Returning borrowers have better default rates

Andrey Kamenov

Andrey Kamenov, Ph.D. Probability and Statistics

We saw in a recent post that Prosper’s own rating system provides relatively accurate results. However, there is some confusion as to whether it takes returning borrowers into account. As we will show in this post, it is possible to improve upon the standard rating system, thanks to the fact that the number of previous Prosper loans is readily available.

Once we look at the average number of Prosper loans for each of the possible seven rating grades (or, alternatively, the percentage of returning borrowers), we immediately notice a strange pattern. It seems that something in the way Prosper calculated its rating changed between 2011 and 2012.


Note how the shape of the curve differs significantly between years. For example, very few first-time borrowers had a “4” rating in 2011 (only 191, compared to 2,321 borrowers with a “3” rating).

Surprisingly, however, this radical change in the shape of the curve doesn’t affect the default rates. On the following chart, you can see the difference between the average number of previous loans for completed and defaulted loans. The positive numbers here correspond to the larger default probability for first-time borrowers.

As you can see, the mean value is positive for each of the seven groups. Granted, for the largest two rating values (the most creditworthy borrowers) the difference is not large enough to be statistically significant as shown by the confidence interval (we used the Student two-sample test for this purpose). But for the other five groups, it appears, you can increase the chance of getting your money back by sticking to returning borrowers whenever possible.

Source: Prosper downloadable data

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About Andrey Kamenov

Andrey Kamenov

Andrey Kamenov, Ph.D. Probability and Statistics

Andrey Kamenov is a data scientist working for Advameg Inc. His background includes teaching statistics, stochastic processes and financial mathematics in Moscow State University and working for a hedge fund. His academic interests range from statistical data analysis to optimal stopping theory. Andrey also enjoys his hobbies of photography, reading and powerlifting.

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