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PART I: SYSTEMIC RISK? LET’S UNDERSTAND THE FOUNDATION TO GAUGE THE NEED OF SYSTEMIC RISK REGULATION.

This is part I of my series on systemic risk. Hold on to Part 3 for my final take on systemic risk regulation. The series analyzes the systemic risk; try to understand its current assessment through statistical models and dynamic with regard to history and the current financial crisis. List and propose methods to assess and anticipated the increase of the systemic risk. Another objective in this series of articles is to demonstrate that there are tools that can help assess, anticipate or signal some of the systemic risk and anticipate its consequence through regulation, provided there is an authority to analyze this risk. The systemic risk has become at the center of the current financial crisis, after the collapse of Lehman brothers and the near collapse of AIG, no financial industry sector is immune from the systemic risk. Regulation of the financial system is a critical issue. The question today is it possible to create a regulatory mechanism that is successful in reducing systemic risk, but not too costly?
 
DEFINITION OF SYSTEMIC RISK
I believe it is important to set first the foundation:
 
"Systemic risk" refers to 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. Property Casualty Insurers Association Of America
 
Systemic risk arises when a disturbance occurs which can lead to credit losses and result in the failure of a group of financial firms. Such disturbances can threaten the functioning of the financial markets as a whole. ….In order for systemic risk to arise, many financial institutions must have made loans the risks of which are correlated and at the same time, the economic environment must be such that losses actually occur. AV Felice Marlor, Payment Systems Department, Sverige Riksbank.
 
Systemic risk is modeled as the endogenously chosen correlation of returns on assets held by banks. The limited liability of banks and the presence of a negative externality of one bank's failure on the health of other banks give rise to a "systemic risk-shifting" incentive where all banks undertake correlated investments, thereby increasing aggregate risk. …….A financial crisis is “systemic” in nature if many banks fail together, or if one bank’s failure propagates as a contagion causing the failure of many banks. A Theory of Systemic Risk and Design of Prudential Bank Regulation, Viral V. Acharya, London Business School, NYU-Stern and CEPR.
 
CLASSIFICATION OF SYSTEMIC RISKS.
I have not found clear classification of systemic risk, but it seems intuitive for me to classify the systemic risk as following:
 
Intern to the financial system (endogenous)
(1)    Too Big to Fail: The institution may be too big and has enormous exposure such that its failure may negatively affect the larger economy such that unusual and extreme federal intervention would be required. This characterization focus on the size of operations and less on the number of interconnection of the institutions.
 
(2) Too Interconnected to Fail: risk that the interconnection of a financial institution which default negatively impact to the larger economy. The institution may not be big but the leverage and multiplier effect can diffuse the effect (domino effect) to the larger economy.
 
(3) Endogenous cycle with euphoric and panic behavior in the financial sector
 
External to the financial system (extraneous)
(4) Macro economical and political risk. A macroeconomic shock, induced by domestic imbalances or an external impulse. Disturbance in the economy or the market which can lead to credit losses and result in the failure of a group of financial firms. For instance unexpected changes in the economic policy or regulation can alter economic fundamentals and thereby substantially change the outcomes of financial institutions’ lending decisions. Regulatory changes have contributes to banking crises in many countries.
 
(5) Natural or human made catastrophes that can disturb the entire financial system. Example of Katrina or September 11.
 
SYSTEMIC RISK ASSESSMENT THROUGH STATISTICAL MODELS
There are several flaws in current risk conceptualization. Before we review the limits of today systemic risk assessment, let’s recognize the important role statistical risk conceptualization or the lack of risk modeling has played in past crisis. The growing importance of risk management is seen in regulatory design where risk regulations are more and more model based. Risk modeling brought tremendous progress in the understanding and the quality of risk assessment. Risk management helped understand the dynamic of previous crisis and the complexity of banks exposures and off/on-balance sheet derivatives trades. It was the misunderstandings of quantitative risk and bank exposures that have contributed to amplify the crises in the nineties and eighties. For instances:
 
  • In many countries banking crises in the late eighties, early nineties and today had resulted from a failure to properly recognize risks and correlations of risks in real-estate, small-business lending and among financial institutions. In many case it is the proper use of risk modeling and the ability to think outside the general framework that were at question
 
  • The absence of risk modeling resulted in a failure to understand the maturity mismatch between assets and liabilities and its implications played an important role in banks defaults in early eighties.
 
  • The development of Value at Risk (VaR) models significantly enhanced banks ability to measure and hedge their trading book risks. An important consequence of VaR is that it has been used by regulators to set rules on prudential capital and avoid the distortionary impact of this capital.
 
But as someone said the devil is in the details, risk models work well as far as the condition are normal, stationary, the models reliability are questionable or the models collapse in specifics and extreme cases. Statisticians know very well the realities do not often exhibit the Gaussian, stationary and independence properties that the statistical theory assumes. And as regulatory environment (Basel II, Solvency II) are based on imperfect models, it is not surprising that those limitations in risk modeling technology, coupled with imperfect regulatory design, may increase rather than prevent systemic failure. To me this, intrinsic human/model/economist imperfection makes the need of systemic risk surveillance important.
 
Assumption of independent Stochastic Process
To understand the limit of current risk approach to measure systemic risk it is interesting to realize some flaws in their initial design. An explicit assumption of many risk models is that the market data or the considered variables follow a stochastic process. Statistical models and efficient market theory usually made the assumptions that past observations predict the futures or all information is embedded in the in the market price. We know market participants’ behavior is not always rational and can be driven by many behavioral and outside considerations that the statistical models don’t incorporate. It is therefore more difficult to incorporate a systemic variable in the modeling. An independent stochastic process assumption break down in time of crisis, when systemic risk arisen. At time of crisis market participants could behave in a similar fashion leadings to collapse of all models. This correlated behavior or systemic risk is not properly modeled or it is omitted in number of risk models. Also unfortunately, regulatory action rather than limiting the risk can be source of systemic risk increase. When identical model based risk capital, constraints are imposed; regulatory demands may perversely lead to the amplification of the crisis by reducing liquidity.
 
Judgment and subjectivity of modeler
Risk assessment is not only based on statistical or economical models but also on the modeler ability to represent the real world and its judgment. This imperfection may be source of systemic risk, if models are used blindly. This observation should lead any risk manager, financial institution regulators to be humble in its modeling ability and put internal and external safeguard to monitor discrepancy. Similarly the regulator should put in place mechanism to observe unusual behavior in the markets. For instance a price that is removed from the fair value or real value of the asset.
 
Correlation as measure of systemic risk
Jon Danielson, of the Financial Markets Group, London School of Economics, www.RiskResearch.org, wrote an excellent paper on the subject that deserve to be read. Some of ideas I shared: correlation in times of stability does not provide the correct measure of assets and financial institutions relationships risk in times of crisis. Correlations models rely on normal distribution assumption and oversee the left tail or extreme risk. Empirical studies and literature review show that correlations and other risk metrics are not robust in time of crisis and are too volatile. And even the wrong comfort these risk metrics gave lead to misinformation and even risk metrics can participate in increasing the systemic risk. When many of the market participants execute the same trading strategies during crisis, they change the distributional properties of risk. As a result, the distribution of risk is different during crisis than in other periods, and standard risk model become not only useless but may amplify the crisis, by leading to large price swings and lack of liquidity. This was the case in the 1987 crash, the Russia crisis of 1998 and the subprime crisis of 2007. The elaboration of a systemic risk regulations could not relied uniquely on those metrics. In particular, correlations are subject to change over time. Even with the best of data, correlations are therefore hard to model. The recent tentative to model correlation such as the copula function showed worrying limitations that participated in the collapse of the CDs market: the mortgages showed non predicted common dependence unanticipated by the most sophisticated risk models. This common factor or systemic factor has been overlooked for too long because of its complexity of modeling.
 
"Risk comes from not knowing what you're doing". Warren Buffett
 
Understand the copula function to understand one of the factors of the CDS collapse: What is copulas function? Copula function played a significant part important part in the acceleration of the credit default swap collapse. As statistician, I love copula because of its elegance and ability to aggregate and simplify the multidimensional correlation concept, I recognize it difficult to model under extreme scenario. But the most important part of a model is not its ”elegance” or “beauty” but assumptions underlying this model that many statisticians and modelers know very well, some are unrealistic. The Gaussian copula is a statistical function introduced by David X. Li in 1998, a New York banker that was initially praised to simplify the complex concept of correlation to a simple number. With copulas no more need to pay close attention to the underlying assets and simulate myriads of scenarios and covariance matrix to capture the correlation: It was a gift as the “le Chaînon manquant or missing link” for statistician, traders, rating agencies, banks and regulators trying to price CDS tranches. As a single number was now almost enough to derived the CDS price, the model was immediately used by practitioners with less considerations for its underlying flaws as the CDS market grow exponentially and there were so many money to be made. Unfortunately copula function fuels the CDS market, contributing to give false sentiment of fair pricing and understanding of risk. Millions of CDS tranches deemed rated AAA, based on their default correlation derived from copulas were created. Without being modelers there can be certain uncomfort to think that a single number so remote from the underlying assets could tell the full story of the default probability of a CDS tranche. The copulas also implicitly made the assumption that CDS market price the default risk appropriately. But as expected when the market freeze and the copulas functions become irrelevant as the CDS tranches correlation exploded, which I called correlation break-down. Li himself certainly clearly understand the limits of the models, but we all buy in the euphoria of increasing home price,   risk diversification and profit underlying the growth of the CDS market.
 
Some comments of renowned experts:
  • Paul Wilmott: “the correlations between financial quantities are notoriously unstable.” The copula model may have give false confidence of little risk, and push to overlook the tail risk or extreme event.
 
  • Nassim Nicholas Taled (Black Swan is one of my favorite book) added "Anything that relies on correlation is charlatanism."  
 
  • And Goodhart (1974) “Any statistical relationship will break down when used for policy purpose “
 
Is Value at Risk an endogenous systemic risk factor?
Value–at–Risk (VaR) is a fundamental component of the current regulatory environment, and financial institutions in most countries are reporting VaR to their supervisory authorities. The simplicity of calculation is the strongest advantage of the VaR. Under some assumptions VaR, provides an adequate representation of risk; however again the Gaussian and independence assumptions underlying VaR are not realistic and may result in misrepresentation of risk especially at time of crisis. There are couple of evident flaws in the VaR, I won’t develop in this article, note that  VaR is not a coherent risk measure as it lacks the subadditivity property and the reliance of VaR on a single quantile of the profit and loss distribution implies it is easy to manipulate reported VaR with clever trading strategies. Also, VaR overlook tail risk or extreme event.
 
SOME STATISTICAL ASSESSMENT OF SYSTEMIC RISK
 
  • Extreme Value dependence to measure systemic risk
Most current risk models did not performed well during crisis, however new models grounded in the extreme value, microeconomic and macroeconomic theories may be useful to explore. Extreme Value Theory (NYSE:EVT) or the analysis of variables behavior under extreme or stress scenario, works provided we have the probability distribution of the variables under consideration. Extreme value dependence focuses on the relation of variables in the tails of their distributions. Existence of extreme realization of variables together or not irrespective of how strongly they might be correlated in their more normal range. Extreme value dependence behaves differently from the basic notion of dependence often refers as correlation
 
  • Stress-testing
To make up for the lack of knowledge of extreme losses and insufficient of data, it can be useful to artificially generate extreme scenarios of the main factors driving returns and then assess the resulting outcome. Stress tests are more accurate when it is possible to calculate the probability of the extreme scenarios, which often is not the case.  Geithner conducted stress-test on the biggest banks to evaluate the systemic risk the system may face.
 
  • Leverage in the system
Because of leverage, financial institution positions are often considerably larger than the collateral against those positions. Leverage has the effect of a magnifying glass, expanding small profit opportunities into larger ones but also expanding small losses into larger losses. And when adverse changes in market prices reduce the market value of collateral, credit is withdrawn quickly, and the subsequent forced liquidation of large positions over short periods of time can lead to widespread financial panic, as in the aftermath of the default of Russian government debt in August 1998 and Lehman Brothers collapse in September 2008.
 
  • Liquidity exposure
Generalize illiquidity play an important part in general market collapse. The more illiquid the portfolio, the larger the price impact of a forced liquidation or fire sale, which erodes the bank’s risk capital that much more quickly. Now if many hedge funds or financial institutions face the same “death spiral” at a given point in time—that is, if they become more highly correlated during times of distress and as financial institutions are interrelated for instance obligors of other financial institutions the illiquidity crisis can cascade quickly into a global financial crisis. This is systemic risk. Along with the many benefits of a truly global financial system is the cost that a financial crisis in one country can have dramatic repercussions in several others—that is, contagion. The subprime mortgage and CDS market collapse have spilled over. A method for assessing the illiquidity risk exposure of a given financial institution can be examined through the autocorrelation coefficients of the institution returns.  Samuelson’s (1965) in his paper—“Proof that Properly Anticipated Prices Fluctuate Randomly”—provides a succinct summary for the motivation of the martingale property: In an informationally efficient market, price changes must be unforecastable if they are properly anticipated, that is, if they fully incorporate the expectations and information of all market participants. Measure of aggregate serial correlation can be used as a proxy of illiquidity in the context of systemic risk.
 
  • Performance smoothing
A more prosaic channel by which serial correlation may arise in the reported returns of hedge funds or financial institution is through “performance smoothing,” the unsavory practice of reporting only part of the gains in months when a fund has positive returns so as to partially offset potential future losses and thereby reduce volatility and improve risk adjusted performance measures such as the Sharpe ratio. For funds containing liquid securities that can be easily marked to market, performance smoothing is more difficult and, as a result, less of a concern. Indeed, it is only for portfolios of illiquid securities that managers and brokers have any discretion in marking their positions. Such practices are generally prohibited by various securities laws and accounting principles and great care must be exercised in interpreting smoothed returns as deliberate attempts to manipulate performance statistics. Managers do have certain degrees of freedom in valuing illiquid securities
 
  • Liquidation of a financial institution
Since the collapse of LTCM in 1998 and Lehman Brothers in September 2008, it has become clear that hedge fund liquidations can be a significant source of systemic risk. By analyzing factors driving financial institutions liquidations, regulators may develop a better understanding of the likely triggers of systemic risk in the financial system.
 
  • Regime switching model
Another measure of systemic risk is motivated by the phase locking example of Lo (1999), where the return-generating process exhibits apparent changes in expected returns and volatility that are discrete and sudden—for example, the Mexican peso crisis of 1994–95, the Asian crisis of 1997, and the global flight to quality precipitated by the default of Russian GKO debt in August 1998. Linear models are generally incapable of capturing such discrete shifts; hence, more sophisticated methods are required. A regime-switching process in which two states of the world are hypothesized and the data are allowed to determine the parameters of these states and the likelihood of transitioning from one to the other. Regime-switching models have been used in a number of contexts, ranging from Hamilton’s (1989) model of the business cycle to Ang and Bekaert’s (2004) regime-switching asset allocation model, and NICHOLAS CHAN and al proposed to apply it to the CSFB/Tremont indexes to obtain another measure of systemic risk, that is, the possibility of switching from a normal to a distressed regime.
 
  • Expected shortfall
From a regulator’s perspective it may not be relevant just to look at VaR and other metrics, but also at expected shortfall, which is the present value of the amount of debt that cannot be covered by the assets of the bank in case of default. In the simple Merton (1977) framework, this is given by the value of a put option. Because of this variation, the regulator might not only be concerned about the level of the expected shortfall but also about its dynamics. In an economy with uncorrelated bank portfolios a shock to the assets of one bank will increase the regulator’s liability towards this bank directly but it will not affect the values of the guarantees the regulator has given to other banks’ depositors. With highly correlated asset portfolios a shock will again hit the regulator directly but will also adversely affect the liabilities towards other banks. It is thus important to look at the liability of the deposit insurance agency and at the potential future shortfall in a banking system from a portfolio perspective and not just at the level of individual banks. In a low correlation banking system, in which the shocks to the bank asset portfolios are mainly idiosyncratic, the volatility in the regulator’s portfolio of guarantees should be low whereas high systemic risk will imply high volatility.
 
The take away of this part s the complexity of the systemic risk concepts that goes beyond modelers and market participant’s expertise. By definition as the individual institution behave to maximize individual profit, someone one needs to be in between to identify friction and systemic risk arisen.
 
 
"Risk comes from not knowing what you're doing". Warren Buffett
 
 
TO BE CONTINUED………………………PART II: How the current systemic crisis could have been averted should we had a systemic risk manager (I do prefer systemic risk manager versus regulatory authority)?
 

Co-author : George Gvishiani

References:
 
1-       Many of the ideas developed in this part result by empirical study conducted by Jon Danielson, of the Financial Markets Group, London School of Economics, RiskResearch.org
2-       Based on article Recipe for Disaster: The Formula That Killed Wall Street By Felix Salmon,
3-       Why VAR Fails: Long Memory and Extreme Events in Financial Markets, Cornelis A. Los Kent State University, Department of Finance, BSA 430, Kent, OH 44242-0001. Email: los500@cs.com
4-       For complete analysis of subadditivity of VaR see Coherence of VaR as risk measure: PRM Handbook–Volume III
5-        The Emperor has no Clothes: Limits to Risk Modeling, Jon Danielson, Financial Markets Group, London School of Economics, www.RiskResearch.org.
6-       NICHOLAS CHAN, MILA GETMANSKY, SHANE M. HAAS, AND
ANDREW W. LO “hedge role in increasing systemic risk”