Banking Systems Simulation E-Book

Stefano Zedda

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Modeling and Simulation
• Sprache: Englisch

Seitenzahl: 325

Veröffentlichungsjahr: 2017

Beschreibung

Presents information sources and methodologies for modeling and simulating banking system stability Combining both academic and institutional knowledge and experience, Banking Systems Simulation: Theory, Practice, and Application of Modeling Shocks, Losses, and Contagion presents banking system risk modeling clearly within a theoretical framework. Written from the global financial perspective, the book explores single bank risk, common bank exposures, and contagion, and how these apply on a systemic level. Zedda approaches these simulation methods logically by providing the basic building blocks of modeling and simulation, and then delving further into the individual techniques that make up a systems model. In addition, the author provides clear and detailed explanations of the foundational research into the mathematical and legal concepts used to analyze banking risk problems, measures and data for representing the main banking risk sources, and the major problems researchers are likely to encounter. There are numerous software descriptions throughout, with references and tools to help readers gain a proper understanding of the presented techniques and possibly develop new applications and research. The book concludes with an appendix that features real-world datasets and models. In addition, this book: * Provides a comprehensive overview of methods for analyzing models and simulating risk for banking and financial systems * Provides a clear presentation of the technical and legal concepts used in banking regulation * Presents unique insights from an expert's perspective, with specific coverage of assessing risks and developing what-if analyses at the systems level * Concludes with a discussion of applications, including banking systems regulation what-if tests, cost-benefit analysis, evaluations of banking systems stability effects on public finances, dimensioning, and risk-based contributions for Deposit Guarantee Schemes (DGS) and Resolution Funds Banking Systems Simulation: Theory, Practice, and Application of Modeling Shocks, Losses, and Contagion is ideal for banking researchers focusing on computational methods of analysis as well as an appropriate reference for graduate-level students in banking, finance, and computational methods. Stefano Zedda is Researcher in Financial Mathematics at the University of Cagliari in Italy and qualified as associate professor in banking and corporate finance. His research is mainly focused on quantitative analyses for banking and finance, with a particular focus on banking systems modeling and simulation. In 2008, Zedda developed the mathematical modeling and software implementation of the Systemic Model for Banking Originated Losses (SYMBOL), further developed during his activity at the European Commission. The Commission subsequently adopted it as a standard tool for testing banking regulation proposals. Stefano Zedda's research interests include banking, financial mathematics, and statistics, specifically simulation of banking and financial systems stability, banking regulation impact assessment, and interactive agent simulation.

Leseprobe

CONTENTS

Cover

Wiley Series in Modeling and Simulation

Title Page

Copyright

Dedication

Foreword

Introduction

Chapter 1: Banking Risk

1.1 Single Bank Risk

1.2 The Basel Committee on Banking Supervision Approach to Regulation

1.3 Banking Risk Modeling and Stress Testing

1.4 Contagion

1.5 System Modeling

Chapter 2: Simulation Models

2.1 Simulating Shocks: Idiosyncratic Shocks, or Exogenous Failure of Individual Banks

2.2 Simulating Shocks: Stress Testing

2.3 Simulating Shocks: Systematic Common Shocks

2.4 Simulating Shocks: Common Shocks

2.5 Estimation of Losses Variability and Assets Riskiness

2.6 Simulating Shocks: Correlated Risk Factors

2.7 Simulating Shocks: Combining Idiosyncratic and Common Shocks

2.8 Correlation

2.9 The Interbank Matrix

2.10 Loss Given Default

2.11 Interbank Losses Attribution

2.12 Contagion Simulation Methods

2.13 Data and Applied Problems

Chapter 3: Real Economy, Sovereign Risk, and Banking Systems Linkages

3.1 Effects of Bank Riskiness on Sovereign Risk

3.2 Effects of Sovereign Risk on Bank Riskiness

3.3 Linkages to the Real Economy

3.4 Modeling

3.5 Implementation

Chapter 4: Applications

4.1 Testing for Banks–Public Finances Contagion Risk

4.2 Banking Systems Regulation What-If Tests

4.3 Banks' Minimum Capital Requirements: Cost–Benefit Analysis

4.4 Deposits Guarantee Schemes (DGS)/Resolution Funds Dimensioning

4.5 Computing Capital Coverage from Assets PD and Bank PD

4.6 Computing Banks Probability to Default from Capital Coverage and Assets PD

4.7 Risk Contributions and SiFis

4.8 The Regulator's Dilemma

Appendix: Software References and Tools

References

Index

End User License Agreement

List of Tables

Table 1.1

Table 1.2

Table 1.3

Table 1.4

Table 1.5

Table 1.6

Table 1.7

Table 1.8

Table 1.9

Table 1.10

Table 2.1

Table 2.2

Table 2.3

Table 2.4

Table 2.5

Table 2.6

Table 2.7

Table 2.8

Table 2.9

Table 2.10

Table 2.11

Table 2.12

Table 2.13

Table 2.14

Table 2.15

Table 2.16

Table 2.17

Table 2.18

Table 2.19

Table 2.20

Table 2.21

Table 2.22

Table 2.23

Table 2.24

Table 2.25

Table 2.26

Table 2.27

Table 2.28

Table 2.29

Table 2.30

Table 2.31

Table 2.32

Table 2.33

Table 2.34

Table 2.35

Table 2.36

Table 2.37

Table 2.38

Table 2.39

Table 2.40

Table 2.41

Table 2.42

Table 2.43

Table 2.44

Table 2.45

Table 2.46

Table 2.47

Table 2.48

Table 2.49

Table 2.50

Table 2.51

Table 2.52

Table 2.53

Table 2.54

Table 2.55

Table 2.56

Table 2.57

Table 2.58

Table 2.59

Table 2.60

Table 4.1

Table 4.2

Table 4.3

Table 4.4

Table 4.5

Table 4.6

Table 4.7

Table 4.8

Table 4.9

Table 4.10

Table 4.11

Table 4.12

Table 4.13

Table 4.14

Table 4.15

Table 4.16

List of Illustrations

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 1.5

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 2.7

Figure 2.8

Figure 2.9

Figure 2.10

Figure 2.11

Figure 2.12

Figure 2.13

Figure 2.14

Figure 2.15

Figure 2.16

Figure 2.17

Figure 2.18

Figure 2.19

Figure 2.20

Figure 2.21

Figure 3.1

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Guide

Cover

Table of Contents

Begin Reading

Chapter 1

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Banking Systems Simulation

Theory, Practice, and Application of Modeling Shocks, Losses, and Contagion

Stefano Zedda

University of CagliariCagliari, Italy

This edition first published 2017

© 2017 John Wiley & Sons, Inc.

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The book “BANKING SYSTEMS SIMULATION” intuitively presents essentials tools for integrating risks in banks and bank systems that are essential for risk professionals and regulators.

Prof. Harald Scheule,

University of Technology Sydney, Australia

Stefano Zedda succeeds in illustrating a wide array of state of the art techniques to set up effective models of bank management, risks and contagion. Real life applications show how the book's key concepts can be used to overcome data limitations and develop parsimonious, yet accurate representations of how outside shocks and policy changes affect lenders.

Prof. Andrea Resti,

Università Bocconi, Italy

The book offers a comprehensive analysis of bank and banking system risks by adopting a simulation framework and an integrated approach between the micro and macro dimension of risk management. The analysis provides important insights for academics, regulators and practitioners.

Prof. Francesco Vallascas,

University of Leeds, UK

Foreword

Why write (or read) another book about models of banking? It sometimes seems that banking is passé — that the real financial action lies elsewhere. A recent survey (R. Greenwood and D. Scharfstein, “The Growth of Finance,” J. of Econ. Perspectives, 2013) documents the explosive growth in non-bank financial products and services. Securities markets more than quadrupled in size, from 0.4 to 1.7 percent of GDP between 1980 and 2007, on the eve of the crisis. Surely this is where we should focus — the busy secondary markets for bonds, equities, securitized products, and over-the-counter derivatives.

Yet, reports of the demise of traditional banking have been greatly exaggerated. Credit intermediation, which includes traditional deposit-taking and lending alongside banks' transactional services such as credit-card accounts and ATM activity, have also grown. Starting from a much larger share, Greenwood and Scharfstein (2013) calculate that credit intermediation grew from 2.6 to 3.4 percent of GDP over the 1980–2007 period. When the dust has settled on a quarter century of remarkable growth, banking is still roughly twice the size of securities markets.

One key reason that banking has been able to keep pace with the booming secondary markets is that banking is a key player in them. Banks provide custodial services for investors and asset managers, prime brokerage services for hedge funds, and much of the loan origination at the front end of asset securitization pipelines. Banks also still dominate the wholesale funding markets that manage much of the financial sector's liquidity provision every day.

Perhaps most importantly, banks provide the crucial cornerstone of financial capital upon which much of the edifice of credit expansion is built. The ability to leverage capital to extend liquidity (by expanding lending) during an economic expansion is critical to the functioning of the system. But the possibility of overleveraging and aggregate liquidity shocks are critical dangers. The crisis of 2007–09 demonstrated that these are not idle fantasies. The challenges of defining “adequate” capital and liquidity levels and ensuring that banks meet this standard are the driving forces behind the often highly technical conversations around the new Basel III, supervisory stress testing, and orderly resolution protocols.

In short, the management and regulation of banks and banking remain important, challenging, and timely topics, worthy of our attention.

Why is simulation a useful approach for addressing these topics? Simulation has two key features that make it an appropriate methodology in this context. First, the financial sector in general, and banking in particular, are evolving rapidly. In addition to the growing volumes of activity, there are significant innovations in both institutions and practice. For example, an entrepreneurial wave of fintech innovation is working to disrupt retail payments and traditional lending channels; supervisors are forging ahead with major new efforts in stress testing and data-driven regulation; and post-crisis institutional reforms are forcing the clearing and settlement of many over-the-counter transactions onto central counterparties. The upshot of these changes is that past is not prologue for many important questions. Moreover, the pace of innovation is such that market participants and regulators alike continue to wrestle with yet new counterfactual proposals. When simple historical patterns cease to be reliable, a higher-order model is vital. Second, many of these issues, especially at the system level, involve intricate interactions and nonlinear feedback effects that pose insurmountable tractability challenges for more traditional theoretical models.

Simulations can be implemented poorly, of course, but when done well, they have the potential to provide us guidance on this turbulent voyage. Books like the one you are reading help move us toward this better practice.

Mark D. Flood

Washington, D.C.

February 2017

Introduction

Simulation methods have recently received great attention, and many studies based on this approach have been developed in the last decade for assessing banking systems stability, determinants, and possible consequences.

Different approaches have been developed to address the main problems, but no single paper aimed at analyzing some specific aspect gives a complete picture or an orderly presentation of the topic.

The aim of this book is to present in an orderly manner the main steps, information sources, and methodologies developed for modeling and simulating banking systems stability and its applications.

The recent financial crises have led to the realization of the importance of simulations, as on one hand systemic risks are really important, and on the other hand it is not possible to make all analyses based on actual data, as the available data are limited by case number, early intervention of supervisors, and the framework evolution.

The modeling and simulation approach, which has been particularly described and developed in this book, is based on a theoretical representation of the fundamental mechanisms of risk managing of banks, and it aims at simulating the possible outcome of the banking sector as a consequence of important shocks, or for having some clue about what the consequences can be in case of regulation changes, modifications in the system structure, introduction or modification of the safety net, and other possible interventions or policies.

This book also includes the main references for banking systems risk simulation, including the models used for representing and quantifying the main banking risk sources, the banking network linkages representation and estimation, correlation and contagion mechanisms, simulation models and methods, and the most important applications for evaluating and testing the effects of possible interventions and regulation changes, and contributes to a better understanding of the banking systems risks and stability.

1Banking Risk

A bank's core business, credit activity, is centered on borrowing and lending, thus mainly dealing with two components: money and risks.

The first component, money, seems to be the simplest to measure, as all balance sheets and income statements report only money values. In fact, the different contracts, timing, and liquidity require much more attention than expected.

Every economic activity implicitly includes risk, as the economic framework always includes uncertainty. But a bank's activity is centered on risk, as its core business is in borrowing money, and lending it, bearing all risks of counterpart: default, maturity transformation, market values variation, liquidity, and so on.

Diverse layers of bank activity are cross-linked, and take part in maintaining the equilibriums in terms of revenue, economic stability, and operational activity. As a consequence, the bank's activity analysis is always complex.

The ways for analyzing credit activity are multiple.

On one hand, the banking activity is a specification of firms management, so it can be analyzed with the same attitude in terms of internal processes, costs and income, business models, personnel management, and so on.

Another possibility is to evaluate the activity results of banks from the outside, by means of regression analyses, so as to find a posteriori a description of their actual activity, results, and business models distribution and evolution.

Banks play a key role in financing the real economy, thereby sustaining and promoting the economic growth; their activity is often considered to be of national interest, and in some countries it is directly held by public companies.

In fact, the credit support of a firm or sector can substantially change its evolution and growth; choosing which firm to finance or which sector to support can be in some cases more effective than some public policy interventions.

Other fundamental aspects of banks activity are related to the volume of money managed in stock exchange and bonds markets, where the buying and selling activity can significantly affect values. Even when considering issuers of large dimensions, as in the case of sovereign bonds, the bank's attitude to buying or holding bonds to maturity can be of fundamental importance, and often the interest of governments in keeping the availability of banks in this can sometimes affect the government policy toward the banking sector.

This key role in sustaining the economic growth and the fact that banks are typically large firms induces specific attention toward the bank's activity, as the banks' default not only stops the support of economic growth but also can induce huge effects of market instability, lack of confidence in banks and in savings, bank runs, and disruptive effects on the real economy.

Thus, the analysis of a bank's activity, and of its different layers and interconnections, and the supervision and regulation of banks, are of fundamental importance for preserving savers' confidence in banks, the bank's action in channeling savings to firms, thus sustaining economic growth and preserving economic and financial stability.

The credit activity also carries a specific characteristic, as it involves buying and selling money—different maturity, contracts, risks, but always money. There is no actual goods production or transformation. This simplifies some aspects, but also induces a greater interrelationship between the different activity layers; so, as an example, there can be no strict separation, as it happens in industrial or commercial activities, between real goods or services production, and financial activities.

At a first glance, a bank's balance sheet seems to be quite similar to any other firm's balance sheet: The assets side mainly includes customer loans, bonds, interbank credits, and some other assets such as cash, buildings, and so on. As banks do not buy, transform, or sell goods, there is no motivation for quantifying the values of goods at the beginning and end of each year. The liabilities side includes deposits, interbank debts, issued bonds, and capital.

A more significant difference with respect to nonfinancial activities, such as the industrial activity, appears when comparing the assets side with the income statement: For banks, the total revenue is only a fraction of total assets, while industries typically register sales revenues in value closer to the total assets.

As an example, the FCA 2015 group's consolidated balance sheet1 reports total assets of €105,040 million, equity of 16,255 (15.5% of TA), and net revenues of €110,595 million (105% of TA), while the Deutsche Bank 2015 balance sheet2 reports total assets of €1,436,029 million, capital of 45,828 (3.2% of TA), and main income values (interest income, current income, commission income, and other operating income) summing up to a total of €31,086 million, around 2% of total assets.

It is evident that when analyzing a bank's activity, our attention is more on the assets volume than on income. It is worth noting that Germany's GDP for 2015 was estimated to be €3,025,900 million,3 while Deutsche Bank's total assets in 2015 were about 47% of its home country's GDP.

This assets dimension also explains why risks are so significant in banking activity. Referring to the values above, a reduction of 3.5% in value for FCA assets will reduce the equity value from 15.5 to 12.4% of total assets, while in the case of Deutsche Bank the capital will be completely wiped out.

Another signal of banks' central role is shown by the number of governments' interventions in rescuing banks during financial crises: Interventions on capital are absolutely fundamental when a large bank is likely to fail, and the cost of nonintervention is typically much higher than the cost of capital injection needed for rescuing the bank.

In fact, not only can the effects of uncertainty in assets and liabilities deeply affect income, and thus banking stability, but also dealing with risks is the basis of the banking activity.

So, even if the primary focus with respect to a bank's activity is toward their assets value, the uncertainty of values intrinsically inherent in the lending activity is the key reference for understanding why banking is almost a synonym for risk management.

1.1 Single Bank Risk

The first reference for analyzing a bank's activity is in considering its balance sheet main values.

(JPMorgan Chase & Co./2015 Consolidated Annual Report)

Starting from the assets side (Table 1.1), the most important exposure of banks is for customer financing, by means of loans.

Table 1.1 Bank balance sheet: assets.

Assets

Cash and due from banks

20,490

Deposits with banks

340,015

Federal funds sold and securities purchased under resale agreements

212,575

Securities borrowed

98,721

Trading assets

343,839

Securities

290,827

Loans

837,299

Allowance for loan losses

13,555

Loans, net of allowance for loan losses

823,744

Accrued interest and accounts receivable

46,605

Premises and equipment

14,362

Goodwill

47,325

Mortgage servicing rights

6,608

Other intangible assets

1,015

Other assets

105,572

Total assets

2,351,698

Loans are the traditional banks' core business, which brings a fundamental part of revenues and carries the most significant risks.

In fact, the main activity of banks consists in evaluating whom to lend money, how, and how much to lend. Analyzing a firm's balance sheets, cash flows, and tendencies (hard information), or verifying the firm's reputation, management capabilities, and reference market stability (soft information) are some of the important ways of evaluating the firm's credibility: that is, if there is a strong probability that the firm will meet its obligations and pay back the debts as scheduled.

It is evident that this evaluation cannot be exact. On one hand, it depends on future events that are not possible to forecast exactly, and moreover speculating the reactions of the firm management on these unforeseeable events will be even more difficult. On the other hand, it is not possible to analyze in depth all the firm's aspects and details, and this intrinsically results in widening the confidence intervals of the creditworthiness estimation.

As a consequence, it is fundamental for banks to use all possible strategies to reduce the total risk of the lending activity.

The traditional, and still fundamental, strategy is based on diversification. In fact, if the exposures are affected by different risk sources, the total risk is lower than the sum of individual risks. In practice, this means that it is unlikely that all exposures will default at the same time; instead, a good diversification ensures that the fraction of defaults tends to remain near the expected value. In this way, it is possible to maintain the bank's financial stability covering the expected value of defaults by means of interest spreads, and store a capital buffer for possibly absorb losses when its value is higher than expected.

It is worth noting that the bank risk is due to the uncertainty of loss value, and not due to its intrinsic value. For clearer evidence, we can consider the example of two banks of the same size, $100 million—the first exposed to firms with higher default probability, say 10%, and strong diversification (or other risk covering), so the total loss variance is of 2%; the second exposed to less risky firms, with a default probability of 5%, but no diversification (or other risk covering), so a higher variance in total losses, say of 5%. In the first case, there are expected losses of 10 and an uncertainty of 2, while in the second we have expected losses of 5, but an uncertainty of 5. The second is much more exposed to risk, even if the first bank's exposures are for riskier firms, and the expected value of losses is higher, as the second case is more subject to uncertainty.

The second important value in our simplified representation of a bank's balance sheet is for bonds, either held to maturity or for trading.

In traditional bank activity, bonds were one way of lowering the average risk, as typically bonds are issued by large firms or by governments (sovereign bonds), so the risk of counterpart default is typically lower, and as bonds are traded on financial markets, they also have a liquidity reserve role, fundamental for covering unexpected cash needs. Evidently, the lower the risk, the lower the expected income on these investments.

More recently, and in particular for large banks, the trading activity has had an important evolution, visible in the balance sheet as a movement from bonds “held to maturity,” to bonds “held for trading.” Evidently, this activity is really different from the traditional banking activity, as it is aimed not at financing an investment, but at having an income in buying and selling bonds (or shares, or derivatives) so as to profit from a price differential, thus much more similar to the commercial activity. This kind of operation is mainly exposed to market risk (in addition to the counterpart risk, always present).

Another fundamental value in our representation refers to interbank loans. In fact, banks often lend money to other banks, here also for liquidity management, for investing some momentary money excess, or for covering some momentary cash need. But it can also be due to a specific business model, for which some banks attract deposits, only using part of this savings volume for direct lending, while some prefer instead to invest in the interbank wholesale market, thus concentrating their activity on lending. This role distinction in some countries is between different bank categories, while in other cases it is just a role distinction within a banking group. Banking groups also tend to have a centralized treasury/liquidity management, so that the interbank lending within the group is typically much higher than the lending outside the group.

With reference to liabilities (Table 1.2), the main funding source is in deposits, typically available at sight or on short-term contracts, which provide the bank the funds, but also introduce a mismatching between funding and lending, typically lent with higher maturities.

Table 1.2 Bank balance sheet: liabilities and equity side.

Liabilities

Deposits

1,279,715

Federal funds purchased and securities loaned or sold under repurchase agreements

152,678

Commercial paper

15,562

Other borrowed funds

21,105

Trading liabilities

126,897

Accounts payable and other liabilities

177,638

Beneficial interests issued by consolidated variable interest entities

41,879

Long-term debt

288,651

Total liabilities

2,104,125

Stockholders' equity

Preferred stock

26,068

Common stock

4,105

Additional paid-in capital

92,500

Retained earnings

146,420

Accumulated other comprehensive income

192

Shares held in restricted stock units (RSU) trust, at cost

(21)

Treasury stock, at cost

(21,691)

Total stockholders' equity

247,573

Total liabilities and stockholders' equity

2,351,698

The stockholders' equity includes common and preferred stock, and retained earnings and other capital reserves, which represent two main sources of bank capital: the issuing of new shares and the retaining of (part of) the earnings produced by the banking activity. The equity is the main shock absorber for banks, and its value is the first reference for limiting the risk of bank default.

The other side of a bank's activity includes reporting the income statement (Table 1.3). It is typically presented starting from the interest income, interest costs, and deriving the interest differential, the net interest income. This value is then corrected for considering the provisions for credit losses. The second layer includes commissions and trading activity for having the noninterest income.

Table 1.3 Bank income statement.

+

Interest and similar income

−

Interest expense

=

Net interest income

−

Provision for credit losses

=

Net interest income after provision for credit losses

+

Commissions and fee income

+/−

Net gains (losses) on financial assets/liabilities

+/−

Other income (loss)

=

Total noninterest income

−

Compensation and benefits

−

General and administrative expenses

−

Other noninterest expenses

=

Total noninterest expenses

=

Income (loss) before income taxes

−

Income tax expense

=

Net income (loss)

The third layer is mainly devoted to operational costs, but also includes the other values that sum up to the total noninterest expenses. The taxes are then computed for obtaining the net income.

The final result of all the activity is kept by the net income (or loss).

As is well known from the accounting standards, the net income can be distributed among the shareholders, or stored for raising the capital value; however, if the bank registers a loss, it must be accounted as a reduction of the capital value.

An important detail with reference to the bank's activity reporting is that some categories of financial investments (in particular, the change in value of “available for sale” investments) are directly imputed on equity, so they do not affect the total and net income, but impact the final equity value. Thus, when evaluating the bank's activity result, it is necessary to reconcile the two, as is done by some commercial databases like Bankscope that specifically takes it into account in its “Fitch Comprehensive Income” value (see Andrew Fight, Understanding International Bank Risk, Wiley Finance, 2004).

The banking activity includes several fundamental mechanisms, which are briefly presented here.

The first one is the money channeling from the actors and sectors with more money than needed, mainly depositors but also bondholders or other banks, to the sectors investing in economic activities and producing an income sufficient to pay both the debt and interest.

The evaluation of the firm's ability to pay back debts, so as to have sufficient income and to afford the evolution of the economic framework, is the most important and specific activity of the bank.

This funding transfer needs some specific attention, as the depositors typically have the right to withdraw all of their own deposits without notice, even if they normally need only a fraction of their current account values. So, the bank has to properly quantify which fraction of deposits must be kept available as cash, and which part can be invested in loans or other interest-bearing activities. This quantification is fundamental, since if the cash requests from depositors are higher than the available cash, the bank has to sell some of its activities to obtain the money. But as the ability to evaluate the counterpart creditworthiness is complex, estimating the value of a loan is not simple, and so selling loans contracts in a short time often results in fire selling, thus losing part of the expected interest income. Thus, on one hand, banks continuously monitor the total amount or deposits and cash needs, and, on the other hand, part of their investments is in “liquid” assets, typically in highly traded bonds that can be easily sold at reasonably stable prices.

This is due to another specific aspect of a bank's activity: the maturity transformation. In fact, the liabilities, and mainly deposits, have a short maturity (days), while investments, and loans in particular, are often characterized by a longer maturity (years). This side of the bank's activity is fundamental for the real economy financing, as firms not only need money for financing their investments, but also need it for all the planned investment time. Thus, the bank has to deal with possible deposit volume changes over time, so it is fundamental to attentively monitor the turnover of investments and the related cash needs, so as to maintain the equilibrium in their assets–liability management.

So, on the basis of the actual ongoing deposits volume and stability, banks have to continuously adapt both the volume of high income and high maturity investments (loans) and the low income but highly liquid investments (as sovereign bonds).

Liquidity management can be crucial for banks, as the lack of liquidity is one of the causes of loss of confidence in banks by depositors, which can cause bank runs.

A bank run, even when not justified by actual difficulties in the bank, forces the bank to sell first the liquid assets, and then, if it is insufficient to cover the cash request, to fire sell the high income investments, resulting in important losses, and possibly causing the bank to default. If caution is not exercised, even the false suspicion that a bank is likely to fail can cause a bank run, which can cause the bank eventually to fail!

For this reason, in almost all countries a deposit guarantee scheme is implemented so that depositors may know that their deposits are covered by a guarantee, and any rumors of a possible bank failing would cause less worry and nervous reactions.

Other possible sources of risk are related to the difference between the contracts held on two sides of the balance sheet. For example, as the liabilities side is typically oriented to shorter maturities, it is more exposed to the variability of the interest rate, while the assets side quite often is oriented to fixed interest rates. This mismatching between assets and liabilities brings an interest rate risk, which can be a source of income, when the average interest rates differentials are higher for the bank, but also a possibility of suffering from significant losses in case the floating rate goes above the fixed one.

Similar problems are related to currencies and also to other risk sources.

So, a bank's soundness must be evaluated on different sides, as in the FDIC approach that includes the consideration of capitalization, assets quality, management capabilities, earnings, liquidity, and sensitivity, commonly known as CAMELS.

Finally, banks have to hold equilibriums on different layers, but banks' problems quite often originate from income difficulties or from losses caused by risk exposures, which only become evident later as liquidity problems. In fact, a low income induces banks to take higher risks, such as raising the share of high income operations, with higher rigidity, thus with more exposure to liquidity shortage, while on the liabilities side the low income can induce a reduction in confidence by possible lenders and difficulties in funding.

The risk management activity is evidently of fundamental importance for banks, and needs a detailed and continuous attention for maintaining subtle equilibriums on each of the different risk factors, each one affecting the others. One complete and detailed description of the techniques adopted with this aim is in Resti and Sironi (Risk Management and Shareholders' Value in Banking, Wiley Finance, 2007).

If, instead, we analyze a bank's results as the outcome of the whole activity without detailed information on each contract, we can analyze its distribution and evaluate the actual capability of the bank to manage and control the risk equilibriums and, subsequently, to assess the bank's default risk.

If we look at a time series of bank results, we will have something like that shown in Figure 1.1.

Figure 1.1 Profit/loss (P/L) values and frequencies.

In Figure 1.1a, we present the time series of bank results in terms of profits or losses. In Figure 1.1b, we report the frequencies for each percentage, so 0% occurs in year 4, 6, and 8, with a frequency of 3, while −1% only happens once in year 5.

The graph in Figure 1.1a, rotated, gives the standard frequency representation of the profit/loss distribution reported in Figure 1.2.

Figure 1.2 Profit/loss frequencies.

This distribution is due to the risks affecting the bank's activity, which on the right side is bell-shaped with a maximum possible loss given by the total value of exposures, while on the left side, as the minimum value of losses is zero, the shape is different. Depending on the exposures riskiness, the left side can decrease from the origin, in case of low riskiness, or it can first increase and then decrease, in case of higher riskiness, similar to what happens in a Poisson distribution depending on the expected frequency of the event.