### Author Topic: Loan Status Markov Chain  (Read 11859 times)

#### Fred

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##### Loan Status Markov Chain
« on: July 11, 2013, 02:10:14 AM »
Got a few of hours of spare time last week, and analyzed LC payment data to construct the transitional probabilities of the various loan status (i.e., Markov Chain -- http://en.wikipedia.org/wiki/Markov_chain).  See attached.

Some things to consider:

1. Each node (state) represents a Loan Status in Lending Club.

2. Current is the root state; all loan initially starts in this state.

3. Fully Paid and Charged Off are the sink states; once a loan comes to this state it cannot get out.  This is supported by data.

4. For each state, the total percentage of all out-going transitions (out arrows) is 100%.

5. The percentages are generated using the monthly payment data.  For example, loan that was Current in month m, and then Fully Paid in month m+1 is included in the arrow from Current to Fully Paid.  The number 1.61% represents the probability of loans that are Current this month to become Fully Paid the following month.

6. Looking at the out-arrows of initial state Current, there is a 97.59% probability the loan will stay Current next month, 1.61% will be Fully Paid next month, etc.

There are a lot of interesting "transitions" in the diagram; but I'd let the data speak for itself.  Anyone with payment data should be able to reproduce this.  Naturally, this chain will change slightly every month as additional payment data becomes available.

Hopefully, this is useful to some of the Forum readers.

#### brycemason

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##### Re: Loan Status Markov Chain
« Reply #1 on: July 11, 2013, 02:50:26 AM »
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.

#### rawraw

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##### Re: Loan Status Markov Chain
« Reply #2 on: July 11, 2013, 06:14:46 AM »
Man I love threads like these.  Interesting stuff Fred and Bryce -- I was unfamiliar with this before this thread.

#### yaoyao

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• Posts: 102
##### Re: Loan Status Markov Chain
« Reply #3 on: July 11, 2013, 08:07:27 AM »
There is only 0.0001% chance the current loan would be in IGP next month?  I would think that the probability would be much higher.

#### Rob L

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##### Re: Loan Status Markov Chain
« Reply #4 on: July 11, 2013, 09:35:55 AM »
Why is it that every time I think of Markov Chains I think of frogs and lilly pads? Is that the classical example they throw at you in school?

#### lender_john

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• Posts: 88
##### Re: Loan Status Markov Chain
« Reply #5 on: July 11, 2013, 10:17:07 AM »

Its an interesting way to to think about it, but I have to agree with Bryce.

Even if it was memoryless, which it isn't, this doesn't account for some of the major payment delays recently that are entirely due to processing.  I believe that May 8th?was a big one when I had dozens of loans go into grace period, only to be paid within the next day or two.

#### Fred

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##### Re: Loan Status Markov Chain
« Reply #6 on: July 11, 2013, 10:42:56 AM »
The next state is dependent on the sequence of event preceding it...

This is the core of our differences.   In my opinion, loan status transition is similar to the price transition in stock market.

Yes, there can be a lot of price "history" that might determine what the next price should be, but as you might recall in Black Scholes option pricing, and the Brownian motion assumption, this can also be considered memoryless.

However, the Brownian motion assumption (for stock prices) has also been challenged in the past; and yes, hedge funds make a lot of money based on "momentum" or "mean reversion" strategies; nevertheless, the Black Scholes provides a convenient analytic tool to use.  This is a goal of this exercise.

#### Fred

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##### Re: Loan Status Markov Chain
« Reply #7 on: July 11, 2013, 10:45:40 AM »
There is only 0.0001% chance the current loan would be in IGP next month?  I would think that the probability would be much higher.

Yep, this is one of those "interesting" transitions I referred to in my original post.

The "cure transitions" -- transitions from late16-30, late31-120, and Default to Current -- are also interesting.

#### GS

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• Posts: 413
##### Re: Loan Status Markov Chain
« Reply #8 on: July 11, 2013, 11:26:07 AM »
Did you pick a certain date for all notes (I.e. m = 1/1/2013), or is m based on the something like the posting date of each individual note?  The later might explain why GP notes are so low, since you'd expect notes to either be 15-30 days late, or back to current, by m+1.

#### Fred

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##### Re: Loan Status Markov Chain
« Reply #9 on: July 11, 2013, 11:44:00 AM »
Did you pick a certain date for all notes (I.e. m = 1/1/2013), or is m based on the something like the posting date of each individual note?  The later might explain why GP notes are so low, since you'd expect notes to either be 15-30 days late, or back to current, by m+1.

I used all LC monthly payment data (not available in LC site, but Zachs has a link to this); I believe it has complete payment information from the beginning of LC until sometime early 2013.  I'll confirm when I get home.

#### TonySaunders

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##### Re: Loan Status Markov Chain
« Reply #10 on: July 11, 2013, 01:19:55 PM »
There is no transition from "Grace Period" to "Late"?

#### rawraw

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##### Re: Loan Status Markov Chain
« Reply #11 on: July 11, 2013, 01:41:50 PM »
Why don't they add up to 100% at every node?

#### Fred

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##### Re: Loan Status Markov Chain
« Reply #12 on: July 11, 2013, 01:48:08 PM »
There is no transition from "Grace Period" to "Late"?

This was another interesting phenomenon based on data.  For all the monthly payments that started from the Grace Period status, the next status was either stayed in Grace Period (80%), or became Current.

What is not obvious from the diagram is the size of each node.  The number of payments that start from Grace Period status is actually much smaller than the number of payments that start from, say, Current.

Also, it is important to note, that for a 3-yr loan that consistently stayed in the Current status for 36-month, this is reflected as 36 counts in the self loop Current to Current transition.

#### Fred

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##### Re: Loan Status Markov Chain
« Reply #13 on: July 11, 2013, 01:53:09 PM »
Why don't they add up to 100% at every node?

For each node, only the outgoing transitions (including the self-loop to the same state) should add up to 100%.  Some small rounding errors might appear, but errors should be less than 0.01%.

I tried to be careful when copying data to this diagram, so did it miss something?

#### rawraw

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##### Re: Loan Status Markov Chain
« Reply #14 on: July 11, 2013, 02:48:28 PM »
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?