# Systemic risk

Not to be confused with systematic risk.

In finance, systemic risk is the risk of collapse of an entire financial system or entire market, as opposed to risk associated with any one individual entity, group or component of a system, that can be contained therein without harming the entire system.[1][2] It can be defined as "financial system instability, potentially catastrophic, caused or exacerbated by idiosyncratic events or conditions in financial intermediaries".[3] It refers to the risks imposed by interlinkages and interdependencies in a system or market, where the failure of a single entity or cluster of entities can cause a cascading failure, which could potentially bankrupt or bring down the entire system or market.[4] It is also sometimes erroneously referred to as "systematic risk".

## Explanation

Systemic risk has been associated with a bank run which has a cascading effect on other banks which are owed money by the first bank in trouble, causing a cascading failure. As depositors sense the ripple effects of default, and liquidity concerns cascade through money markets, a panic can spread through a market, with a sudden flight to quality, creating many sellers but few buyers for illiquid assets. These interlinkages and the potential "clustering" of bank runs are the issues which policy makers consider when addressing the issue of protecting a system against systemic risk.[1][5] Governments and market monitoring institutions (such as the U.S. Securities and Exchange Commission (SEC), and central banks) often try to put policies and rules in place with the justification of safeguarding the interests of the market as a whole, claiming that the trading participants in financial markets are entangled in a web of dependencies arising from their interlinkage. In simple English, this means that some companies are viewed as too big and too interconnected to fail. Policy makers frequently claim that they are concerned about protecting the resiliency of the system, rather than any one individual in that system.[5]

Systemic risk should not be confused with market or price risk as the latter is specific to the item being bought or sold and the effects of market risk are isolated to the entities dealing in that specific item. This kind of risk can be mitigated by hedging an investment by entering into a mirror trade.

Insurance is often easy to obtain against "systemic risks" because a party issuing that insurance can pocket the premiums, issue dividends to shareholders, enter insolvency proceedings if a catastrophic event ever takes place, and hide behind limited liability. Such insurance, however, is not effective for the insured entity.

One argument that was used by financial institutions to obtain special advantages in bankruptcy for derivative contracts was a claim that the market is both critical and fragile.[1][5][6][7]

Systemic risk can also be defined as the likelihood and degree of negative consequences to the larger body. With respect to federal financial regulation, the systemic risk of a financial institution is the likelihood and the degree that the institution's activities will negatively affect the larger economy such that unusual and extreme federal intervention would be required to ameliorate the effects.[8]

A general definition of systemic risk which is not limited by its mathematical approaches, model assumptions or focus on one institution, and which is also the first operationalizable definition of systemic risk encompassing the systemic character of financial, political, environmental, and many other risks, was put forth in 2010.[9]

## Measurement of systemic risk

### TBTF/TICTF

According to the Property Casualty Insurers Association of America, there are two key assessments for measuring systemic risk, the "too big to fail" (TBTF) and the "too interconnected to fail" (TICTF) tests. First, the TBTF test is the traditional analysis for assessing the risk of required government intervention. TBTF can be measured in terms of an institution's size relative to the national and international marketplace, market share concentration, and competitive barriers to entry or how easily a product can be substituted. Second, the TICTF test is a measure of the likelihood and amount of medium-term net negative impact to the larger economy of an institution's failure to be able to conduct its ongoing business. The impact is measure beyond the institution's products and activities to include the economic multiplier of all other commercial activities dependent specifically on that institution. The impact is also dependent on how correlated an institution's business is with other systemic risks.[10]

Too Big To Fail: The traditional analysis for assessing the risk of required government intervention is the "Too Big to Fail" Test (TBTF). TBTF can be measured in terms of an institution's size relative to the national and international marketplace, market share concentration (using the Herfindahl-Hirschman Index for example), and competitive barriers to entry or how easily a product can be substituted. While there are large companies in most financial marketplace segments, the national insurance marketplace is spread among thousands of companies, and the barriers to entry in a business where capital is the primary input are relatively minor. The policies of one homeowners insurer can be relatively easily substituted for another or picked up by a state residual market provider, with limits on the underwriting fluidity primarily stemming from state-by-state regulatory impediments, such as limits on pricing and capital mobility. During the recent financial crisis, the collapse of the American International Group (AIG) posed a significant systemic risk to the financial system. There are arguably either no or extremely few insurers that are TBTF in the U.S. marketplace.

Too Interconnected to Fail: A more useful systemic risk measure than a traditional TBTF test is a "Too Interconnected to Fail" (TICTF) assessment. An intuitive TICTF analysis has been at the heart of most recent federal financial emergency relief decisions. TICTF is a measure of the likelihood and amount of medium-term net negative impact to the larger economy of an institution's failure to be able to conduct its ongoing business. The impact is measured not just on the institution's products and activities, but also the economic multiplier of all other commercial activities dependent specifically on that institution. It is also dependent on how correlated an institution's business is with other systemic risk.[11]

### SRISK

A financial institution represents a systemic risk if it becomes undercapitalized when the financial system as a whole is undercapitalized. In a single risk factor model, Brownlees and Engle,[12] build a systemic risk measure named SRISK. SRISK can be interpreted as the amount of capital that needs to be injected into a financial firm as to restore a certain form of minimal capital requirement. SRISK has several nice properties: SRISK is expressed in monetary terms and is, therefore, easy to interpret. SRISK can be easily aggregated across firms to provide industry and even country specific aggregates. Last, the computation of SRISK involves variables which may be viewed on their own as risk measures, namely the size of the financial firm, the leverage (ratio of assets to market capitalization), and a measure of how the return of the firm evolves with the market (some sort of time varying conditional beta but with emphasis on the tail of the distribution). Because these three dimensions matter simultaneously in the SRISK measure, one may expect to obtain a more balanced indicator than if one had used either one of the three risk variables individually.

Whereas the initial Brownlees and Engle model is tailored to the US market, the extension by Engle, Jondeau, and Rockinger[13] allows for various factors, time varying parameters, and is therefore more adapted to the European market. One factor captures worldwide variations of financial markets, another one the variations of European markets. Then this extension allows for a country specific factor. By taking into account different factors, one captures the notion that shocks to the US or Asian markets may affect Europe but also that bad news within Europe (such as the news about a potential default of one of the countries) matters for Europe. Also, there may be country specific news that do not affect Europe nor the USA but matter for a given country. Empirically the last factor is found to be less relevant than the worldwide or European factor.

Since RISK is measured in terms of currency, the industry aggregates may also be related to Gross Domestic Product. As such one obtains a measure of domestic systemically important banks.

The SRISK Systemic Risk Indicator is computed automatically on a weekly basis and made available to the community. For the US model SRISK and other statistics may be found under the Volatility Lab of NYU Stern School website and for the European model under the Center of Risk Management (CRML) website of HEC Lausanne.

## Valuation of assets and derivatives under systemic risk

### Inadequacy of classic valuation models

One problem when it comes to the valuation of derivatives, debt, or equity under systemic risk is that financial interconnectedness has to be modelled. One particular problem is posed by closed valuations chains, as exemplified here for four firms A, B, C, and D:

B might hold shares of A, C holds some debt of B, D owns a derivative issued by C, and A owns some debt of D.[14]

For instance, the share price of A could influence all other asset values, including itself.

#### The Merton (1974) model

Situations as the one explained earlier, which are present in mature financial markets, cannot be modelled within the single-firm Merton model,[15] but also not by its straightforward extensions to multiple firms with potentially correlated assets.[14] To demonstrate this, consider two financial firms, ${\displaystyle i=1,2}$, with limited liability, which both own system-exogenous assets of a value ${\displaystyle a_{i}\geq 0}$ at a maturity ${\displaystyle T\geq 0}$, and which both owe a single amount of zero coupon debt ${\displaystyle d_{i}\geq 0}$, due at time ${\displaystyle T}$. "System-exogenous" here refers to the assumption, that the business asset ${\displaystyle a_{i}}$ is not influenced by the firms in the considered financial system. In the classic single firm Merton model,[15] it now holds at maturity for the equity ${\displaystyle s_{i}\geq 0}$ and for the recovery value ${\displaystyle r_{i}\geq 0}$ of the debt, that

${\displaystyle r_{i}=\min\{d_{i},a_{i}\}}$

and

${\displaystyle s_{i}=(a_{i}-d_{i})^{+}.}$

Equity and debt recovery value, ${\displaystyle s_{i}}$ and ${\displaystyle r_{i}}$, are thus uniquely and immediately determined by the value ${\displaystyle a_{i}}$ of the exogenous business assets. Assuming that the ${\displaystyle a_{i}}$ are, for instance, defined by a Black-Scholes dynamic (with or without correlations), risk-neutral no-arbitrage pricing of debt and equity is straightforward.

#### Non-trivial asset value equations

Consider now again two such firms, but assume that firm 1 owns 5% of firm two's equity and 20% of its debt. Similarly, assume that firm 2 owns 3% of firm one's equity and 10% of its debt. The equilibrium price equations, or liquidation value equations,[16] at maturity are now given by

${\displaystyle r_{1}=\min\{d_{1},a_{1}+0.05s_{2}+0.2r_{2}\}}$
${\displaystyle r_{2}=\min\{d_{2},a_{2}+0.03s_{1}+0.1r_{1}\}}$
${\displaystyle s_{1}=(a_{1}+0.05s_{2}+0.2r_{2}-d_{1})^{+}}$
${\displaystyle s_{2}=(a_{2}+0.03s_{1}+0.1r_{1}-d_{2})^{+}.}$

This example demonstrates, that systemic risk in the form of financial interconnectedness can already lead to a non-trivial, non-linear equation system for the asset values if only two firms are involved.

#### Over- and underestimation of default probabilities

It is known that modelling credit risk while ignoring cross-holdings of debt or equity can lead to an under-, but also an over-estimation of default probabilities.[17] The need for proper structural models of financial interconnectedness in quantitative risk management - be it in research or practice - is therefore obvious.

### Structural models under financial interconnectedness

The first authors to consider structural models for financial systems where each firm could own debt of any other firm were Eisenberg and Noe in 2001.[18] In their model, no equity could be cross-owned, and debt had to be of one seniority level, only. In 2002, Suzuki published a model in which equity could be cross-owned as well.[19] His model was developed independently of Eisenberg and Noe's. Elsinger's publication of 2009[20] was the first in which debt could be of different seniorities, hence allowing to model, for instance, senior and junior debt, while correctly accounting for the order of priority. His model allowed equity cross-ownership, too. With Fischer (2014), the first model which also allowed derivatives was introduced.[16] The fact that Elsinger was unaware of Suzuki's publications, Fischer was unaware of Elsinger's, and the fact that other authors re-discovered parts of Suzuki's and Elsinger's results[14][21][22] shows that the research in this field is still somewhat unconsolidated.

### Risk-neutral valuation: price indeterminacy and open problems

Generally speaking, risk-neutral pricing in structural models of financial interconnectedness requires unique equilibrium prices at maturity in dependence of the exogenous asset price vector, which can be random. While financially interconnected systems with debt and equity cross-ownership without derivatives are fairly well understood in the sense that relatively weak conditions on the ownership structures in the form of ownership matrices are required to warrant uniquely determined price equilibria,[14][19][20] the Fischer (2014) model needs very strong conditions on derivatives - which are defined in dependence on any other liability of the considered financial system - to be able to guarantee uniquely determined prices of all system-endogenous liabilities. Furthermore, it is known that there exist examples with no solutions at all, finitely many solutions (more than one), and infinitely many solutions.[14][16] At present, it is unclear how weak conditions on derivatives can be chosen to still be able to apply risk-neutral pricing in financial networks with systemic risk. It is noteworthy, that the price indeterminacy that evolves from multiple price equilibria is fundamentally different from price indeterminacy that stems from market incompleteness.[16]

## Factors

Factors that are found to support systemic risks[23] are:

1. Economic implications of models are not well understood. Though each individual model may be made accurate, the facts that (1) all models across the board use the same theoretical basis, and (2) the relationship between financial markets and the economy is not known lead to aggravation of systemic risks.
2. Liquidity risks are not accounted for in pricing models used in trading on the financial markets. Since all models are not geared towards this scenario, all participants in an illiquid market using such models will face systemic risks.

## Diversification

Risks can be reduced in four main ways: avoidance, diversification, hedging and insurance by transferring risk. Systematic risk, also called market risk or un-diversifiable risk, is a risk of a security that cannot be reduced through diversification. Participants in the market, like hedge funds, can be the source of an increase in systemic risk[24] and the transfer of risk to them may, paradoxically, increase the exposure to systemic risk.

Until recently, many theoretical models of finance pointed towards the stabilizing effects of a diversified (i.e., dense) financial system. Nevertheless, some recent work has started to challenge this view, investigating conditions under which diversification may have ambiguous effects on systemic risk.[25][26] Within a certain range, financial interconnections serve as a shock-absorber (i.e., connectivity engenders robustness and risk-sharing prevails). But beyond the tipping point, interconnections might serve as a shock-amplifier (i.e., connectivity engenders fragility and risk-spreading prevails).

## Regulation

One of the main reasons for regulation in the marketplace is to reduce systemic risk.[5] However, regulation arbitrage – the transfer of commerce from a regulated sector to a less regulated or unregulated sector – brings markets a full circle and restores systemic risk. For example, the banking sector was brought under regulations in order to reduce systemic risks. Since the banks themselves could not give credit where the risk (and therefore returns) were high, it was primarily the insurance sector which took over such deals. Thus the systemic risk migrated from one sector to another and proves that regulation of only one industry cannot be the sole protection against systemic risks.[27]

## Project risks

In the fields of project management and cost engineering, systemic risks include those risks that are not unique to a particular project and are not readily manageable by a project team at a given point in time. These risks may be driven by the nature of a company's project system (e.g., funding projects before the scope is defined), capabilities, or culture. They may also be driven by the level of technology in a project or the complexity of a project's scope or execution strategy.[28]

## Systemic risk and insurance

In February 2010, international insurance economics think tank, The Geneva Association, published a 110-page analysis of the role of insurers in systemic risk.[29]

In the report, the differing roles of insurers and banks in the global financial system and their impact on the crisis are examined (See also CEA report, "Why Insurers Differ from Banks").[30] A key conclusion of the analysis is that the core activities of insurers and reinsurers do not pose systemic risks due to the specific features of the industry:

• Insurance is funded by up-front premia, giving insurers strong operating cash-flow without the requirement for wholesale funding;
• Insurance policies are generally long-term, with controlled outflows, enabling insurers to act as stabilisers to the financial system;
• During the hard test of the financial crisis, insurers maintained relatively steady capacity, business volumes and prices.

Applying the most commonly cited definition of systemic risk, that of the Financial Stability Board (FSB), to the core activities of insurers and reinsurers, the report concludes that none are systemically relevant for at least one of the following reasons:

• Their limited size means that there would not be disruptive effects on financial markets;
• An insurance insolvency develops slowly and can often be absorbed by, for example, capital raising, or, in a worst case, an orderly wind down;
• The features of the interrelationships of insurance activities mean that contagion risk would be limited.

The report underlines that supervisors and policymakers should focus on activities rather than financial institutions when introducing new regulation and that upcoming insurance regulatory regimes, such as Solvency II in the European Union, already adequately address insurance activities.

However, during the financial crisis, a small number of quasi-banking activities conducted by insurers either caused failure or triggered significant difficulties. The report therefore identifies two activities which, when conducted on a widespread scale without proper risk control frameworks, have the potential for systemic relevance.

• Derivatives trading on non-insurance balance sheets;
• Mis-management of short-term funding from commercial paper or securities lending.

The industry has put forward five recommendations to address these particular activities and strengthen financial stability:

• The implementation of a comprehensive, integrated and principle-based supervision framework for insurance groups, in order to capture, among other things, any non-insurance activities such as excessive derivative activities.
• Strengthening liquidity risk management, particularly to address potential mis-management issues related to short-term funding.
• Enhancement of the regulation of financial guarantee insurance, which has a very different business model than traditional insurance.
• The establishment of macro-prudential monitoring with appropriate insurance representation.
• The strengthening of industry risk management practices to build on the lessons learned by the industry and the sharing experiences with supervisors on a global scale.

Since the publication of The Geneva Association statement, in June 2010, the International Association of Insurance Supervisors (IAIS) issued its position statement on key financial stability issues. A key conclusion of the statement was that, "The insurance sector is susceptible to systemic risks generated in other parts of the financial sector. For most classes of insurance, however, there is little evidence of insurance either generating or amplifying systemic risk, within the financial system itself or in the real economy."[31]

Other organisations such as the CEA and the Property Casualty Insurers Association of America (PCI)[32] have issued reports on the same subject.

## Discussion

Systemic risk evaluates the likelihood and degree of negative consequences to the larger body. The term "systemic risk" is frequently used in recent discussions related to the economic crisis, such as the Subprime mortgage crisis. The systemic risk of a financial institution is the likelihood and the degree that the institution's activities will negatively affect the larger economy such that unusual and extreme federal intervention would be required to ameliorate the effects. The failing of financial firms in 2008 caused systemic risk to the larger economy. Chairman Barney Frank has expressed concerns regarding the vulnerability of highly leveraged financial systems to systemic risk and the US government has debated how to address financial services regulatory reform and systemic risk.[33][34]

## References

1. ^ a b c Banking and currency crises and systemic risk, George G. Kaufman (World Bank), Internet Archive
2. ^ What is systemic risk anyway?, Gerald P. Dwyer
3. ^
4. ^ Systemic Risk, Steven L. Schwarcz
5. ^ a b c d Containing Systemic Risk, CRMPG III, August 6, 2008
6. ^ What is Systemic Risk
7. ^ The Economics of Legal Tender Laws, Jorg Guido Hulsmann (includes detailed commentary on systemic risk inherent in FRB)
8. ^ Systemic Risk, Property Casualty Insurers Association of America
9. ^ Market Dynamics & Systemic Risk, Milan Boran
10. ^ PCI Definition of Systemic Risk
11. ^ Too Big to Fail, Property Casualty Insurers Association of America
12. ^ Brownlees, C.T., Engle, R.F., 2010. Volatility, correlation and tails for systemic risk measurement, [1]
13. ^ Engle, R.F., Jondeau, E., Rockinger, M., 2012. Systemic Risk in Europe
14. Fischer, Tom (2014). "Valuation in the structural model of systemic interconnectedness" (PDF). Presentation at the Frankfurt MathFinance Colloquium, November 27, 2014.
15. ^ a b Merton, R.C. (1974). "On the pricing of corporate debt: the risk structure of interest rates". Journal of Finance. 29 (2): 449–470. doi:10.1111/j.1540-6261.1974.tb03058.x. line feed character in `|title=` at position 53 (help)
16. ^ a b c d Fischer, Tom (2014). "NO-ARBITRAGE PRICING UNDER SYSTEMIC RISK: ACCOUNTING FOR CROSS-OWNERSHIP". Mathematical Finance. 24 (1): 97–124 (Published online: 19 Jun 2012). doi:10.1111/j.1467-9965.2012.00526.x.
17. ^ Karl, S.; Fischer, T. (2014). "Cross-ownership as a structural explanation for over- and underestimation of default probability". Quantitative Finance. 14 (6): 1031–1046 (Published online: 18 Nov 2013). doi:10.1080/14697688.2013.834377.
18. ^ Eisenberg, L.; Noe, T.H. (2001). "Systemic Risk in Financial Systems". Management Science. 47 (2): 236–249. doi:10.1287/mnsc.47.2.236.9835.
19. ^ a b Suzuki, T. (2002). "Valuing Corporate Debt: The Effect of Cross-Holdings of Stock and Debt" (PDF). Journal of the Operations Research Society of Japan. 45 (2): 123–144.
20. ^ a b Elsinger, H. (2009). "Financial Networks, Cross Holdings, and Limited Liability". Working Paper 156, Oesterreichische Nationalbank, Wien.
21. ^ Gouriéroux, C.; Héam, J.-C.; Monfort, A. (2012). "Bilateral exposures and systemic solvency risk". Canadian Journal of Economics. 45 (4): 1273–1309 (Published online: 09 Nov 2012). doi:10.1111/j.1540-5982.2012.01750.x.
22. ^ Gouriéroux, C.; Héam, J.-C.; Monfort, A. (2013). "Liquidation equilibrium with seniority and hidden CDO". Journal of Banking & Finance. 37: 5261–5274. doi:10.1016/j.jbankfin.2013.04.016.
23. ^ Reto R. Gallati. Risk management and capital adequacy. Retrieved 2008-09-18.
24. ^ Systemic risk and hedge funds
25. ^ Rethinking the Financial Network
26. ^ Paolo Tasca and Stefano Battiston. "Diversification and Financial Stability". SSRN .
27. ^ Franklin Allen and Douglas Gale. "Systemic Risk and Regulation" (PDF). Retrieved 2008-09-18.
28. ^ Systemic Risks in Projects
29. ^ Systemic Risk in Insurance—An analysis of insurance and financial stability (2010) The Geneva Association
30. ^ CEA (June 2010) Insurance: a unique sector—Why Insurers Differ from Banks
31. ^
32. ^ PCI (2009) Systemic Risk Defined
33. ^ Systemic Risk Focus