Print

[lenderguy]

Ok.  For a class project, I decided to calculate the roll rates of Prosper loans.  In one of Prosper's data dumps, they provide a table of all payments made.  Right now, the calculations are done on a payment by payment basis.  The significance is that a loan consists of more than one payment.  This is a "Beta" version of my project, so I will obvious make some changes to data processing and presentation. 

Prosper records a current payment on the day a loan is issued, so all loans start out as current.  Loans are counted only The way one should read the data is to look down the column for the status in a current month, and look across the row for the status in the next month.  The intersection are the odds of that occurrence happening.  For instance, a payment that is presently one month late has a 72.2% chance of being 2 months late next month.

The data does suggest that just over half of the payments that go < 15 recover, but almost two thirds (65.7%) of the loans that go late go one month late.

Because of the way Prosper handles 4+ month late loans, I have some issues with the way to present that data.  Since it can go multiple months in that stage, I'm not sure how to show that statistic in a meaningful way.  (I could actually show rows for 5 mos, 6 mos, 7 mos,etc if I felt like it.  I just didn't feel like it, because it takes a bit more work.)

The natural extension of this data is to do a long run analysis of the table, and it would show the % of loans that pay off early, pay off on time, default, or file bk.  The odd thing is, in the long run, we don't concern ourselves about the nuances of any particular payment -- the long run equilibrium has the same values for each column.

Current   <15        Late   1 mo        2 mo     3 mo     4 mo    Early PIF   FT PIF   BK   Default

Current   91.3%   7.40%   0.00%   0.00%   0.00%   0.00%   0.00%   1.30%   0.00%   0.00%   0.00%

<15        52.0%   1.30%   46.4%   0.00%   0.00%   0.00%   0.00%   0.20%   0.00%   0.00%   0.00%

Late        31.4%   2.60%   0.20%   65.7%   0.00%   0.00%   0.00%   0.10%   0.00%   0.00%   0.00%

1 mo       13.4%   10.1%   2.90%   1.30%   72.2%   0.00%   0.00%   0.10%   0.00%   0.00%   0.00%

2 mo       2.80%   4.50%   0.80%   7.50%   0.90%   83.40%   0.00%   0.10%   0.00%   0.10%   0.00%

3 mo       1.90%   2.80%   0.00%   2.50%   3.30%   0.70%   88.3%   0.00%   0.00%   0.40%   0.00%

4 mo       0.70%   3.00%   0.10%   1.40%   0.20%   1.00%   69.5%   0.00%   0.00%   0.90%   23.2%

[Fred93]

Shouldn't each row sum to 100% ?  The "late" row sums to 97.2%

[lenderguy]

Shouldn't each row sum to 100% ?  The "late" row sums to 97.2%

thanks...fixed it.

[ira01]

According to this data, 6.4% of 4 month late loans overall improved the next month.  So sb92075's data in this thread showing a monthly rate of about 9.5% in the last 6 weeks (93 of 697 4+ month lates improving during a 6 week period) shows about a 50% improvement over the historical average lately.  I wonder how much of that is caused by recent events (e.g., the New Agency Test and the Penncro/AmSher substitution), and how much is caused by the historical data containing NC's and "low" (now cut-off) HR's (who presumably are more likely to default than higher grade borrowers)?

[lenderguy]

According to this data, 6.4% of 4 month late loans overall improved the next month. 

No, it doesn't... be very careful how you interpret that data.  I know what those %'s add up to, but what they mean and what you think it means are two different things.  FWIW, the raw number associated with the "habitual" 4+ mo lates is 4043 (that equates to the 69.5% figure you see in the last row.)  The raw number associated with Current/Current 91.3% is 129863.  Given that Prosper has only originated 18,836 loans, we have to be careful how we interpret that.  (The data set I work off of has 261,908 entries.)  I guess one way to think of what that 4043 number means is that every time a single loan hangs in there an extra month, it increases that count.  So a loan that is in the 4+ stage for 8 months would count 8 times.

I suppose I could recode my reader to count a loan only once when it reaches the 4+ stage.

I wonder how much of that is caused by recent events (e.g., the New Agency Test and the Penncro/AmSher substitution), and how much is caused by the historical data containing NC's and "low" (now cut-off) HR's (who presumably are more likely to default than higher grade borrowers)?

Those are projects for another class this quarter... I want to map the extended credit details onto actual performance and do some sort of regression analysis.

[HollowOak]

Very interesting work. If you don't mind sharing, what course/degree are you taking at university?

I played with this a little, to try and understand it better. I've attached a screenshot from my spreadsheet program that has formatting and some color applied to it.

The normal status of a loan should be "current." Does a loan that runs to maturity have one count in this column and then 1 count in the FT_PIF column? In other words, for a loan that performs as we all hope, should I see 97% in the "Current" column and 3% in the "FT_PIF" column?  That's about the only way I can explain the low numbers I see in the "Early PIF" column, since I looked at my stats and a few other long-term lenders and we all have about 15-20% of our loans showing as having being repaid.

Now I assume the bright green "Current" data point (91%) is what we really want our loans to show up as. After that it becomes a little bit unclear. I suppose the yellow diagonal line is to show the loans that deteriorate, in other words, of all the loans, about 7% will then go "<15 late." Of this 7% about 52% (or 4% of the 7%) will flip back to "current" and 46% will deteriorate further into"late." Then of the 46%, 66% will deteriorate into "1 month late," and so on? Is this interpretation correct? This seems to be extraordinary low rates, and I suppose it can be accounted for only if you count all the current loans for each presentation of current.  So in effect you're counting state changes in the Prosper loans database?  That would also then account for the 70% of "4Month late" loans remaining in this status and only 23% seemingly exit this process?

If my understanding is incorrect, would you talk me (and others as uncomprehending as I), through your table in more detail?

[lenderguy]

Very interesting work. If you don't mind sharing, what course/degree are you taking at university?

I'm studying for a Masters of Science - Quantitative Analysis.  Think Doug Fuller.  This project is for a course I'm taking in Stochastic Modeling.  My next project (for a different course) is performing a regression analysis of the extended credit scoring against default rates.  One thing I want to examine is whether the PD07 extra data makes a difference in defaults.

The normal status of a loan should be "current." Does a loan that runs to maturity have one count in this column and then 1 count in the FT_PIF column? In other words, for a loan that performs as we all hope, should I see 97% in the "Current" column and 3% in the "FT_PIF" column?  That's about the only way I can explain the low numbers I see in the "Early PIF" column, since I looked at my stats and a few other long-term lenders and we all have about 15-20% of our loans showing as having being repaid.

This is hard to think about conceptually, because there are a couple of regularly recurring states.  The FT_PIF column (I don't know why I didn't explain that earlier) stands for "full term pay in full."  We have had no loans reach full term, so there should be zeros in that column.  Early PIF is early pay in full.  Because of regularly recurring states, a loan can run up 36 counts in the current column before transition to a "1" in the PIF column.

As I said about the difficulty in conceptualizing this, and this is something I have to talk to my prof about, is whether I defined my states properly.  See, this is a "month to month" roll rate.  The way you read the data is looking at that first row and column and saying "if a payment is current this month, it has a 97% chance of being current next month."  But a loan can only become "FT PIF" once it has made the 36th payment.  The way the math behind this model really works, if I want to differentiate between payoff states, I have to have a state for month 36.

So to directly comment on the numbers we "should" see, I'm not sure... a loan would rack up 36 counts in the current column before transitioning over to the "FT PIF" column.

Now I assume the bright green "Current" data point (91%) is what we really want our loans to show up as. After that it becomes a little bit unclear.

Actually, conceptually, the lines <15, late, 1 mo, 2 mo, 3 mo lates are the easiest to understand.  They don't contain any regularly recurring states in ways that "Current" and "4+" do.  Remember, a loan that is always current will count 36 times in the current column and then once in the FT PIF column.  The 4+ column holds loans that have sat there for several months, and every month a single loan hangs out there, it racks up another count in the column before changing states. 

I suppose the yellow diagonal line is to show the loans that deteriorate, in other words, of all the loans, about 7% will then go "<15 late."

Technically, what the chart shows is that if a loan (more technically the payment) is current one month, it has a 7% chance of going <15 the next month.

Of this 7% about 52% (or 4% of the 7%) will flip back to "current" and 46% will deteriorate further into"late." Then of the 46%, 66% will deteriorate into "1 month late," and so on? Is this interpretation correct?

No.  The proper interpretation is "for a payment in state x, the odds of it being in state y next month are z%."  You might ask me what the difference is, but I really don't know.. 

This seems to be extraordinary low rates, and I suppose it can be accounted for only if you count all the current loans for each presentation of current.  So in effect you're counting state changes in the Prosper loans database?  That would also then account for the 70% of "4Month late" loans remaining in this status and only 23% seemingly exit this process?

Yes, I'm counting state changes, with the understanding that some states are recurring.

If my understanding is incorrect, would you talk me (and others as uncomprehending as I), through your table in more detail?

If you want more detail, PM me your phone number and a good time.  I'll call you.  This is a lot to write, and sometimes not intuitively obvious to understand.

[Mtnchick]

Think Doug Fuller.

Don't belittle yourself - you know proper grammar and spelling.

[Tokyo Joe]

Ok.  For a class project, I decided to calculate the roll rates of Prosper loans. 

Glad to see you're getting some practical benefit from prosper after all this time.  I bet you're kicking ass at school this semester.

[HollowOak]

Thanks for the lengthy reply. I think I understand the data sufficiently now.

[yankeefan]

That looks like a useful analysis of roll rates.  Thanks for sharing.

A couple of questions-
At what point in the month are you capturing the data?  This matters most for the current to <15, the <15 to late, and the late to 1 month late roll rates.  A loan monthaversary  (we made that up in the early universal life days) look would seldom have a <15 status, for instance.

An additional view at the loan level of "what percentage of 1month lates ever catch up to current" etc. would be useful, but a different job.

Differential analysis by credit grade or other indicators would be of interest, but would probably quickly deteriorate into noise.


When you're ready to publish, I'd like a copy.  I'll pm you my e-mail.

[lenderguy]

A couple of questions-
At what point in the month are you capturing the data?  This matters most for the current to <15, the <15 to late, and the late to 1 month late roll rates.  A loan monthaversary  (we made that up in the early universal life days) look would seldom have a <15 status, for instance.

I captured state changes as they occurred.  In that regard, I errored when I said these are monthly roll rates, because, you're right... a loan month aniversary would seldom have a < 15 status.  I was at a loss as to how to present that data, as recovery rates from <15 and late are of interest to us.  Perhaps that should be presented separately from the "monthly" roll rates?

An additional view at the loan level of "what percentage of 1month lates ever catch up to current" etc. would be useful, but a different job.

Can't that be inferred from the information provided?

Differential analysis by credit grade or other indicators would be of interest, but would probably quickly deteriorate into noise.

I've been thinking about that, as it would be interesting to see how the "real" stats compare against what Prosper usees in their projected calculations.

When you're ready to publish

You're serious, aren't you?

[yankeefan]

An additional view at the loan level of "what percentage of 1month lates ever catch up to current" etc. would be useful, but a different job.

Can't that be inferred from the information provided?

Maybe- I was thinking that, since we don't know how long loans stay in the 4+ state, we can see the monthly cure rate, but not the "percent of policies ultimately cured." 

Quote
When you're ready to publish


You're serious, aren't you?

There must be, at least, some conferences which you could submit the work to.   Most of the Prosper-generated "stats" would qualify for "The Journal of Irreproducible Results", but yours should be of interest beyond this small group.

[lenderguy]

Maybe- I was thinking that, since we don't know how long loans stay in the 4+ state, we can see the monthly cure rate, but not the "percent of policies ultimately cured." 

Well, isn't a property of a Markov chain the ability to derive the steady state equilibrium and determine the % of loans that ultimately end up in each absorbing state?

There must be, at least, some conferences which you could submit the work to.   Most of the Prosper-generated "stats" would qualify for "The Journal of Irreproducible Results", but yours should be of interest beyond this small group.

So, which school faculty should I talk to?  People in the finance department?

[yankeefan]

I can spell Markov chain, but that's all I know about them

The Finance department sounds like the way to go.

Also see Prosper's 3rd party app pages  http://www.prosper.com/tools/3rdParty.aspx

Especially note the Stanford business school paper.