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Roll Rates Revisited Again:  A look at month by month delinquency transitions across the consumer lending space

In our previous post from July 2014, we analyzed roll rates on the Prosper platform using the explicit roll data provided in their monthly payments file. Looking at month by month roll rates of the consumer unsecured lending space is of interest to many who want to keep an eye on overall trends in the industry, but it is often hard to compare data across different originators who may have different reporting conventions. In this post, we strive to introduce a heuristic for measuring the delinquency status of a loan at any month based on the month-end principal balance, interest rate, original term, and installment amount of the loan.

For any payment month, we can calculate the expected remaining term of a loan given its current outstanding principal balance and its monthly scheduled installment payment. Adding the above calculated remaining term to the payment month date will give us the expected repayment date. If this calculated expected repayment date occurs later than the expected repayment date at origination of the loan, then we label this delinquent.

Let’s turn our focus to 36 month loans. Using our newly calculated delinquency statuses, we can now answer questions such as the following: “If a loan is currently 1-29 days past due, what is the probability of that loan being 30-59 days past due next month?” Let’s take a look at the transition matrix below:

pic1

Status Current 1-29 30-59 60-89 90-119 120+
Current 98.6% 24.2% 3.6% 1.2% 0.5% 1.8%
1-29 1.4% 61.6% 2.9% 0.6% 0.3% 0.6%
30-59 0.0% 14.0% 6.1% 1.1% 0.4% 1.2%
60-89 0.0% 0.0% 83.6% 2.8% 0.8% 1.7%
90-119 0.0% 0.0% 0.0% 87.8% 1.9% 3.7%
120+ 0.0% 0.0% 0.0% 0.0% 5.8% 8.9%
Charged Off 0.0% 0.2% 3.8% 6.6% 90.3% 82.2%

The data underlying the above matrix includes payments from loans originated by various lenders in the consumer unsecured lending space from January 2013 to September 2015. The columns represent the current status of the loan, and the rows represent the probability that the loan will be in the corresponding delinquency status next month. Using the above matrix of probabilities, we see the probability of a loan that is 1-29 days delinquent rolling into 30-59 days delinquent next month is 14%.

This is interesting when thinking about the market as a whole, but what if our portfolio consisted largely of low interest rate or high interest rate loans? See below for the interest rate distribution of 36 month loan originations over our selected period.

pic5

The dashed lines represent the 25th, 50th and 75th percentiles of the distribution. We will denote all loans with interest rate less than 9.2% as Low, loans with interest rates between 9.2% and 15.3% as Medium and loans with interest rates above 15.3% as High.

For Low loans we observe the following matrix:

pic2

Status Current 1-29 30-59 60-89 90-119 120+
Current 99.10% 24.80% 2.50% 1.30% 0.80% 0%
1-29 0.90% 70.20% 3.10% 0.80% 0.30% 0%
30-59 0% 4.90% 4.30% 1% 0.40% 6.70%
60-89 0% 0% 85.50% 2.20% 0.70% 0%
90-119 0% 0% 0% 88.70% 1.70% 6.80%
120+ 0% 0% 0% 0% 1.40% 31.70%
Charged Off 0% 0.10% 4.60% 6% 94.70% 54.80%

Loans in this category which are 1-29 days past due only roll into the next delinquency bucket 4.9% of the time. This implies that for Low loans, one missed payment is not as serious of an indicator of major delinquency as it is for the rest of the market. However, looking at the roll rates between 30-59 dpd, 60-89 dpd, 90-119 dpd, 120+ dpd and eventual charge-off, like the rest of the market, once a Low loan has missed two payments, its future chances of recovery are slim.

For Medium loans we observe the following matrix:

pic3

Status Current 1-29 30-59 60-89 90-119 120+
Current 98.80% 25.20% 3% 1.20% 0.50% 1.90%
1-29 1.20% 60.90% 2.40% 0.60% 0.40% 2.10%
30-59 0% 13.60% 3.40% 0.80% 0.40% 1.30%
60-89 0% 0% 86.60% 2.40% 0.80% 1.50%
90-119 0% 0% 0% 87.70% 1.60% 2.80%
120+ 0% 0% 0% 0% 3.10% 11%
Charged Off 0% 0.30% 4.60% 7.30% 93.40% 79.50%

Loans in this category are largely representative of the overall market, and as expected, their transition probabilities will be quite similar. Loans which are currently in the 1-29 dpd bucket have a 13.6% chance of rolling into the 30-59 dpd bucket next month.

Finally for High loans we observe the following matrix:

pic4

Status Current 1-29 30-59 60-89 90-119 120+
Current 97.80% 22.50% 4.20% 1.10% 0.50% 1.80%
1-29 2.20% 57.10% 3.20% 0.50% 0.20% 0.20%
30-59 0% 20.20% 8.60% 1.40% 0.40% 1%
60-89 0% 0% 80.90% 3.20% 0.90% 1.80%
90-119 0% 0% 0% 87.60% 2.10% 3.90%
120+ 0% 0% 0% 0% 8.50% 7.70%
Charged Off 0% 0.20% 3.10% 6.10% 87.30% 83.60%

Loans in this category have a 20.2% chance of going from 1-29 dpd to 30-59 dpd in the next month. Relative to the rest of the market, one missed payment from a High loan is more indicative of an eventual charge-off.

Looking at roll rates stratified by term and loan interest rate is only one way of looking at overall roll rates of a portfolio. Other potential strats include origination FICO, annual income, DTI, and any other loan characteristics provided by the originator. Having a standardized roll rate measure is not only helpful in performing analytics on individual portfolios but for ongoing monitoring of roll rates in the broader market as well.

  • David Brown

    How do the 36-month roll-rates compare to the 60-month loans? That would be a cool blog follow-up.

  • rupesh

    what code did you used to calculate the roll rate?