"Inverted" correlation of the amount of the loan and the probability of default

Question

My task is to make a machine learning model for predicting the probability of default when taking a loan (binary classification).

But I also want to predict the loan amount. Something like: if the client is very good, then you can give him more money than we usually give. Now the amount is billed based on experience and intuition by the loan portfolio analysts. The problem with adding the "loan amount" feature to the model and training it again is that historically we have given more money to clients who had a low probability of default. Something like:

group	max Probability of default	max money
1	0.05	100
2	0.1	50
3	0.15	25
4	1	0 (reject)

Because of this, the model will observe an 'inverted' correlation. The more money, the more likely the customer will pay back! Although the real situation is exactly the opposite. The more money we give the client, the less likely he is to pay it back, so only good clients should be given large sums.

Can you advise me how to correct this situation, what area of scientific knowledge should be studied, what A/B tests should be performed?

Answer 1

Typically this problem is solved by looking at loans in terms of percentage loss rates. IE if we loan out \$100, how many dollars is lost on defaults. If we loan 300 dollars and $15 is lost, our rate is 15/300 or 5%. This solves the problem of using a raw number. Loaning lots of money would invariably increase losses in raw terms but that's not inherently bad.

Now you have default rates by risk category with risky groups usually having a higher rate. You can then look at the interest rate you charge them and see if you are breaking even or not.

In short, probablity of default is no longer a useful metric here. If I give a riskier person slightly less money or charge a better interest rate, it might become a better or worse deal.

Update per comment "It is the amount of the loan and possibly the interest rate I want to predict."

If this is the case, I would talk to the people writing the loans for a bit more insight. It would appear that the upper limit of the size of the loan is credit worthiness. The lower limit is minimum money needed for a successful loan. Ie, you aren't going to get a car loan for 12k if the car costs 35k.

Linear regression is what I would use. Working in this area, most places in the world require high levels of explainablity so most ML is out. So internal risk managment can feel safe and for legal reasons such as discrimination and avoiding run away economic chaos.