Loan Status Markov Chain

[Fred]

I was misreading the loops that circle back on themselves.  What does that even mean?  For example, its 60.58% in default.  It was in default and kept going into default?  And only 2% got charged off?

It means: loans that are in Default this month will stay in Default next month 60.58% of the time.

Perhaps it is clearer if we use the conditional probabilty notations:

Prob(next_state = Default    | current_state = Default) = 0.6058
Prob(next_state = Current    | current_state = Default) = 0.1731  -- this is an eye-opening to me.
Prob(next_state = Late16-30  | current_state = Default) = 0.0096
Prob(next_state = Late31-120 | current_state = Default) = 0.1923
Prob(next_state = ChargedOff | current_state = Default) = 0.0192

[TonySaunders]

There is no transition from "Grace Period" to "Late"?

This was another interesting phenomenon based on data. 

...

What is the source of the data you are using? Is it your own set of notes?

[Fred]

What is the source of the data you are using? Is it your own set of notes?

See this thread: http://www.lendacademy.com/forum/index.php?topic=1057.0

[TonySaunders]

What is the source of the data you are using? Is it your own set of notes?

See this thread: http://www.lendacademy.com/forum/index.php?topic=1057.0

Well, that explains it. "In grace period" appears in that entire gigantic file a total of 5 times, all for the same note, which went back to current after the 5th month. It makes a certain kind of sense that IGP wouldn't appear in the file (except for that one weird note), since a delinquent note can't possibly be in it's grace period a month after missing a payment, it would have to be either current or late.

In any case, this makes the data in the Markov chain regarding IGP misleading. The .00001% is for the ONE time it has ever happened in the entire history of LC (somehow). The 20% is for the ONE time it ever went back (out of 5).

[rawraw]

I was misreading the loops that circle back on themselves.  What does that even mean?  For example, its 60.58% in default.  It was in default and kept going into default?  And only 2% got charged off?

It means: loans that are in Default this month will stay in Default next month 60.58% of the time.

Perhaps it is clearer if we use the conditional probabilty notations:

Prob(next_state = Default    | current_state = Default) = 0.6058
Prob(next_state = Current    | current_state = Default) = 0.1731  -- this is an eye-opening to me.
Prob(next_state = Late16-30  | current_state = Default) = 0.0096
Prob(next_state = Late31-120 | current_state = Default) = 0.1923
Prob(next_state = ChargedOff | current_state = Default) = 0.0192

Oh okay. I'll have to look closer when I'm not on my phone to make sure that clears up the totaling of nodes

Sent from my SAMSUNG-SGH-I747 using Tapatalk 2

[Fred]

As I indicated in the beginning, the analysis was done based on the payment data, not on the daily snapshot.  If LC provides this daily snapshot data, that would be another good exercise to work on.

I was actually focusing more on the various paths & probabilities to the Charged Off state, because this is where the pains reside.

[TonySaunders]

I do not believe that loan repayment can be modeled via a Markov process because the situation does not meet a fundamental assumption about the system. It is not memoryless. The next state is dependent on the sequence of event preceding it, and thus the transition probabilities are non-constant. The easiest counter example is the fact that once loans become seasoned with a good repayment history, their future chance of being late is greatly reduced.

Good thoughts though. I looked at this carefully a while back when you had mentioned it.

I think the model is useful/interesting, the caveat is pretty dangerous though. If anyone were to use a single metric like "what is a note's status right now" against this chart to predict future performance, then they are obviously taking too naive an approach. I mean, be serious, ONE metric, that's silly.

On the other hand, if you want to model the movement of notes on LC in general and independently of such naive evaluation of individual notes, then I think it's useful enough to consider, and pretty interesting.

[gamassey]

Why is a loan much more likely to go from current to over 31 days late (.77%) than it is to go from current to 16-30 days late (.03%).  I would think the opposite would be true.  Not even sure how it can go from current to over 31 days late.

[Fred]

Good question.

Most of the situations where a loan jumped from Current to Late31-120 happened when some payment was made, but it did not cover the full amount of Principal + Interest + Fees (if any).  It seems LC kept the Current status on the month when the partial payment was made, but assigned the Late31 status the following month.

See for example Loan ID 69251, which was Current on 2009-11-01, but was Late (31-120 days) on 2009-12-01.  It seemed some payment was made late, but it was not enough to cover the additional $15 late fee.

[gamassey]

Thanks Fred, that is very interesting.  Not all what I would have expected to see.

Allen