UK: Tipping Point: Threshold Models In IFRS 9 And Stress Testing Models

Introduction

Under IFRS 9, financial institutions are required to account for loan loss impairment by recognising an allowance for expected future credit losses (IFRS9.5.5.1) in a manner that considers a range of possible outcomes (IFRS9.5.5.17), including current conditions and a range of forecasts of economic conditions (IFRS9.B.5.5.49).

The IFRS 9 standard further sets out that firms should consider all "reasonable and supportable information" (IFRS9.5.5.17), which includes (IFRS9.B.5.51) statistics and historical information.

Therefore, in loan portfolios where instruments' cash flow performance exhibits a dependency on macro-economic variables, compliant approaches to loss estimation would need to consider the dependency between the state of the macro-economy and credit losses.

This article compares two alternative econometric models, a linear and a threshold model, in the context of unsecured personal lending. The objective is to understand the predictive power of the two models and the degree to which they can sufficiently capture the relationship between credit risk and the macro-economy.

Quantification Methods

Neither the IFRS 9 standard, nor regulatory guidance, are prescriptive as to the methodology for how expected credit losses should be estimated, nor the type of macro-economic variables that should be considered. Indeed, the IFRS 9 standard does not explicitly mandate the use of any model. Nevertheless, in the time that has elapsed since publication of the draft standard, a consensus is beginning to emerge whereby:

• Econometric models are developed to quantify the historical relationship between macroeconomic factors and generate some number of forward-looking scenarios; and
• Scenario-conditional expected credit loss quantification models are developed to quantify the impact of a given scenario on credit losses.

One of the least developed areas remains the interface between econometric modelling and credit modelling. Here, one of the least-examined areas is non-linearity. Whilst many firms have introduced non-linear mapping functions into the relationship between credit losses and the macro-economy, comparatively few have explored the possibility that the macroeconomic system might exhibit significantly different responses during normal versus stressed periods. This variability in response can be modelled using a "regime-switching" approach. This family of models in-effect runs two-separate sub-models and produces a blended result. The blending can be continuous, or a simple switch between sub-models that occurs at some pre-determined threshold. In the following section, we explore whether a threshold model can provide better forecasts of UK market unsecured write-off rates.

Unsecured Write-Offs

Amongst credit portfolios, unsecured personal lending stands out as one of the most challenging to model. Contractual features such as an unbounded period of risk and lack of collateral can lead to stress losses (as well as variability of estimates) that exceed those seen in typical secured lending.

We have compared two approaches to estimating the impact of macro-economy on market unsecured write-off rates in the UK:

1. Linear model: A change in GDP growth from 0% to -2% has the same impact on credit losses as a change from -4% to -6%, for example.
2. Threshold model: Allows for impacts to change once underlying variables cross a pre-determined threshold – this may reflect that in reality, falls in real income can be sustained to a certain level before an individual has to default. In our example above, these models enable the change in GDP from -4% to -6% to have a far stronger impact on credit losses than a change from 0% to -2% would have.

For this article, we trained a pair of models that established a statistical relationship between unsecured write-offs and the output gap, using a sample comprising the 90 quarters from 1994. The only difference is that our threshold model establishes different relationships above or below a certain threshold value.

The appropriate choice of model can be assessed on the basis of goodness-of-fit, which measures how strongly the model describes the underlying data generating process. We have used three goodness-of-fit criteria:

• Akaike Information Criterion (AIC) expresses the log-likelihood of the observed data points occurring under a given model, but introduces a penalty for free parameters. Therefore, if two models have the same log-likelihood, AIC will favour the model with fewer free parameters.
• Bayesian Information Criterion (BIC) expresses the log-likelihood of the observed data points occurring for a given model, but introduces penalties for free parameters and the number of data points. BIC can be interpreted as an extension of AIC.
• R-squared, or coefficient of determination, expresses the proportion of variation in the dependent variable that is explained by the input predictions. Although R-square is an intuitive metric, it does not consider model complexity. Therefore, the model with the highest R-square may also be the model with greatest risk of over-fit.

The table below compares the three goodness-of-fit statistics for a) our linear model; and b) our threshold model. All three models favour a threshold model.

Next, we estimate unsecured cumulative 2016-2017 net write-offs under three scenarios:

1. Bank of England baseline – c.2% annual growth in real GDP on average until 2018;
2. Bank of England stress – c.1% annual growth in real GDP on average until 2018; and
3. A recession shock scenario, simulating the 2008-09 recession with c.-1% annual GDP growth until 2018.

The results suggest that the linear and threshold models give similar results in a relatively benign set of current and forecasted economic conditions. However, the results suggest that linear models are likely to dramatically under-estimate stress losses in a recession scenario. This finding is particularly pertinent when we consider that the simple sum of quarterly credit losses from 2008-2009 numbered c.10%.

The time series comparison of predicted losses as a proportion of credit is shown below for the linear and threshold models during the recession simulation period. What can be seen is that the threshold model (green) is considerably more responsive to underlying macroeconomic fundamentals than the linear alternative (blue). To put this finding in context, a 1% gap between the forecast series in a particular quarter would represent c.£600m difference if applied to 2016 levels of credit.

The risk of a linear model leading to a misstatement therefore depends on the likelihood of the stress loss occurring. If the macroeconomic forecast is benign then the likelihood of a serious estimation error is low. However, if the likelihood of the stress loss occurring increases, then a linear model is likely to significantly under-state future losses.

A final word of caution, however: This class of model is predicated on the assumption that future variability in macroeconomic indices and credit risk metrics will obey the same relationship as has been observed historically. With many series exhibiting non-stationary behaviour, and a long period of low interest rates, the only inference that can be drawn with any degree of certainty is that the next recession is unlikely to look anything like the previous one. Credit modelling therefore remains just as much of a judgemental art, as a precise science.

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