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Appendix

Published onApr 08, 2020
Appendix
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A.1  Asset Interconnectedness Literature Review

Much of the recent literature on asset connectedness provides theoretical support for the conjecture of Haldane (2009) that a densely connected financial system is “robust yet fragile” so that “[w]ithin a certain range [of negative shocks], connections serve as a shock-absorber [and] [c]onnectivity engenders robustness, [but outside that range] the system [flips to] the wrong side of the knife-edge” and distress spreads.1 So asset connectedness may actually be a way to absorb shocks rather than a cause for meltdown. For example, Acemoglu, Ozdaglar, and Tahbaz-Salehi (2015)2 study a banking network connected by a cross-holding of unsecured debt contracts. This model includes a “small shock” regime and a “large shock” regime. In the small shock regime, “a more diversified pattern of interbank liabilities implies that the burden of any potential losses [from a borrowing bank] is shared among more banks, creating a more robust financial network.”3 However, in the large shock regime, “dense interconnections act as a channel through which shocks to a subset of the financial institutions transmit to the entire system creating a vehicle for instability and systemic risk.”4 The dividing line between the large and small shock regimes is a negative shock equal to the “total excess liquidity available to the financial network as a whole.”5 Specifically, the dividing line is an idiosyncratic shock equal to all cash held by banks that is not required to meet external liabilities.6 Like other models of asset connectedness, this dividing line is too high to offer a plausible explanation of the 2008–2009 financial crisis, or prospective future crises.

Other recent literature has added some insight to the relationship between asset connectedness and contagion. For example, Elliot, Golub, and Jackson (2014)7 analyze a model of connectedness that looks at the effects of integration (i.e., a measure of a firm’s asset exposure to other firms) and the effects of diversification (i.e., the number of firms that a given firm is exposed to). Under this model, an initial shock can be amplified when one bank loses value discontinuously after its value falls below a certain critical threshold. Elliot, Golub, and Jackson offer a variety of explanations for the sharp drop in value. For example, a bank might be downgraded, pushing up its cost of capital. More generally, “many of these discontinuities stem from … illiquidity which then leads to an inefficient use of assets.”8 In other words, a small initial shock can be amplified by a sudden withdrawal of liquidity (runs on the bank) that destroys value and magnifies an otherwise minor event into a systemic crisis. They find that an economy is most susceptible to the chain reaction of failures (cascading failures) in the middle region—a system that include firms that are both partially integrated and partially diversified.9 While asset connectedness plays an important role in shaping the propagation and magnitude of the crisis, the root cause of collapse is value destruction related to illiquidity and contagion. Although they focus on chain reaction failures, which were not observed during the crisis, it may be the case that their results could apply to “cascading losses” that fall short of actual insolvency. For example, suppose Bank A owns the debt of Bank B. If Bank B suffers a shock, which is amplified by illiquidity costs, Bank A will also experience a discontinuous drop in asset prices, as the value of its Bank B debt holdings also dropped discontinuously. Importantly, the mechanism driving the cascade is amplification of the initial shock by run behavior.

Simulation studies are a partial substitute for empirical studies of bank failure, which are often impractical owing to the infrequency of financial crises and the tendency of governments to intervene when they do occur. Upper (2011) reviews a large body of literature that uses “counterfactual simulations to estimate the danger of [cascading failures] owing to exposures in the interbank loan market.”10 He finds that the vast majority of this literature “focus[es] on the unanticipated failure of individual banks,” but observes that historical banking crises were not caused by “the domino effects of idiosyncratic failures.”11 Upper observes that one important shortcoming of these models is the assumption that “banks sit tight as problems at their counterparties mount,” until an unanticipated default triggers a cascade of failures.14 However, in reality, counterparties “react by cutting credit lines, [by] not rolling over maturing debt, [and] by novating derivatives contracts.”12 These simulation studies cannot account for the events witnessed in the 2008–2009 financial crisis.

A.2  Liability Interconnectedness Literature Review

This literature can be broadly categorized into two groups. The first group uses network theory to evaluate how an illiquidity shock to one firm propagates to others. The second group identifies liability connectedness through reliance on a “common liquidity pool.”

A.2.1  Liability Connectedness through the Lens of Network Theory

One body of literature uses the tools of network theory to examine how a funding shock to one firm spreads to other firms through the interbank lending market. These papers attempt to characterize how the structure of linkages between individual institutions affects the likelihood and severity of a systemwide funding dry up. According to this literature, the complexity of direct and indirect linkages between institutions within a financial network is a critical component of a network’s resilience. Many studies have analyzed how direct funding linkages, while introducing the possibility of systemic failure, can also prevent such failure where banks engaging in cross-holdings of deposits effectively insure each individual bank against an idiosyncratic liquidity shock. For example, if Bank A and Bank B each hold one another’s deposits, a liquidity shock to Bank A can be met simply by liquidating its holdings in Bank B.13 Such a network works well when there is sufficient aggregate liquidity in the system to meet demand, but in the case where demand exceeds supply even a small, localized liquidity shock to one bank can spread rapidly through the entire financial network through direct interbank lending arrangements. When an initial shock causes a bank to fail, this failure reduces the overall pool of common liquidity available for the remaining solvent banks in the network. A negative feedback cycle can afflict the system whereby insolvency reduces liquidity, which then causes further insolvency, and so on. The end result can be complete systemic collapse. To a degree, the numerous interconnections between banks within a network serve as a “shock absorber,” diffusing the shock throughout the vastness of the financial system, much as does asset connectedness as discussed above. The network provides mutual insurance to each institution, and negative shocks dissipate with no systemic consequences. However, the range of absorbable shocks is bounded by a “tipping point.” Beyond this point, interconnections no longer dampen the shock to the system but rather serve to amplify and propagate the damage; this is the same analysis as discussed above for asset connectedness. “The system acts not as a mutual insurance device but as a mutual incendiary device.”14 While the precise threshold of absorbable shocks can be difficult to specify, the existence of such “tipping points” in a connected network can be shown.15

The concentration of institutions within a financial network also plays an important role in the propagation of a shock through the system. A more concentrated (“fat-tailed”) network is one with a small number of highly connected key players, where connectedness refers to both the number of interbank relationships and the total value of those relationships.16 A concentrated network is more robust to random shocks than less concentrated networks, provided the shocks are within a given range.17 However, for shocks outside that range, “higher concentration in the network makes the system more susceptible to a systemic liquidity crisis.”18 Furthermore, since concentrated networks are vulnerable to shocks targeting the key players, when the initial shock hits the most connected interbank lender, the likelihood of systemic failure increases.19 However, it may require an exceptionally large liquidity shock to destabilize the system. For example, in Gai, Haldane, and Kapadia (2011) instability is triggered by a sudden doubling of repo haircuts.20 The only plausible explanation for such a tremendous liquidity shock is run-like behavior (i.e., contagion), so connectedness absent contagion would not be a serious problem.

Over the decade preceding the 2008 financial crisis, US financial networks increased in complexity, concentration, connectedness, and homogeneity. From a network theory perspective, such a combination leads to fragility.21 Securitization and derivatives have lengthened the network chains, while also multiplying the number of links between institutions. Over the past two decades, nodes in the financial network have increased fourteen-fold and “links have become fatter and more frequent, increasing roughly 6-fold.”22 As firms diversified and engaged in risk management strategies with common characteristics, the diversification of individual firms created less diversity in the aggregate system. The network became more homogeneous. Finally, the international finance network has increasingly displayed the characteristics of a fat-tailed network, comprising a relatively small number of highly connected financial institutions.23

These features have resulted in a “robust-yet-fragile” system, well equipped to absorb adverse shocks within a given range but vulnerable to failure in the case of shocks outside that range. In addition to the relative magnitude of the shock, the location of a shock in the network (i.e., hitting a so-called super-spreader) can have catastrophic consequences for systemic stability.24 The basic fragility of the US financial network is best illustrated by the fact that, while the system demonstrated resilience to “fairly large shocks prior to 2007 (e.g., 9/11, the Dotcom crash and the collapse of Amaranth to name a few),”25 the past fifteen years were in fact a “lengthy period of seeming robustness (the Golden Decade from 1997 to 2007) ... punctuated by an acute period of financial fragility.”26

Importantly, in most theoretical network models of liability connectedness, the destabilizing mechanism is not a cessation of lending due to default of a lender. Instead, the financial system is disrupted by contagious waves of liquidity hoarding. The structure of the network determines how an initial shock is transmitted throughout the system, but the fundamental destabilizing force is an abrupt onset of liquidity hoarding behavior, often without regard the credit quality of a bank’s counterparties. Hence liability connectedness itself is less problematic than contagious run-like behavior.

A.2.2  Liability Connectedness through Reliance on a Common Pool of Liquidity

A second body of literature examines how banks are exposed to funding shocks through reliance on a common pool of liquidity. Empirical studies have documented that market liquidity (the ease with which an asset is traded) co-varies with market prices and volatility,27 and that an asset’s sensitivity to market liquidity is priced (e.g., the less liquid, the lower price).28 The value of liquidity provides some explanation for the “flight to quality” or “liquidity hoarding” that takes place during crises. Archarya and Pedersen (2005) set forth an equilibrium model that explains these phenomena. Brunnermeier and Pedersen (2009) propose a model that further explains these phenomena and includes a feedback mechanism that illustrates how this need for liquidity can create financial fragility. In their framework, an “asset’s market liquidity is linked with investors’ “funding liquidity (i.e., the ease with which a firm or more generally an investor can obtain funding).” When market liquidity decreases, and the value of assets decrease as a result, margin requirements will increase. But, if funding liquidity also decreases, it will be difficult to obtain such margin. Thus a small shock to market liquidity can produce outsize effects on market prices through “margin spirals” and “loss spirals.” In a loss spiral, firms are forced by a drop in market prices to liquidate assets, which further impairs market liquidity and also asset prices. As a result firms are faced with ever more increased demands for collateral. In a margin spiral, increased demands for collateral prompt firms to sell into an illiquid market, feeding back into the loss spiral. This mechanism creates multiple equilibria in which “a small change in fundamentals can lead to a large jump in illiquidity” and a corresponding decline in asset prices. These spirals may be transmitted between markets and institutions. According to Kodres and Pritsker (2002), “the correlated liquidity shock channel posits that when some market participants need to liquidate some of their assets to obtain cash, perhaps due to a call for collateral, they chose to liquidate assets in a number of markets, effectively transmitting the shock.” This illustrates how contagion can spread throughout the financial sector via fire sales, even absent direct balance sheet links between institutions. A similar point is made in Liu (2015), that “indirect interconnectedness” can occur though fire sales and mark-to-market accounting practices.29 However, these are really consequences of contagion and not the chain reaction of failures that is the key feature of interconnectedness. While Liu (2015) also posits that correlation of CDS spreads is evidence of interconnectedness, that is more indicative of correlation, discussed below.

A.3  Measures of Systemic Risk

Adrian and Brunnermeier’s (2010) CoVaR estimates the value at risk of a given financial institution conditional on financial distress occurring at other financial institutions in the industry.30 A financial insititution’s systemic risk measure is therefore defined as the difference between the firm’s CoVaR when in a distressed state and the firm’s CoVaR when in a stable state. Adrian and Brunnermeier attempt to use firm characteristics such as size, leverage, and maturity mismatch to construct forward-looking measures of CoVar and therefore predict systemic risk (systemic risk as defined by the authors). In effect, the CoVar analysis is really predicting changes in correlation without providing any direct measure of connectedness or contagion. The measure therefore leaves a wide hole in systemic risk predictions since it does not predict systemic risk that results from contagion or connectedness. While the CoVaR measure may be a useful tool in monitoring correlation, its failure to address the most significant driver of systemic risk—contagion—is a major limitation.

Acharya et al.’s (2011) systemic expected shortfall (SES) estimates a given financial institution’s expected loss conditional on substantial losses to the rest of the financial industry.31 In particular, the SES measure focuses on the likelihood of losses large enough to result in a firm’s undercapitalization, namely failure. The higher a firm’s SES, the more it contributes to systemic risk under this analysis. Further Acharya et al. propose a “systemic risk tax” on financial institutions based on their SES. However, similar to the issues with the CoVaR measure, the SES measure is merely a conditional loss-probability-based measure, in that it primarily captures correlation among financial institutions without providing any quantifiable measure of connectedness or contagion. While there is value in the SES measure for purposes of correlation, the risk of contagion is absent in the analysis.

Finally, Billio et al. (2012) attempt to complement the conditional loss-probability-based CoVaR and SES systemic risk measures by providing a measure of connectedness for financial institions.32 They use a principal component analysis to estimate the return correlations among financial institutions, finding that the monthly returns of hedge funds, banks, broker-dealers, and insurance companies have become more correlated over the past ten years. While Billio et al. declare that their return correlation measurements are “metrics [gauging] the degree of connectedness of the financial system,” the analysis does not in fact directly measure connectedness, but merely makes an inference that connectedness must be present to explain the return correlations. As I have explained above, connectedness, contagion, and correlation are distinct factors in systemic risk that should not be conflated. The presence of one factor does not imply the other. Therefore Billio et al. (2012) have provided evidence of correlation, but they fail to measure connectedness or contagion.

A.4  Correlation Literature Review

The potential for widespread correlated losses is intimately related to the degree of herding behavior exhibited by banks and other investors. If bank portfolios are homogeneous across individual firms, for example, if all banks lend to the same type of borrower, they can become vulnerable to a correlated shock. Scharfstein and Stein (1990)33 study mechanisms that can lead to this herding behavior in investment decisions. They suggest that individual managers may have an incentive to follow herd behavior, even despite “substantive private information” suggesting that the path is ill-advised. They believe there is safety in just being part of a herd. In addition to maximizing value for their current employer, managers have an incentive to preserve their reputations. As a result managers may make suboptimal investments because “an unprofitable decision is not as bad for reputation when others make the same mistake.” This reasoning is equally applicable to asset managers who, during times of market distress, “rush to the exit” and collectively shun many asset classes. Archarya and Yorulmazer (2008) construct a model in which rational profit-maximizing banks have an incentive to herd into similar positions, because contrarian banks that do not follow the herd may face higher borrowing costs, and therefore lower profits.

Reinhart and Rogoff (2009) document 800 years of systemic crises and identify real estate price bubbles as a major contributor to systemic risk.34 Allen and Carletti (2009) “argue that the main cause of the crisis was that there was a bubble in real estate in the U.S.”35 In addition to the papers that identify correlated shocks as the proximate cause of crisis, another body of literature identifies correlated losses as the trigger of an amplification mechanism. For example, Elsinger Lehar and Summer (2006)36 study the effects of a correlated shock on a banking network connected through asset connectedness. They find that studying the effects of a single idiosyncratic shock “underestimates the impact of bank defaults on the rest of the system by a considerable margin.”37 However, losses in the housing market amounted to roughly $100–200 billion. This correlated shock alone is insufficient to explain the $8 trillion loss of equity market capitalization witnessed during the crisis. As previously argued, indiscriminate waves of run-like behavior depressed asset prices far below their fundamental values. Although correlation played an important role in this process, contagion is what transformed an otherwise minor shock into a major systemic crisis.

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