WHEN IS GINI A GENIE? Summary Advanced Basel 2 retail credit risk status, requires ‘good’ models…that is models which have a ‘high’ level of discrimination between defaulting and non-defaulting potential borrower populations. The industry standard for assessing discrimination is the GINI co-efficient. Unfortunately, some of the more powerful approaches to risk model development lead to apparently lower GINI co-efficiency rather than higher ones. This article explains what going on so that firms can properly demonstrate the strength of their risk model to managers and regulators. Introduction The industry standard approach to measuring the power of a risk model is in the GINI co-efficient. The GINI co-efficient compares the “Lorenz” curve (the cumulative distribution) with the line of perfect randomness. A schematic example is set out as figure 1. Figure 1: The GINI Curve There are in fact several ways of assessing the power of risk model to discriminate between population segments of higher or lower risk, for example Discriminant Analysis. GINI has become the industry standard partly because • It can be applied across a wide variety of situations • It is as accurate a measure of discrimination power as any of the other approaches • It is simple to apply and interpret In the usual approach taken to retail risk assessment, a ‘scene’ is calculated for each borrower. Such that a low score represents a high probability of default and a high score forecasts a low probability of default. A GINI co-efficient for a virtually perfect credit risk model will look like figure 2. Chart 2: The Ideal Gini Curve Producing Powerful Retail Risk Measures Retail credit risk measurers, or scorecards consist of a chosen group of characteristics determined statistically to separate ‘good’ and ‘bad’ accounts. Typically characteristics are not applied continuously but instead are broken down into sub- brackets (or attributes) and points are assigned such that the overall score of a borrower can be mapped directly to a probability if by ‘bad’. The ‘power’ of the scorecard is then assessed by a GINI co-efficient with 50% widely perceived as a minimum target for regulatory model acceptability. (As an aside, I should mention that GINI co-efficient for commercial credit situations are often lower). Several approaches can be used to improve the power of retail risk measures. • Use more data: This enables development of richer models with attributes used more continuously. • Consider cause and effect: before developing a score card, a firm should ensure that it reflects predictive futures. For example many ‘behavioural’ scorecards based on current account information can demonstrate a GINI co- efficient of 90% - because the account has already reached a stage where default is inevitable and the lender has no opportunity to react. In summary, a retail credit risk scorecard that does not include income-in-relation-to-debt and nature-of-employment, either directly or through proxy variables is not genuinely predictive, however high its apparent GINI. • Improved statistical techniques (for example, multivariate regression, logit, probit, neural networks, etc): These can be very powerful but an important constraint in their use is the need for simplicity and transparency, both in implementation and in explaining outcomes to customers. • Segment on overall population using a different scorecard for each segment: this is very powerful wherever data is sufficiently powerful to support it. Unfortunately; it is easy to do this in such a way that GINI co-efficient deceive, giving the impression that discriminatory power is by host. GINI co-efficient for Multiple Scorecards Figure 4 shows a risk measure applied to a particular population. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 Graph 4: GINI Curve of population with even probabilities of default For this scorecard the GINI coefficient is calculated to be 0.59 Let us consider a segmentation into people with an annual income of more than £30,000 and people with an annual income of less than £30,000. Let us assume that 20% of the population have an annual income of less than £30,000; with a default probability of 60%. The remaining 80% of the population with an annual income of more than £30,000 has a default probability of 40%. This data is summarised in the following table: Income % of population Default Probability Less than £30,000 20% 60% More than £30,000 80% 40% If scorecards are re-developed for each segment, using the same techniques one actives a GINI co-efficient of 0.433 for the first 30% of the population and a GINI co- efficient of 0.22 for the second segment. Apparently, discriminating power has declined! The reality however, is summarised by figure 5. In figure 5, you can see that the 2 segmented GINI co-efficient exclude area C. In reality, the GINI co-efficient for the overall population – i.e. including A, B and C – is now <0.67> 1 0.9 0.8 B 0.7 0.6 C 0.5 0.4 A 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 Figure 5: Gini curves of the 2 factor model In fact an increase in overall GENIE will always be achieved where populations can be segmented by output probability of default. Conclusion Scorecards add value when they are predictive. There is great scope to increase discriminatory power by segmenting populations but only if one understands how a GINI co-efficient can be turned into a GENIE.
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