# AnalyticBridge

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# Credit Limits Model

Hi,
Does anyone have experience in developing credit limit model that assigns credit limits in dollars to customers? Suppose I have build a credit scoring model that assign credit score to my customers, how do I assign credit limit based on the credit score to each customer?

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### Replies to This Discussion

I think it is completely a management decision task that how much amount should be assigned with a particular score. Once a credit scoring model is developed and back tested and then accepted the job of a modeler is over. Next is the management task what to do with that model................obviously you can make your own comments, notes, but it is upto them only.

Best,
Arun Kumar Saha
Hi, Arun:
I agree with you totally. However, it is part of my project to determine the credit limit once I got a credit score model. I suppose that assign a credit limit has something to do with optimization techniques as I heard from the instructor in SAS who told me some people use MDP (Markow Decision Process) to determine the optimal credit limits. Any idea on this optimization front?
After first developing a proprietary behavioral score, we used the new score along with a credit bureau score to assign credit limit that was pseudo optimized.

Based on some historical analysis, we settled on a percentage of revenue that should be allocated to cover bad debt costs in order to achieve profitability. Then, assuming a certain level of utilization of the credit line at charge off (something like 105% in our case), we developed a simple formula that calculated an "optimal" credit limit for each account based on historical scores (proprietary behavioral and bureau) and revenue and charge off data.

Next we grouped the historical data by 5% groupings for each score (20 each, up to 400 when groups intersect). For each of these groups, we calculated the optimal credit limit based on the average revenue and charge off rates. The optimal limit was rounded to something like the nearest 200 (our limits are fairly low) and regrouped by the rounded number. This reduced the number of groups from almost 400 to about 25-30.

With a little smoothing and judgemental modification based on management input, we reduced the number of groups a little further, and finalized a matrix that assigns credit limits based on the two scores.

This isn't a terribly elegant technique, but it was easy to do. More importantly, management understood it and bought in. It is also pretty easy to look at the financial benefits of developing/purchasing the scores when you can demonstrate higher charge off rates and balances for the accounts with credit limits that are outside of recommendations.
Hi, David:
Thanks. Do you use any optimization techniques like linear programming in calculation?
No, we're not using any true optimization because we only have one variable (credit limit) in this scenario. The credit limit is directly related to the balance in the event of a charge off. For everything else we're using historical averages for the groups.

Our philosophy, as we have started to do modelling in house, has been to start simple and add complexity iteratively.

In the future, we'll probably add a separate score to predict revenue to the mix. In that scenario, we may need to do some more sophisticated optimization.

Hi, have you some more material on this topic, we are interested in to use optimization techniques like linear programming in calculalation.
We want to find optimal credit limit that  make possible increase revenue and remain the same or lower the percent of bad loans.