Some Basic Credit Risk Modelling Concepts

As the world's banking and financial systems become increasingly stressed - and distressed, a common reaction is to blame the models that are used by banks to quantify risk. This article is about some of those techniques, which can provide a strong basis for a sound risk management framework. However they are unfortunately often misunderstood, abused, and used naively

There are several important terms that often arise, particularly in the context of credit portfolio risk analysis, which include:

• Economic Capital.
• Risk-Appetite.
• Risk-Adjusted Returns.

Economic Capital

This term is often used for quantitative measures which attempt to put a number on the capital that would be required to 'cover' the riskiness of a portfolio. There are several variations, some essentially based on empirical 'rules of thumb', and some based on sophisticated statistical models.

Risk-Appetite

This term should be self-explanatory. By quantifying 'risk-appetite' it is possible to put flesh on a business strategy which involves the taking of financial risk, by identifying how much risk a business is prepared to take.

Risk-Adjusted Returns

Different financial institutions take different amounts of risk, and make different returns. By looking at 'risk-adjusted' returns, we try to account for the riskiness of a return, so that we can measure the quality, rather than just the size of a financial return.

What Causes A Portfolio to Suffer Large Credit Losses ?

Before considering some of the modelling issues, it is perhaps worth 'getting back to basics', and stating the obvious - which is why a large credit portfolio can suffer significant losses. To understand this at the most basic level, we do not need to consider any complex or 'toxic' financial instruments. There are two possible causes:

• There are large individual losses.
• Many smaller losses occur together.

What this means is that two of the critical 'inputs' to any portfolio risk model are: (i) the probabilities of default, and (ii) the factors which drive the probabilities of multiple defaults occurring together - 'correlation' effect in general terms.

Some Problems with Using Economic Capital Models to Manage Portfolio Credit Risk

In the author's opinion, the most frequent problems that arise when using this type of model are as follows:

1. What the Model Results Mean is frequently Misunderstood.

   The first and most important problem is that these models are frequently misunderstood, even by those that use them. These misunderstandings do not just relate to their complex inner-workings, but much more fundamentally to what the results actually mean, what they can be used for, and perhaps more importantly, what they can not.

   The role of these models are primarily to produce a measure of risk, often called a 'risk metric' - which is not to say that they are necessarily meant to be 'predictive'.

2. The Statistical Measures that are Used are Often not Ideal

   The risk models which are based on some kind of statistical risk analysis often internally compute probability distributions for loss, and then calculate various statistical 'risk' figures based on these distributions.

   Unfortunately, the particular measures that are often used have some serious practical flaws. One measure that is often used in the context of 'Value-At-Risk' is the 'Confidence Level'. Unfortunately, this type of measure is in statistical-speak 'non-coherent'. In practical terms this means that they can be quite unstable, and the aggregation and disaggregation of these numbers can behave very strangely.

3. Estimates of Some Key Input Parameters are Often Rather Questionable

   The most obvious examples of this are the probabilities of default, or 'PD's that are used by such models. This is particularly true for the better credit grades (lower PDs), where there are often too few recent historical default events - if any - to get a proper estimate using simple statistics. This then feeds through to a disproportionately high dependence of the overall risk figures to changes to these input figures in relative-terms.

   In addition, the influence of 'Correlation Effects' usually depends on a range of input parameters in a rather complex way, which is not always especially robust.

4. Models Often Under-Estimate Extreme Risks Due to Inappropriate Risk-Diversification Effects

   One of the key factors in almost any portfolio modelling is the way in which 'diversification' - or looking at it from the opposite perspective - 'concentration' effects are taken into account. By having a diversified portfolio, the riskiness (in relative terms) is generally reduced - this is because it is less likely that many bad things will occur together.

   However, it is the author's view that these effects are often not always taken into account properly - and that for more extreme situations - these models can significantly over-estimate the sanitising impact of diversification, and therefore greatly under-estimate the real risk.

   This is essentially because such models often do not capture the way in which correlation effects can change dramatically under particularly adverse or extreme market conditions. In the author's view, it is not sensible to trust such a model - even if it is properly calibrated (which is rare) - for computing risk figures for events that occur less often than about once every ten or twenty years.

5. Risk Model Calibration Issues

   These models generally have significant 'calibration' issues - these arise because there are often a range of inputs which configure the models, and whose values are open to question. Unfortunately, this process is not always as objective as it might be.

   This type of situation can arise especially if a manager is unwilling to accept the risk figures that are calculated - because they appear to be high - even without properly including some of the effects that lead to increased values. These circumstances can lead to the credibility of the analysis to be questioned, and methodologies to be adjusted, so that the outputs match pre-conceived values.

   In the worst cases 'model calibration' becomes a euphemism for adjusting the inputs to achieve a desired output, which can mean that not only are the results misleading, but the changes to the computed risk figures do not change as they should in response to changes that are made to other input parameters.

6. 'Cascade' Effects are Often not Accounted For

   These models often only include 'first-order' correlation effects between the various factors that drive risk. They rarely properly include 'cascade' effects, which are common in the real work under extreme circumstances. Attempts are sometimes made to undertake multi-factor 'scenario analysis' to capture some of these effects - but it is questionable to what extent they succeed.

All of these issues do not mean that such models cannot make a valuable contribution to quantifying and managing risk; they simply mean that they need to be properly understood by those that make use of them.

The worst outcome is when such models are not used properly, and the appearance of sound quantitative risk-management is then used as a justification for reducing other complementary risk management mechanisms, resulting in even more risk being taken.