, distinct from focusing on individual banks". This quest to understand has been extraordinary, outpacing the growth in world gross domestic the network dynamics of what might be called 'financial ecosystems' has product (GDP) by a factor of three. In some derivatives markets, such as interesting parallels with ecology in the 1970s. Implicit in much eco- credit default swaps (CDS), growth has outpaced Moore's Law. These nomic thinking in general, and financial mathematics in particular, is developments contributed significantly towards an unprecedented influx the notion of a 'general equilibrium. Elements of this belief underpin, ofmathematically skilled people (quantitative analysts) into the financial/ for example, the pricing of complex derivatives. But, as shown below, banking industry. These people produced very sophisticated tech- deeper analysis of such systems reveals explicit analogies with the con- niques (including APT), which seemingly allowed you to put a price on cept that too much complexity implies instability, which was found future risks, and thus to trade increasingly complex derivative contracts— earlier in model ecosystems. bundles of assets—with risks apparently decreasing as the bundles grew. There are, of course, major differences between ecosystems and However, recent empirical and theoretical studies have indicated that financial systems. For one thing, today's ecosystems are the winnowed the trading activity associated with derivatives can have significant effects survivors of long-lasting evolutionary processes, whereas the evolution on markets"-".More specifically, Brock and colleaguesw have shown that of financial systems is a relatively recent phenomenon". Nor have proliferation ofhedging instruments can destabilize markets. Building on selective pressures been entirely dispassionate, with the hand of govern- this, Caccioli and colleague?' note that APT makes several conventional ment a constant presence shaping financial structures, especially among assumptions upon which everything else depends: "perfect competition, institutions deemed "too big to fail"". In financial ecosystems, evolu- market liquidity, no-arbitrage and market completeness". Crucially, this tionary forces have often been survival of the fattest rather than the adds up to the implicit assumption that trading activity has no feedback fittest. on the dynamical behaviour of markets. And indeed, in the APT-fuelled 'Bank of England.Threadneedle Steer.London EC2R BAHUlt 2Zoolow Department Oxford Unirersdy. Oxford OKI 3PS. UK. 20 JANUARY 2011 I VOL 469 I NATURE 1 351 02011 Macmillan Publishers limited. All rights reserved EFTA00610315  RESEARCH PERSPECTIVE 700 For n > n•, the average supply increases with increasing n (that is, increasing proliferation of financial instruments) if c > 0. Conversely, 600- for c < 0 the supply decreases with increasing complexity once n > n•.It 500 - is emphasized" that such sensitivity in market behaviour in the neigh- bourhood of the singularity can easily produce very strong fluctuations— 400 either positive or negative—in the volume of trading in derivative markets. g - Note that the consequences of this singularity are not easily intuited 200 - from the competitive equilibrium setting. It seems to us that the basic process—in grossly simplified terms—is that once there are enough deri- 100- vatives to span the space of available states of nature (the net supply of derivatives within the system necessary to meet true hedging demand 0 from non-banks), the market is essentially complete in the sense of the 1999 1999 2000 2001 2002 2005 2004 2005 2006 2007 2006 '1009 Year Arrow-Debreu" model. Once that happens, gross derivatives positions within the system are essentially unbounded. So long as there is an Figure I I Notional principal value of outstanding derivative contracts, as incentive to supply new instruments—a positive premium to trading— recorded at year end. These include foreign exchange, interest rates, equities, banks will continue to expand gross positions, independent of true commodities and credit derivatives. Data from UK Department for Business. hedging demand from non-banks. Such trades are essentially redundant, Innovation and Skills. International Monetary Fund and Bank of England calculations. increasing the dimensionality and complexity of the network at a cost in terms of stability, with no welfare gain because market completeness has boom time that preceded the bust, APT seemed to be very successful.Inits already been achieved. imaginary world, market failures are caused by regulatory carelessness, Caccioli and colleagues" also examine a measure ofmarket volatility as resulting in a focus on creating institutional arrangements that seek to the risk premium parameter c varies. If they calculate this quantity under guarantee the premises upon which APT is bestir". To the contrary, the approximation that the fluctuations in the values of the individual Caccioli and colleagues argued" that APT is not a 'theory' in the sense 'supply variables' (s,; derivatives,etc) are completely uncorrelated, they in habitually used in the sciences, but rather a set ofidealized assumptions on effect recover the happy world of APT, with no singularities. This which financial engineering is based; that is, APT is part of the problem strongly indicates that the highly important singularities in their accurate itself. and self-consistent calculations, with market dynamics included, are Caccioli and colleagues" illustrate their point by exploring the associated with the supplies ofdifferent derivatives being strongly corre- dynamical properties of a model that gives a more realistic caricature lated in this domain, as has found to be the case among derivatives of markets, going beyond the idealized world of APT to include the markets in practice. effects of individual trades on prices. Prices now depend on the balance In summary, Caccioli and colleagues suggest that the idealized between demand and supply. The outcome is that "the road to efficient, assumptions upon which recent financial engineering has been based arbitrage-free, complete markets can be plagued by singularities which can give a misleading account of potential instabilities in markets. They arise upon increasing financial complexity"". also note that these instabilities echo those that can develop in ecosys- tems as complexity increasest". Figure 2 illustrates the main results of the analysis by Caccioli and colleagues". Here n is essentially a measure of the proliferation of deriva- Propagation of shocks within financial systems tives or similar financial instruments, and s is the overall average value of the supply ofany one such derivative/financial instrument. The parameter In ecology's models of food webs, aimed at qualitative understanding of their dynamical response to perturbation, the nodes are simply species, c encodes the risk premium that banks require for trading derivatives". linked to other nodes/species as prey, predator, competitor or mutualist. we see from Fig. 2 that if,' is less than fie (here rie = 4.14), the average Inepidemiological networks, the nodes are susceptible, infected/infectious supply of derivatives, s, is relatively steady and essentially independent or recovered/immune individuals linked by sexual or other contacts. But of the banks' risk premium (as measured by a). But as market complexity in a minimally realistic caricature of financial networks—henceforth increases, so that n approaches n", there is a sharp singularity at a = 0. called banks—the nodes have a more complex structure. FollowingNier and colleagues' and Gai and Kapadia30, we define such 0.9 a bank/node as schematically illustrated in Fig. 3. In this deliberately 0.8 0.01 oversimplified scheme, a bank's activities are partitioned among four categories. Two represent assets: interbank loans (4) and external assets 0.7 (ed. The other two represent liabilities: interbank borrowing (6,) and 0.6 deposits (4).11m subscript i labels the specific bank (i = 1, 2, ..., N for a total ofNbanks). Solvency requires that the difference between a bank's 0.5 assets and its liabilities (the capital reserve or 'net worth', labelled 7, in 0.4 Fig. 3) be positive. That is, i5 = (e, + - (d, + LJ a 0. These banks are now assumed to be interlinked in a random, Erd6s- 0.3 • Renyi network, with any one of the N banks connected to any other as 0.2 • lender or borrower, or possibly both, each with probability p. A bank's 0.1 average number of incoming/borrowing or outgoing/lending links is 11141,4*-•—•- then z = p(N - 1). 0 Various further assumptions are now made to carry these Bank of 10 England/Federal Reserve Bank of New York models to the point where Figure 21Discontinuous transition to instability of derivatives as the knock-on effects of a single bank failure can be explored in numerical complexity increases. Average supply ofany one derivative. s. at competitive simulations. Much ofthe essential findings ofsuch studies can be captured, equilibrium as a function of the number, n, ofdifferent derivatives being traded, and made more transparent, by a 'mean-field' approximation in which for various values ofbanks' risk premium, c. Adapted with permission from re(. each bank has exactly average behaviour". This means all banks are the 21. For fuller discussion, see text. same size (resealed to I), every bank is linked to exactly z others, all loans 3S2 I NATURE I VOL 469 120 JANUARY 2011 0201i Macmillan Publishers Limited. All rights reserved EFTA00610316  PERSPECTIVE RESEARCH SMOCK of z banks go down; in the red triangle (0, 1, B) there is a third phase of (to e, or?) roughly 22 failures; and so on. Note that, when (as above) the initial Lab.(Les shock is to external assets, the system's fragility is maximized (failures for relatively large values of y) by 0 having values intermediate between 0 Net worth Er) and 1, which in some ways very roughly corresponds to banks substan- tially engaged in both retail and investment (high-street and casino) Deposits activity. As seen earlier and in Fig. 4, an increase in the system's con- (or) 0 -0,19, nectivity, z, causes the coloured region of instability to shrink; high connectivity distributes, and thereby attenuates risk On the other hand, when later-phase failures do occur, they will then involve more banks. A second, and almost surely more important, source of shock pro- 1 pagation arises from losses in the value of a bank's external assets, caused Interbank by a generalized fall in market prices, a rise in expected defaults or a borrowing (b) failing bank's 'fire sale' actions. Such market liquidity shocks are con- ventionally and sensibly represented by discount factors that, for a given asset class, are proportional to the number of failing banks holding the asset. This may be generalized to distinguish between strong liquidity shocks, associated with discounting specific asset classes, and weak Figure 3 1 Schematic model for a node in the interbank network Adapted liquidity shocks, resulting from the expectation of further defaults or a with permission front ref. 25. more general loss of confidence". In all cases and in sharp contrast to the attenuation in interbank loan shocks, liquidity shocks amplify as more banks fail. Thus, relatively small initial liquidity shocks have the poten- have the same magnitude, as do the capital reserves, 7, and the ratios of tial to make strong contributions to systemic risk loans to total assets, 0. A third mechanism of shock propagation, which has been a marked— As illustrated in Fig. 3, all these models study the consequences of a and in many peoples' opinion the most important—feature of the recent shock that initially hits a single bank, wiping out a fraction, f, of its crisis has been the diminished availability of interbank loans, or in the external assets. If the magnitude of this shock exceeds the capital reserve, jargon of the trade, 'funding liquidity shocks'. This has often taken the f(l — 0) > 7, the bank fails. This is a deliberate oversimplification, aimed form of liquidity hoarding in interbank funding markets. Gai and at a clearer understanding of how an initial failure can propagate shocks Kapadia" have recently shown how such liquidity hoarding can cascade throughout the system. through a banking network with severe consequences. As one bank calls The most direct effect of such a failure is that its z creditor banks will in or shortens the term of its interbank loans, affected banks tend in turn lose part or all of their loans. If such losses exceed y, these banks in turn to do the same. The result is a liquidity-hoarding shock that is not will fail, propagating a third phase of shocks to those remaining, and so subject to the attenuation characteristic of interbank default shocks. on. Note, however, that a failing bank's losses are in effect divided among All three propagation mechanisms can be drawn together within the its z creditors, so that each subsequent phase of loan-driven shocks is framework defined by Fig. 3 (see also N. Arinaminpathy, S. Kapadia and attenuated, approximately by a factor z. M., manuscript in preparation). The model can also be generalized Figure 4 illustrates one of the tentative messages emerging from this to treat banks of varying size, including the extreme but realistic case of a toy model, showing regimes of failure in terms of the critical parameter). few very large all-purpose banks, each connected to many smaller banks; (capital reserves relative to bank size) and 0 (interbank activity as a interconnectivity within real banking networks is far from random"-", fraction of total assets). Within the unhatched triangle (0, I, f), the with long-tailed degree distributions. It also seems that these networks initially shocked bank fails; in the blue triangle (0, 1, A) a second tranche tend to be disassociative rather than proportionately connected: that is, big banks are disproportionately linked to smaller ones, and conversely. Such a 'wiring up' of a network is known, unfortunately, to maximize the number of individuals infected by an agent that is transmitted by inter- =a(1 +zo)y personal contact". On the other hand, such disassociative structures are 8 likely to support a larger number of coexisting banks (another link Y = zy s between ecology and banking"), and can make the network more robust to random losses". Some of this work, particularly that on liquidity shocks, echoes an important insight from pervious work".'" (N. Beale and colleagues, manuscript in preparation). This is that excessive homogeneity within a 1- z a financial system—all the banks doing the same thing—can minimize = risk for each individual bank, but maximize the probability of the entire system collapsing. A very simple toy model illustrates this. Suppose you have N banks and N distinct, uncorrelated asset classes, each of which has some very small probability, e, of having its value decline to the extent that a bank holding solely that asset would fail. At the inhomo- f I +z(1 +raj 1. -Vz Net worth (y) geneous extreme, assume each bank holds the entirety of one of the N assets: the probability for any one bank to fail is now s, whereas that for Figure 4 I Domains of interbank lending. Domains arc expressed as a the system is a vastly smaller e j. At the opposite, homogeneous extreme, fraction of total assets. O. and capital reserves or net worth, y, which result in the assume all banks are identical, each holding IIN of every one of the N propagation of interbank loan shocks. The triangle (I, 0,f) defines the region where loss of a fractionfof a bank's external assets will cause it to fail. The blue assets: the probability for any one bank to fail can now be calculated as triangle(1, 0, A) depicts the region in which creditors of the initially failing bank NN EN/N!, and this is obviously also the probability for all N of these will receive phase II shocks which cause them also to fail, and the red area (I, 0, banks to fail. This homogeneous, 'herding behaviour' limit clearly makes B) shows the region in which phase HI shocks cause failure. Adapted with each individual bank safer, but the systemic risk is much larger. More permission from ref. 27. realistic versions of this scenario consistently show the same unhappy 20 JANUARY 2011 I VOL 569 I NATURE 1 353 02011 Macmillan Publishers Limited. All rights reserved EFTA00610317  RESEARCH PERSPECTIVE conclusion. Tentative evidence comes from the fact that the world's five on 'super-spreaders' within the network to limit the potential for sys- largest banks have shown increasing concentrations of assets over the tem-wide spread. Although initially applied in the study of contagious last ten years, in contrast to the top five hedge funds, whose less con- diseases, such as HIV/AlDs, this same insight has since been applied in centrated systems can give greater scope for diversity. The former are in managing the dynamics of the world wide web, power grids and bio- trouble, the latter much less so. logical ecosystems"'. If anything, this same logic applies with even greater force in banking. Implications for public policy There has been a spectacular rise in the size and concentration of the All the studies described earlier involve numerical simulations, but financial system over the past two decades, with the rapid emergence of many combine such work with analytic results of the kind exemplified 'super-spreader institutions' too big, connected or important to fail by Fig. 4. Such analysis of the dynamics of deliberately oversimplified (Fig. 5). The collateral damage, to both the real economy and financial models of financial ecosystems carries potentially far-reaching implica- system, following the failure of Lehman Brothers in October 2008 is tions for the design and implementation of public policy. These impli- testimony to the force of such super-spreader dynamics. Protecting cations include the following. the financial system from future such events would require the key super-spreader nodes to run with higher—potentially much higher— Setting regulatory capital/liquidity ratios buffers of capital and liquid assets, which are then proportional to the The cornerstone of the current international regulatory agenda is the system-wide risk they contribute. setting of higher requirements for banks' capital and liquid assets. The A second source of system-wide risk, in addition to super-spreader traditional rationale for such requirements is that they reduce idio- failures, arises from aggregate external events, such as booms and busts syncratic risks to the balance sheets of individual banks. An alternative in the real economy. Indeed, historically this has been the largest single and more far-reaching interpretation is that they are a means of source of banking problems. If regulation could be operated counter- strengthening the financial system as a whole by limiting the potential cyclically, with buffers rising in booms and falling in recessions, this for network spillovers. With this wider objective, prudential regulation would lessen systemic risk from this particular source. Why? Because is following in the footsteps of ecology, which has increasingly drawn on increasing insurance in a boom would increase system-wide resilience a system-wide perspective when promoting and managing ecosystem against the subsequent bust, as well as providing an incentive for banks resilience. to curb risk-taking during the boom. Operating regulation in this way The systemic rationale for financial regulatory intervention is well illu- would be a new departure for prudential policy—so-called macro- strated by the dynamic modelsoutlined earlier. Consider banks' buffers of prudential policy—but a potentially important ones"' from a systemic capital or net worth (y). These capital ratios have been in secular decline in risk perspective. relation to banks' total assets for at least the past 150 years in the United Kingdom and United States". Reversing these trends by setting higher Netting and clearing derivatives required capital ratios strengthens the absorptive capacity of each of the The rapid growth in the size and complexity of the derivatives market nodes in the financial network in response to external shocks. As impor- contributed importantly to the destabilizing dynamics of the system tantly, however, it also lessens the risk of idiosyncratic defaults cascading under stress during the recent financial crisis. This begs questions about around the system, as illustrated in Fig 4. the underlying structure and dimensionality of the derivatives market. Broadly, the same arguments apply in the setting of regulatory One means of simplifying the complex web of interactions between requirements on banks' liquid assets. These liquidity ratios have also banks in derivatives markets is to centralize the trading and clearing been in secular decline in the United Kingdom and United States, for at of these instruments. For example, central counterparties interpose least the past half century. Typically, liquidity requirements are specified themselves between every bilateral transaction, thereby replacing a as a minimum ratio of banks' liquid assets to their short-term liabilities. cat's-cradle of financial network interactions with a single hub-and- This liquidity ratio can be seen as a means of short-circuiting the poten- spokes configuration. Provided the central counterparty is extremely tial for systemic liquidity spillovers arising from fire sales on the asset robust—to prevent it becoming a super-spreader itself—the upshot is side of the balance sheet (liquidity shocks) or liquidity hoarding on the liabilities side (liquidity-hoarding shocks). In particular, holdings of 45 liquid assets reduce the potential for market liquidity risk to propagate around the system, while limits on short-term liabilities reduce the 40 spread of funding liquidity risk around the system. 35 Setting systemic regulatory requirements 30 Looking at financial risk through a network lens indicates a fundament- 25 ally different rationale for prudential regulation. It also indicates a quite different calibration of such regulation. Prudential regulation has 20 become increasingly risk-based with the advent of first Basel I and 15 latterly Basel II. But the risk in question to which regulation was then calibrated has tended to be institution-specific rather than systemic risk. 10 To give an example, as conventionally calibrated, capital regulation 5 seeks to equalize failure probabilities across individual institutions to a 0 given tolerance threshold—such as a 0.1% probability of failure. 1896 18M 093 1947 961 1166 0091033 1347 1971 1091139 1910 107 091190 191/12oo Nor Approaching this problem from a system-wide angle indicates a rather Year different calibration. Instead, the objective would be to set firms' capital requirements to equalize the marginal cost to the system as a whole of Figure 5 I Recent rise in the size and concentration of the United States their failure. In other words, regulatory requirements would be set financial system. This figure illustrates the marked increase in assn concentration within the United States banking system since the Glass-Steagal higher for those banks bringing greatest risk to the system; for example, restrictions were revoked in 1999. Red line represents the Gramm-Leach- because of their size or connectivity. Wiley Act (1999). which revoked Glass-Steagal restrictions. Data include only Although new in the context of banking, the essential insight here is the insured depository subsidiaries of bariks to ensure consistencyover time; for an old one in the study of epidemiological networks. Anderson and example. non-deposit subsidiaries arc not included. Data from the Federal May" established the theoretical case for focusing preventative action Deposit Insurance Corporation. 364 I NATURE I VOL 469 20 JANUARY 201 1 02011 Macmillan Publishers Limited. All rights reserved EFTA00610318  PERSPECTIVE RESEARCH a less complex and lower-risk financial network Efforts are underway 7. Dunne, J. A. et at Network struchre and robustness of marine food webs.Mar.Ecot Prog. Sec 273.291-302 (2004). internationally to extend the scope and reach of central counterparty 8. May, R. M. Network structure and the biology of populations. Trends foot Evol 21, clearing, in particular to ensure it covers transactions in complex over- 394-399 (2006). the-counter derivative instruments, such as CDS (D. Duffle and H. Zhu, 9. Bascompte. J. Disentangling the web of life. Science 325, 416-419(2009). 10. Suithara,G.8Ye, H.Coopemtive network dynamics.Nature458,979-980(2009). manuscript in preparation). 11. Dunne, J.A.ef at. Compilation andnetwork analyses of Cambrian (cod webs.PLoS In parallel, there are international efforts to reduce the dimensionality of Blot 6, e102 (2008). derivatives contracts by eliminating redundant trades and through netting. 12. Haldane. A G. Rethinking the financial network (http:/Avonv.ban kofengland.co. This redundancy might arise either because contracts have been reassigned uk/publkations/speeches/2003/speech386.pif) (2009). 13. lanes-C. Preventing system failure. Cent Banking 21, 69-75 (2010). to participants (but the claim not extinguished) or because there are per- The survey of recent thinking about financial networks, in lay language. fectly offsetting bilateral transactions between two parties that can be netted. 14. Fanner. J. D. Market force. ecology and evolution. Ind. Co, Change 11, 895-953 For example, the stock of CDS contracts has already been reduced by (2002). 15. Haldane. A G. The 5100 billion question. (http://wvm.bankofengland.cauk/ around S25 trillion since December 2007 as a result of such netting arrange- publicationstspeeches/2010/speech43300 (2010} menu. Looking forward, there may be more sophisticated multilateral net- 16. Buffet. W. E. Chairman's Letter. Berkshire Hathaway Inc 2002 Annual Report 15 ting algorithms that can be used to reduce further derivatives balances. (2002). A prescient and clearly expressed waming of problems inherent in derivatives. 17. Sircar. K. R. & Papanicolau. G. General Black-Scholes models accenting for Shaping the topology of the financial network increased market volatility from hedging strategies. Aopt Math. Finance 5, 45-82 The analytic model outlined earlier demonstrates that the topology of (1998). the financial sector's balance sheet has fundamental implications for the 18. Avellaneda. M. & Lipkin, M. D.A market-induced mechanism for stack pinning. Quantit Finance 3,417-425 (2003). state and dynamics of systemic risk. From a public policy perspective, 19. Osier. C. L Macro lessons from microstructure. Int 1 Finance Econ. 11, 55-80 two topological features are key's. (2006). First, diversity across the financial system. In the run-up to the crisis, 20. Brock. W.A. Hammes. C. H. & Wagner. F. 0.0. More hedging instruments may destabilise markets.!. Econ. Dynan. Cent 33, 1912-1928 (2008} and in the pursuit of diversification, banks' balance sheets and risk 21. Caccioli, F.. Marsiti. M. &Vivo. P. Eroding market stability by proliferation of management systems became increasingly homogenous. For example, financial instrument. Eur. Phys. -I. B 71,467-479 (2009). banks became increasingly reliant on wholesale funding on the liabilities A sophisticated and important analysis of a major flaw in the pricing of side of the balance sheet; in structured credit on the assets side of their derivatives. 22. Pfiska. S. R. fntroduction to MathematicalFinance: Discrete Time Modals (Blackwell. balance sheet; and managed the resulting risks using the same value-at-risk 1997). models. This desire for diversification was individually rational from a risk 23. Arrow, KJ. & Debreu. G. Existence of an equilibrium for a competitive economy. perspective. But it came at the expense of lower diversity across the system £conometrica 22, 265-290 (1954). 24. May, R. M. Stability and Complexity in Model Ecosystems (Princeton Univ. Press. as whole, thereby increasing systemic risk. Homogeneity bred fragility (N. 1973). Beale and colleagues, manuscript in preparation). 25. Nier, E., Yang J.. Yorulmazer. T. & Alentorn. A. Network models and financial In regulating the financial system, little effort has as yet been put into stability./ Econ. Dyn. Control 31, 2033-2060(2007). 26. Gai. P. & Kapadia. S. Contagion in financial networks. Proc. R. Soc. A 466, assessing the system-wide characteristics of the network, such as the 2401-2423(2010). diversity of its aggregate balance sheet and risk management models. 27. May, R. M. & Arinaminpathy. N. Systemic risk: the dynamics of model banking Even less effort has been put into providing regulatory incentives to systems. / R Sac Interface 7, 823-838 (2010). promote diversity of balance sheet structures, business models and risk 28. Gai. P. & Kapadia. S. Liquidity hoarding. network externalities. and interbank market collapse.Proc.R Soc. A 466.2401-2423 (2010). management systems. In rebuilding and maintaining the financial sys- 29. Schweitzer. F. et at Economic networks: the new challenges. Science 325. tem, this systemic diversity objective should probably be given much 422-425 (2009). greater prominence by the regulatory community. 30. May,n.Levin,S.A.&Sugihara,G.Complexsystems: ecology forbankers Nature 451, 893-895 (2008). Second, modularity within the financial system. The structure of A brief overview of the 2006 NAS/FRBNY study on systemic risk. many non-financial networks is explicitly and intentionally modular. 31. Kyriakopoulos. F. et at. Network and eigenvalue analysis of financial transaction This includes the design of personal computers and the world wide web networks. Eur. Phys.& B 71, 523-631(2009).