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I am analyzing LendingClub data with two available loan terms: 36 and 60 months. In the course of my analysis I have spotted that both the interest rates associated with each loan and the default probabilities, obtained from my logistic regression, are higher for the longer term. Interest rates and probability of default for different loan terms

I am thinking about a way of explaining why both interest rates and PDs are higher for the longer term. For the former the only thing I can come up with is that considering the assets are frozen for longer time lender expects to obtain higher premium.

Is there any formal way to explain these relations?

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There are two reasons why the interest rate is higher for the 60 months loans:

1- Liquidity premium Like you said, since the money is immobilized for a longer period of time, it's normal to expect a higher return on the investment. It's also a way of protecting itself in case the interest rate increases, because the longer the term of your loan, the more you are exposed to changes in the interest rate.

2- Risk Like you said yourself, the risk of default is significantly higher when the term of the loan is longer. Following the basic rule that more risk means higher returns, it's clear that the rates will be higher for 60 months than for 36 months loans.

As for why the default rate is higher for 60 months loans than for 36 months, I'm not very knowledgeable on the subject, but if we imagine that there is a fixed chance that the borrower defaults each month, we can easily imagine why more months means more chances of default.

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due to an accumulation of a higher amount of interest in the longer time period, the total payout obligation of the buyer increases; the amount to be repaid is higher in comparison to the shorter term(through interest calculation on the term). As a result, the probability of the borrower defaulting the payment is higher, simply resulting from a higher payout obligation. the rise in interest rates as rightly explained by you has a simple cause and effect relationship with the PD.

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