# WHEN IS GINI A GENIE Summary Advanced Basel 2 retail credit risk by crunchy

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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.

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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>

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C
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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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