Macro Stress Testing of the Financial System

Danmarks Nationalbank, like many other central banks, is developing models for macro stress testing of the financial system. This chapter presents an overall model architecture and discusses the methodology and choice of population, as well as the sectoral and geographical demarcation. Some preliminary model specifications are also discussed.

INTRODUCTION

Macro stress testing, as described in Box 12, is the stress testing of the financial system, typically in relation to macroeconomic shocks.

The financial system is illustrated in Chart 43. The system is a complex network of hundreds of financial enterprises with thousands of counterparties. To be manageable and understandable, a model for stress testing of the financial system in Denmark necessitates simplification of the real world's complex network.

The process of developing the model involves numerous choices concerning the geographical and sectoral delineation of the financial system, as well as the degree of coverage and detail, and the risk sources to be focused on. Danmarks Nationalbank's overall model architecture and preliminary model specifications are described below.

OVERALL MODEL ARCHITECTURE

The planned model architecture for macro stress testing is open and flexible, with a toolbox of stress test models that can be used end to end, cf. Chart 44.

The five risk modules in the model architecture focus on:

• The resilience of the banking institutions (module 2 in the Chart). The initial focus is on operating profit and excess capital adequacy, but the module could be expanded to cover liquidity risk buffers.
• Market and credit risks (modules 3 and 4 respectively). This includes application of the failure-rate model (KIM) and macro stress testing of households.
• Two potential sources of systemic risk: common risk factors (module 1) and domino effects via counterparty exposures (module 5). A third source of systemic risk – feedback effects via credit crunch or fire sale – is discussed at the end of this chapter.

Through-processing using the five risk modules will require a set of overall model specifications.

Population
The preliminary population for the implementation of the model is the Danish Financial Supervisory Authority's categories 1 and 2.

The combined market share of categories 1 and 2 is shown in Chart 45 as the blue column plus the yellow column, and totals more than 75 per cent for all business areas.

These 14 banking institutions represent a relatively broad selection of institutions with different business strategies, balance-sheet structures and risk profiles. In sectoral terms, the population is limited to banking institutions. The balance-sheet structure of the banking institutions (i.e. short-term deposits and longer-term lending), and their role in payment systems and the overall economy, make them " special" and potentially " systemic" . Furthermore, from a modelling perspective it is easier to limit the population to institutions of the same type that are subject to the same legal and supervisory regime. The banking institutions' exposures to other financial intermediaries may to some extent be incorporated in the credit-risk module.

Geographical delineation
The model's geographical focus is the financial system in Denmark, so the analysis of the population relates first and foremost to Danish banking institutions. For foreign-owned banks in the population, the model will disregard any support from the parent company. For Danish financial groups with foreign units, the model may cover international credit exposures, depending on data availability.

Since the geographical focus is on Denmark, in the first instance the internationalisation of the financial system is disregarded. The two largest banking groups in Denmark have a significant volume of foreign activities. The market share of foreign banks' units in Denmark is around 30 per cent.^[1] Overall, Danish banks have financed a large proportion of their widening deposit shortfall via international borrowing and securities issuance. At the same time, the financial markets in Denmark are directly influenced by developments in the global markets. Internationalisation has positive consequences for financial stability in terms of diversification of risk and the diversity of institutions in the financial system. On the other hand, it also increases the complexity of financial activities and can heighten the risk of contagion from financial problems in other countries, especially if several countries are affected by the same shock.

The geographical focus on the domestic financial system reflects the need to simplify the model by reducing its complexity. In addition, Danmarks Nationalbank has no comparative advantage in analysing business and credit risks in other countries. The international perspectives should nevertheless be borne in mind, for example through dialogue and cooperation with other central banks^[2] and with banks that have international activities and incorporate their international exposures into their own internal stress tests. In the longer term, the macro stress test model may be extended to cover more broadly the international interlinkages of the financial system.

Preliminary model specifications
A key challenge in the development of macro stress test models is to link up the various modules in a way that utilises the information in the various available data. The exact data and model specifications are decided during this process.

Module 1: Common risk factors
Common risk factors are an important source of systemic risk and thus form the basis for the specification of risk scenarios for macro stress tests. The model framework must be flexible enough to accommodate changes to the risk-factor specifications, e.g. in order to improve the explanatory power of the model or to analyse new types of risk. The risk factors are chosen and specified on the basis of the following criteria:

• They must be able to quantify the risk scenarios implemented in the macro stress test.
• They must be relevant input to the other modules in the macro stress test model (i.e. a potential direct or indirect impact on the market risk, credit risk or operating profit of the banks).
• They must ideally be calibrated and projected in Danmarks Nationalbank's macroeconomic model, MONA, so as to ensure internal consistency in the projection of risk scenarios. As a minimum, there must be a historical data basis for the risk factors with which the projection in the risk scenarios can be compared.

Calibration of risk scenarios for macro stress testing is a delicate balance. The scenarios must be extreme enough to affect system stability, but plausible enough to be taken seriously.

In stress tests, a distinction is generally made between sensitivity analysis of the effect of changes in an individual risk factor and scenario-based stress tests involving changes to several risk factors.

Sensitivity analysis is applied to stress testing of market risk, e.g. the beta of an equities portfolio against a market index, or the duration of a bond portfolio, i.e. its sensitivity to shifts in the yield curve. Sensitivity analyses are typically viewed in an " all-other-things-being-equal" perspective and therefore rarely take account of the risk of indirect effects and changes in correlations, e.g. in connection with extreme changes in market prices.

Scenario-based stress tests entail projection of a number of common risk factors that can affect the financial system. There are several possible approaches to the projection of scenarios:

• Repetition of historical stress episodes, e.g. the recession from 1987 to 1993.
• Hypothetical scenarios, e.g. based on crises in other countries.
• Probability-based scenarios, e.g. based on the 1st percentile for empirical data for the actual development in the risk factors.
• "Reverse engineering" , i.e. calculating back the level of stress needed to cause systemic damage.

So far, historical or hypothetical stress test scenarios have been most commonly used in macro stress tests in other countries.

Module 2: Bank core financials model
The bank core financials model must estimate the scenario-dependent development in the core operating profits of the individual banks. Core operating profit excludes the financial items associated directly with market and credit risk, e.g. valuation changes and write-downs on lending, which are covered by more detailed models in modules 3 and 4.

The banking institutions' current earnings (together with excess capital adequacy) account for a significant share of their buffer against losses. Economic developments in recent years have had very favourable consequences for the banking institutions' earnings, and are not necessarily a reliable indicator of their future earnings potential. On the other hand, it would probably be unfair just to assume in a macro stress test that earnings will disappear.

There is a need to identify the drivers of the banking institutions' earnings and to link them to the development in the common risk factors (e.g. macro and market variables), and to the special characteristics of the individual banking institutions.

Module 3: Market-risk model
The market-risk model must estimate the scenario-dependent development in the individual banking institutions' valuation changes on equities and bonds. Risk scenarios will typically specify the general development in the equity and bond markets. This can be linked to data for the individual banking institutions' holdings of equities and bonds, subject to adjustment for the market sensitivity of these holdings.

The correlation between trends in the financial markets and the banking institutions' market risk exposure, and the resulting valuation changes, will be tested.

The choice of time horizon is a modelling challenge. The banks' financial statements typically cover a quarter, six months or a whole year, which are short horizons for credit-risk models, but very long horizons for market-risk models.

Module 4: Credit-risk model
The credit-risk model must estimate the banking institutions' expected and unexpected credit losses, based on the development in the common risk factors in the risk scenario and the individual banking institution's actual credit-risk exposure. Quantitative credit-risk modelling is a rapidly evolving discipline that offers a wide range of opportunities for implementation in macro stress tests.

The simplest linkage of the banking institutions' losses as a result of macroeconomic risk factors can be illustrated by a single-equation model^[3], cf. Chart 14 in the chapter on the financial sector.

Credit risk is the most important area of risk for the banking institutions. Chart 46 outlines the planned credit-risk model for macro stress testing, based on modelling of loss ratios for each credit risk category as functions of the common risk factors.

The dissection of the credit portfolios and the layout of the exposure tables will be based primarily on the banking institutions' published accounting and risk management data. However, the econometric analysis will also include the historical correlation between the banking institutions' losses, write-downs, risk exposures, market-based risk measures (e.g. distance to insolvency), and interest margins on lending, as well as the macroeconomic development. The risk profiles can be estimated in various ways:

• With regard to the credit risk on business lending, the failure-rate model (KIM) is an appropriate starting point for estimating default frequencies. The linkage to the individual banking institution can be based on companies' indication of " main bank" , and on the banks' indicated industry and sector exposures. A model of expected failure rates at sector level can also be estimated from historical failure rates as a function of the development in macro variables.
• Regarding the credit risk on lending to households, the overall risk structure of the banking institutions can be calculated on the basis of the data and models that are presented in the chapter on macro stress testing of Danish households. The linkage to each individual banking institution can be based on an estimate of the banking institution's credit risk appetite based on recent years' growth in lending to households, key credit risk figures and data for interest margins on lending to households.

The chapter on the financial sector applies a credit-risk measure to the exposure-weighted credit risks of the individual banking institutions. For stress testing purposes, this credit-risk measure should be refined to describe the banking institutions' loss-distribution, i.e. their expected and unexpected losses both in general and under specific risk scenarios.

Module 5: Interbank systemic contagion model
If stress testing of the banking institutions' earnings, market risk and credit risk results in a capital shortfall, this may have systemic consequences via e.g. uncollateralised day-to-day money-market exposures among the banking institutions. In such case, the balance sheets of the other banking institutions should be recalculated with losses (or the freezing of funds) on their exposures to the crisis-stricken institution(s).

The individual bilateral money-market exposures are not known, but payment data in Kronos^[4] has been used to estimate a significant proportion of the banking institutions' uncollateralised interbank assets.

Further processing of systemic risk in macro stress tests
Macro stress tests should focus on systemic risk, and the model architecture presented here takes account of common risk factors (module 1) and interbank contagion channels (module 5) – two of the three sources of systemic risk shown in Chart 47.

The third source of systemic risk – feedback effects from financial sector behaviour to the macroeconomy via credit crunch or fire sale – is harder to incorporate into macro stress test models. There are several possible approaches, e.g.:

• A satellite model for financial stability variables (e.g. bankruptcies, house prices, profit margins), of which the results are included in the recalculation of the risk scenario in the macro model.
• Bottom-up stress test exercises whereby financial institutions base their calculations on the risk scenario for one year at a time, and where their risk management decisions are included in the scenario projections for the following year.
• Explicit modelling in the macro model of credit-crunch mechanisms (e.g. via capital accelerator effects) and financial market feedback (via demand equations).^[5]
• A separate general equilibrium model for financial stability analysis purposes, with heterogeneous, utility-optimising borrowers and banking institutions, and default risk and uncertainty.^[6]
• Pragmatic choice of risk scenarios.^[7]

Danmarks Nationalbank will continually assess the optimum implementation of the stability analysis and macro stress tests for the financial system in Denmark.