RDP 2022-03: Macrofinancial Stress Testing on Australian Banks 2. Model Framework

Nicholas Garvin, Samuel Kurian, Mike Major and David Norman

September 2022

At its heart, the stress testing model involves estimating how adverse macroeconomic conditions effect bank capital ratios, using various assumptions and balance sheet decision rules. These connections are illustrated in Figure 1. The three key components in this process (which are captured in the three shaded boxes) are the flow of bank profits (i.e. revenues minus losses), the extent to which any profits are retained as capital or instead paid out, and growth in risk-weighted assets. The first two components determine the numerator in the capital ratio – that is, the amount of Common Equity Tier 1 (CET1) capital – while the third determines the denominator.

Most connections in the model occur within a single period, although asset growth and end-period capital ratios may have implications for funding spreads and net interest income (hence profitability) in the next period. These intertemporal connections can then be used to trace the effects of a shock over subsequent quarters.

Figure 1: Overview of the Stress Testing Model
Figure 1: Figure 1 is a stylised representation of the stress testing model. It contains a series of boxes that represent exogenous variables that feed into the model and endogenous variables that are calculated within the model. Between these boxes are a series of arrows that connect variables to each other to illustrate the effect a certain variable has on another (such as the effect of credit losses on profits). These effects can either happen in the current period or the next period. The macroeconomy (four an exogenous variables) affects credit losses and provisions (an endogenous variable), funding spreads (an endogenous variable), and risk densities (an endogenous variable). Funding spreads and lending spreads (an exogenous variable) affect net interest income (an endogenous variable). Net interest income, credit losses and provisions, non-interest income (an endogenous variable), the tax rate (an exogenous variable) and operating expenses (an endogenous variable) all affect profits (an endogenous variable). A decision rule links profits to dividends (an endogenous variable) and to retained earnings (an endogenous variable). Retained earnings affect the amount of capital (an endogenous variable) and the total assets (an endogenous variable). Total assets and risk density affect risk-weighted assets (an endogenous variable). Capital and risk-weighted assets affect the capital ratio which is key metric that the model calculates. In addition, total assets affect net interest income, operating expenses, and non-interest income in the following period. The capital ratio affects dividends paid in current period and funding spreads in the next period.

Macroeconomic conditions in the model are summarised by four variables: GDP growth, the unemployment rate, housing prices and commercial property prices. The model is currently specified to be invariant to fiscal policy, the level of the cash rate and exchange rates, which are therefore omitted to keep it simple. In reality, each of these influence credit losses and (potentially) funding spreads, but we follow the conventional practice when conducting bank stress tests of abstracting from policy responses that mitigate stress (such as the monetary easing that would likely occur during a downturn). This approach has become conventional because it enables a clear separation of the effects of various shocks on banks' balances sheets from the effects of the possible responses. In making this separation clear, it better highlights to policymakers when action on their behalf is warranted, but this does push the model to overstate the extent of capital loss in a real-life scenario. The four variables in our macroeconomic block can be endogenously determined by applying a shock to a simple set of macroeconomic equations that constitute the macroeconomic model. (This is discussed in more detail in Appendix A.) However, it is also possible to exogenously determine these based, for example, on forecasts derived from a more fully specified model such as that documented in Ballantyne et al (2019).

The primary effect of macroeconomic conditions in the model is on credit losses and hence profits. This mapping of the macroeconomy into credit losses forms one foundation of the model, and is discussed in more detail in Section 3. Likewise, the effect of macroeconomic conditions on the risk rating of banks' assets – that is, risk weights – is discussed in more detail in Section 4.

Macroeconomic conditions also feed into profitability via their effect on banks' average funding costs. This mechanism captures the historical pattern that marginal spreads on wholesale funding – debt securities and deposits of large wholesale/institutional customers – rise quickly when economic activity drops and uncertainty rises. We calibrate this mechanism based roughly on historical experience of the spread between the three-month bank bill swap rate and the cash rate during economic downturns.[2] Wholesale funding costs are also influenced by the extent of decline in banks' capital ratios in the prior period, both their own and those at other banks. (The influence of each bank's capital ratios on other banks' funding costs is discussed in more detail in Section 5.1.) The model could also include the potential for (retail) deposit rates to increase in response to declining bank capital ratios, but this is not currently modelled on the basis that the Financial Claims Scheme protects depositors from loss in the event of bank failure. More generally, we do not explicitly model changes in the size or composition of banks' liabilities. Rather, banks' liabilities are assumed to move in line with changes in the asset side of their balance sheets, while the composition of these liabilities stays constant. This reflects that our focus in this model is on bank solvency (i.e. net worth); we use separate models to consider the potential effect of shocks to banks' liquidity.

Other components of banks' profits – non-interest income and operating expenses – are assumed to grow in line with balance sheet growth with a one quarter lag. The decision to not model non-interest income and operating expense in a more complicated way is based on the absence of any clear historical evidence of how non-interest income responds to economic stress. However, the model has the ability to impose exogenous shocks for both non-interest income and operating expenses if warranted, including as a way to simulate the effect of operational risk losses. The decision to not allow banks to reduce operating expenses (except in proportion to any falls in their balance sheet size) is consistent with the decision to limit banks' ability to take actions to mitigate the decline in bank capital (as discussed below). A 30 per cent tax rate is then applied to banks' pre-tax profits. Collectively, these components (net interest income and credit losses, along with the profile for non-interest income, operating expenses and tax rates) determine the profits (or losses) banks generate each quarter.

The core of the stress testing model is then how this profit flows into new lending, capital accumulation and dividends. The split between capital accumulation and dividends is determined by a decision rule in the model that determines the share of profits that is retained (and hence available to grow banks' credit assets) rather than paid out as dividends. A second decision rule then determines the extent to which retained earnings are used to grow lending rather than strengthen capital ratios. These decision rules are founded on a principal that banks will choose to maintain their current balance sheet profile when their capital ratio is sufficiently high, but that their ability to make decisions becomes increasingly constrained by regulatory settings as their capital ratio falls into the ‘capital conservation buffer’.[3] Accordingly, banks that are profitable and well capitalised will both pay out dividends and grow their assets at a healthy rate, banks that are under-capitalised will retain most earnings and increase assets only marginally, and banks that are loss-making only roll over maturing loans. (The specifics of this decision rule in discussed in more detail in Section 4.1.)

The allocation of profits between dividends and retained earnings, how quickly banks grow assets and the effect of the macroeconomy on risk weights then combine to determine end-of-period capital ratios – the key output of the model. However, end-period capital ratios and revised total asset values have consequences for the next period that go beyond just updating the starting balance sheet. Specifically, the end-period capital ratios are an input to the wholesale funding spread that banks pay in the next period; banks with low capital ratios are charged more for wholesale funding than banks with high capital ratios (as per the earlier discussion). And growth in total assets positively contributes to next period's net interest income calculation. These linkages over time are depicted in Figure 1 (using double line arrows).

Before exploring the model in more detail, it is worth discussing the role that mitigating actions are allowed to play in the model. For the most part, these are prohibited: banks are assumed to never raise capital externally; they cannot improve their profitability by raising lending spreads or by reducing operating costs more than warranted by changes in the size of their balance sheet; and they are not permitted to sell assets or contract their balance sheet. This leaves them with only one mitigating action – reducing dividend payments.[4] (Banks would generate CET1 capital if their CET1 capital ratio falls below the 5.125 per cent trigger at which point Additional Tier 1 capital is automatically converted to CET1, but this is not a discretionary action.)

The decision to prohibit banks in the model from engaging in a broader range of mitigating actions is consistent with standard stress testing approaches. It is motivated by an aim of observing how well banks can withstand stress without needing to take drastic action (i.e. selling assets) or doing things that mean they are not effectively performing their role in supporting the economy (which motivates the prohibition on contracting lending or raising lending rates). Furthermore, we judge it best to be conservative on actions that may not be available in a crisis (such as raising external capital). A prime reason for this view is that history shows that some options available to banks that are healthy (such as issuing new equity) can quickly become unavailable when their capital ratio drops sharply. However, the exclusion of these options means that any results from the stress test should be seen as worst case. Banks could soften the effect of an adverse economic shock by responding promptly, and before they become stressed.

The model covers the balance sheets of the nine largest banks operating in Australia (ANZ, CBA, NAB, Westpac, Macquarie, Suncorp-Metway, Bank of Queensland, Bendigo and ING). These nine banks account for around 80 per cent of banking system assets in Australia. Each bank differs only in the composition and size of their balance sheet; they are otherwise assumed to have the same sensitivity to macroeconomic conditions and to adopt the same decision rules. This means that the model is less suited to monitoring idiosyncratic stress than APRA's approach (consistent with the differences in institutional mandates). The one exception is for risk weight calculations where the internal rulings-based (IRB) banks (ANZ, CBA, NAB, Westpac, Macquarie and ING) have a different method for calculating changes in risk weights relative to their standardised peers (as discussed in Section 4). More generally, parameters in the model can typically be adjusted as desired to test the sensitivity of results to various assumptions.

The data underlying the model is a subset of what is reported to APRA by banks on a monthly or quarterly basis. The model is set to provide quarterly capital ratio projections over a set horizon, which is typically specified to be three years.

Footnotes

Our calibration results in wholesale funding spreads rising by 80 basis points for every percentage point of reduction in quarterly GDP growth relative to the starting period. Wholesale funding accounts for over one-third of total funding. [2]

The capital conservation buffer is an amount of capital above the regulatory minimum that serves to protect the minimum capital requirement. In Australia, it includes a 1 per cent domestic systemically important banks (D-SIB) buffer above the typical capital conservation buffer for major banks. [3]

Additional Tier 1 (AT1) capital coupons are also discretionary but, for simplicity, we do not allow for banks to reduce these. In practice, it is very unlikely that a bank will restrict AT1 coupons unless it comes under severe stress. [4]