SAS is used by many banks and other financial institutions to perform the necessary statistical analysis used to create intelligence from a company's data. From data cleansing and audits to scorecard builds SAS is essential throughout the whole development lifecyle of the tools banks use to assess risk.

## Measures of Discrimination Used In Credit Risk

For the sake of illustrating the measures below the imaginary an imaginary score has been used wilth the following good bad distribution.

### The Gini

The Gini is a common measure that is often used in Credit Risk to measure the effectiveness of a scorecard in discriminating between goods and bads. There are various ways of interpreting the Gini Graph one common way of interpreting and defining the Gini is that it is the area between the Lorenze Curve and the bottom left to top right diagonal divided by the area under the bottom left to top right diagonal. So in the graph below this works out as (Area A)/(Area A + AreaB).

### Somer's D

A statistic that works out mathematicallythe same as the Gini is Somer's D, this statistic is defined as (the number of Concordant Good Bad Pairs - the Number of Discordant Pairs) / (Total Number of Pairs Including Ties). A concordant pair is a good bad pair where the Good has a higher score than the bad, a discordant pair is where the good has a lower score than the bad and a tie is where the good has and equal score to the bad.

You should be able to from the Graph below that taking the discordant pairs from the concordant pairs will give double area A from the Graph above. The denominator will be the entire area of the graph which is double (Area A + Area B) from the graph above so the statistics will work out equal.

### The Kolmogorov-Smirnoff Statistic

The Kolmogorov-Smirnoff Statistic when used to measure the dicrimatory power of a score card, looks at how the distribution of the score differs among goods and bads. The Kolgomorov Stat measures the maximum point of separation between the CDF of two distributions. See Graphs Below:

The Graph Below Shows the cummulative distributions of the observed goods and bads. The K-S Statistic is the maximum separation of these cdfs.

The K-S Statistic can be calculated from the gini graph by taking the maximum vertical distance of the lorenze curve from the line y=x.