Stress Test of the Financial System

The purpose of Danmarks Nationalbank's stress test model is to assess the resilience of the financial system to extreme, but plausible shocks to the economy in general and to the financial sector in particular. At the same time, the model helps to identify weaknesses in the financial system in Denmark by illustrating how shocks to the economy spread through the financial system.

Danmarks Nationalbank's stress test model takes the individual bank as its point of departure, but allows for the fact that banks can influence each other. A 3-year scenario is set up for the macroeconomic and financial market developments that are consistent with a given level of stress from one or more economic risk factors. On the basis of this scenario, the model provides an estimate of the impact on the banks' Tier 1 capital and solvency. Three years' financial statements are projected and the consequences for the financial system assessed for each year. The assessments are solely based on the development in the banks' profits and solvency.

The stress test model is developed on an ongoing basis. At present e.g. liquidity risk and operational risk are not explicitly modelled. The modelled outcomes are not a precise description of the consequences of a given development, but rather an estimate of the resilience of the financial sector to various types of economic and financial shocks.

MODEL ARCHITECTURE

The model for macro stress testing is based on a number of submodels for bank earnings, market risk, credit risk and interbank systemic contagion risk, respectively. The model architecture is illustrated in Chart 48.

Dynamics of the stress test model
The first step of the model is to set up a coherent scenario – i.e. a consistent development in macroeconomic and financial variables – that provides the desired level of stress. Danmarks Nationalbank's macroeconomic model, MONA, is used to project the economic development.

For each bank, the correlation is estimated between a number of risk factors and the bank's earnings, valuation changes and loan losses. This makes it possible to estimate the banks' annual profits in the scenarios analysed. The profits are used to project the balance-sheets, which are used to assess whether the banks will be able to meet the statutory capital requirement. If all banks meet their capital requirements, the model progresses to the second year of the scenario, using the projected balance-sheets and stressed risk factors as input.

If, following update of the balance-sheets after a period, one or more banks can no longer meet the capital requirement, it is assumed that the bank(s) will close down. The stress test model then shifts to the interbank systemic contagion model, in which the losses of the closed bank(s) may spread through the financial system via interbank exposures. The banks' balance sheets are then updated to take into account any losses on the closed bank(s). If this leads to further closures, the procedure is repeated until no more banks are closed. The model then progresses to the next period. The stress test model operates with a 3-year horizon.

Delineation of the model population
The population of the stress test model is limited to banks in the Danish Financial Supervisory Authority's groups 1 and 2, i.e. the largest 16 banks in the Danish market in terms of working capital. The model is based on publicly available data.^[1] With this delineation of the population, the model covers 93 per cent of the Danish banking market in terms of balance-sheet assets and 77 per cent of total bank lending in Denmark. It also ensures that a wide range of bank business strategies are represented.

At present the stress test model comprises only banks. Other financial institutions, such as mortgage-credit institutes and insurance companies, are disregarded. This potentially affects the models results due to cross-ownership within the Danish financial sector. For example, a bank that is a subsidiary of an insurance company may have a smaller capital buffer than other, comparable banks, because the buffer lies in the parent company, which is able to inject capital if required. The opposite may apply if banks have ownership of e.g. insurance companies.

SUBMODELS OF THE STRESS TEST MODEL

The submodels for core earnings^[2], market risk and credit risk each comprise one or more items in a bank's basic financial statements. The latter is illustrated in Chart 49. In combination, these submodels provide estimates of the banks' profits. The estimated model relations are based on data from the banks' financial statements for the period 1990-2006. The projections of balance-sheets totals and solvency are based on the estimated results and ad-hoc assumptions.

Core-earnings model
The core-earnings model is used to estimate the banks' core earnings in the scenario. Net interest income, net fee income and costs are modelled explicitly, while the minor items under "Other" are assumed to constitute the same share of the Tier 1 capital in each year of the scenario.^[3]

The banks' net interest income, net fee income and costs are modelled separately. For each of the three items it is estimated how the general development in the item is influenced by the development in the risk factors. In order to project the general development, the development in the risk factors is entered into the estimated relations. The projected developments are adjusted for each bank in order to obtain a bank-specific development.

The relations of the core earnings model are described in more detail in Box 9.

RELATIONS OF THE EARNINGS MODEL	Box 9
In the core earnings model, the development in the income-statement items is determined in two steps. Net interest income is broken down into eight items that are treated separately.1 Each income-statement item is normalised by an appropriate balance-sheet item.2 The first step is to estimate how the development in the macroeconomic variables affects the implied interest rates, net fee income and costs for the banking sector. The second step is to estimate how the development in these items for the individual banks relates to the overall sector development. Step 1: For each of the ten dependent variables, a median value is calculated for each year in the estimation period. This results in a time series for each variable. An error-correction model is set up for each variable with a set of macrovariables as exogenous variables. The interest-rate relations are estimated using SUR (Seemingly Unrelated Regression). Net fee income and costs are estimated using OLS (Ordinary Least Squares). The variables are projected by inserting the projected macrovariables into the estimated relations. Step 2: For each variable, a calculation is performed for each bank of the median spread over the last three years to the variable for the sector overall. In the projections, it is assumed that for each bank the spread to the variable in relation to the sector overall corresponds to the median spread over the most recent three years of the estimation period. Projections are made by projecting the development in the sector conditionally on the macrodevelopment in the scenario and individually adjusting the development for each bank. This is illustrated in the chart below.
PROJECTION IN THE EARNINGS MODEL
1  Net interest income comprises four income items (receivables, lending, bonds and other) and four expense items (central banks and other financial institutions, deposits, subordinated debt and other). 2  For example, interest income from bonds is normalised by the bond portfolio. Other interest income and expenses, net fee income and costs are normalised by equity. The normalised values are calculated as the profit/loss on the item in question in the year t divided by the average of the portfolios at the beginning and end of the year t. Conversely, projections are based solely on the portfolios at the beginning of the year.

Market-risk model
The market-risk model provides an estimate of bank revenue and losses resulting from changes in asset values due to changing market conditions. Market risk comprises interest-rate, equity market, foreign-exchange and commodity risks. For the banks in the model population, the foreign-exchange and commodity risks are so small that they have been assumed to be zero. The market-risk model therefore operates only with interest-rate and equity market risks.

Interest-rate risk is the risk that the value of a portfolio of interest-bearing assets changes as a result of changes in interest rates. In the stress test model, the portfolio of interest-bearing assets is measured as the banks' bond portfolios. The risk on a bank's bond portfolio is stated using the interest-rate risk measure published in the bank's financial statements. The model thus allows different degrees of interest-rate risk for the various banks. It is assumed that the individual bank's measure remains unchanged throughout the scenario. Based on the banks' Tier 1 capital and the projected change in interest rates, the interest-rate risk measure expresses the effect of the banks' interest-rate risk.

Equity market risk is the risk that the value of a bank's equity portfolio changes due to price fluctuations in the market. For each bank, it is estimated how the value of the equity portfolio co-varies with the development in the market. Thus, the model allows banks to have different risk profiles on their equity portfolios. To project the effect of the banks' equity market risk, the development in the equity market and in interest rates is entered into the estimated relations.

The relations of the market-risk model are described in more detail in Box 10.

Credit-risk model
Credit risk is the risk of losses because borrowers or other counterparties default on their obligations to the bank. Credit risk is typically the greatest risk factor for retail banks. The credit-risk model models the banks' credit losses on loans to 10 sectors.

The loss ratios for the various sectors are treated separately, i.e. different loss ratios are stated for each sector. To determine a bank's losses on loans, its exposure to each sector is multiplied by the projected loss ratio for that sector. This method assumes identical loss ratios in given sectors for all banks in the population. That is, credit quality is assumed to be the same for all banks lending to a given sector.

The relations of the credit-risk model are described in more detail in Box 11.

The banks' financial results
Combined, the estimates from the core earnings model, the market-risk model and the credit-risk model make up the point estimates on a bank's profit/loss before tax. It is assumed that a bank making a profit pays 25 per cent in tax and distributes 50 per cent of the profit after tax as dividend. The rest of the profit for the year after tax is transferred to the bank's Tier 1 capital.

A bank making a loss is assumed to pay neither tax nor dividend. The loss is offset directly against the bank's Tier 1 capital.

Balance sheets and solvency
The banks' balance sheets are updated on the basis of a simple rule of thumb. It is assumed that each bank has targets for gearing, risk profile and portfolio composition and that these targets are met in the banks' most recent financial statements.

This means that a bank that makes a profit and meets its portfolio targets has the same portfolio structure, gearing and risk on the portfolio as it had the year before and in the baseline year (i.e. balance-sheet items are scaled by the same factor as the Tier 1 capital). Thus, the solvency ratio also remains unchanged.

For banks reporting losses, the Tier 1 capital is reduced by the loss for the year. The decrease in Tier 1 capital is matched by an equivalent fall in assets. At the same time, it is assumed that downward adjustment of the banks' exposures is sluggish so that it is not possible to gear down activities. This means that assets yielding losses are reduced while assets not yielding losses remain unchanged. The assets are reduced so as to reflect the relative sizes in the baseline year as well as possible. The solvency ratio therefore declines for loss-making banks. Banks that do not meet their portfolio targets do not begin to gear any profits until these targets are, once again, met.

After each update of the banks' balance sheets it is checked that the banks still meet their capital requirements.^[4] Where this is not the case, it is assumed that the bank in question closes and that its remaining assets lose 10 per cent of their value.^[5] Thus, any bank not meeting its capital requirement is automatically insolvent in the sense that it imposes losses on its creditors. It is assumed that the banks in the model population are each other's lowest-ranking creditors and thereby bear the first losses.

Interbank systemic contagion model
How severely the liquidation of a bank affects other banks within the system depends on their interbank exposures. The total interbank exposures from the banks' financial statements are combined with data for uncollateralised day-to-day lending to estimate each bank's relative exposure to the other banks. If a bank becomes insolvent, the loss is distributed on the other banks on the basis of their relative exposures.

Next period …
In the subsequent period, the projected balance-sheets and the projected macrovariables for the subsequent period are the point of departure for assessing the banks' profits/losses. This procedure continues until the end of the third year in the scenario.

Against that background it is possible to apply dynamic effects to assess the exposure of the banks to various stress scenarios.