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

http://cmi.comesa.int/

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

Micro and Macro Stress Testing Guideline

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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.


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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.


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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.


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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.


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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


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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


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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


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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


~ 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


~ 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.


~ 16 ~

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).


~ 18 ~

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.


~ 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


~ 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.


~ 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


~ 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).


~ 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.


~ 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


~ 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


~ 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


~ 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

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Inve

stm

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tse

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Tota

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BANK 1 BANK 2 BANK 3

BANK 4 BANK 5 OTHERS

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20%

40%

60%

80%

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~ 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


NPL ratio



~ 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.


~ 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.


~ 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.


~ 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


~ 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


~ 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

https://support.office.com/en-us/article/sumproduct-function-16753e75-9f68-4874-94ac-4d2145a2fd2e

https://support.office.com/en-us/article/sumproduct-function-16753e75-9f68-4874-94ac-4d2145a2fd2e


~ 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.


~ 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


~ 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.


~ 41 ~


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.


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


~ 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


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


~ 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.


~ 44 ~

Figure 19: Computing banks’ post-shock core CAR for the direct foreign exchange shock

Results of the direct foreign exchange shock


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


~ 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


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


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


~ 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.


~ 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).


~ 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


~ 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.


~ 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.


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).


~ 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.


~ 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.


~ 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.


~ 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.


~ 55 ~


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


~ 56 ~


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.


~ 57 ~

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.



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


~ 58 ~

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.




~ 59 ~

Table 6: Scenarios and shock sizes for liquidity risk stress tests


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:


~ 60 ~

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


~ 61 ~

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


~ 62 ~

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.


~ 63 ~

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.


~ 64 ~

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.



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


~ 65 ~

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


~ 66 ~

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.



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.


~ 67 ~

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).


~ 68 ~

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


~ 69 ~

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.




~ 70 ~

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


NPL ratio


Direct foreign exchange risk

Depreciation of the local currency by 50 percent


Direct interest rate risk

Increase in nominal interest rate of 2 percentage points




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.


~ 71 ~

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


~ 72 ~

limited data. Furthermore, it sets the pace for the application of scenario

analysis in the setting of macro stress tests.



Chart 15: Liquidity ratio (%)


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


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



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



~ 73 ~

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.


~ 74 ~

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


~ 75 ~

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 (%)


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


~ 76 ~

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))


~ 77 ~

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)


Date: 09/25/18 Time: 10:24




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



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


~ 78 ~

Table 11: NPL ratio

Dependent Variable: NPLR


Date: 09/25/18 Time: 10:22




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






Durbin-Watson stat 1.834694

Table 12: Deposit growth

Dependent Variable: DEPS_GR


Date: 09/25/18 Time: 10:26




RGDP_GR 0.985618 0.050540 19.50169 0.0000






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


~ 79 ~

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


~ 80 ~

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.


~ 81 ~

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.


~ 82 ~

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


~ 83 ~

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.


~ 84 ~

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.


~ 85 ~

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.


~ 87 ~

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


~ 90 ~

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


~ 92 ~

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.


~ 93 ~

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).


~ 94 ~

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 24: Net profit-after-tax (millions)


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

0

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~ 96 ~

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.


~ 97 ~

Figure 63: Results from shock calibration using historical changes

Chart 26: Deposit growth (%)

Chart 27: Credit growth (%)

Chart 28: Lending rates (%)


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.


~ 99 ~

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.


~ 100 ~

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


~ 101 ~

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:


~ 102 ~

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.


~ 103 ~

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


~ 104 ~

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.


~ 105 ~

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.


~ 106 ~

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.

Basel Committee on Bank Supervision. (2001). Principles for the management and

supervision of interest rate risk. Supporting Document to the New Basel Accord.

Bank for International Settlements.

Basel Committee on Bank Supervision. (2012). A framework for dealing with domestic

systemically important banks.

Basel Committee on Banking Supervision. (2009). Principles of sound stress testing practices

and supervision. Bank for International Settlements.

Bunn, P., Cunningham, A., & Drehmann, M. (2005, June). Stress testing as a tool for

assessing systemic risks. Financial Stability Review. Bank of England.

Čihák, M. (2005). Stress Testing of Banking Systems. Czech Journal of Economics and

Finance, 9-10.

Čihák, M. (2007). Introduction to Applied Stress Testing. IMF Working Paper,

WP/07/59.

Degryse, H., & Nguyen, G. (2004). Interbank exposures: An empirical examination of

systemic risk in the Belgian banking system. International Journal of Central

Banking 3(2), 123-171.

Demirgüç-Kunt, A., & Detragiache, E. (1998). The determinants of banking crises in

developed and developing countries. IMF Staff Papers Vol.45 No. 1.

Espinosa-Vega, M. A., & Sole, J. (2014). Introduction to the network analysis approach

to stress testing. A guide to IMF stress testing. International Monetary Fund.

Haldane, A., Hall, S., & Pezzini, S. (2007). A new approach to assessing risks to

financial stability. Financial Stability Paper No. 2. Bank of England.

Havrylchyk, O. (2010). A macroeconomic credit risk model for stress testing the South

African banking sector. South African Reserve Bank Working Paper WP/10/03.

Hilbers, P. L., Leone, A. M., Gill, M. S., & Evens, O. (2000). Macroprudential

indicators of financial system soundness. International Monetary Fund Occasional

Papers. International Monetary Fund.

Hilbers, P., & Jones, M. T. (2004). Stress testing financial systems. International Monetary

Fund, WP/04/127.


~ 108 ~

International Monetary Fund. (2004). Compilation Guide on Financial Soundness Indicators.

International Monetary Fund.

International Monetary Fund. (2018). Financial Sector Assessment Program (FSAP).

Retrieved from International Monetary Fund:

https://www.imf.org/en/About/Factsheets/Sheets/

2016/08/01/16/14/Financial-Sector-Assessment-Program

Minoui, C., & Reyes, J. (2013). A network analysis of global banking: 1978-2010 .

Journal of Financial Stability 9, 168-184.

Mistrulli, P. (2010). Assessing financial contagion in the interbank market: maximum

entropy versus observed interbank lending patterns.

Moretti, M., Stolz, S., & Swinburne, M. (2008). Stress Testing at the IMF. IMF Working

Paper, WP/08/206.

Ong, L. L., & Čihák, M. (2014). Stress testing at the International Monetary Fund:

Methods and models. A guide to IMF stress testing: Methods and models.

International Monetary Fund.

Ong, L. L., Maino, R., & Duma, N. (2010). Into the great unknown: stress testing with

weak data. IMF Working Paper WP/10/282. International Monetary Fund.

Documents

Micro and Macro-Stress Testing User Guide