# Calculate the implied loss rate on a loan, given the interest charged

My bank has a retail credit portfolio of 100 million in loans. I know the payment history,balance history of all these loans since inception. Are there any tools to calculate an expected loss, a loss distribution either at the loan level or at the portfolio level from the interest charged?

My thinking is that a higher interest charged relates to a higher expected loss qualitatively. What I want to do is reverse engineer the expected loss based on the interest and see if the number matches with the official numbers from the Group Risk folks.

• I suspect you will want to use the python library pandas. Essentially your problem is a data preprocessing and processing task, which this will do for you. The next part of your problem is a Regression or Classification machine learning task which the python library Scikit-Learn can do. I highly doubt there to be any ready made softwares which you can slot your data into. The learning curve of python tools is probably better and more useful than a localised software package. – Attack68 Apr 22 at 17:11
• What I am asking is for a high level methodology, not the tools/software. – Victor123 Apr 22 at 17:17
• Apologies, I was confused when you wrote; Are there any tools to calculate an expected loss, a loss distribution either at... – Attack68 Apr 22 at 17:23

## 1 Answer

If you have access to the payment history then would not it be better to estimate the loss rate using historical payment data? The thing with the interest rate is it will include compensation for a lot of other factors as well, such as funding cost, capital charge, servicing cost etc. And some of these would vary by vintage, for example the funding cost would differ depending on when the loan was booked. And if you want to prove the relationship between risk and price, then why don’t you score the accounts using payment history, and then plot the average interest rate against the score.

If you don’t have access to risk scores, then you can use some rule of thumb. For example, get the number of missed payment indicators over the past 12 months, and add the indicator values over the previous 6 months or 1 year, and this will give a reasonable rough indicator of risk.

Alternatively if you can make an assumption around the other add-ons that I mentioned before, then you can strip out the loss component of the interest rate charges.