Project "PN-II-ID-PCE-2011-3-1054 - Uncertainty, Complexity and Financial Stability"

 

 

The financial crash of 2008-9 has been the most damaging economic event since the Great Depression – affecting the lives of hundreds of millions of people. The most immediate problem now is to prevent a repeat performance. Much has been written about reforming the world financial system. But it is rarely based on a searching in-depth analysis of the underlying weaknesses within the system. Nor does it usually tackle the key question of what a financial system is for. The issues at stake are extraordinarily difficult and profound. The central question is what the financial system is for? Standard texts list five main functions – channeling savings into real investment, transferring risk, maturity transformation (including smoothing of life-cycle consumption), effecting payments and making markets. But if we study how financial companies make their money, it is extraordinarily difficult to see how closely this corresponds to the stated functions, and it is often difficult to explain why the rewards are often so high. Any explanation must also explain why the system is so prone to boom and bust.

Our Research Project deal with these fundamental issues: the ideal functions of the system; the way the system has actually operated; and the sources of boom and bust. To answer these questions much of the abstract theory of finance has to be abandoned in favor of a more realistic model of how the different agents actually behave. Central to this is opacity and asymmetric information, combined with uncertainty and complexity of Financial System. The financial system is composed of intermediaries, markets and the infrastructure of payment, settlement and trading mechanisms that support them. Intermediaries are connected with each other through direct transactions, as in interbank markets, and through similar investment and financing decisions with third parties such as other intermediaries or end investors. Financial markets, in turn, are connected with each other through the trading activities of financial intermediaries and through end investors active in more than one market. Systemic risk within the financial system relates to the risk that these inter-connections and similarities render emerging financial instability widespread in the system. Even if the original problem seems more contained, important amplification mechanisms can be at work. This complex network of financial connections is extended through the savings and financing needs of all economic sectors, notably non-financial firms, households and the government. By reallocating savings from individuals and sectors with a surplus of funds to individuals and sectors in need of funds, the financial system plays a central role in the economy. So, systemic risk, in a broader sense, relates to the risk that widespreading stabilities in the financial system translate into adverse effects on growth and welfare in the economy at large.
The Financial System is an extremely complex system, interconnected through multiple connections with the system of the real economy. ‘Complexity’ is a widely used term to describe the difficulties of analysing large systems with many components. Complexity is more than just ‘complicated’ (Sajeva and Masera, 2006); it is qualitatively more than the difficulty involved in analysing systems with many sub components with complicated behavioural functions. It refers to systems which have features which make the prediction of system behaviour extremely difficult even if the properties of the component parts are well understood.
The features of complexity include ‘nonlinearities, multiple stable states, hysteresis, contagion, and synchrony’ which ‘are features common to all complex adaptive systems’ (Kambhu, Weidman et al., 2007). Complex systems also manifest the characteristics of ‘chaos’, one reading of which is high sensitivity to initial conditions meaning outcomes can be practically impossible to predict. Abrupt regime shifts can occur which in the economy, for example, can lead to a ‘transition to an inferior but stable equilibrium’ (Kambhu, Weidman et al., 2007).
As Durlauf (2001) points out, four properties highlighted by Complexity Theory are relevant for economic-financial systems, namely: non-ergodicity, phase transition, emergent properties and universality. Applying methodologies worked out within Complexity Theory to the study of economic-financial phenomena allows analyzing new types of processes, especially those with high volatility and complicated dynamics. Thus, the dynamics of certain systems which are hypersensitive with respect to initial conditions, i.e. systems for which small changes of initial conditions lead to a critical change of trajectories, is studied at present by means of Chaos Theory - an important chapter of Complexity Theory. Obviously, the study of uncertainty, volatility and risk factors for non-stochastic systems with chaotic behaviour is a very complex problem. For this very reason, Chaos Theory found numerous applications in the analysis of economic-financial phenomena.
Perhaps most importantly, systems with a high degree of complexity apparently cannot be understood fully by scientific methods which means uncertainty becomes a distinctive feature. Uncertainty ‘reduces the strength of confidence in the estimated cause and effect chain’ (Klinke and Renn, 2006). Systemic risk therefore appears to be replete with uncertainty; it appears to limit the effectiveness of statistical probabilistic analytical techniques and raises questions about how risk should be managed. It has been noted that ‘many quantitative risk management approaches rely too heavily on data from relatively benign periods and thus allow history to grant a false sense of security’ (Kambhu, Weidman et al., 2007).
A crucial problem in modeling financial-economic phenomena is clarifying the ontological and gnoseological connections between the concepts of uncertainty and probability. In a recent paper (February 2008), Gilboa, Postlewaite and Schmeidler from the Economic Research Institute of Pennsylvania University analyze the way in which the understanding of the concepts of uncertainty and probability evolved, as well as the way how this is reflected in financial-economic modeling. Thus, the classical approach assumed that the occurrence probabilities of several elements are known or can be estimated on the basis of historical data, even deriving the probability law governing the phenomenon analyzed. As concerns uncertainty, it is related to the cases when the occurrence probabilities of the events are not known and there is no possibility of estimating them, either.
The so-called Bayesian approach tries to solve the problems connected with uncertainty by introducing the concept of subjective probability. In this way, the Bayesian approach reduces the problems of decision - making under uncertainty to decision- making under risk. The Bayesian paradigm, although using an elegant scientific apparatus, does not clarify the mechanism by which economic agents substantiate their subjective probabilities. At the same time, the Bayesian paradigm has obtained few successes concerning the mechanisms of expectations formation. As early as 1951, Leo Hurwicz ( Nobel laureate for Economics-2007) pointed out that economic agents face a high degree of uncertainty concerning the evolution of future events, which prevents them from formulating a unique apriori Bayesian distribution. An important event in the development of the scientific apparatus regarding uncertainty was the publishing, in 1988, of a paper in which they create a new paradigm, namely studying uncertainty, volatility and risk on the basis of a multitude of apriori distributions (“Multiple Prior”).
The results obtained by using the so-called “Multiple Prior” model are more plausible than those obtained by the standard Bayesian model. On the basis of an axiomatics due to Gilbao, Lieberman and Schneidler (2006) and of the so-called similarity function, the “Multiple Prior” model can be used for optimization of financial decisions, as well as for substantiating expectations of economic agents. In order to drop the hypothesis, which appears to be false, according to which the economic agent knows the real model of the economy, Hansen and Sargent (2001, 2003, 2006) applied the “Multiple Prior “ model to work out a new theory aimed at mastering the phenomena of uncertainty, volatility and risk. The new theory, known under the name Robustness, was successfully applied for substantiating several macroeconomic policy decisions (Dennis-2007, Giannoni-2005). In 2007, Peter Tillmann applies Robustness to substantiate monetary policy in the Euro Zone countries, in a paper published at the European Commission (DGECFIN).

The well-known adage that “one cannot manage what one cannot measure” is particularly timely with respect to the notion of systemic risk, a term that has come into common usage but which has so far resisted formal definition and quantification. Systemic risk is usually taken to mean the risk of a broad-based breakdown in the financial system, often realized as a series of correlated defaults among financial institutions, typically banks, which occurs over a short period of time and typically caused by a single major event.
There is a vast literature on systemic risk, which is rapidly growing since the onset of the financial crisis. Bandt et al. (2009) distinguish between a broad and a narrow sense of systemic risk. In their nomenclature contagion effects on interbank markets pose a systemic risk in the narrow sense, whereas the broad sense of systemic risk is characterized as a common shock to the financial markets, that affects many institutions or markets. A large part of the literature on systemic risk focuses on systemic risk through contagion effects. Rochet and Tirole (1996) for instance state that “Systemic risk refers to the propagation of an agent’s economic distress to other agents linked to that agent through financial transactions.”, emphasizing the role of interbank markets for systemic risk. Iori et al. (2006) present a network model of interbank markets and analyze the effects of the bank sectors’ heterogeneity on financial stability. Financial networks and especially interbank markets exhibit a robust-yet-fragile property, as for example Haldane (2009) argues. This behaviour of connected networks can be best explained as a knife-edge property. Up to a certain point, financial networks and interbank connections serve as a mutual insurance of the financial system and thus contribute to systemic stability. Beyond this point the same interconnections might serve as a shock-amplifier and thus increase systemic fragility. This is in line with Fernando (2003), Cifuentes et al. (2005) and Gai and Kapadia (2008) who argue that increasing connectivity on the interbank market leads to increasing contagion in times of crisis. The broad sense of systemic risk (as defined by Bandt et al. (2009)) has become increasingly important in recent years. Adrian and Shin (2008) address the issue of financial contagion through fire-sales and marked-to-market accounting and argue that this can amplify the potential impact of a shock and therefore pose a systemic risk.
Acharya (2009) models systemic risk as the endogenously chosen correlation of returns on assets held by banks. Two types of externatlities are introduced: if a bank fails, there is a reduction of aggregate deposit supply in the economy, resulting in a recessionary spillover (a negative externality). The surviving banks, however, have a strategic benefit from the failure of other banks (positive externality) due to an increase in scale, resulting from the migration of the failed bank’s depositors. Banks strategically decide to invest in similiar assets if the negative externality exceeds the  positive externality. In this case there is a correlation between the bank’s assets which exposes them to common shocks. Acharya (2009) defines systemic risk as “the joint failure risk arising from the correlation of returns on asset side of bank balance sheets”. Acharya argues that bank regulation mechanisms that are based on a bank’s own risk only might fail to mitigate systemic risk. The
conclusion is that common shocks are not subordinated to contagion, but are in fact a coequal form of systemic risk. Whelan (2009) argues in the same direction, giving a simple example where a small initial trigger leads to a large common shock. Wagner (2009) states that one key reason behind the severity of the financial crisis of 2007/2008 was that many financial institutions had invested in the same assets (e.g. subprime mortgages), therefore exposing them to a common shock. Irrespective of their importance, common shocks have not yet received the same attention in the literature, as contagion has.
A prerequisite for financial crisis prevention and management is to assess both types of systemic risk in an appropriate framework. Brunnermeier et al. (2009) propose to apply leverage, maturity mismatch or the rate of expansion to measure systemic risk. Lehar (2005) estimates the risk of a common shock by the correlation between institution’s asset portfolios. Acharya et al. (2009) recommends to measure an institution’s contribution to aggregate risk based on it’s marginal value-at-risk and it’s marginal expected shortfall. Acharya et al. (2010) propose to assess the systemic expected shortfall which indicates how much an institution is prone to undercapitalize when the financial system is undercapitalized as well. Haldane (2009) suggests to measure contagion based on the interconnectedness of each institution within the financial system, whereas Adrian and Brunnermeier (2009) focus on Co-VaR, which is the value-at-risk of the whole financial sector in times of crisis. They argue to interpret the difference between CoVar and the institution’s specific value-at-risk as the institution’s contribution to systemic risk. Tarashev et al. (2009) propose to apply the Shapley value methodology to asses this contribution. Thomson (2009) provides a scoring model to categorize each institution according to it’s contribution to systemic risk. Eligible criteria are size, contagion, correlation, concentration and economic conditions.
A new approach to systemic risk in financial markets comes from network theory. As for example Allen and Babus (2008) argue, linkages between financial institutions stem from both the asset side (through holding similiar portfolios) and the liabilities side (by sharing the same mass of depositors). These linkages can be direct (as in the case of interbank loans) and indirect (as in the case of similar portfolios). Allen and Babus (2008) investigate the resilience of financial networks to shocks and the formation of financial networks. Network theory has been successfully applied in the analysis of payment systems (see e.g. Soramaki and Galbiati (2008) or Markose et al. (2010)). Castren and Kavonius (2009) apply network theory to study accounting-based balance sheet interlinkages at a sector level. Canedo and Jaramillo (2009) propose a network model to analyse systemic risk in the banking system that seeks to obtain the probability distribution of losses for the financial system resulting both from the shock/contagion process. Nieret al. (2007) construct a network model of banking systems and find that (i) the better capitalised banks are, the more resilient is the banking system against contagious defaults and this effect is non-linear; (ii) the effect of the degree of connectivity is non-monotonic; (iii) the size of interbank liabilities tend to increase the risk of knock-on default; and (iv) more concentrated banking systems are shown to be prone to larger systemic risk. In Gai and Kapadia (2009) the authors investigate systemic crises with a network model and show that on the one hand the risk of systemic crises is reduced with increasing connectivity on the interbank market. On the other hand, however, the magnitude of systemic crises increases at the same time.