Micro and Macro-Stress Testing User Guide
Transcript of Micro and Macro-Stress Testing User Guide
Micro and Macro-Stress Testing
User Guide
MICRO AND MACRO-STRESS
TESTING
User Guide
Prepared by
PAMELA KAHWA
Senior Analyst
Bank of Uganda
Published By
COMESA Monetary Institute (CMI)
First Published 2018 by
COMESA Monetary Institute C/O Kenya School of Monetary Studies P.O. Box 65041 – 00618 Noordin Road Nairobi, KENYA Tel: +254 – 20 – 8646207 http://cmi.comesa.int
Copyright © 2019, COMESA Monetary Institute (CMI)
All rights reserved. Except for fully acknowledged short citations for purposes of research and teaching, no part of this publication may be reproduced or transmitted in any form or by any means without prior permission from COMESA.
Disclaimer
The views expressed herein are those of the author and do not in any way represent the official position of COMESA, its Member States, or the affiliated Institution of the Author. Typesetting and Design
List of Figures ......................................................................................................... vii
List of Tables ........................................................................................................... ix
List of Acronyms ...................................................................................................... x
Preface ...................................................................................................................... xi
Acknowledgements ................................................................................................ xii
CHAPTER 1: INTRODUCTION TO STRESS TESTING .................. 1
1.1 Defining Stress Testing ................................................................................... 1
1.1.1 Approaches to stress testing ................................................................................... 1
1.2 Data Requirements for Stress Testing .......................................................... 4
1.3 Stages of the Stress Testing Process .............................................................. 6
1.3.1 Identification of risks ............................................................................................ 7
1.3.2 Designing scenarios and calibrating shocks ............................................................ 9
1.3.3 Mapping the transmission of shocks to the banking system .................................. 11
1.3.4 Interpretation and reporting of results .................................................................. 14
CHAPTER 2: APPLICATION TO INDIVIDUAL RISK FACTORS ... 15
2.1 Credit Risk ....................................................................................................... 15
2.2.1 Approaches to assessing credit risk ...................................................................... 16
2.2 Exchange Rate Risk ....................................................................................... 17
2.3 Interest Rate Risk ........................................................................................... 19
2.3.1 Direct interest rate risk ....................................................................................... 19
2.3.2 Indirect interest rate risk ..................................................................................... 21
2.4 Liquidity Risk .................................................................................................. 22
2.5 Contagion Risk ............................................................................................... 23
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CHAPTER 3: APPLICATION OF STRESS TESTING
METHODOLOGIES: PRACTICAL EXAMPLES .......................... 27
3.1 Applications of Micro Stress Testing .......................................................... 27
3.1.1 Review of the data set ......................................................................................... 28
3.1.2 Credit risk ......................................................................................................... 30
3.1.3 Direct foreign exchange rate risk ......................................................................... 41
3.1.4 Interest rate risk ................................................................................................. 45
3.1.5 Liquidity risk .................................................................................................... 58
3.2 Combined Shock Scenario ............................................................................ 69
3.2.1 Results of the combined scenario stress test ........................................................... 71
3.3 Practical Application of Macro Stress Testing ........................................... 73
3.3.1 Identifying risks in the banking sector and deriving a shock scenario .................... 74
3.3.2 Mapping the scenario to the banking system ........................................................ 76
3.3.3 Computing shock magnitudes .............................................................................. 79
3.3.4 Transmission of risks to the balance sheet and income statement .......................... 85
3.3.5 Analysis of the results ......................................................................................... 94
3.4 Practical Application of Contagion Risk Stress Testing ........................... 98
3.4.1 Review of the data set ....................................................................................... 100
3.4.2 Implementation of the contagion shock ............................................................... 101
REFERENCES...................................................................... 107
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Figure 1: Typical stress testing framework (Source: IMF) .................................................................. 3
Figure 2: Summary of macroprudential indicators ............................................................................ 6
Figure 3: Different types of risks covered in stress tests ................................................................... 7
Figure 4: Summary of steps involved in stress testing ...................................................................... 8
Figure 5: Generic risk transmission map (Source: Bank of England) ............................................... 12
Figure 6: Propagation of shocks in the interbank market (Source: IMF) ......................................... 25
Figure 7: Inputting assumptions and computing additional NPLs for the aggregate credit
shock................................................................................................................................. 32
Figure 8: Computing additional provisions for the aggregate credit shock ..................................... 33
Figure 9: Computing the impact of the aggregate credit shock on banks’ capital adequacy .......... 33
Figure 10: Computing banks’ post-shock core CAR for the aggregate credit shock .......................... 34
Figure 11: Computing the new level of NPLs following an aggregate credit shock ........................... 34
Figure 12: Inputting assumptions and computing additional NPLs for the sectoral credit
shock................................................................................................................................. 36
Figure 13: Computing additional provisions for the sectoral credit shock ........................................ 37
Figure 14: Computing the impact of the sectoral credit shock on banks’ capital adequacy ............. 38
Figure 15: Computing banks’ post-shock core CAR for the sectoral credit shock ............................. 39
Figure 16: Computing the new level of NPLs following a sectoral credit shock ................................ 39
Figure 17: Inputting assumptions and computing impact on capital of the direct foreign
exchange shock ................................................................................................................ 42
Figure 18: Computing banks’ post-shock core capital for the direct foreign exchange shock .......... 43
Figure 19: Computing banks’ post-shock core CAR for the direct foreign exchange shock ............... 44
Figure 20: Inputting assumptions for all interest rate risk stress tests .............................................. 46
Figure 21: Computing banks’ repricing gaps ..................................................................................... 47
Figure 22: Computing banks’ cumulative repricing gaps ................................................................... 48
Figure 23: Computing the impact of interest rate changes on banks’ net interest income .............. 48
Figure 24: Computing the impact of interest rate changes on banks’ core capital ........................... 49
Figure 25: Computing banks’ post-shock core capital for the repricing shock .................................. 50
Figure 26: Computing the average duration for each bank’s holdings in long-term
government bonds ........................................................................................................... 51
Figure 27: Computing the change in the value of bonds held by banks ............................................ 52
Figure 28: Computing banks’ core capital following an increase in interest rates ............................ 53
Figure 29: Computing the post-shock capital adequacy for the direct interest rate shock ............... 54
Figure 30: Computing the change in banks’ net interest income ...................................................... 56
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Figure 31: Computing the impact of a reduction in net interest income on banks’ capital
adequacy .......................................................................................................................... 57
Figure 32: Assumptions for the simple bank run ............................................................................... 60
Figure 33: Computing the balance of deposits after day 1 of the bank run ...................................... 60
Figure 34: Computing the new cash outflow for day 1 of the bank run ............................................ 61
Figure 35: Computing the balance of liquid assets after covering for withdrawn deposits on
day 1 ................................................................................................................................. 62
Figure 36: Computing the net cash inflow for day 1 of the bank run ................................................ 63
Figure 37: Liquidity ratio at the end of day 1 of the bank run ........................................................... 63
Figure 38: Computing the amount of foreign-owned funds withdrawn ........................................... 64
Figure 39: Computing total deposits and liquid assets following the loss of foreign depositor
funds ................................................................................................................................. 65
Figure 40: Computing the post-shock liquidity ratio due to loss of foreign-owned funds ................ 65
Figure 41: Computing the amount of insurance sector deposits withdrawn .................................... 66
Figure 42: Computing total deposits and liquid assets following the loss of insurance sector
deposits ............................................................................................................................ 67
Figure 43: Computing the post-shock liquidity ratio due to loss of insurance sector deposits ......... 67
Figure 44: E-Views work file containing data and estimated equations for macro scenario ............. 76
Figure 45: Estimation results for the banking variables in the macro stress tests ............................ 77
Figure 46: Transmission mechanism for the rise in short-term interests .......................................... 78
Figure 47: Input coefficients from model estimations ...................................................................... 81
Figure 48: Computing projected baseline bank variables ................................................................. 82
Figure 49: Computing standard deviation for macroeconomic variables in
Figure 50: Shock calibration using the standard deviation approach ................................................ 83
Figure 51: Deriving the largest historical quarterly change in the policy rate ................................... 84
Figure 52: Shock calibration using historical values .......................................................................... 85
Figure 53: Selecting shock calibration method .................................................................................. 86
Figure 54: Computing projected loan loss reserves .......................................................................... 87
Figure 55: Computing projected interest income .............................................................................. 88
Figure 56: Computing projected interest expenses ........................................................................... 89
Figure 57: Computing projected non-interest income ...................................................................... 90
Figure 58: Computing projected non-interest expenses ................................................................... 91
Figure 59: Computing projected loan loss provisions ........................................................................ 92
Figure 60: Computing projected core capital .................................................................................... 93
Figure 61: Computing projected risk-weighted assets ...................................................................... 94
Figure 62: Results from shock calibration using standard deviation ................................................. 95
Figure 63: Results from shock calibration using historical changes................................................... 97
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Figure 64: Matrix of interbank exposures before the contagion shock ............................................. 99
Figure 65: Network schematic of the interbank market ................................................................... 99
Figure 66: Execution of scenario (a) of the contagion shock ........................................................... 102
Figure 67: Propagation of contagion due to the failure of Bank 3 .................................................. 103
Figure 68: Execution of scenario (a) of the contagion shock with a 5 percent haircut on
capital ............................................................................................................................. 104
Figure 69: Results of the failure of Bank 3 with a 5 percent haircut on capital ............................... 105
Figure 70: Propagation of scenario (a) of the contagion shock with a 5 percent haircut on
capital ............................................................................................................................. 105
Figure 71: Results of the failure of Banks 2 and 10 with a 10 percent haircut on capital ............... 106
Table 1: Summary of worksheets in spreadsheet for micro stress testing ..................................... 27
Table 2: Selected financial soundness indicators ........................................................................... 28
Table 3: Scenarios and shock sizes for credit risk stress tests ........................................................ 31
Table 4: Scenarios and shock sizes for direct foreign exchange risk stress tests ........................... 42
Table 5: Scenarios and shock sizes for interest rate risk stress tests ............................................. 45
Table 6: Scenarios and shock sizes for liquidity risk stress tests .................................................... 59
Table 7: Shock sizes for the combined scenario stress test ........................................................... 70
Table 8: Summary of variables included in macro stress testing exercise ..................................... 74
Table 9: Average lending rate ........................................................................................................ 77
Table 10: Total loans ........................................................................................................................ 77
Table 11: NPL ratio ........................................................................................................................... 78
Table 12: Deposit growth ................................................................................................................. 78
Table 13: Summary of banks’ interbank exposures as at end of December 2017 ......................... 100
Table 14: Summary of the results of a contagion shock triggered by the failure of Bank 3 ........... 106
Table 15: Summary of the results of a contagion shock triggered by the failure of Banks 2
and 10 ............................................................................................................................. 106
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IMF International Monetary Fund
FSIs Financial Soundness Indicators
NPLs Non-Performing Loans
CAR Capital Adequacy Ratio
RWA Risk-Weighted Assets
FSAP Financial Sector Assessment Programme
GDP Gross Domestic Product
DSIBs Domestic Systemically Important Banks
OLS Ordinary Least Squares
REER Real Effective Exchange Rate
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The preparation of this User’s Guide followed a directive to COMESA Monetary
Institute (CMI) by the 23rd Meeting of the COMESA Committee of Governors of
Central Banks which was held in March, 2018 in Djibouti. Governors observed that
the financial crisis of 2008 necessitated the development and enhancement of
frameworks, tools, and techniques to assess the stability of financial systems. These
approaches combine the analysis of relevant macroeconomic data, structural
information about the financial system, market developments, and the degree of
compliance with international financial sector standards to understand the
vulnerabilities of financial systems.
The overall objective of the User’s Guide is to equip users with practical understanding
of Macro and Micro stress testing of Banks. Specifically, the Guide elaborates on the
different methodologies and techniques currently used for macro and micro stress
testing, and advices on some of the best practices to follow in applying these
techniques in small developing economies with noncomplex financial system, from
identifying vulnerabilities, to constracting scenarios, and to interpreting the results.
The User’s Guide draws extensively from several works by the International Monetary
Fund (IMF) on applied stress testing for banking systems, although the methods and
models have been widely customised to relate to experiences in the COMESA region.
Readers will familiarise themselves with how common types of stress tests can be
implemented in practice. The User’s Guide illustrate how to conduct stress testing
using concrete examples.
It is hoped that the User’s Guide will be a useful tool in assisting financial institutions
in the region to undertake macro and micro stress testing. It is also hoped that the
Guide will be used by COMESA member central banks as a reference material to train
their staff.
Ibrahim Zeidy
Director and Chief Executive Officer
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The Guidline benefited emensely from staff of COMESA Member States
Central Banks who participated in a number of trainings on the subject of stress
testing. Participants during the trainings provided critical inputs that informed
the content and scope of the User’s Guide.
The Author thanks the Director, Mr. Ibrahim Abdullahi Zeidy and the Senior
Economist, Dr. Lucas Njoroge for providing technical and expert assistance,
and all the staff of the Institute for the facilitation and logistical support
towards the completion of the User’s Guide.
The Author especially acknowledges comments from the participants of the
Validation Workshop held from 29th October to 1st November, 2018 in
Nairobi, Kenya that provided the final inputs to the User’s Guide. The
workshop was attended by participants from the following COMESA member
countries’ Central Banks: Burundi, Djibouti, DR Congo, Egypt, Eswatini,
Kenya, Malawi, Sudan, Uganda, Zambia, and Zimbabwe.
One of the key techniques for quantifying vulnerabilities in any physical system
is stress testing. In the context of financial sector analysis, the term stress
testing refers to a range of techniques used to help assess the vulnerability of
financial institutions or the financial system to exceptional but plausible events
(Čihák, 2005). Stress tests cover a range of methodologies whose complexity
can vary, which aim to assess the impact of severe stress events on the
performance and stability of the financial system. The findings of stress testing
exercises could then be applied in macroprudential policy decisions aimed at
reducing systemic risk.
1.1.1 Approaches to stress testing
There exist a wide range of methods and models for estimating the impact of
financial or economic shocks on financial systems. Hence, stress tests need to
be tailored to country-specific circumstances, the complexity of the financial
system, and data availability. Compared to complex banking systems in
emerging and advanced economies, simple banking systems such as those in the
COMESA region often have relatively small credit and market risk exposures,
and they tend not to be highly interconnected. The nature of these financial
systems suggests that the stress testing approaches implemented should involve
simple, less sophisticated models that would adequately capture the important
risk drivers, while taking into consideration the typical data and resource
constraints associated with financial stability analysis within the region.
The methodology for stress testing that is selected determines the nature and
complexity of the task. For the case of the COMESA region, two approaches
are most applicable, the balance sheet-based approach and the macrofinancial approach,
as discussed by Ong and Čihák (2014). The balance sheet-based approach uses
accounting data from the financial statements of individual institutions or
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systems. For financial sector supervisors and regulators, it is the more
convenient approach to stress testing in that the information is usually readily
and publicly available. The macrofinancial approach focuses on linkages
between the financial and the non-financial sectors of the economy, aiming to
understand how major changes in the economic environment may affect the
financial system as a whole. It can be implemented with accounting, market and
macroeconomic data by estimating models that directly connect
macroeconomic assumptions and financial risk parameters.
For any chosen approach, decisions have to be made regarding the institutional
coverage and the techniques used to determine how various risk factors
translate into banking system impact. Stress tests may be performed at varying
degrees of aggregation, from the level of an individual instrument, to
institutional level, and up to systemic level. Notwithstanding the ultimate focus
on the system level, stress tests can be either bank-by-bank, run on the
portfolios of individual financial institutions, or based on an aggregate system-
wide model (Moretti, Stolz, & Swinburne, 2008). Micro stress tests are designed
to assess resilience of individual financial institutions, and they are mainly run
by or on individual institutions. Macro stress tests, on the other hand, are
system-focused and involve aggregation or comparison of heterogeneous
institutions, often based on different assumptions and methods of calculation.
They are used to quantify financial stability assessments, to challenge
calculations that banks provide in supervisory stress tests and to reinforce the
link between macroeconomic risk assessment and microprudential actions. The
ultimate intent of system-focused approaches is to identify common
vulnerabilities across institutions that could undermine the overall stability of a
financial system. If data availability allows, conducting both micro and macro
provides maximum information about a system’s vulnerabilities.
Introduction to Stress Testing
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Figure 1: Typical stress testing framework (Source: IMF)
The analysis of any risk factor’s impact on a banking system involves modelling
the way in which the risk would be likely to affect different aspects of banks’
performance. Risk factors can be imposed on the banking system by either
sensitivity analysis or scenario analysis. With sensitivity analysis, the stress tests
aim to evaluate banks’ resilience to individual risk factors, while scenario
analysis introduces two or more risk factors simultaneously into the banking
system. Furthermore, there are two main approaches to translating
macroeconomic shocks and scenarios into financial sector variables: the
“bottom-up” approach, where the impact is estimated using individual banks’
data, and the “top-down” approach, where the impact is estimated using
aggregated banking sector data (Čihák, 2005). The bottom-up approach ideally
captures the concentration of risks and contagion, unlike the top-down
approach which could overlook the concentration of exposures at the level of
individual institutions and linkages among the institutions. While having
detailed information on exposures of individual banks to individual borrowers
should in principle lead to more accurate results than using aggregated data, the
bottom-up approach may be hampered by insufficient data and calculation
complexities. And, where the bottom-up stress tests involve calculations are
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done by many institutions, it may be a major challenge to ensure that all banks
implement the assumed shocks or scenarios in a consistent fashion.
Given various technical challenges, no single model can hope to generate
robust answers. Instead, there is a role for judgement at each step of the stress
testing process. The technical challenges in modelling financial stresses mean
that there is bound to be considerable uncertainty around the precise numbers
derived from any stress test. Notwithstanding this uncertainty, a key benefit of
stress tests is that they impose a coherent structure in which to discuss risks and
the potential impact of structural changes on the stability of a financial system.
It is by ensuring the consistency of the scenario that stress testing exercises can
add rigour to systemic financial stability analysis.
Measuring financial system soundness requires good quantitative inputs:
information on the structure of the system, general macroeconomic indicators,
and macroprudential indicators. Ideally, the data inputs should include
indicators of overall financial sector performance, covering key aspects such as
the financial infrastructure, risks from the macroeconomy, trends in credit
quality, funding and liquidity conditions, risk exposure in the financial markets,
and profit and capital buffers. Collectively, this information can be used to
broadly define, assess and monitor systemic risk within the financial sector.
Including non-banking sector indicators reflects the interconnection of the
financial and real sectors, as unfavourable developments in the real sector may
have a negative effect on financial stability. Notably, the analysis of these
indicators largely involves identifying changes in trends, major disturbances and
other outliers in order to characterise their behaviour in normal times and
during periods of stress.
Broad macroprudential indicators are essential to evaluating strengths and
weaknesses in the financial system, taking measures at both the aggregated
financial system and at the macroeconomic level since financial crises often
occur when vulnerabilities are identified in both (Hilbers, Leone, Gill, & Evens,
2000). Knowledge of the macroeconomic environment provides overall context
for the performance of the financial system and indicates potential sources of
shocks by making use of data on the real sector, such as economic growth,
inflationary pressures, and measures of indebtedness and debt-servicing ability.
Introduction to Stress Testing
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Useful information on the government sector includes measures of the deficit,
debt stock, fiscal impulse, and how the government budget is financed. The
external sector can also provide important information on vulnerabilities, using
indicators of the magnitude of the current account deficit; the relative size,
maturity structure, and currency composition of external debt, and the extent of
exchange rate misalignment and whether there are any pressures on the
exchange rate.
In addition to using macroeconomic and structural indicators, a range of
financial soundness indicators (FSIs) can be used to understand vulnerability to
shocks and capacity to absorb the resulting losses. The IMF developed a core
set of FSIs covering the banking sector, reflecting the central role of the
banking sector in many financial systems (International Monetary Fund, 2004).
In addition, an encouraged set of FSIs covers key nonfinancial sectors because
weaknesses in these sectors are a source of credit risk for banks and, thus, help
to detect banking sector vulnerabilities at an earlier stage. The health of the
financial sector can be analysed by looking at levels and trends in FSIs—
typically of capital adequacy, asset quality, profitability, liquidity, and exposure
to market risks.
A variety of indicators of the structure of the financial system can provide
important insights into the location of risks in the financial system. Data on
ownership and market shares helps to identify systemically important
institutions and sectors. Balance sheet structures, derived from aggregate
financial statements, can indicate significant exposures to particular classes of
assets and liabilities or income sources. Flow-of-funds accounts can provide
insights into major changes in the patterns of intermediation in the economy
and trends in fundraising by different sectors and instruments.
Micro and Macro Stress Testing Guideline
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Figure 2: Summary of macroprudential indicators
More frequently than not, the availability and quality of data imposes major
constraints on the nature of the stress tests that can be performed. There may
be basic data limitations in countries where information on balance sheet
exposures is not available. Also, some risk measures may be difficult to obtain
in countries where risk management systems are less sophisticated. To
overcome these difficulties, collaboration between financial and economic
sector regulators is necessary to aid the process of information sharing. It may
also be valuable to work with the institutions in the system that operate more
sophisticated surveillance and risk management frameworks to obtain better
data or to support the more analytical parts of the stress testing exercise.
Stress testing can be seen as a multi-step process of examining the key
vulnerabilities in the financial system. This process involves identifying the
major risks and exposures in the system and formulating questions about the
resilience and stability of the financial system in the face of sudden, adverse
shocks. Stress tests complement traditional financial risk models with estimates
of how banks’ balance sheets change in response to exceptional but plausible
changes in the underlying risk factors.
Introduction to Stress Testing
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1.3.1 Identification of risks
The process of designing macroprudential stress tests typically begins with
identifying potential risks to and arising from the macroeconomy and within
the banking system. At this point, it is also important to define the objective
and scope of the stress tests, that is, the selection of institutions to be included
and the coverage of risks. The coverage of the stress-testing exercise should be
broad enough to represent a significant part of the financial system, while
keeping the number of institutions involved at a feasible level. Besides
commercial banks, systemically important non-bank financial institutions may
also be included in the analysis, although this may present some difficulties if
they are supervised by different entities or have different financial reporting
practices. The discussion around identifying vulnerabilities in the system
suggests that certain types of shocks are more plausible than others, and thus
helps to narrow the focus of the exercise as it is unrealistic to attempt to stress
every possible risk factor.
Figure 3: Different types of risks covered in stress tests
Stress tests are performed for different risk types including market, credit,
operational and liquidity risk. Stress tests make use of a range of numerical
indicators to help isolate potential weaknesses, including macro-level and broad
structural indicators, together with institution-focused or micro-level indicators.
Qualitative information on the institutional and regulatory frameworks that
govern financial activities also helps to interpret developments in a range of
indicators.
Micro and Macro Stress Testing Guideline
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Analysis of the macroeconomy focuses on three major sectors: real, external
and fiscal. The indicators considered should mainly reflect the ability of the
economy to create wealth and sustain output, and its exposure to price
movements. The health of the household and corporate sectors is gauged
through proxies of their outstanding debt and disposable income which indicate
their ability to withstand sudden economic downturns (Demirgüç-Kunt &
Detragiache, 1998). Furthermore, conditions in the external sector are reflected
by real exchange rates, the current account, capital flows and maturity/currency
mismatches. These variables can be reflective of sudden changes in the
direction of capital inflows, of loss of export competitiveness, and of the
sustainability of the foreign financing of domestic debt. It should be noted,
however, that the fact that there are macroeconomic risks that could result in
shocks to the financial system does not necessarily mean that the impact of the
shocks would be large. The impact on banks depends on the size of their
exposures to the macroeconomy. Hence, it is the purpose of the stress tests to
assess how the risks combine with the exposures.
Figure 4: Summary of steps involved in stress testing
Introduction to Stress Testing
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The assessment of the banking system is characterised by quantitative indicators
of financial system soundness and stability. The objective is for the indicators
to be reflective of potential problems in the banking system, and to gauge the
impact of a crisis on the real economy. Information collected on the structure
of the financial system is used to monitor changes in the size and concentration
of financial sector assets. This is because rapid growth in size, complexity, and
diversity of financial markets can present new dimensions and challenges to the
process of maintaining financial stability.
Ideally, credit risk is analysed in terms of the banks’ ability to withstand
moderate and adverse rises in their non-performing loans (NPLs) due to
increased default rates by their borrowers. The assessment of funding and
liquidity risk should address the reliance of banks on both short- and long-term
funding sources. Overall, funding and liquidity risk in the banking sector is
quantified by the level of deposit liabilities and liquid assets held by commercial
banks. The liquidity indicators measure banks' resilience to cash flow shocks
and are hence designed to detect any liquidity disruptions which may be a
materialisation of the market’s ability to efficiently intermediate funds to
investment opportunities within the economy.
The analysis of market risk (interest rate risk and exchange rate risk) aims to
determine the impact of interest rate and exchange rate movements on the
performance of financial markets and the structure of banks’ balance sheets.
The calculations for interest rate risk should consider the presence of any
possible maturity mismatches, and the effect of interest rate sensitivities on
banks’ balance sheets. The indicators, which include short- and long-term
interest rates, exchange rates, interest spreads, and country credit risk ratings,
can indicate a loss of investors’ risk appetite and possibly financing problems
within the financial system and for the rest of the economy.
1.3.2 Designing scenarios and calibrating shocks
A key element of any stress test is the selection of the initial shock, or
combination of shocks, which draws on the main vulnerabilities identified. This
step of the exercise helps to identify stress scenarios that could expose these
vulnerabilities with potential consequences for the financial system as a whole.
The behaviour of the system in the stress scenarios is examined and the
financial sector impact of the scenarios can be compared with some baseline
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projection to gauge the scale of each vulnerability. In most cases, the baseline
scenario is an assessment of the performance of the banking sector, assuming
the most likely evolution of the macroeconomy (Haldane, Hall, & Pezzini,
2007). The scenarios considered in a stress test should be beyond the “normal”
business operating environment because stress testing involves discovering the
impact of exceptional but plausible events.
In this User’s Guide, emphasis is placed on determining the impact of any
shock on the soundness of the banking sector, rather than on deriving the
probability of a given shock scenario occurring. The expected impact is based
on banks’ exposure to a particular sector, type of asset, or dependence on
funding. In order to adequately determine the probability of any risk occurring,
one would have to perform econometric analyses or generate mathematical risk
models to quantify the relationships between key macroeconomic events and
the performance of the banking sector; this technique is beyond the scope of
the User’s Guide. Instead, through a combination of quantitative and qualitative
approaches, adverse yet plausible scenarios are developed to link each risk-type
to appropriate risk indicators and impact measures.
The stress scenarios are representations of banks’ operating environment, in
which a shock (or combination of shocks) leads to the exposure of a
vulnerability. Each scenario comprises a shock which triggers a change in some
specific risk factor. One key issue is how large a shock to consider. Note that
the objective of stress testing is not to apply shocks until some or all financial
institutions fail, although it is such exceptional outcomes that precipitate
financial instability. So, for any policy conclusions to be meaningful, the shock
should adequately highlight vulnerabilities to stresses but not be so extreme as
to be implausible. In this respect, a range of techniques can be used to develop
scenarios. At the most basic level, there are sensitivity tests which shock a single
parameter, holding constant all other factors. Given that these scenarios ignore
multiple risk factors or feedback effects, their main benefit is that they can
provide a fast initial assessment of portfolio sensitivity to a given risk factor and
identify certain risk concentrations (Basel Committee on Bank Supervision,
2001). However, stress scenarios are likely to involve adjustments in multiple
rather than single risk factors. Simultaneously capturing the correlation between
variables and through time is a key benefit of a model-based scenario approach
to stress testing which involves developing a simulation model that provides a
Introduction to Stress Testing
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forward-looking and internally consistent framework for analysing key linkages
between the financial system and the real economy (Hilbers & Jones, 2004).
Depending on the structure and features of the model, the simulation can
produce a range of economic and financial variables as outputs. However, the
effectiveness of this approach will vary according to the quality of data and
range of modelling expertise available.
Choosing appropriate stress scenarios requires historical and empirical analysis
to guide in their design and calibration as well as a significant degree of expert
judgement. Scenarios can be based on historical data (e.g., using the largest
observed changes or extreme values over a specified period), or they can be
hypothetical and involve large movements thought to be plausible. Historical
scenarios can be more intuitive because they were actually observed, but
hypothetical scenarios may be more realistic, especially if the financial structure
has changed significantly. Experiences of other countries can be a useful guide
as well (Hilbers & Jones, 2004). Another alternative sometimes used in systemic
stress testing is to ‘reverse engineer’ shocks: assessing how large a shock would
need to be to generate losses in excess of some threshold (Ong, Maino, &
Duma, 2010).
1.3.3 Mapping the transmission of shocks to the banking system
Assessing the significance of vulnerabilities in the way in which they affect the
functioning of the financial system involves identifying which parts of the
financial sector would be affected initially, as well as second-round feedback
and interaction effects between the real economy and the financial system. This
step is important as it enforces an explicit modelling of correlations of the
macroeconomic determinants of financial risk and is thus fundamental to a
clear and consistent understanding of the nature of various vulnerabilities and
the risk they poses to the system. In addition, where stress testing does identify
material impacts, the feedback mechanism may be more important and warrant
further analysis. However, modelling feedback and the interaction between
banks, households and companies is complex because of the many channels
through which such feedback may operate, and the critical role of expectations
and information.
The process of determining the impact of identified risks on the stability of the
financial system culminates in drawing risk transmission maps for each
Micro and Macro Stress Testing Guideline
~ 12 ~
vulnerability, that identify some key propagation channels through which risks
may affect individual institutions and the financial system as a whole. Figure 5 is
a schematic of how risks to financial stability might flow through to the
financial system. To the left of the transmission map are the triggers — or
‘shocks’ — that might cause a vulnerability to crystallise. They can be broken
down into shocks to the macroeconomy or financial system as a whole
(aggregate shocks) or shocks to individual firms or sectors (idiosyncratic
shocks). The central part of the map — ‘transmission’ — shows where the
effect of shocks is initially felt, capturing the sectoral and behavioural
interactions that might take place if a vulnerability materialises. The first part of
that block shows the sectors affected, broken down between the financial and
real sectors; the real sectors are public, corporate and household. The financial
sector is split between infrastructure and other financial institutions.
Figure 5: Generic risk transmission map (Source: Bank of England)
The second part of the transmission block captures propagation mechanisms,
including behavioural effects that may amplify the impact of an initial shock.
These can take a variety of forms and are broken down here between
transmission effects working through asset prices and through financial activity.
Asset price channels involve price changes, such as changes in interest and
foreign exchange rates that have knock-on effects on balance sheets and
behaviour, typically in the form of increased exposure to credit risk and balance
sheet valuation losses. Financial activity channels are characterised by volatility
in financial markets and reduced access to market liquidity and funding. On the
Introduction to Stress Testing
~ 13 ~
right of the transmission map is the ‘impact’ column which, through relevant
impact measures, captures the impact of stress events on individual firms’
balance sheets and on the functioning of the financial system as a whole.
Impact measures may be derived by aggregating estimates of potential losses on
credit and market exposures, from reductions in income generation, and from
additional funding costs.
In essence, this approach amounts to identifying a low probability stress
scenario that might cause a given vulnerability to crystallise, and then
quantifying the associated risk channels identified in a risk transmission map. In
some cases, well-articulated macroeconomic and financial models can be used
to gauge the scale of these channels. In other cases where it is not yet possible
to quantify the channels with any accuracy, typically as a result of insufficient
data or modelling difficulties, more informal approaches or historical
experience can be used.
1.3.3.1 Balance sheet implementation
There are two main approaches to translating macroeconomic shocks and
scenarios into financial sector variables through banks’ balance sheets: the
“bottom-up” approach, where the impact is estimated using data on individual
portfolios, and the “top-down” approach, where the impact is estimated using
aggregated data (Čihák, 2007). Under the bottom-up approach, the response to
various shocks in a scenario is estimated using highly disaggregated data from
individual financial institutions and may be carried out by the institutions
themselves, under the guidance of their regulators. The results of the bottom-
up approach can then be aggregated or compared to analyse the sensitivity of
the entire sector or group of institutions. This type of stress test also provides
useful information on the sensitivity of individual institutions to different
shocks, as well as information on concentrations of risks in the financial
system. Having institutions cooperate in a stress-testing exercise allows banks
to benchmark their own results against their peer groups and learn from other
participants.
The top-down approach, which is the focus of this User’s Guide, is used to
estimate the responsiveness of a group of institutions to a particular scenario.
This approach provides information on the overall sensitivity of the system to
Micro and Macro Stress Testing Guideline
~ 14 ~
broad financial and macroeconomic developments. The top-down approach is
often easier to implement, because it requires only aggregated data; however,
applying the tests only to aggregated data could disguise concentration of
exposures at the level of individual institutions that could lead to failures of
these institutions and then contagion to the rest of the system. Hence, it is
useful to perform macroprudential stress tests that attempt to combine both
approaches.
1.3.4 Interpretation and reporting of results
Stress tests should be interpreted as rough indicators of exposures rather than
as forecasts of financial institutions’ failures. By their nature, stress tests focus
on extreme events, not on the most probable events. When interpreting stress
tests, their limitations and assumptions need to be taken into account. A
complete examination of vulnerabilities must take into account also the fact
that financial institutions adapt dynamically to shocks in the environment. An
important limitation of stress tests is that they typically assume no reaction by
the institutions or supervisors, viewing all participants as static portfolios.
Nevertheless, stress tests can be particularly useful when they are conducted
regularly, because this can provide information about changes in the risk profile
of the system over time. Although stress test results are useful in evaluating
effects of large movements in key variables, care should be taken not to portray
them as providing a precise measure of the magnitude of losses.
This part of the User’s Guide provides theoretical details of computations and
specifications that are specific to the different financial risk factors in stress
testing, such as equations and definitions of risk and impact variables. The
practical examples in Part E below are presented such that readers have an
opportunity to apply these techniques as part of the simulated stress testing
exercises laid out in that section.
Credit risk is the loss associated with unexpected changes in the quality of
banks’ loan books and is typically the most significant source of risk for any
banking sector. Credit risk arises mostly from loans, but also from positions in
corporate bonds or from over-the-counter transactions that involve the risk of
a counterparty default. Measuring credit risk involves the estimation of a
number of different parameters: the likelihood of default on each instrument
both on average and under extreme conditions; the extent of the losses in the
event of default; and the likelihood that other counterparties will default at the
same time.
Credit risk stress tests aim to address two main issues: identifying which banks
could withstand the assumed shocks, and determining the associated potential
costs for the economy given the failure of banks in times of stress (Čihák,
2007). Both these factors can be addressed by assessing banks’ capital adequacy
ratio (CAR), defined as the ratio of total regulatory capital to risk-weighted
assets (RWA). According to the Basel Core Principles, a bank has to hold a
minimum CAR, of 12 percent. Hence, below this minimum, (or the value
prescribed in the respective country jurisdiction), a bank would be considered
to be failing the stress test and would be required to inject more capital to
improve its solvency and remain operational.
Micro and Macro Stress Testing Guideline
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To illustrate the computations involved in a typical stress test for credit risk, let
nplt represent the level of existing NPLs at time t, and plt the level of performing
loans. Then, a shock to a bank’s loan portfolio assumes that a certain portion of
their performing loans ∆pl become NPLs such that nplt+1 = nplt+∆pl. The bank
would now have to make provisions ∆p for the new NPLs ∆npl at a
predetermined provisioning rate π such that ∆p = π. ∆npl. The new provisions
∆p would then impact the bank’s profitability and hence capital. With c as the
bank’s existing total regulatory capital, and w as its existing risk-weighted assets,
the bank’s capital adequacy ratio ρ following the shock at time t+1 is computed
as:
𝜌t+1 =ct + ∆p
wt + ∆p (1)
Now consider the following relationship:
c + i
w + (𝑞. i)= 𝜌𝑚𝑖𝑛 (2)
Here, i is equivalent to the total capital injection required, q is the percentage of
the capital injection that is immediately used to increase risk-weighted assets,
and ρmin is the regulatory minimum CAR. From equation (2), we can derive the
necessary capital injection as:
(𝜌𝑚𝑖𝑛. w) − c
1 − (𝑞. 𝜌𝑚𝑖𝑛)= {
i if c < (𝜌𝑚𝑖𝑛. w)
0 otherwise (3)
2.2.1 Approaches to assessing credit risk
There are two general approaches to macroprudential stress tests for credit risk;
one is based on loan performance data, and the other on balance sheet or
income statement data about financial institutions’ borrowers. This User’s
Guide focuses on the approaches based on loan performance data, similar to
those employed by the IMF in their financial sector assessment programme
(FSAP) missions (International Monetary Fund, 2018). The advantage of using
loan performance data, which is data on the classification of loans into the
various categories of performing and non-performing loans, is that it is readily
available to supervisors. Still under using loan performance data, supervisors
can use two approaches: asset reclassification, and econometric modelling
Application to Individual Risk Factors
~ 17 ~
including NPLs and a number of macroeconomic factors such as real interest
rates and GDP growth. With the asset reclassification approach, a
predetermined share of the existing loans is modelled to deteriorate into NPL
status, whereby the magnitude of the increase in NPLs can be determined
mechanically, or derived from historical observations. The effect of the asset
reclassification on the banks’ capital adequacy is calculated after deducting the
additional provisions from capital and from assets.
The econometric modelling approach attempts to account for channels of
interplay between bank lending and the risk of default by borrowers as
determined by the impact of key macroeconomic factors on their debt-servicing
capabilities. The choice of explanatory variables for the model can be guided by
several sources in literature where it has been demonstrated that adverse
changes in macroeconomic variables have a significant impact on the credit
losses of banks (Demirguc-Kunt and Detragiache (1998), Havrylchyk (2010)).
The regressions can be run on the level of economic sectors if there are sectoral
data on NPLs, or on the individual financial institution level to capture the
financial institutions’ different sensitivities to macroeconomic developments.
However, the institution-by-institution approach can be too resource intensive.
It is therefore more common to estimate regressions for aggregated data and to
apply the estimated parameters onto the individual financial institutions’
positions. A typical problem with the regression approach includes the lack of
long and consistent time series data on NPLs, and even where the data are
available for a long time period, they may exhibit structural breaks due to
changing definitions of NPLs or policy changes.
Exchange rate risk is the risk that exchange rate changes affect the local
currency value of financial institutions’ assets, liabilities, and off-balance sheet
items. Exchange rate risk consists of a direct risk, arising from positions in
foreign currency, and an indirect risk, resulting from the impact of foreign
exchange positions taken by borrowers on their creditworthiness and ability to
repay, and thereby on financial institutions. The computations in this section
focus on direct foreign exchange risk. Direct exchange rate risk can be assessed
using the net open position in foreign exchange, one of the IMF’s core FSIs
(International Monetary Fund, 2004).
Micro and Macro Stress Testing Guideline
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To illustrate this test, let f denote the net open position in foreign exchange, c
the total regulatory capital, w the risk-weighted assets (all in domestic currency
units), and e the exchange rate in units of foreign currency per unit of domestic
currency. A depreciation (decline) in the exchange rate leads to a proportional
decline in the domestic currency value of the net open position, that is,
∆𝑒 𝑒 = ∆f f⁄⁄ (for f ≠ 0). Let us assume that this translates directly into a
decline in capital, that is, ∆c ∆f⁄ = 1. The capital adequacy ratio following the
exchange rate shock would then be:
𝜌 = c + (∆𝑒. f)
w (4)
For simplicity, and in the absence of quantitative models, it is assumed that the
changes in the exchange rate have no direct impact on the existing risk-
weighted assets. This is because any changes in the value of the assets are
reflected in the changes to the banks’ net open position in foreign currency. A
depreciation will benefit banks that have a long (positive) open position in
foreign currency and hurt banks that have a short (negative) position in foreign
currency.
Given that most central banks impose limits on foreign exchange positions to
capital, for most banking systems, the direct foreign exchange solvency risk is
rather small. Banks in some countries have explicit limits on these positions as a
percent of the bank’s capital. In general, the open positions tend to be rather
small and consequently the direct impact of an exchange rate depreciation (or
appreciation) is small.
Application to Individual Risk Factors
~ 19 ~
Interest rate risk is the exposure of a bank to adverse movements in interest
rates such as a shift in the absolute level of interest rates, in the spread between
two rates, in the shape of the yield curve, or in any other interest rate
relationship. Interest rate changes affect interest income and interest expenses
as well as the balance sheet through changes in market prices of financial
instruments. Changes in interest rates affect a bank's earnings by changing its
net interest income and the level of other interest-sensitive income and
operating expenses. Changes in interest rates also affect the underlying value of
the bank's assets, liabilities and off-balance sheet instruments because the
present value of future cash flows (and in some cases, the cash flows
themselves) change when interest rates change (Basel Committee on Bank
Supervision, 2001).
2.3.1 Direct interest rate risk
Direct interest rate risk is the risk incurred by a financial institution when the
interest rate sensitivities of its assets and liabilities are mismatched. Most banks
operate by transforming short-term, low interest rate liabilities into long-term,
higher-interest rate assets. Thus, an increase in interest rates has a negative
impact on the institutions’ net worth and capitalization, leading to increased
financial sector vulnerability. Banks encounter interest rate risk mostly arising
from timing differences in the maturity (for fixed rate) and repricing (for
floating rate) of bank assets, liabilities and off-balance-sheet positions. Such
repricing mismatches can expose a bank's income and underlying economic
value to unanticipated fluctuations as interest rates vary. For instance, a bank
that funded a long-term fixed rate loan with a short-term deposit could face a
decline in both the future income arising from the position and its underlying
value if interest rates increase. These declines arise because the cash flows on
the loan are fixed over its lifetime, while the interest paid on the funding is
variable, and increases after the short-term deposit matures.
The impact of changes in the interest rate on net interest income can be
measured using two models: the repricing gap model and the duration gap model. The
repricing gap model allocates interest-bearing assets and liabilities into buckets
according to their time to repricing, and the gap between assets and liabilities in
each bucket is used to estimate the net interest income exposure to interest rate
Micro and Macro Stress Testing Guideline
~ 20 ~
changes. The duration gap model focuses on the impact of interest rate changes
on the market value of assets and liabilities.
2.3.1.1 The repricing gap model
Variation in earnings is an important focal point for interest rate risk analysis
because reduced earnings or outright losses can threaten the financial stability
of a bank by undermining its capital adequacy and by reducing market
confidence.
The repricing gap model calculates the changes in interest income and interest
expenses resulting from the “gap” between the flow of interest on the holdings
of assets and liabilities sorted into time-to-repricing “buckets” for floating-rate
instruments, and the time until payments are due on fixed-rate instruments. The
net present value of assets and liabilities can be derived by discounting the net
cash flows in each time bucket, and the effect of an interest rate shock
estimated by rediscounting the net cash flows using the changed interest rates.
It is expected that the repricing gap is closed when the repricing of rate-
sensitive assets and liabilities is adequately matched.
To illustrate the implementation of the repricing gap model for the purposes of
stress testing, we define a bank’s holdings of assets A and liabilities L by their
length of time I to repricing or to payment. Then, the repricing gap for period t
is given as Rgap = At – Lt. The impact on the bank’s net interest income N due
to a change in interest rates r is computed as ∆N = ∆r.Rgap. Hence, the bank’s
capital adequacy ratio following a change in interest rates is computed as:
𝜌 = c + ∆N
w (5)
Here, c is the bank’s existing total regulatory capital, and w are its existing risk-
weighted assets.
Application to Individual Risk Factors
~ 21 ~
2.3.1.2 The duration model
To reflect the constraints on financial markets data in the COMESA region, the
duration model presented in this User’s Guide focuses on the impact of interest
rate changes on the value of bonds held by the commercial banks as illustrated
by Čihák (2007). The calculations assume that the bonds are “marked-to-
market”, that is, changes in their market value have a direct impact on the
capitalisation of the banks.
Duration of a bond is a measure of the average number of years it takes to
receive the bond’s cash flows, and it also helps to estimate how much the price
of a bond is likely to rise/fall if interest rates change. Therefore, if a bond has a
high duration, investors would need to wait a long period to receive the coupon
payments and principal invested, and the higher the duration, the more
sensitive the price of the bond is to changes in interest rates. The reverse is true
for both of these conditions. Typically, if interest rates change by 1 percent, a
bond’s price is likely to experience an inverse change by approximately 1
percent for each year of duration.
To illustrate the implementation of the duration model for purposes of stress
testing, we have to determine the impact of a change in interest rates on the
value of a bank’s bond portfolio and hence its solvency. We define the bank’s
total bond portfolio value as B and the average duration of that portfolio as D.
Then, the change in the bond portfolio value due to a change in interest rates
∆r is given by ∆B = ∆r.B.D. Hence, the bank’s capital adequacy ratio following
a change in interest rates is computed as:
𝜌 = c + ∆B
w (6)
Here, c is the bank’s existing total regulatory capital, and w are its existing risk-
weighted assets.
2.3.2 Indirect interest rate risk
Banks are exposed to indirect interest rate risk resulting from the impact of
interest rate changes on borrowers’ creditworthiness and ability to repay loans,
thus making it part of credit risk. The exact impact depends on factors such as
the borrowers’ disposable income in relation to the cost and degree of
Micro and Macro Stress Testing Guideline
~ 22 ~
collateralization of the loans. It is difficult to implement the analysis of indirect
interest rate risk with direct calculations on income and capital; rather, the use
of a regression model is more ideal. Hence, one would apply regression
modelling to determine the impact of nominal interest rate changes on real
interest rates and thereby on the creditworthiness and ability to repay of the
borrowers.
Liquidity risk is the risk that assets are not readily available to meet a short-term
demand for cash. The presentation of the stress test impact of liquidity risk is
different from the solvency tests described for credit and market risks. The
impact of a liquidity shock to a bank is expressed in terms of the adequacy of its
liquidity buffers to absorb a sudden, short-term liquidity drain without resorting
to alternative funding sources from other financial institutions or the central
bank. Although this is a relatively narrow approach to liquidity stress testing, it
is one that allows for an introductory exposition to the concept.
Modelling liquidity risk is often considered to be much more difficult than
modelling market or credit risk. Designing a liquidity stress test is challenging
due to the difficulty in identifying which assets that are normally considered
liquid may become illiquid in periods of financial stress. A straightforward
approach to stress testing liquidity risk is to shock the value of a bank’s liquid
resources by a certain percentage or amount which could be determined based
on past bank runs or on a rule of thumb.
For a typical liquidity stress test, consider a bank’s existing liquid assets L
whose adequacy is analysed by a suitable indicator such as the ratio of liquid
assets to total deposits. Then, it is assumed that the bank is faced with a sudden
shock to its available funding sources; the shock could be in form of a bank
run, a sudden withdrawal of institutional funds, or lack of access to wholesale
funding from the interbank market. It is further assumed that the bank would
draw down on its stock of liquid assets, an amount equivalent to the lost funds,
in order to sustain the liquidity drain. This relationship is presented as ∆D =
∆L, whereby D represents the value of deposit liabilities held by the bank.
Hence, a bank is considered to have failed the stress test when its liquid assets
are depleted. As a rule of thumb, a bank should be able to survive at least five
days of a moderate liquidity run without outside support (Čihák, 2005).
Application to Individual Risk Factors
~ 23 ~
One of the most important issues that financial sector supervisors have to
address when an institution is in distress is whether its failure will trigger the
subsequent failure of other financial institutions. The global financial crisis of
2008 showed how intertwined the financial system has become, thus
highlighting the potential for widespread losses and instability in case of
vulnerability in one part of the system. It became clear that interactions
between banks are critical to understanding systemic risk.
Empirical and theoretical evidence has shown that the proportion and direction
of bank contagion is heavily dependent on not only the structure of the
interbank network and the size of counterparty exposures, but also the capacity
of the banking system to absorb contagious shocks as defined by the level of
capitalisation (Mistrulli (2005), Degryse and Nguyen (2004), Minoiu and Reyes
(2013)). Robust interbank markets are important for the well-functioning of
modern financial systems because they ensure bank liquidity and efficient
monetary policy implementation. However, the interbank market may also
serve as a channel for contagion, through which solvency and liquidity
problems are transmitted through the banking system, and thus possibly
creating the risk of a banking crisis. Overall, several studies suggest that
contagious defaults in interbank markets are improbable but cannot be fully
eliminated. Contagion could lead to the breakdown of a substantial fraction of
the banking system, thus imposing high costs to the economy as a whole. In
order to assess the contagion risk in the banking system, simulations of
idiosyncratic bank failures have to be performed.
Interbank stress testing complements the standard set of stress tests by
measuring the risk that the failure of a bank or a group of banks triggers failures
of other banks in the system. There are a number of interbank contagion
channels. The most direct one is contagion through uncollateralized interbank
lending. Other plausible channels of contagion include reputational effects,
whereby a perceived stability problem in a bank could make it difficult or more
expensive for other banks in the system to access funds in money markets. The
reputational effect of a failure of a bank can also lead to liquidity runs on other
banks that are perceived as weak.
Micro and Macro Stress Testing Guideline
~ 24 ~
To begin contagion risk analysis, we define a matrix of interbank exposures,
capturing bilateral liabilities and claims. If the banking system consists of N
banks, the matrix X will be of the order NxN, where xij represents the claims of
bank i in a row against bank j in a column, such that 𝑎𝑖 = ∑ 𝑥𝑖𝑗𝑗 is the sum of
assets due to bank i and 𝑙𝑖 = ∑ 𝑥𝑖𝑗𝑖 is the sum of liabilities due from bank i.
𝑋 =
[
0 ⋯ 𝑥1𝑗 ⋯ 𝑥1𝑁
⋮ ⋱ ⋮ ⋱ ⋮𝑥𝑖1 ⋯ 0 ⋯ 𝑥𝑖𝑁
⋮ ⋱ ⋮ ⋱ ⋮𝑥𝑁1 ⋯ 𝑥𝑁𝑗 ⋯ 0 ]
∑ 𝑖
𝑎1
⋮𝑎𝑖
⋮𝑎𝑛
(7)
∑ 𝑗 𝑙1 ⋯ 𝑙𝑗 ⋯ 𝑙𝑁
A pure interbank contagion stress test models the impact of the failure of one
or more banks on the stability of the rest of the banking system through their
interbank exposures. The triggers in the scenario are introduced arbitrarily into
the interbank network, representing individual bank failures, shocks
endogenous to the banking system, or macroeconomic shocks directly affecting
the sector. A bank is then considered to have failed the test if it becomes
insolvent as a result of the propagation of the shock through the banking
system.
To initiate the contagion simulation test, it is assumed that there is a failure in a
bank, Bank 1. The first round of the contagion calculation derives the direct
impact of Bank 1’s failure on each of the other banks in the system, assuming
that Bank 1 fails to honour all or part of its interbank obligations with its direct
counterparties. If some banks fail as a result of Bank 1’s failure, the second
round of the calculation derives the impact on each of the remaining banks of
these newly failed banks not repaying their unsecured interbank exposures. The
interbank market is subjected to further shocks until there are no more failures.
Then, the overall impact on the sector’s solvency is obtained, along with the
total number of failures.
The analysis of how shocks propagate throughout the system is important to
get a sense of how a crisis could unravel once the initial shocks have taken
place (Espinosa-Vega & Sole, 2014). While the analysis of banking sector
Application to Individual Risk Factors
~ 25 ~
interconnectedness may not reveal the probability of a crisis occurring,
including an analysis of interlinkages may help to identify institutions that need
further scrutiny in terms of their vulnerability and/or level of systemic risk.
With the right data set, the extent of the domino effects can be determined, and
this could help in distinguishing which banks should be placed under
supervisory scrutiny.
Figure 6: Propagation of shocks in the interbank market (Source: IMF)
Hence, financial sector regulators need to strengthen their understanding of
systemic linkages and improve their gathering of relevant data.
This subsection provides practical examples for applying micro stress tests
using single factor analysis. Readers are provided with simulated individual bank
data and appropriately set-up Microsoft Excel spreadsheets in order to execute
the exercises for each specified risk-type. Readers are also expected to closely
follow the steps as prescribed in Section C above, as well as apply the formulae
and concepts provided in Section D above.
This part of the exercise is implemented using the MS Excel spreadsheet titled
“Micro_ST_ex.xlsx”, and the data therein contained is hypothetical. The sheet
contains five worksheets whose contents are summarised in the table below:
Table 1: Summary of worksheets in spreadsheet for micro stress testing
SHEET NAME CONTENTS
A.DATA Summary of bank data from financial statements reported as at December 2017, as well as selected financial soundness indicators
B.CREDIT RISK Illustration of credit risk stress tests
C.MARKET RISK Illustration of interest rate and foreign exchange risk stress tests
D.LIQUIDITY
RISK Illustration of liquidity risk stress tests
E.COMBINED Illustration of simplistic combined risk stress tests
The spreadsheet provides financial data for a hypothetical banking system for
which the total number of banks is unknown. It is assumed that the central
bank carries out micro stress tests for only those banks which are systemically
important (Basel Committee on Bank Supervision, 2012), and for this banking
sector, five banks (banks 1-5) were identified as being domestic systemically
Micro and Macro Stress Testing Guideline
~ 28 ~
important banks (DSIBs). Data for the rest of the banks in the sector are
aggregated and analysed as such.
Stress tests are performed on the data provided in worksheet A.DATA which is
assumed to depict the baseline operating conditions of the banking system. It is
further assumed that the central bank has yet to develop econometric models to
map the macroeconomic environment to the performance of the banking
sector and as such, it is worth noting that no macroeconomic variables are
included in these examples. Also, the shocks applied in the micro stress tests
are arbitrary. The aim of this approach is to provide users with insight into
performing banking system risk analysis while working with limited data.
3.1.1 Review of the data set
In this sub-section, a brief analysis of the performance of the banking system as
at end of December 2017 is provided in order to identify some sources of risks
(Charts 1-4 and Table 2).
Table 2: Selected financial soundness indicators
Selected financial soundness indicators (%)
ALL B1 B2 B3 B4 B5 OTHERS
Regulatory capital to risk-weighted assets
21.8 20.7 24.2 29.6 11.3 29.1 26.5
Core capital to risk-weighted assets
18.3 19.5 19.9 22.5 10.4 24.2 20.4
NPLs to total gross loans 10.5 5.8 7.5 5.2 23.8 6.9 7.7
Return on assets 0.7 4.4 3.1 -2.4 -3.1 0.9 1.3
Return on equity 6.0 31.0 17.5 -6.9 -20.4 6.2 8.3
Cost to income 91.9 69.0 73.3 112.3 118.8 93.0 84.8
Liquid assets to total deposits
29.4 37.4 29.3 28.6 45.9 36.2 19.6
Forex exposure to regulatory tier 1 capital
-1.4 4.0 -9.7 -5.1 10.6 -2.9 -5.2
Forex assets to forex liabilities
97.2 111.6 95.3 97.3 80.9 94.6 103.4
The following observations can be made from the data provided in worksheet
A.DATA:
Application of Stress Testing Methodologies: Practical Examples
~ 29 ~
a) The five DSIBs account for 58.8 percent of the banking system’s total
assets (Chart 1).
b) Banks’ assets are predominantly split between extending credit and
investing in government securities. Notably, Bank 4’s holdings in
government securities are much smaller relative to the loan portfolio, a
possible indication of lack of diversification in their assets (Chart 1).
c) Banks lend mostly to three business sectors: agriculture, construction and
real estate, and households (Chart 2). Of the DSIBs, Bank 2 holds the
largest share of loans to the agriculture sector; Bank 5 the largest share of
loans to the construction and real estate sector; and Bank 4 holds the
largest share of loans to the household sector. Also, the DSIBs collectively
account for 69.8 percent of all loans to households. The high credit
exposure to households represents heightened credit risk since the banking
sector has high NPLs to a sector that consumes more than it is productive
(Chart 3). The household sector’s NPL ratio stands at 16.1 percent and,
DSIBs also account for the majority of NPLs to the sector.
d) Bank 4 has the highest NPL ratio of the DSIBs, of 23.8 percent (Table 2).
e) The banking sector’s profitability appears low, with two of the DSIBs
(Bank 3 and Bank 4) reporting losses as at end-December 2017 (Table 2).
The sector’s cost-to-income ratio is 91.9 percent, suggesting that operating
costs were high across the sector relative to banks’ earnings.
f) Regarding banks’ funding sources, the central bank closely analyses
deposits held for non-resident financial institutions and deposits from the
insurance sector as they are the key sources of institutional funding for the
banking system. The data shows that of the DSIBs, Bank 4 has the largest
share of deposits held for non-residents, and close to 60.0 percent of the
insurance deposits are held by the DSIBs.
g) The liquidity ratio for the rest of the banking sector as a whole, excluding
DSIBs, is 19.6 percent, 0.4 percentage points below the central bank’s
prescribed regulatory minimum of 20 percent (Table 2). A liquidity ratio
this low is indicative of funding and liquidity pressures during the reporting
period.
h) All DSIBs except Bank 4 reported capital adequacy ratios above the central
bank’s regulatory minimum requirements (Table 2); 10 percent for the core
Micro and Macro Stress Testing Guideline
~ 30 ~
capital to risk-weighted assets and 15 percent for total regulatory capital to
risk-weighted assets.
Chart 1: Breakdown of bank assets Chart 2: Bank loans by sector
Chart 3: Bank NPLs by sector Chart 4: Types of deposits held by banks
3.1.2 Credit risk
Stress tests for credit risk are performed in worksheet B.CREDIT RISK;
Table B contains a summary of the all the data relevant for the credit risk stress
tests. Column B in the sheet is reserved for entries of the assumptions to be
applied to the data, while column C contains the aggregate results of the stress
0%
20%
40%
60%
80%
100%
Tota
l ass
ets
Inve
stm
ent
ingo
vern
men
tse
curi
ties
Tota
l lo
ans
BANK 1 BANK 2 BANK 3
BANK 4 BANK 5 OTHERS
0%
20%
40%
60%
80%
100%
Agr
icu
ltu
re
Co
nst
ruct
ion
&re
al e
stat
e
Ho
use
ho
lds
BANK 1 BANK 2 BANK 3
BANK 4 BANK 5 OTHERS
0%
20%
40%
60%
80%
100%
Agr
icu
ltu
re
Co
nst
ruct
ion
&re
al e
stat
e
Ho
use
ho
lds
BANK 1 BANK 2 BANK 3
BANK 4 BANK 5 OTHERS
0%20%40%60%80%
100%
Dep
osi
ts h
eld
for
no
n-
resi
den
ts
Insu
ran
cese
cto
r d
epo
sits
BANK 1 BANK 2 BANK 3
BANK 4 BANK 5 OTHERS
Application of Stress Testing Methodologies: Practical Examples
~ 31 ~
tests for the entire banking system, the values of which are computed
automatically. Column I contains the aggregated position of the rest of the
banking system excluding the DSIBs.
Two scenarios are considered for credit risk stress tests; a shock to banks’ aggregate
loan portfolio (Table B1) and, a shock to banks’ sectoral loans (Table B2). For each
scenario, we determine the impact on banks’ solvency if a portion of their
existing performing loans becomes NPLs. We also assume that a share of their
existing NPLs deteriorate further, thus increasing the overall outstanding
amount of NPLs and attracting more provisions. Furthermore, it is assumed
that additional provisions are made for the new NPLs at a rate of 50.0 percent.
It should be noted that the choice of provisioning rate on new NPLs should be
aligned with the banking regulatory requirements in the user’s jurisdiction.
A bank is assumed to fail a credit risk test if it breaches the core CAR’s
regulatory minimum requirement of 10 percent, and the results represent the
banking sector conditions after a period of six months following the shock,
with all other factors remaining constant. For purposes of this exercise, we
assume that the following shock sizes are applied uniformly to all banks’ loan
books:
Table 3: Scenarios and shock sizes for credit risk stress tests
SCENARIO MAGNITUDE OF SHOCK IMPACT
VARIABLES
Shock to aggregate loan portfolio
10 percent of performing loans become NPLs
0.5 percent of existing NPLs deteriorate further
NPL ratio
Core capital adequacy ratio
Shock to sectoral loans
The following shares of loans become NPLs: o 3 percent for agriculture
o 4.5 percent for construction & real estate
o 2 percent for households
0.2 percent of existing NPLs deteriorate further
NPL ratio
Core capital adequacy ratio
Micro and Macro Stress Testing Guideline
~ 32 ~
A shock to the aggregate loan portfolio
This test is performed in Table B1 in worksheet B.CREDIT RISK, with the
following steps:
1. To start with, input the assumptions provided in Table 3. In Figure 7, the
10 percent share of performing loans becoming NPLs is entered in cell
B20; the 0.5 percent share of NPLs deteriorating further is entered in cell
B21 and; the provisioning rate on new NPLs is entered in cell B22.
Figure 7: Inputting assumptions and computing additional NPLs for the aggregate credit shock
2. For each bank, compute the additional NPLs due to 10 percent of
performing loans becoming NPLs and the additional NPLs due to 0.5
percent of the existing NPLs experiencing further defaults. In Figure 7, this
is illustrated for Bank 1 in cell D24. The value in cell B20 is multiplied by
the bank’s performing loans in cell D4 to obtain the value of performing
loans converted to NPLs; the value in cell B21 is multiplied by the bank’s
existing NPLs in cell D8, and both values are summed together to obtain
the additional NPLs due to the shock.
3. For each bank, compute the additional provisions required to cover the new
NPLs by applying the provisioning rate of 50 percent. In Figure 8, this is
illustrated for Bank 1 in cell D25. The provisioning rate of 50 percent in cell
B22 is multiplied by the new NPLs in cell D24.
Application of Stress Testing Methodologies: Practical Examples
~ 33 ~
Figure 8: Computing additional provisions for the aggregate credit shock
Figure 9: Computing the impact of the aggregate credit shock on banks’ capital adequacy
4. Determine the impact of the shock on the banks’ capital adequacy by
deducting the new provisions from both the outstanding levels of core
capital and risk-weighted assets.
5. Figure 9 shows the new provisions in cell D25 being deducted from the
Bank 1’s reported risk-weighted assets in cell D14. Similarly, the impact on
the bank’s core capital in D26 is obtained by subtracting the new provisions
from the reported core capital in cell D12.
6. In line 28, we compute the core capital adequacy ratio for all banks
following the shock. In Figure 10, the core CAR for Bank 1 is calculated as
the new core capital in cell D26 divided by the new level of risk-weighted
assets in cell D27.
Micro and Macro Stress Testing Guideline
~ 34 ~
Figure 10: Computing banks’ post-shock core CAR for the aggregate credit shock
Figure 11: Computing the new level of NPLs following an aggregate credit shock
7. In line 30, we compute the new level of NPLs for all banks following the
shock. This is then used to acquire the new NPL ratio due to a shock to
banks’ aggregate loans. In Figure 11, Bank 1’s post-shock NPLs are
computed by adding the NPLs due to the shock in cell D24 to its existing
NPLs in cell D8. Then, the bank’s NPL ratio following the shock is derived
as the new outstanding NPLs level in cell D30 divided by its existing loans
in cell D3. Note that gross loans are kept constant in the stress test as
changes in bank credit are non-linear and hence would have to be estimated
analytically.
Application of Stress Testing Methodologies: Practical Examples
~ 35 ~
Results of the aggregate credit shock
Overall, the results reveal that the banking system is vulnerable to sudden yet
uniform increased credit default. In addition, this banking system holds
sufficient capital buffers to withstand a shock of this type, although the low
profitability suggests that any further losses would erode profit buffers which
are essential for boosting banks’ solvency.
It should be noted that this shock may be deemed severe as the likelihood of
the banking sector experiencing credit losses of this magnitude in a period of
six months is very low, although this would depend on factors affecting the
banks’ operating environment, which are not considered in this approach.
Chart 5: NPL ratio (%)
10 percent of the banking system’s
performing loans becoming NPLs
would increase the sector’s NPL
ratio from 10.5 percent to 19.5
percent.
Bank 3 would experience the largest
increase in their NPL ratio, of 9.5
percentage points.
Bank 4 registers the highest NPL
ratio due to the shock, at 31.5
percent.
The sector’s core capital adequacy
ratio decreases to 14.6 percent
following the shock, with Bank 3
registering the largest decline in the
ratio, of 3.0 percentage points.
Bank 4 fails the test as its core CAR
falls to 7.6 percent which is below
the regulatory minimum of 10
percent, and would thus need to be
recapitalised.
Chart 6: Core CAR (%)
10
.5
5.8 7.5
5.2
23
.8
6.9 7.7
19
.5
15
.2
16
.8
14
.7
31
.5
16
.3
17
.0
0.0
10.0
20.0
30.0
40.0
TOTA
L
BA
NK
1
BA
NK
2
BA
NK
3
BA
NK
4
BA
NK
5
OTH
ERS
Pre-shock Shock to aggregate loans
18
.3
19
.5
19
.9 22
.5
10
.4
24
.2
20
.4
14
.6 17
.1
17
.3
19
.5
7.6
21
.3
13
.0
0.05.0
10.015.020.025.030.0
TOTA
L
BA
NK
1
BA
NK
2
BA
NK
3
BA
NK
4
BA
NK
5
OTH
ERS
Pre-shock Shock to aggregate loans
Micro and Macro Stress Testing Guideline
~ 36 ~
A shock to sectoral loans
This test is performed in Table B2 in worksheet B.CREDIT RISK, with the
following steps:
1. To start with, input the assumptions provided in Table 3. In
2. Figure 12, the respective shares of sectoral performing loans becoming
NPLs are entered in cell range B36:B38; the 0.2 percent share of NPLs
deteriorating further is entered in cell B39 and; the provisioning rate on
new NPLs is entered in cell B40.
Figure 12: Inputting assumptions and computing additional NPLs for the sectoral credit shock
Application of Stress Testing Methodologies: Practical Examples
~ 37 ~
Figure 13: Computing additional provisions for the sectoral credit shock
3. For each bank, compute the additional NPLs due to the sectoral
performing loans becoming NPLs and the additional NPLs due to 0.2
percent of the existing NPLs experiencing further defaults. In
4. Figure 12, this is illustrated for Bank 1 in cell D42. The values in cell range
B36:B38 are multiplied by the bank’s sectoral performing loans in cell range
D5:D7 using MS Excel’s SUMPRODUCT array function1 to obtain the
value of performing loans converted to NPLs; the value in cell B39 is
multiplied by the bank’s existing NPLs in cell D8, and both values are
summed together to obtain the additional NPLs due to the shock.
5. For each bank, compute the additional provisions required to cover the new
NPLs by applying the provisioning rate of 50 percent. In Figure 13, this is
illustrated for Bank 1 in cell D43. The provisioning rate of 50 percent in cell
B40 is multiplied by the new NPLs in cell D42.
1 https://support.office.com/en-us/article/sumproduct-function-16753e75-9f68-4874-94ac-
4d2145a2fd2e
Micro and Macro Stress Testing Guideline
~ 38 ~
Figure 14: Computing the impact of the sectoral credit shock on banks’ capital adequacy
6. Determine the impact of the shock on the banks’ capital adequacy by
deducting the new provisions from both the outstanding levels of core
capital and risk-weighted assets. Figure 14 shows the new provisions in cell
D43 being deducted from the Bank 1’s reported core capital in cell D12.
Similarly, the impact on the bank’s risk-weighted assets in D45 is obtained
by subtracting the new provisions from the reported risk-weighted assets in
cell D14.
Application of Stress Testing Methodologies: Practical Examples
~ 39 ~
Figure 15: Computing banks’ post-shock core CAR for the sectoral credit shock
7. In line 46, we compute the core capital adequacy ratio for all banks
following the shock. In Figure 15, the core CAR for Bank 1 is calculated as
the new core capital level in cell D44 divided by the new level of risk-
weighted assets in cell D45.
Figure 16: Computing the new level of NPLs following a sectoral credit shock
Micro and Macro Stress Testing Guideline
~ 40 ~
8. In line 48, we compute the new level of NPLs for all banks following the
shock. This is then used to acquire the new NPL ratio due to a shock to
banks’ sectoral loans. In Figure 16, Bank 1’s post-shock NPLs are
computed by adding the NPLs due to the shock in cell D42 to its existing
NPLs in cell D8. Then, the bank’s NPL ratio following the shock is derived
as the new outstanding NPLs level in cell D48 divided by its existing loans
in cell D3. Note that gross loans are kept constant in the stress test as
changes in bank credit are non-linear and hence would have to be estimated
analytically.
Results of the sectoral credit shock
The results reveal that the banking system is resilient to sudden, combined
increased default on loans extended to the agriculture, construction and
household sectors. This is because the banking system holds sufficient capital
buffers to withstand a shock of this type, although the low profitability suggests
that any further losses would erode profit buffers which are essential for
boosting banks’ solvency. In addition, the impact of the shock on each bank
depends on that’s banks level of credit exposure to the affected sectors.
This shock may be deemed moderate as it is plausible for the banking sector to
experience diversified credit losses from different business sectors within a
period of six months, although this would depend on specific factors affecting
the credit worthiness and debt-servicing capabilities of the borrowers in the
different sectors, which are not considered in this approach.
Application of Stress Testing Methodologies: Practical Examples
~ 41 ~
Chart 7: NPL ratio (%)
The sectoral shock represents 9.5
percent of the banking system’s
performing loans becoming
NPLs, and this would increase
the sector’s NPL ratio from 10.5
percent to 12.7 percent.
Bank 5 would experience the
largest increase in their NPL
ratio, of 3.1 percentage points.
Bank 4 registers the highest NPL
ratio due to the shock, at 25.3
percent.
The sector’s core capital
adequacy ratio decreases to 17.4
percent following the shock,
with Bank 5 registering the
largest decline in the ratio, of 0.9
percentage points.
Bank 4 fails the test as its core
CAR falls to 9.8 percent which is
below the regulatory minimum
of 10 percent, and would thus
need to be recapitalised.
Chart 8: Core CAR (%)
3.1.3 Direct foreign exchange rate risk
The stress test for direct foreign exchange risk is performed in worksheet
C.MARKET RISK; Table C contains a summary of the all the data relevant
for the market risk stress tests. Column B in the sheet is reserved for entries of
the assumptions to be applied to the data, while column C contains the
aggregate results of the stress tests for the entire banking system, the values of
which are computed automatically. Column I contains the aggregated position
of the rest of the banking system excluding the DSIBs.
One scenario is considered for direct foreign exchange risk; the impact of a change
in the exchange rate on banks’ net open position in foreign currency (Table C1). For this
scenario, we determine the impact on banks’ solvency if the exchange rate
Micro and Macro Stress Testing Guideline
~ 42 ~
depreciates. A bank is assumed to fail the stress test if it breaches the core
CAR’s regulatory minimum requirement of 10 percent, and the results
represent the banking sector conditions after a period of six months following
the shock, with all other factors remaining constant. For purposes of this
exercise, we assume that the following shock size is applied uniformly to all
banks’ net open positions in foreign currency:
Table 4: Scenarios and shock sizes for direct foreign exchange risk stress tests
SCENARIO MAGNITUDE OF SHOCK IMPACT
VARIABLES
Shock to net
open position in
foreign
currency
Depreciation of the local
currency by 50 percent
Core capital
adequacy ratio
This test is performed in Table C1 in worksheet C.MARKET RISK, with the
following steps:
1. Input the assumptions provided in Table 4. In Figure 17, the depreciation
in the local currency of 50 percent is entered in cell B23.
Figure 17: Inputting assumptions and computing impact on capital of the direct foreign exchange shock
Application of Stress Testing Methodologies: Practical Examples
~ 43 ~
2. For each bank, compute the impact on core capital due to losses or gains
caused by the exchange rate depreciation. In Figure 17, this is illustrated for
Bank 1 in cell D25. The exchange rate depreciation in cell B23 is multiplied
by the bank’s reported net open position in foreign currency in cell D3 to
obtain the equivalent absolute change in core capital.
3. In line 26, compute the post-shock level of core capital for each bank. In
4. Figure 18, Bank 1’s core capital following the shock is calculated by adding
its gains due to the exchange rate shock in cell D25 to its existing core
capital in cell D16. Note that the operation is an addition instead of a
subtraction because a depreciation will benefit banks that have a long
(positive) open position in foreign currency and hurt banks that have a
short (negative) position in foreign currency.
Figure 18: Computing banks’ post-shock core capital for the direct foreign exchange shock
5. In line 27, compute the post-shock core CAR for all banks. In Figure 19,
Bank 1’s core CAR following the shock in cell D27 is derived as its post-
shock core capital level in cell D47 divided by its risk-weighted assets in cell
D18. Note that it is assumed the changes in the exchange rate have no
direct impact on the existing risk-weighted assets. This is because any
changes in the value of the assets are reflected in the changes to the banks’
net open position in foreign currency.
Micro and Macro Stress Testing Guideline
~ 44 ~
Figure 19: Computing banks’ post-shock core CAR for the direct foreign exchange shock
Results of the direct foreign exchange shock
Chart 9: Core CAR (%)
A depreciation in the local exchange rate of 50 percent results in the banking
sector’s core CAR reducing from 18.3 percent to 18.0 percent.
Of the DSIBs, banks 1 and 4 make gains while the other three make losses
on their capital.
To conclude on this stress test, the results show that impact of foreign
exchange risk would be minimal on the banking system and hence, banks are
not vulnerable to this type of market risk. This is because banks hold small
open positions in foreign currency relative to their capital.
TOTALBANK
1BANK
2BANK
3BANK
4BANK
5OTHER
S
Pre-shock 18.3 19.5 19.9 22.5 10.4 24.2 20.4
Direct FX Risk 18.0 19.9 18.9 21.9 10.9 23.8 19.8
0.0
5.0
10.0
15.0
20.0
25.0
30.0
Pre-shock Direct FX Risk
Application of Stress Testing Methodologies: Practical Examples
~ 45 ~
3.1.4 Interest rate risk
The stress tests for interest rate risk are performed in worksheet C.MARKET
RISK; Table C contains a summary of the all the data relevant for the market
risk stress tests. Column B in the sheet is reserved for entries of the
assumptions to be applied to the data, while column C contains the aggregate
results of the stress tests for the entire banking system, the values of which are
computed automatically. Column I contains the aggregated position of the rest
of the banking system excluding the DSIBs.
Three scenarios are considered for interest rate risk; the impact of a change in
nominal interest rates on banks’ net interest income (Table C2); the impact of a change in
nominal interest rates on the value of long-term bonds held by banks (Table C2) and; the
impact of an autonomous shock on banks’ net interest income (Table C3). For each
scenario, we determine the impact of changes in interest rates on banks’
solvency. A bank is assumed to fail the stress test if it breaches the core CAR’s
regulatory minimum requirement of 10 percent, and the results represent the
banking sector conditions after a period of six months following the shock,
with all other factors remaining constant.
For purposes of this exercise, we assume that the following shock sizes are
applied uniformly to all banks:
Table 5: Scenarios and shock sizes for interest rate risk stress tests
SCENARIO MAGNITUDE OF SHOCK IMPACT
VARIABLES
Impact of a change in
nominal interest rates
on banks’ net interest
income
Increase in nominal interest
rate of 2 percentage points
Core capital
adequacy ratio
Impact of a change in
nominal interest rates
on the value of long-
term bonds held by
banks
Increase in nominal interest
rate of 2 percentage points
Duration of Bond 1 is 3 years
Duration of Bond 2 is 5 years
Core capital
adequacy ratio
Autonomous shock on
banks’ net interest
income
A reduction in banks’ net
interest income of 10 percent
Core capital
adequacy ratio
Micro and Macro Stress Testing Guideline
~ 46 ~
Impact of an increase in nominal interest rates on banks’ net interest income
Under the scenario to determine the impact of an increase in nominal interest
rates on banks’ net interest income, we implement the repricing gap model as
discussed in Chapter 7, where we focus on determining the gains or losses
made by banks on assets and liabilities due to be repriced within one year from
December 2017. This test is performed in Table C2 in worksheet
C.MARKET RISK, with the following steps:
1. Enter the assumptions provided in Table 5. In Figure 20, the duration for
the bonds are entered in cells B32 and B33; the expected change in
nominal interest rates is entered in cell B34 and; the autonomous shock to
net interest income is entered in cell B35.
Figure 20: Inputting assumptions for all interest rate risk stress tests
2. In order to implement the repricing gap, we must compute the cumulative
repricing gap for banks’ interest-bearing assets and liabilities grouped in
time-to-repricing buckets of 3, 6 and 9 months. In Figure 21, we compute
the repricing gap for Bank 1’s assets and liabilities that are due to be
repriced within 3-6 months; this would be the difference between the assets
in this time bracket (cell D6)and the liabilities in the same time bracket (cell
D10). Similarly, the repricing gap for Bank 1’s assets and liabilities in the 3-
month bucket is calculated by subtracting the liabilities in cell D9 from the
assets in cell D5.
Application of Stress Testing Methodologies: Practical Examples
~ 47 ~
Figure 21: Computing banks’ repricing gaps
3. Next, compute the cumulative repricing gap for each time-to-repricing
bucket for each bank. For instance for Bank 1 in Figure 22, the cumulative
gap for all assets and liabilities due to be repriced within three months from
December 2017 is simply the value in cell D37 (blue box). Then, the
cumulative gap for all assets and liabilities due to be repriced within six
months is the sum of the repricing gap for all those assets and liabilities due
to be repriced within three and six months (red box). The same concept is
then applied to the cumulative gap for one year (green box).
Micro and Macro Stress Testing Guideline
~ 48 ~
Figure 22: Computing banks’ cumulative repricing gaps
4. Compute the gains or losses made by banks on assets and liabilities due to
be repriced within one year from December 2017. In Figure 23, this
amount is calculated for Bank 1 in cell D46 as the cumulative gap for time-
to-pricing of 12 months in cell D45, multiplied by the change in nominal
interest rates in cell B34. The repricing gap computation suggests that the
impact on banks’ net interest income is directly proportional to the impact
on the repricing gap.
Figure 23: Computing the impact of interest rate changes on banks’ net interest income
5. Compute the impact of banks’ gains or losses on their core capital. The
impact on core capital is determined by adding gains or deducting losses
directly from core capital. In Figure 24, Bank 1’s gains due to the interest
rate change in cell D46 are added to their reported core capital in cell D16.
Note that the operation is an addition instead of a subtraction because an
increase in interest will benefit banks that have a positive gap and hurt
Application of Stress Testing Methodologies: Practical Examples
~ 49 ~
banks that have a negative gap. This is because an increase in nominal
interest rates increases potential interest earned on assets and interest
expenses on liabilities with variable rates; hence, a bank whose liabilities
exceed their assets is likely to experience losses as they spend more on
funding than they earn on their assets.
Figure 24: Computing the impact of interest rate changes on banks’ core capital
1. In line 48, compute the post-shock core CAR for all banks. In Figure 25,
Bank 1’s core CAR following the shock in cell D48 is derived as its post-
shock core capital level in cell D47 divided by its risk-weighted assets in
cell D18. Note that the impact on risk-weighted assets is accounted for in
the repricing gap computation.
Micro and Macro Stress Testing Guideline
~ 50 ~
Figure 25: Computing banks’ post-shock core capital for the repricing shock
Impact of a change in nominal interest rates on the value of banks’ holdings in
long-term government bonds
Under the scenario to determine the impact of a change in nominal interest
rates on the value of long-term bonds held by banks as at end-December 2017,
we implement the duration model as discussed in Chapter 7. The data provided
shows that banks had holdings in two long-term government bonds, Bond 1
and Bond 2, as at end-December 2017. The duration of the bonds is 3 years
and 5 years respectively.
This test is performed in Table C2 in worksheet C.MARKET RISK, with the
following steps:
1. In line 52, compute the average duration for each bank’s holdings in long-
term government bonds. In Figure 26, this is obtained for Bank 1 in cell
D52 as the sum-product of the bank’s holdings in the bonds (cell range
D13:D14) and the bonds’ duration (cell range B32:B33), divided by the
banks’ total investment in the bonds (cell D12).
Application of Stress Testing Methodologies: Practical Examples
~ 51 ~
Figure 26: Computing the average duration for each bank’s holdings in long-term government bonds
2. For each bank, compute the change in the value of bonds held, following
the increase in interest rates. In Figure 22, the change in Bank 1’s value of
bonds in cell D53 is obtained by multiplying the average duration of their
bond portfolio in cell D52 by total value of their bond portfolio in cell D13,
and applying the increase in interest rates in cell B34.
Micro and Macro Stress Testing Guideline
~ 52 ~
Figure 27: Computing the change in the value of bonds held by banks
3. Calculate the post-shock core capital for all banks. In Figure 28, the core
capital level for Bank 1 following a change in interest rates (cell D54) is
computed as the difference between their reported core capital levels in cell
D16 and the change in the value of their bond portfolio in cell D53.
Application of Stress Testing Methodologies: Practical Examples
~ 53 ~
Figure 28: Computing banks’ core capital following an increase in interest rates
4. Calculate the resultant capital adequacy for all banks due to the change in
bond value. In Figure 29, this is achieved by dividing the value of post-
shock core capital in line 54 by the risk-weighted assets in line 18. Also,
derive the overall capital adequacy level of the shock, that is, impact of asset
repricing and change in bond value. Figure 29 illustrates this for Bank 1,
where the change in bond value in cell D53 is deducted from the post-
shock core capital impacted by the repricing effect in cell D47, and the
resulting amount is divided by the bank’s risk-weighted assets in cell D18.
Micro and Macro Stress Testing Guideline
~ 54 ~
Figure 29: Computing the post-shock capital adequacy for the direct interest rate shock
Results of the direct interest rate shock
The results of the direct interest rate shock suggest that the banking system is
resilient against changes in nominal interest rates. While the effect on the
industry’s bond portfolio is negative due to the relatively long average duration
of the bonds held, these losses are offset by the gains in net interest income due
to the sector’s positive one-year repricing gap.
Application of Stress Testing Methodologies: Practical Examples
~ 55 ~
Chart 10: Core CAR (%)
The impact of a rise in nominal interest rates on the aggregate banking
sector’s net interest income is positive, resulting in the core CAR increasing
to 19.0 percent.
Of the DSIBs, only Bank 4 makes losses due to the repricing effect.
The impact of the shock on the value of banks’ bond portfolios is negative,
with Bank 5 registering the largest drop in the core CAR, of 2.3 percentage
points.
The combined effect of the shock on banks’ earnings and value of bond
investments is largely negative.
Impact of an autonomous decline in net interest income
Under this scenario, the aim is to determine the impact of an arbitrary decline
of 10 percent in banks’ net interest income on their capital adequacy. This
scenario is ideal for when granular data on interest-bearing assets and liabilities,
such as their maturity and repricing profiles, is unavailable. Then, the test
provides information on the resilience of banks in the event that their profit
buffers are diminished.
TOTAL BANK 1 BANK 2 BANK 3 BANK 4 BANK 5 OTHERS
Pre-shock 18.3 19.5 19.9 22.5 10.4 24.2 20.4
Repricing effect on netinterest income
19.0 20.3 20.5 22.7 10.2 24.9 22.5
Change in bond value 17.2 18.7 19.1 20.9 10.3 21.8 18.4
Overall impact 17.9 19.4 19.7 21.2 10.1 22.5 20.6
0.0
5.0
10.0
15.0
20.0
25.0
30.0
Pre-shock
Repricing effect on net interest income
Change in bond value
Overall impact
Micro and Macro Stress Testing Guideline
~ 56 ~
This test is performed in Table C3 in worksheet C.MARKET RISK, with the
following steps:
1. For each bank, calculate the absolute change in net interest income. In
Figure 30, the absolute reduction in Bank 1’s net interest income is
obtained by multiplying the reduction of 10 percent in cell B35 by their net
interest income reported for the year 2017 in cell D15.
Figure 30: Computing the change in banks’ net interest income
2. The post-shock capital is then obtained by subtracting the loss in net
interest income from the reported core capital as at December 2017 (cell
D64, Figure 31), and the core CAR is calculated as the new level of core
capital in line 64, divided by the risk-weighted assets in line 18.
Application of Stress Testing Methodologies: Practical Examples
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Figure 31: Computing the impact of a reduction in net interest income on banks’ capital adequacy
Results of the indirect interest rate shock
The results of the indirect interest rate shock suggest that the banking system is
resilient against a sudden decline in net interest income.
Chart 11: Core CAR (%)
TOTAL BANK 1 BANK 2 BANK 3 BANK 4 BANK 5 OTHERS
Pre-shock 18.3 19.5 19.9 22.5 10.4 24.2 20.4
Reduction in NII 16.7 18.3 18.5 20.9 9.5 23.0 17.4
0.0
5.0
10.0
15.0
20.0
25.0
30.0
Pre-shock Reduction in NII
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A reduction of 10 percent in banks’ net interest income results in an industry
core CAR of 16.7 percent.
Bank 3 registers the largest decline in their core CAR, of 1.6 percentage
points.
Bank 4 fails the test as its core CAR falls to 9.5 percent, breaching the
minimum regulatory requirement.
3.1.5 Liquidity risk
The stress tests for liquidity risk are performed in worksheet D.LIQUIDITY
RISK; Table D contains a summary of the all the data relevant for the liquidity
risk stress tests. Column B in the sheet is reserved for entries of the
assumptions to be applied to the data, while column C contains the aggregate
results of the stress tests for the entire banking system, the values of which are
computed automatically. Column I contains the aggregated position of the rest
of the banking system excluding the DSIBs.
The assessment of funding and liquidity risk attempts to address the reliance of
banks on both short- and long-term funding sources. The risk tests model
liquidity drains that affect all banks in the system proportionally, depending on
their volumes of demand and time deposits. Overall, funding and liquidity risk
in the banking sector is quantified by the level of liquid assets held by banks,
the share of their deposit liabilities that belong to institutional depositors, and
their reliance on funding from non-resident financial institutions.
Three scenarios are considered for liquidity risk; a simple bank run on the banking
system (Table D2); the sudden withdrawal of funds held for foreign institutions (Table D3)
and; the sudden withdrawal of deposits held for the insurance sector (Table D4). For each
scenario, we determine the impact of the withdrawal of different types of
funding on banks’ liquidity conditions. A bank is assumed to fail the stress test
if it breaches the regulatory minimum requirement for the ratio of liquid assets
to deposits (liquidity ratio), of 20 percent. The impact of the simple bank run is
evaluated after a period of stress of five days, and the results of the latter two
scenarios represent the banking sector conditions after a period of six months
following the shock, with all other factors remaining constant.
For purposes of this exercise, we assume that the following shock sizes are
applied uniformly to all banks:
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Table 6: Scenarios and shock sizes for liquidity risk stress tests
SCENARIO MAGNITUDE OF SHOCK IMPACT
VARIABLES
Simple bank run
Daily withdrawal rate of 5
percent on demand and savings
deposits
Daily withdrawal rate of 3
percent on time deposits
Share of liquid assets available
for conversion daily is 5 percent
Other non-liquid assets are not
available for conversion
Liquidity ratio
Sudden withdrawal
of funds held for
foreign institutions
A reduction of 20 percent in
funds held for foreign
institutions
Liquidity ratio
Sudden withdrawal
of deposits held for
the insurance sector
A reduction of 10 percent in
deposits held for insurance
companies
Liquidity ratio
A simple bank run on the banking system
The simulated bank run models the banks’ ability to survive a systemic liquidity
drain during a 5-day period of stress without resorting to funding from sources
external to the domestic banking system. Bank runs are normally triggered by
diminished confidence by depositors in the stability of the affected institutions.
It is assumed that banks are faced with a daily withdrawal rate of 5 percent on
their demand deposits and 3 percent on time deposits. The time deposits have a
lower daily withdrawal rate because their withdrawal before the contractual
maturity date has been reached is bound by strict requirements and penalty fees
which may deter some depositors during a bank run. Furthermore, we assume
that banks are only able to readily liquidate 5 percent of their total liquid assets
in order to cover for lost funds and meet their daily funding obligations.
This test is performed in Table D1 in worksheet D.LIQUIDITY RISK, with
the following steps:
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1. Enter the assumptions for stress test as in Figure 32. Note that for this
test, although the withdrawal rates are imposed uniformly on all banks,
users have the option to apply varying rates for the different banks on the
premise that banks are not affected equally by such an event.
Figure 32: Assumptions for the simple bank run
2. For each bank on day 1, calculate the following:
a) The balance of total of deposits on the day: In Figure 33, the level of
demand deposits withdrawn from Bank 1 on the first day of the run is
computed by multiplying the withdrawal rate on demand deposits in cell
D14 by their existing demand deposits in cell D5. This amount is then
subtracted from the existing deposits in cell D5 in order to obtain the
remaining level of demand deposits after day 1 in cell D21. The same
approach is applied for the balance of time deposits in cell D22.
Figure 33: Computing the balance of deposits after day 1 of the bank run
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b) The cash outflow for the day: In
c) Figure 34, the cash outflow for Bank 1 on day 1 is computed as the
difference between the reported deposits in cell range D5:D6 and the
new level of deposits on day 1 in cell range D21:D22.
d) The balance of liquid assets after covering funds withdrawn on the
day: In Figure 35, the level of liquid assets that are converted (liquidated)
to cover for lost deposits from Bank 1 on the first day of the run is
computed by multiplying the share of liquid assets available to the bank
in cell D16 by their total liquid assets in cell D9. This amount is then
subtracted from the existing liquid assets in cell D9 in order to obtain the
remaining level of liquid assets after day 1.
Figure 34: Computing the new cash outflow for day 1 of the bank run
Micro and Macro Stress Testing Guideline
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Figure 35: Computing the balance of liquid assets after covering for withdrawn deposits on day 1
e) The net cash inflow for the day: In Figure 36, the new cash inflow for
Bank 1 is calculated in cell D25 as the difference between the bank’s
existing total assets in cell D3 and the new level of liquid assets on day 1
in cell D24. Then, the net cash inflow for day 1 for Bank 1 is the
difference between the new cash inflow in cell D25 and the new cash
outflow in cell D23.
Application of Stress Testing Methodologies: Practical Examples
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Figure 36: Computing the net cash inflow for day 1 of the bank run
f) The liquidity ratio at the end of day: In Figure 37, the liquidity ratio
for Bank 1 at the end of day 1 of the bank run (cell D28) is computed as
the balance of liquid assets in cell D24, divided by the balance of total
deposits in cell range D21:D22.
Figure 37: Liquidity ratio at the end of day 1 of the bank run
3. The process described in step 2 is repeated for days 2-5, computing changes
in deposits, liquid assets and cash flows compared to the previous day, to
attain the liquidity ratio for each bank at the end of each day of the run.
Micro and Macro Stress Testing Guideline
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Then, the liquidity condition of each bank is assessed at the end of day 5 of
the run.
The sudden withdrawal of funds held for foreign institutions
This scenario models the impact on banks’ funding conditions, of the sudden
withdrawal of 20 percent of the deposits belonging to foreign institutions
(Table 6). This type of scenario can take the form of capital outflows by foreign
investors, possibly triggered by instability with the domestic financial system, or
the emergence of low-risk high-return investment opportunities in other
economic regions.
This test is performed in Table D2 in worksheet D.LIQUIDITY RISK, with
the following steps:
1. Enter the share of foreign-owned deposits to be withdrawn in cell B73
(Figure 38).
2. For each bank, compute the absolute amount of funds withdrawn by
foreign institutions. In Figure 38, this is illustrated for Bank 1 by
multiplying the percentage share of 20 percent in cell B73 by the level of
deposits held for non-residents by the bank in cell D7.
Figure 38: Computing the amount of foreign-owned funds withdrawn
3. Determine the post-shock level of total deposits and liquid assets for each
bank by deducting the withdrawn funds from both items; the deduction
from the liquid assets suggests that the amount of liquid assets required to
Application of Stress Testing Methodologies: Practical Examples
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fund the sudden withdrawal is directly proportional to the actual deposits
taken out by the depositors. Figure 39 shows the computation of post-
shock liquid assets for Bank 1 in cell D77, which is gotten by subtracting
the amount of funds withdrawn by foreign depositors in cell D75 from the
bank’s existing liquid assets in cell D9.
Figure 39: Computing total deposits and liquid assets following the loss of foreign depositor funds
4. Derive the post-shock liquidity ratio for each bank by dividing the new level
of liquid assets in line 77 by the new total deposits in line 76 (Figure 40).
Figure 40: Computing the post-shock liquidity ratio due to loss of foreign-owned funds
The sudden withdrawal of funds held for insurance companies
This scenario models the impact on banks’ funding conditions, of the sudden
withdrawal of 10 percent of the deposits belonging to insurance companies
(Table 6). The aim of this scenario is to illustrate how banks can be affected by
Micro and Macro Stress Testing Guideline
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over-reliance on wholesale funds from other financial institutions such as
insurance companies and pension funds, in the event that these funding sources
suddenly become unavailable. In the case of the insurance sector, the trigger of
such an event may arise from the occurrence of a disaster event that would
result in an influx of claims, thus prompting insurance companies to recall their
deposits.
This test is performed in Table D3 in worksheet D.LIQUIDITY RISK, with
the following steps:
1. Enter the share of insurance sector deposits to be withdrawn in cell B83 (
2. Figure 41).
Figure 41: Computing the amount of insurance sector deposits withdrawn
3. For each bank, compute the absolute amount of funds withdrawn by
insurance companies. In
4. Figure 41, this is illustrated for Bank 1 by multiplying the percentage share
of 10 percent in cell B83 by the level of deposits held for insurance
companies by the bank in cell D8.
Application of Stress Testing Methodologies: Practical Examples
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Figure 42: Computing total deposits and liquid assets following the loss of insurance sector deposits
5. Determine the post-shock level of total deposits and liquid assets for each
bank by deducting the withdrawn funds from both items; the deduction
from the liquid assets suggests that the amount of liquid assets required to
fund the sudden withdrawal is directly proportional to the actual deposits
taken out by the depositors. Figure 42 shows the computation of post-
shock liquid assets for Bank 1 in cell D87, which is gotten by subtracting
the amount of funds withdrawn by insurance companies in cell D85 from
the bank’s existing liquid assets in cell D9.
Figure 43: Computing the post-shock liquidity ratio due to loss of insurance sector deposits
6. Derive the post-shock liquidity ratio for each bank by dividing the new level
of liquid assets in line 87 by the new total deposits in line 86 (Figure 43).
Micro and Macro Stress Testing Guideline
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Results of the liquidity risk stress tests
While the DSIBs appear to hold sufficient liquid assets to withstand the shock
scenarios presented, this is not the case for the rest of the banking system
which collectively breaches the regulatory minimum liquidity ratio of 20
percent. In particular, that portion of the banking industry is significantly
affected by the loss of foreign-owned deposits, which is an indicator of over-
reliance on these types of funds by the banks.
Chart 12: Liquidity ratio (%)
The simple bank run results in a reduction in banks’ total deposits of 20.1
percent by day 5, with a liquidity ratio of 28.5 percent.
The withdrawal of foreign-owned funds has the largest impact on the
banking system, resulting in a liquidity ratio of 26.6 percent.
All DSIBs are able to withstand the liquidity shock scenarios imposed on
them.
TOTAL BANK 1 BANK 2 BANK 3 BANK 4 BANK 5OTHER
S
Pre-shock 29.4 37.4 29.3 28.6 45.9 36.2 19.6
Simple bank run 28.5 36.1 28.6 27.3 43.1 33.7 19.4
Loss of foreign funds 26.6 35.0 29.1 28.6 42.1 34.5 15.2
Loss of insurance deposits 28.6 36.6 28.4 27.7 45.3 35.5 18.6
0.05.0
10.015.020.025.030.035.040.045.050.0
Pre-shock
Simple bank run
Loss of foreignfunds
Loss of insurancedeposits
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The combined shock scenario illustrates how shocks to the various risk factors
can be combined into a single scenario, and how this scenario impacts the
capital adequacy and liquidity of the banking system. The main reason for using
scenarios rather than single factor shocks is that in the macroeconomic context,
changes in several risk factors are typically interrelated (Čihák, 2007).
The stress tests for the combined shock scenario are performed in worksheet
E.COMBINED; Table E contains a summary of the all the relevant pre- and
post-shock data. Column B contains the aggregate results of the stress tests for
the entire banking system, and Column H contains the aggregated position of
the rest of the banking system excluding the DSIBs. Note that the worksheet
contains only formulas linked to the other worksheets. In the sheet, the impacts
of the selected shocks are summed up to arrive at an aggregate impact. The
aggregation approach applied in the worksheet takes into account concentration
of risks in institutions. Simply adding up aggregate losses caused by individual
shocks could overlook situations when risks are concentrated in an institution
or a group of institutions. This issue is addressed by calculating the impacts
bank-by-bank, allowing us to see how each bank is affected by the selected
combination of shocks. Also, it is not trivial to combine solvency and liquidity
risks and hence, this is not attempted in the worksheet.
For purposes of this exercise, we assume that the following shock sizes are
applied uniformly to all banks:
Micro and Macro Stress Testing Guideline
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Table 7: Shock sizes for the combined scenario stress test
RISK TYPE MAGNITUDE OF SHOCK IMPACT VARIABLES
Credit risk
5 percent of total performing loans become NPLs
The following shares of sectoral loans become NPLs: o 2 percent for agriculture o 3.5 percent for construction & real
estate o 1 percent for households
0.5 percent of existing NPLs deteriorate further
NPL ratio
Core capital adequacy ratio
Direct foreign exchange risk
Depreciation of the local currency by 50 percent
Core capital adequacy ratio
Direct interest rate risk
Increase in nominal interest rate of 2 percentage points
Duration of Bond 1 is 3 years
Duration of Bond 2 is 5 years
Core capital adequacy ratio
Liquidity risk
Daily withdrawal rate of 2 percent on demand and savings deposits
Daily withdrawal rate of 1 percent on time deposits
Share of liquid assets available for conversion daily is 5 percent
Other non-liquid assets are not available for conversion
A reduction of 5 percent in funds held for foreign institutions
Liquidity ratio
The following serves as an example of the type of scenario quantified by the
shock magnitudes in Table 7: a depreciation of the local currency, of 50 percent
triggers an increase in nominal interest rates of 2 percent (possibly through
increased inflationary pressures), which leads to an increase in real interest rates
that eventually contribute to 5 percent of banks’ aggregate performing loans
becoming NPLs as the cost of credit rises. The impending instability in the
domestic financial markets then leads to a fire sale of government securities and
capital outflows in the short-term which manifest in the form of a bank run and
the withdrawal of deposits for held for foreign institutions.
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This test is performed with the following steps:
1. Enter the assumptions presented in Table 7 in their respective worksheets
and as described for the stress tests for each type of risk. The assumption
for the loss of insurance sector deposits is left as 0 percent because these
deposits remain unaffected in the scenario. Also, for the credit risk
assumptions in worksheet B.CREDIT RISK, the share of existing NPLs
that deteriorates further should be entered either in cell B21 or cell B39 but
not both, to avoid double counting.
2. For each risk, if not already completed as in Chapter 11, compute the
impact of the shocks on capital and liquidity where applicable, and review
the results in worksheet E.COMBINED. Note the following:
a) The results for post-shock NPLs in line 15 aggregate the results for
both the aggregate and sectoral credit risk shocks.
b) The results for post-shock capital in lines 16 and 17 aggregate the
results for the credit, foreign exchange and interest rate risks.
c) The results for post-shock risk-weighted assets only represent the
impact of the credit risk shocks.
d) The post-shock results for liquidity reflect the impact of the liquidity
shocks only.
3.2.1 Results of the combined scenario stress test
The results show that the banking system may indeed be vulnerable to a
systemic risk event such as the one imposed on it in the combined shock
scenario. The sector’s core CAR drops to 13.7 percent which, still being above
the regulatory minimum requirement of 10 percent, represents the impact of
the shock on the rest of the banking sector excluding the DSIBs. The other
banks in the system report a post-shock core CAR of 10.7 percent, meaning
that many of the banks were adversely affected by the shock. A suitable
response to these results by the banking sector supervisors and regulators
would be to require all banks to acquire additional core capital in order to guard
against the effects of a similar event.
The combined shock scenario illustrated in this chapter is an example of how
scenario analysis as described in Chapter 2 can be applied in an environment of
Micro and Macro Stress Testing Guideline
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limited data. Furthermore, it sets the pace for the application of scenario
analysis in the setting of macro stress tests.
Chart 13: Core CAR (%)
Chart 14: NPL ratio (%)
Chart 15: Liquidity ratio (%)
TOTAL BANK 1 BANK 2 BANK 3 BANK 4 BANK 5 OTHERS
Pre-shock 18.3 19.5 19.9 22.5 10.4 24.2 20.4
Post-shock 13.7 16.7 15.8 18.0 9.4 18.5 10.7
0.0
5.0
10.0
15.0
20.0
25.0
Pre-shock Post-shock
TOTAL BANK 1 BANK 2 BANK 3 BANK 4 BANK 5OTHER
S
Pre-shock 10.5 5.8 7.5 5.2 23.8 6.9 7.7
Post-shock 16.5 12.0 13.6 11.7 28.5 13.9 13.8
0.05.0
10.015.020.025.030.0
Pre-shock Post-shock
TOTAL BANK 1 BANK 2 BANK 3 BANK 4 BANK 5OTHER
S
Pre-shock 29.4 37.4 29.3 28.6 45.9 36.2 19.6
Post-shock 24.0 30.8 24.7 23.9 37.0 29.5 15.5
0.010.020.030.040.050.0
Pre-shock Post-shock
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Of the DSIBs, Bank 5 faces the largest decline in their core CAR of 5.6
percentage points.
Bank 4 fails the combined scenario test as its core CAR falls to 9.4 percent,
which is below the regulatory minimum requirement.
Regarding credit risk, Bank 5 reports the largest increase in their NPL ratio,
from 6.9 percent to 13.9 percent, possibly due to the impact from the
sectoral credit shock as was noted in section 11.2.
The rest of the banking sector, excluding the DSIBs, collectively fails the
combined liquidity stress test as their liquidity ratio falls to 15.5 percent,
which is below the regulatory minimum requirement.
This subsection introduces the fundamental concepts of an ideal macro stress
testing framework and provides one detailed practical example for
implementing macro stress tests. It is vital that readers closely follow the steps
as prescribed in Sections B and C above, as well as apply the formulae and
concepts provided in Section D above.
The exercise is performed in the MS Excel spreadsheet named
MacroST_ex.xlsx. The ALL DATA worksheet contains aggregated bank data,
as well as data for selected relevant macroeconomic variables for a fictional
country (summarised in Table 8). The data is of quarterly frequency, from
March 2001 to December 2017. For all the macroeconomic variables, projected
values are provided from March 2018 to December 2019; it is assumed that the
central bank has a macroeconomic projection model that produces forecasts for
up to two years from any reporting period.
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Table 8: Summary of variables included in macro stress testing exercise
Level data is in millions of local currency units, while all growth rates are based
on annual changes. In the SHOCKS worksheet, the shock magnitudes for the
selected scenario that is projected onto the banking system are computed. The
results arising from the exercise are then presented in the RESULTS
worksheet. In addition to the MS Excel file, the E-Views file named cmi_mast
is provided, within which regression analysis is performed to quantify
relationships between selected bank and macroeconomic variables.
In the following sub-sections, readers are taken through the key steps involved
in performing a typical stress test, as discussed in Chapter 3 of this User’s
Guide.
3.3.1 Identifying risks in the banking sector and deriving a shock
scenario
By analysing the data provided in worksheet ALL DATA, we can derive the
key risks faced by this particular banking system.
The data shows that the economy is going through a period of recovery
following a gradual decline in economic output that started in 2016 (Chart 16).
The central bank projects that real GDP will grow at annual rate of 6.8 percent
in the year to March 2018 and peak at 7.6 percent in September 2018. From
Chart 17, it seems that the central bank was exercising expansionary monetary
policy in order to boost economic activity, with the policy rate falling from 19.5
percent in March 2016 to 8.8 percent in December 2017. The average lending
Bank variables
Average lending rate
Total loans (levels & growth rates)
Deposit growth
NPL ratio
Macroeconomic variables
Real GDP growth
Real M3 (level & growth rates)
Policy rate
Change in REER
Inflation rate
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rate offered by banks closely tracked the policy rate during this period, implying
that banks’ lending activity responded to the applied monetary policy actions.
However, despite the pronounced drop in interest rates, credit growth
remained sluggish, growing at a rate of 1.5 percent during 2017 (Chart 18). The
slow credit growth could possibly be explained by both reduced demand by
borrowers and retracted supply by banks as they concentrated on cleaning up
their loan books. Indeed, the NPL ratio hit 10.5 percent in December 2015,
before falling back to 6.5 percent in December 2017, likely due to high write-
offs following increased default rates.
Chart 16: Annual real GDP growth and inflation (%)
Chart 17: Interest rates (%)
Chart 18: Annual credit growth (%)
Chart 19: NPL ratio (%)
Looking ahead, the central bank anticipates that annual inflation is expected to
remain subdued for the next two years even as the economy continues to
recover. However, in the face of rising global interest rates, they project that the
policy rate will rise gradually to reach 11.3 percent in March 2019. Based strictly
on the available information, the banking sector is primarily faced with
increased credit risk in the short- to medium – term, arising from a possible rise
-30
-20
-10
0
10
20
30
Dec-01 Dec-05 Dec-09 Dec-13 Dec-17
Inflation - projectedInflation - historicalGDP - projected
0
5
10
15
20
25
30
35
Mar-01 Mar-05 Mar-09 Mar-13 Mar-17
Policy rate - Projected
Policy rate - Historical
Lending rate
-10
10
30
50
Mar-01 Mar-05 Mar-09 Mar-13 Mar-17 0
10
20
30
Mar-01 Mar-05 Mar-09 Mar-13 Mar-17
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in loan defaults due to an increase in the cost of funding and credit. The next
step is to design a shock scenario that adequately captures the impact of an
increase in short-term interest rates on the performance of the banking system.
3.3.2 Mapping the scenario to the banking system
This step of the exercise is performed using the E-Views work file cmi_mast.
Figure 44: E-Views work file containing data and estimated equations for macro scenario
Based on the central bank’s macroeconomic projections, we are able to map the
impact of changes in the policy rate to the performance of the banking system
by estimating relationships between the macroeconomic and banking sector
variables provided. All the variables from the MS Excel worksheet ALL DATA
are loaded into the E-Views work file provided. Using this data, four equations
are estimated using the ordinary least squares (OLS) technique, the results of
which are included in the E-Views work file (Figure 44), and they are laid out in
Figure 45. The bank variables are estimated as follows:
1) NPL ratio (t) = f (NPL ratio (t-1), lending rate (t), real GDP growth (t-1))
2) ln (loans (t)) = f (ln (loans (t-1), ∆ln (real M3 (t)), lending rate (t))
3) lending rate (t) = f (policy rate (t), REER change (t))
4) deposit growth (t) = f (real GDP growth (t))
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An increase in the policy rate directly translates into a rise in banks’ lending
rates (equation 3, Table 9), which are also affected by changes in exchange rates
as represented by the real effective exchange rate (REER). The lending rates
then affect banks’ credit growth and asset quality. In this banking system,
banks’ lending activity is driven by annual changes in broad money supply
within the economy and banks’ lending rates (equation 2, Table 10). This is
expected as broad money supply transforms into retail deposits from which
banks can extend credit and a shortage of which would hamper credit growth,
as well as disposable income for borrowers to adequately service their loans.
Also, credit demand increases as interest rates fall.
Figure 45: Estimation results for the banking variables in the macro stress tests
Table 9: Average lending rate
Dependent Variable: AVGLENDR
Method: Least Squares
Date: 09/25/18 Time: 10:25
Sample (adjusted): 2005Q1 2017Q4
Included observations: 52 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 16.68512 0.556692 29.97193 0.0000
POLRATE 0.459755 0.049651 9.259810 0.0000
REER_CHG -0.118373 0.034737 -3.407728 0.0013
R-squared 0.636474 Mean dependent var 21.51538
Adjusted R-squared 0.621637 S.D. dependent var 2.224585
S.E. of regression 1.368370 Akaike info criterion 3.521079
Sum squared resid 91.74939 Schwarz criterion 3.633651
Log likelihood -88.54805 Hannan-Quinn criter. 3.564236
F-statistic 42.89553 Durbin-Watson stat 0.581127
Prob(F-statistic) 0.000000
Table 10: Total loans
Dependent Variable: LOG(LOANS)
Method: Least Squares
Date: 09/25/18 Time: 10:24
Sample (adjusted): 2001Q2 2017Q4
Included observations: 67 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.203819 0.051364 3.968136 0.0002
LOG(LOANS(-1)) 1.002178 0.005265 190.3556 0.0000
D(LOG(RM3)) 0.410078 0.140502 2.918652 0.0049
AVGLENDR -0.008604 0.002787 -3.087118 0.0030
R-squared 0.998914 Mean dependent var 4.132320
Adjusted R-squared 0.998862 S.D. dependent var 1.067265
S.E. of regression 0.036002 Akaike info criterion -3.752652
Sum squared resid 0.081656 Schwarz criterion -3.621028
Log likelihood 129.7138 Hannan-Quinn criter. -3.700568
F-statistic 19312.89 Durbin-Watson stat 1.582666
Prob(F-statistic) 0.000000
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Table 11: NPL ratio
Dependent Variable: NPLR
Method: Least Squares
Date: 09/25/18 Time: 10:22
Sample (adjusted): 2002Q1 2017Q4
Included observations: 64 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
NPLR(-1) 0.700353 0.079144 8.849100 0.0000
AVGLENDR 0.187222 0.054266 3.450066 0.0010
RGDP_GR(-1) -0.360010 0.134870 -2.669304 0.0097
R-squared 0.750976 Mean dependent var 5.856250
Adjusted R-squared 0.742812 S.D. dependent var 4.406592
S.E. of regression 2.234748 Akaike info criterion 4.491875
Sum squared resid 304.6401 Schwarz criterion 4.593073
Log likelihood -140.7400 Hannan-Quinn criter. 4.531742
Durbin-Watson stat 1.834694
Table 12: Deposit growth
Dependent Variable: DEPS_GR
Method: Least Squares
Date: 09/25/18 Time: 10:26
Sample (adjusted): 2001Q4 2017Q4
Included observations: 65 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
RGDP_GR 0.985618 0.050540 19.50169 0.0000
R-squared 0.311835 Mean dependent var 6.049758
Adjusted R-squared 0.311835 S.D. dependent var 3.136894
S.E. of regression 2.602233 Akaike info criterion 4.765882
Sum squared resid 433.3836 Schwarz criterion 4.799334
Log likelihood -153.8912 Hannan-Quinn criter. 4.779081
Durbin-Watson stat 1.103522
The banking sector’s level of credit risk, as measured by the NPL ratio, is
determined by banks’ lending rates and real economic output (equation 1, Table
11). Indeed, it is expected that as the cost of credit rises, borrowers’ debt
burden increases and may result in loan defaults which can be exacerbated in an
environment of slow economic growth as borrowers’ disposable income is
diminished. Table 12 reveals that banks’ deposit mobilisation is supported by
strong economic activity, which is expected since savings by retail depositors
such as households and private sector companies are driven by increased
earnings generated from firm economic productivity.
Figure 46: Transmission mechanism for the rise in short-term interests
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3.3.3 Computing shock magnitudes
The coefficients obtained from the estimations in Figure 45 enable readers to
acquire projected values for all the banking sector variables included in the
exercise. Then, the projected data set is the basis for the baseline scenario, that
is, the assumed “normal” operating conditions for both the economy and the
banking system, for up to two years from December 2017. At this point, the
objective is to determine how deviations from the baseline affect the banks’
solvency; these deviations are presented in the form of moderate and adverse
changes in the baseline data.
In this part of the exercise, we compute variables for the baseline, moderate
and adverse scenarios, and this is done in the SHOCKS worksheet of the MS
Excel file which contains five tables laid out as follows:
TABLE 1: For inputting coefficients from the estimated equations
TABLE 2: For computing the standard deviation of each of the
macroeconomic variables
TABLE 3: For finding the largest historical quarterly change in the policy
rate
TABLE 4: For deriving values for the baseline scenario
TABLE 5: Implementation of shock calibration methodologies
Two approaches are used to compute the shock values for the moderate and
adverse scenarios:
Standard deviation from the baseline: Standard deviation is used to
quantify the amount of variation or dispersion in a variable. It can also
represent the level of volatility or uncertainty contained within the
variable. For each macroeconomic variable in the data set provided, the
standard deviation is computed. Then, this value is added to or
subtracted from the variable’s baseline values to obtain shock values for
either the moderate or adverse scenarios. Depending on the objective of
the exercise, one can deviate from the baseline by more than one
standard deviation such that the higher the deviation, the more severe the
shock. The interpretation of this approach is as follows: it is assumed that if
the prevailing macroeconomic conditions worsen, the changes in the values are
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equivalent to one standard deviation being added to or deducted from the baseline
values.
Historical values: This approach relies on the identification of extreme
events within the economy. Then, the resulting scenario assumes that
these events are repeated, and the objective of the stress test is to
determine how the current banking system is affected by similar
macroeconomic conditions. Hence, from the reporting period, in this
case December 2017, a variable will rise or drop by its highest or lowest
observed quarterly change in value in the following quarter and evolve at
the same rate it would have done for two years from the date of the initial
shock. Since the decline in banking system resilience is triggered by
increasing interest rates, we compute the highest historical quarterly
change in the policy rate and identify the quarter during which it was
observed.
Once values are obtained using both approaches, the moderate scenario is then
defined by the results that display the least negative impact on the banking
sector’s stability in terms of losses in capital adequacy over the forecast horizon
of two years, while the adverse scenario is represented by the largest negative
impact.
Below are the steps involved in this part of the exercise:
1. Generate projected bank variables for the baseline scenario in TABLE 3
(lines 17 to 29). To do this, start by copying and pasting the coefficients
obtained from the estimated equations into TABLE 1 in the worksheet.
Column A in the table contains the dependent variables, while columns B
to E contain the coefficients of the independent variables for each
equation estimated. Where there is no regression constant, enter a value of
zero. In Figure 47, for the equation for the NPL ratio, the coefficients are
entered from the E-Views output seen in Table 11 in Figure 45. This is
repeated for all the other equations.
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Figure 47: Input coefficients from model estimations
2. Upon the insertion of the coefficients in TABLE 1, the projected banking
variables in TABLE 4 are updated (columns H to L). Columns B to G
contain projected macroeconomic variables obtained from the central
bank’s projection model (linked from the ALL DATA worksheet).
As an example, Figure 48 shows the computation of banks’ total loans for
the quarter ending September 2018 (cell I23). As deduced earlier, banks’
loans are dependent on the existing stock of loans (cell B8 x cell I22),
changes in broad money supply (cell D8 x (cell D23 – cell D22)), and the
lending rate (cell E8 x cell H23). Since this is a log-transformed equation,
the exponential must be taken in order to obtain a value in the local
currency unit. The forecasted values for the other variables are computed in
a similar manner to complete the baseline data set.
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Figure 48: Computing projected baseline bank variables
3. Implement the standard deviation methodology of computing shock values
as described above.
In TABLE 2, compute the standard deviation for each macroeconomic
variable for the period March 2001 to December 2017. This is done using
the STDEV() function and by referencing the time series in column D in
the ALL DATA worksheet (Figure 49).
Figure 49: Computing standard deviation for macroeconomic variables in TABLE 2
Next, we generate shock values based on the variables ‘deviation from the
projected baseline obtained in TABLE 3. Recall that it is assumed that if the
prevailing macroeconomic conditions worsen, the changes in the values are
equivalent to one standard deviation being added to or deducted from the
baseline values.
In TABLE 5 (lines 33 to 41), the shock values are computed using the
standard deviation, and this is illustrated in Figure 49 for the policy rate.
Since the scenario is triggered by an increase in short-term interest rates,
readers would have to determine by how much interest rates would rise
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during a period of stress. Under normal conditions, the policy rate is
expected to rise by 1.8 percentage points to 9.0 percent between December
2017 and March 2018. However, under stressful conditions, it is assumed
that the policy rate will deviate from the baseline by one standard deviation,
meaning that the rate will increase to 13.1 percent (cell E34), which is 4.1
percent (cell H7) greater than the baseline of 9.0 percent (cell E21). The
computation is the same for all macroeconomic variables for the forecast
horizon of two years.
Figure 50: Shock calibration using the standard deviation approach
Note, however, that some variables require a negative variance from the
baseline: real GDP growth, real M3 growth and the REER change. This is
because a decline in these values would have a negative impact on the
economy and the banking system. For instance, while GDP growth is
projected to reach 6.9 percent in the year to March 2018 (cell B21), a
deviation from this baseline of 2.2 percent (cell H5) means that economic
output would grow at a slower rate of 4.7 percent (cell B34) during the
stressful period.
Finally, the corresponding shocked bank variables are derived in a similar
way to the baseline scenario (Figure 48), by mapping the coefficients in
TABLE 1 to the newly acquired macroeconomic variables in TABLE 5.
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4. The next step is to compute shock values using the historical approach
described above, and this is done in TABLE 5 (lines 45 to 52). Unlike the
standard deviation approach, the historical approach is not a direct
deviation from the baseline scenario, but rather a simulation of historical
events and how the current banking system would respond to similar
macroeconomic conditions.
First, in TABLE 3, derive the largest historical quarterly change in the
policy rate between March 2001 and December 2017. In Figure 51, cell K4
references the quarterly changes in the policy rate in column F in the ALL
DATA sheet using the MAX() function to gain a value of 6.3 percent as the
largest ever quarterly change in the policy rate, occurring in between
September 2011 and December 2011 (cell K5).
Figure 51: Deriving the largest historical quarterly change in the policy rate
Next, compute the policy rate for March 2018 based on the quarterly
change in TABLE 3. Since we know that the largest change occurred
between September 2011 and December 2011, we apply that change of 6.3
percent (cell F45 in the ALL DATA sheet) to the value of 8.8 percent
observed in December 2017 (cell E44 of SHOCKS sheet). This is
illustrated in Figure 52 in cell E45, such that the policy rate increases to 15.1
percent in March 2018 instead of 9.0 percent as projected in the baseline
scenario. Similarly, the value for June 2018 in cell E46 is the change
between December 2011 and March 2012 applied to the rate in March 2018
in cell E45. The proceeding values for the remaining quarters to December
2019 are computed in a similar manner.
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Figure 52: Shock calibration using historical values
For the remaining macroeconomic variables, we take the values as observed
between December 2011 and September 2013 in the ALL DATA sheet.
This is because the scenario assumes that these variables would respond to
the change in policy rates as they did back in 2011. For instance, for real
GDP growth, the rate increases to 7.7 percent in March 2018 (cell B45) as it
was in December 2011. Note, however, that for real M3, we take the
growth rate and derive the levels from it, as opposed to taking the levels as
they were in 2011. This is because money supply is a stock that gradually
increases over time.
Finally, the corresponding shocked bank variables are derived in a similar
way to the baseline scenario (Figure 48), by mapping the coefficients in
TABLE 1 to the newly acquired macroeconomic variables in TABLE 5.
3.3.4 Transmission of risks to the balance sheet and income statement
Projected selected banking sector variables for both baseline and shocked
scenarios have been obtained. While it can be seen how changes in the policy
rate will affect credit quality, deposit growth and lending rates, it remains to be
determined how they impact banks’ capital adequacy. Therefore, it is essential
to examine how these changes are transmitted through banks’ balance sheets
and income statements.
This part of the exercise is carried out in the RESULTS worksheet which is
laid out as follows:
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TABLE 6: Projected balance sheet, income statement and selected FSIs
from the shock values generated by the standard deviation and historical
methods
TABLE 7: Projected balance sheet, income statement and selected FSIs
from the baseline scenario
In the top left corner of the worksheet (cell range A2:A3, Figure 53), readers
can use a dropdown menu to select the results they wish to view between the
standard deviation and historical methods in TABLE 6.
Figure 53: Selecting shock calibration method
Historical balance sheet and income statement data for the aggregate banking
sector is provided for 2017 on a quarterly basis so that readers are required to
obtain the forecasted values for the period March 2018 to December 2019. In
both tables, all the variables under “Other items”, as well as the NPL ratio, are
determined by the model estimations reviewed above and are drawn from
worksheet SHOCKS. These are then used to get levels for total loans, total
NPLs and total deposits. All the other lines are computed based on simplistic
assumptions because in practice, it may not be possible to develop model
estimations for every single item in banks’ financial statements.
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Assumptions for projected balance sheet and income statement computations
Loan loss reserves: NPLs are not broken down into performance
categories such substandard, doubtful and loss loans so that provisioning
rates are applied to the respective categories as is best supervisory practice.
Hence, an assumed provisioning rate of 80 percent is applied to existing
loans. In Figure 54, the loan loss reserves for the baseline scenario for the
quarter March 2018 are computed in cell F44, amounting to 11.9 million in
local currency units, off of 14.8 million in NPLs projected as at the end of
the quarter.
Figure 54: Computing projected loan loss reserves
Interest income: Total interest income is calculated as the lending rate
charged on the average stock of total loans in the current and previous
quarters, plus 20 percent of the value obtained to reflect income from other
interest-earning assets such as Nostro accounts, fixed income and
government securities. In other words, it is assumed that income on loans
makes up 80 percent of interest income. The lending rate is applied to the
average of loans between quarters to account for gains or losses due to
changes in the loan portfolio.
In Figure 55, interest income earned in March 2018 under the baseline
scenario is calculated in cell F52. First, the average of total loans in
December 2017 (cell E42) and March 2018 (cell F42) is taken. This is then
multiplied by the baseline lending rate for March 2018 of 20.1 percent in cell
F69. Note that the lending rate is divided by four in order to obtain a
quarterly interest rate. Lastly, 20 percent is added to the result to account for
interest income other than that from loans. So, in March 2018, the banking
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system is expected to make 14.4 million in interest income under the
baseline scenario.
Figure 55: Computing projected interest income
Interest expenses: Total interest expense is calculated as the policy rate
paid out on 40 percent of the average stock of deposits in the current and
previous quarters. It is assumed that banks pay interest on approximately 40
percent of their total deposit liabilities. The policy rate is applied to the
average of deposits between quarters to account for gains or losses due to
changes in total deposits. The policy rate is used as a proxy for the average
deposit rate because in practice, a central bank policy rate is used as the
benchmark for the cost of wholesale funding for banks and other financial
institutions.
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Figure 56: Computing projected interest expenses
In Figure 56, interest expenses in March 2018 under the baseline scenario
are calculated in cell F53. First, the average of total deposits in December
2017 (cell E45) and March 2018 (cell F45) is taken. Then, 40 percent of
these deposits are multiplied by the baseline deposit rate for March 2018 of
9.0 percent in cell F70. Note that the policy rate is divided by four in order
to obtain a quarterly interest rate. So, in March 2018, the banking system is
expected to spend 3.2 million in interest expenses under the baseline
scenario.
Non-interest income: Non-interest income is calculated as an annual
moving average. Non-interest income typically consists of fees and charges
on loans, gains on foreign currency operations and earnings on any non-
interest bearing activities. For this banking system, it is assumed that
changes in these amounts are minimal and as such, an annual average can be
used to project the quarterly figures.
In
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Figure 57, the non-interest income earned in March 2018 under the baseline
scenario is calculated in cell F54 as the average of the non-interest income
earned in the four quarters of 2017 (cell range B54:E54). So, banks made 5.1
million in non-interest income during March 2018.
Figure 57: Computing projected non-interest income
Non-interest expenses: Non-interest expenses are calculated as the
quarterly percentage change in annual inflation applied to the previous
quarter’s non-interest expenses. Non-interest expenses for banks are
typically comprised of staff costs, rent and maintenance costs for banks and
other operating costs. It is assumed that most of these costs are expected to
change with the economic environment and so, inflation is chosen as the
variable that is most likely to impact banks’ non-interest expenses.
In
Figure 58, the non-interest expenses for March 2018 under the baseline
scenario are calculated in cell F55 by multiplying the non-interest expenses
for December 2017 in cell E55 by the change in inflation between
December 2017 (cell E71) and March 2018 (cell F71).
Loan loss provisions: Loan loss provisions in the income statement are
calculated as the change in loan loss reserves between the current and
previous quarters to reflect changes in the provisions for bad debts held by
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banks due to write-offs and/or recoveries on their loan portfolios. In Figure
59, the loan loss provisions for March 2018 under the baseline scenario are
calculated in cell F56 by adding the change in loan loss reserves held by
banks between December 2017 (cell E44) and March 2018 (cell F44).
Figure 58: Computing projected non-interest expenses
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Figure 59: Computing projected loan loss provisions
Core and total regulatory capital: Unlike the micro stress testing example in
Chapters 10 and 11 where the impact on banks’ capital is dependent on
changes in single risk factors, macro stress testing attempts to combine the
effects of various risk factors. In the current case study, the macro stress test
reveals the impact on banks’ capital through changes in their profitability
due to:
o Changes in net interest income arising from increasing interest rates
o Changes in loans and deposits affecting the level of net interest income
o Changes in provisioning for bad debts
o Changes in non-interest income and expenses
Hence, projected core and total regulatory capital are adjusted by the
changes in net profits between the current and previous quarters. In Figure
60, the banking sector’s core capital for March 2018 under baseline
conditions is computed in cell F46 as the core capital level of 70.9 million
for December 2017 in cell E46, plus the difference in the net profits
between December 2017 (cell E57) and March 2018 (cell F57). It should be
noted that the calculations for net interest income and net profits follow
basic accounting principles.
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Figure 60: Computing projected core capital
Risk-weighted assets: Risk-weighted assets are computed by adjusting
each asset class in the balance sheet for risk in order to determine a bank's
real world exposure to potential losses. For many COMESA countries, risk-
weighted assets are predominantly comprised of loans. For this reason, in
this exercise, projected risk-weighted assets are calculated as the level of the
previous quarter’s risk-weighted assets, adjusted by the change in loan loss
reserves between the current and previous quarters. Recall that changes in
loan loss reserves between quarters reflect changes in the provisions for bad
debts held by banks due to write-offs and/or recoveries on their loan
portfolios. In Figure 61, the banking sector’s risk-weighted for March 2018
under baseline conditions is computed in cell F48 as the level of 350.0
million for December 2017 in cell E48, plus the difference in loan loss
reserves between December 2017 (cell E44) and March 2018 (cell F44).
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Figure 61: Computing projected risk-weighted assets
3.3.5 Analysis of the results
Results from shock calibration using standard deviation
Under the standard deviation method, it is assumed that all the macroeconomic
variables worsen at a uniform rate equivalent to one standard deviation from
the projected baseline (TABLE 5, SHOCKS sheet). The trigger variable, the
policy rate, rises from 8.8 percent in December 2017 to 13.1 percent in March
2018 and remains in double figures for the duration of the forecast horizon,
probably in response to the inflationary pressures. Between 2018 and 2019, the
local currency persistently loses value, and real money supply growth slows
down despite the moderate growth in economic output. The data set under this
scenario suggests that the projected rate of growth in economic activity is not
sufficient to fend off the volatility in real prices.
As per the model equations, the changes in the policy rate are initially
transmitted to the banking system through the lending rates. Between
December 2017and March 2018, the lending rate increases by 2.5 percentage
points instead of falling by 0.1 percentage points as per the baseline scenario
(Chart 22). Then, the rate remains higher than the baseline for two years, albeit
changing at a relatively stable pace. The sharp decline in credit growth by 25.2
percent in March 2018 is predominantly a result of the slowdown in money
supply growth, with minimal impact from the lending rates (Chart 21). The rise
in lending rates has a small effect on NPLs in the short-term, but the NPL ratio
eventually rises to 9.2 percent in December 2019 as the rising cost of credit
results in increased loan defaults (Chart 23).
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Figure 62: Results from shock calibration using standard deviation
Chart 20: Deposit growth (%)
Chart 21: Credit growth (%)
Chart 22: Lending rates (%)
Chart 23: NPL ratio (%)
Chart 24: Net profit-after-tax (millions)
Chart 25: Core CAR (%)
The banking sector also registers lower deposit growth as compared to the
baseline as a direct reaction to slower economic growth (Chart 20). Slow
deposit mobilisation translates into a contraction in funds available for asset
allocation. Consequently, the high loan defaults and reversal in lending activity
have a significant impact on banks’ profitability such that by the aggregate
banking sector remains loss making for most of the forecast horizon. In 2019
alone, banks would make losses amount to 16.8 million. The large losses are
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reflected in the sector’s capital buffers: the core CAR declines to 20.9 percent in
December 2019, compared to 23.1 percent in the baseline scenario.
Results from shock calibration using historical changes
Under the historical changes approach, the objective of the stress test is to
determine how the current banking system would be affected by previously
observed adverse macroeconomic conditions. Recall that the period being
replicated is from December 2011 to September 2013, during which inflation
and the policy rate were high compared to historical figures.
In this scenario, the policy rate rises by 6.3 percentage points between
December 2017 and March 2018 to reach 15.1 percent. Although the initial
shock is higher compared to that in the standard deviation approach, the policy
rate starts to drop significantly in December 2018, reaching as low as 2.9
percent in December 2019. Annual inflation remains in the double digits for
five consecutive quarters from March 2018 and eventually falls to 4.5 percent in
December 2019, suggesting that real prices respond to the seemingly
expansionary monetary policy actions taken by the central bank. Real money
supply growth is stronger than observed in the standard deviation approach,
although overall economic activity remains sluggish in comparison to the
projected baseline. The simulated changes in the macroeconomic variables
under this approach suggest that there are factors hindering output growth that
cannot be derived from this data set alone.
Analysing the impact of the macroeconomic developments on the banking
sector, it appears that the effects are less severe compared to the standard
deviation approach. A gradual drop in lending rates over the forecast horizon
encourages rapid credit expansion in the medium-term, with annual credit
growth peaking at 35.6 percent in June 2019. On the other hand, deposit
growth remains modest due to the slow economic growth. Despite the low
interest rate environment, NPLs rise gradually throughout the two years such
that the NPL ratio reaches 8.1 percent in December 2019; this phenomenon
can possibly be explained high default rates brought on by relaxed lending
standards practised by banks in order to boost their earnings on credit since
interest rates are historically low.
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Figure 63: Results from shock calibration using historical changes
Chart 26: Deposit growth (%)
Chart 27: Credit growth (%)
Chart 28: Lending rates (%)
Chart 29: NPL ratio (%)
Chart 30: Net profit-after-tax (millions)
Chart 31: Core CAR
Similar to the standard deviation approach, the banking sector registers losses
for most of the forecast horizon, brought on mostly by large loan loss
provisions. However, the sector seems to maintain adequate capital buffers to
withstand this shock, even though the capital adequacy ratios trend below the
baseline projections.
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This subsection provides a simplistic yet effective practical example of stress
testing of contagion risk. The purpose of simulating contagion in a banking
system is to determine the capacity of the system to absorb multiple institution
failures due to common risk exposure. For any given type of shock,
endogenous or exogenous to the system, the stress test helps to identify which
institutions are most vulnerable to counterparty default risk brought on by their
connections within the system, as well as which banks are most likely to cause
the largest losses upon their failure.
Readers are provided with simulated individual bank data on interbank
transactions in appropriately set-up MS Excel spreadsheet. In this exercise,
readers are expected to apply the theoretical concepts from Section D above
regarding the analysis of contagion risk at the banking sector level.
The exercise is performed in the contagion_ex.xlsm sheet. The EXPOSURE
worksheet contains four tables. Table 1 is where the names of the banks that
trigger the contagion are entered; up to three banks can be entered as the
trigger banks. Table 2 contains a summary of the results of the contagion
shock, which include the total losses on capital following a shock, and the total
number of banks affected by the shock. Total losses on capital are computed as
the difference between the sector’s total core capital before the shock, and the
core capital levels following the shock. Tables 3 and 4 are the matrices of
interbank exposures before the contagious shock and following the contagious
shock, respectively. Both tables contain interbank exposures for ten commercial
banks for the period ending December 2017. The rows represent outstanding
amounts lent while the columns represent outstanding amounts borrowed as at
the end of the review period (Figure 64). Note that in the exposure matrices,
the diagonal contains zeros, meaning that a bank cannot transact with itself.
The cells highlighted in blue represent the magnitude on the exposures between
banks. For example, in cell I36, Bank 7 owed Bank 8 6.2 million as at the end of
December 2017.
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Figure 64: Matrix of interbank exposures before the contagion shock
For each bank, the total outstanding amounts borrowed and lent have been
summed up. Furthermore, each table contains each bank’s total core capital and
risk-weighted assets from which the core capital adequacy ratio is computed. In
column Q of Table 4, the ratio of the amount lent by each bank as a share of
their core capital is calculated; the purpose of this ratio is to determine how
much a bank’s core capital can cover potential losses due to counterparty
default.
Figure 65: Network schematic of the interbank market
Table 3 contains the following additional information:
The “health” of each bank is computed in line 25 and column N, where
bank health is defined by their core capital adequacy ratio; a value of “1”
means the bank’s core capital ratio is above the regulatory minimum of 10
percent, and “0” indicates that the bank is breaching this minimum.
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The “shock size” in column P represents the losses incurred by each bank
due to the contagion shock. For each bank, the losses are equivalent to the
amount lent by that bank to other banks, in the event that these banks fail to
repay their debts to that bank.
Since it is assumed that the losses due to contagion are absorbed by a bank’s
core capital, the credit losses are deducted from the initial core capital to
obtain the core capital after the shock in column Q, as well as the
corresponding core capital adequacy ratio in column S.
3.4.1 Review of the data set
Table 13 provides a summary of the data in the worksheet. As at the end of
December 2017, a total amount of 316.7 million local currency units was
outstanding in the interbank market. Bank 3 was both the largest borrower with
135.6 million owed to five banks, and the largest lender with 75.3 million owed
by three banks (Figure 64). The same bank also had the highest core CAR of
34.7 percent, which is well above the regulatory minimum of 10 percent,
suggesting that the bank is adequately capitalised. However, in terms of
exposure to counterparty default risk, Bank 7 had the highest exposure, with
their outstanding funds due from other banks amounting to 67.0 percent of
their core capital, meaning that if the one bank they lent 21.0 million to, Bank 2,
was unable to meet that obligation, that loss would equate to 67.0 percent of
their capital. The bank faced with the least risk would be Bank 5.
Table 13: Summary of banks’ interbank exposures as at end of December 2017
Total borrowed (millions)
Total lent (millions)
Core CAR (%)
Total lent / core capital (%)
BANK 1 6.7 3.2 29.3 35.4 BANK 2 86.4 30.0 12.5 17.9 BANK 3 135.6 75.3 34.7 31.9 BANK 4 10.5 39.7 16.9 55.7 BANK 5 5.0 1.6 30.4 5.4 BANK 6 32.0 10.5 21.3 36.1 BANK 7 6.2 21.0 32.1 67.0 BANK 8 3.2 42.5 25.9 10.5 BANK 9 10.0 66.4 29.7 36.8 BANK 10 22.0 27.3 11.4 13.0
Overall, it appears that as at the end of December 2017, the banking sector was
adequately capitalised, with the exception of Banks 2 and 10 whose core CAR
were close to the regulatory minimum. Hence, the next step is to determine if
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these capital levels are sufficient to help the banks withstand risks arising from
their interlinkages in the interbank market. The contagion scenario is initialised
by failing one or more banks, and then examining if there are any additional
bank failures as result. To this end, two scenarios are considered:
a) The failure of the bank(s) with the highest activity in terms of lending and
borrowing (Bank 3)
b) The failure of the bank(s) with low capital adequacy ratios (Banks 2 and
10)
For each scenario, additional assumptions are made about the availability of the
banks’ capital buffers:
That 100 percent of banks’ capital as at the reporting date is available to
cover the resulting losses.
That prior to the contagion shock, banks’ core capital was previously
depleted by an undefined shock, by the following magnitudes: 5 percent
and 10 percent.
Banks do not respond to the shock by seeking additional funds from
external sources.
These modified scenarios aim to account for stress testing exercises that
involve combined scenarios; in cases where banks’ solvency has been previously
impacted by shocks such as credit losses or the banking system being faced
with tight liquidity conditions, it is beneficial to observe how the banking
system would be affected by additional losses arising from a contagious shock.
Indeed, in practice, it is expected that failures in individual institutions may
become contagious when the affected banks default on their interbank
obligations.
3.4.2 Implementation of the contagion shock
In this simple contagion simulation exercise, a bank’s credit exposure in the
interbank market determines the extent of the potential losses in the event that
its counterparties fail to repay their loans. Hence, a bank is considered to fail
the test if the amount lost due to counterparty default depletes its capital
buffers. The contagion shock is simulated with the following steps:
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1. Start by resetting the EXPOSURE worksheet to ensure that you are
working with a fresh matrix of exposures in Table 3. To reset the
worksheet, click on the black “RESET” button in the top left corner of the
worksheet (Figure 66).
2. Execute scenario (a), that is, the failure of Bank 3 with the respective
haircuts on all the banks’ core capital. From the exposure matrix, it can be
seen that the sudden failure of Bank 3 would affect the following five
banks: Bank 2, Bank 5, Bank 8, Bank 9 and Bank 10.
i. In Table 2 under “initial shock size to capital”, enter a value of “0” in
cell G8 since banks have all their core capital available to cover potential
losses (Figure 66).
Figure 66: Execution of scenario (a) of the contagion shock
ii. In cell C8 in Table 1, enter “BANK 3” as the first and only bank to
trigger the contagion; bank names MUST match the ones provided in
the exposure matrix or else they will not be recognised (Figure 66).
Observe the changes in the “Health” row (line 25) and column (column
N), and note that the failing bank’s health is now denoted with “0”.
This means that Bank 3 is assumed to be insolvent and is left without
any capital or liquidity buffers. Then, the test determines how the bank’s
inability to repay its interbank loans to the five banks it is indebted to
would affect the stability of the rest of the banking system.
Application of Stress Testing Methodologies: Practical Examples
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iii. Initiate the domino effects of Bank 3 failing on the rest of the banking
system by clicking on the blue “SHOCK” button in the top left corner
of the worksheet, right below the “RESET” button. In Table 3, for all
the banks whose health is denoted with “0”, the corresponding cells
containing the total amounts lent/borrowed are set to zero amounts
(columns E and L highlighted with red boxes in Figure 67). Setting
Banks 3 and 10’s outstanding borrowed amounts to zero implies that
these banks are unable to repay their respective creditors and so the
creditors have lost these funds to the failed institutions. For example,
the five banks exposed to Bank 3 lose a combined total of 135.6 million
that they lent to Bank 3, while Banks 2 and 4 lose 22.0 million upon the
failure of Bank 10.
Figure 67: Propagation of contagion due to the failure of Bank 3
iv. In Figure 67, it can be seen that the failure of Bank 5 leads to the failure
of one other bank, Bank 10. This is because Bank 10 was owed 27.3
million by Bank 3 (cell E38 in Table 4). Although this was Bank 10’s
only exposure in the interbank market, amounting to 13.0 percent of its
core capital, this loss reduces its core capital from 210.4 million to 183.0
million (cell Q23 in Table 3) and pushes it into failure as its core CAR
drops from 11.4 percent to 9.9 percent (cell S23 in Table 3) which is
below the regulatory minimum of 10 percent. However, the failure of
Bank 10 does not lead to any further failures as its counterparties
(Banks 2 and 4) hold sufficient capital to absorb the risk.
v. If there still exists some banks with “0” health but with their original
exposure amounts (as seen in Figure 66 in column E for Bank 3 prior to
the shock execution), click on “SHOCK” again until this is no longer
Micro and Macro Stress Testing Guideline
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the case. At this point, there are no more contagious failures in the
banking system.
In summary, the failure of Bank 3 in turn results in the failure of Bank
10, with the total capital losses to the banking system amounting to
394.4 million.
vi. The next step is to reset the worksheet and repeat sub-steps (ii – v)
above for haircuts on banks’ core capital amounting to 5 percent and 10
percent.
In Table 2 under “initial shock size to capital”, enter a value of “5” in
cell G8 (Figure 68); this action implements the assumption that prior to
the contagion shock, the banking system had experienced a loss of 5
percent of their core capital to an unspecified shock, resulting in a
reduction of the sector’s core capital by 68.6 million (cell H8).
Figure 68: Execution of scenario (a) of the contagion shock with a 5 percent haircut on capital
vii. Repeat sub-steps (ii – v) above. Figure 69 shows the results of this
shock. When the system’s capital is reduced by 5 percent, banks become
more vulnerable to contagious failure. Indeed, the shock results in the
failure of four banks; Banks 2 and 10 are impacted by Bank 3, while
Bank 7’s insolvency is brought on by Bank 2’s default (Figure 70). In
addition, the total losses in capital add up to 478.0 million.
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Figure 69: Results of the failure of Bank 3 with a 5 percent haircut on capital
Figure 70: Propagation of scenario (a) of the contagion shock with a 5 percent haircut on capital
Similarly, the contagion shock with a haircut on core capital of 10 percent is
carried out. Table 14 provides a summary of the results corresponding to
the failure of Bank 3. Reducing the sector’s capital by 10 percent before
introducing the contagion shock results in total capital losses of 534.7
million, although the number of failing banks remains at four.
From the results, it can be concluded that the failure of Bank 3 under
normal operating conditions would have minimal impact on the stability of
the interbank market. However, in the face of systemic vulnerability
characterised by inadequate capital buffers, Bank 3’s demise would have
significant impact on the banking system, resulting in the failure of three
other banks. It should be noted, however, that the impact of this shock
would vary in practice as banks are able to take prompt corrective actions to
reduce contagion risk.
Micro and Macro Stress Testing Guideline
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Table 14: Summary of the results of a contagion shock triggered by the failure of Bank 3
Initial shock size to capital (%)
Total change in capital (millions)
Total number of failed banks
0.0 394.0 2
5.0 478.0 4
10.0 534.7 4
3. Execute scenario (b), that is, the failure of Banks 2 and 10 with the
respective haircuts on all the banks’ core capital. The steps are similar to
those under step 2, except that Table 1 now has two entries (Figure 71).
Figure 71: Results of the failure of Banks 2 and 10 with a 10 percent haircut on capital
Table 15: Summary of the results of a contagion shock triggered by the failure of Banks 2 and 10
Initial shock size to capital (%)
Total change in capital (millions)
Total number of failed banks
0.0 466.4 2
5.0 522.5 3
10.0 572.1 3
Table 15 provides a summary of the results corresponding to the failure of
Banks 2 and 10. Under normal conditions, the failure of these banks does not
result in the propagation of contagion risk through the banking system.
However, with reduced capital levels by up to 10 percent, one other bank, Bank
7, would be adversely affected by the failure of Bank 2, with total capital losses
in the system amounting to 572.1 million. Overall, the banking system appears
to be resilient to a contagion shock triggered by the failure of Banks 2 and 10.
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