### Author Topic: Effect of Previous Delinquencies on Probability of Default  (Read 8134 times)

#### dompazz

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##### Effect of Previous Delinquencies on Probability of Default
« on: December 15, 2015, 09:17:01 PM »
I've just started digging into the historic data provided by Lending Club.  I'm currently looking at 36 month notes and only on the data prior to 2015.

I had assumed the the variable delinq_2yrs would be positively correlated with defaults.  I'm finding exactly the opposite.

 Default nLoans 0 311,640 1 26,285

Breaking Defaults downs by having a delinquency reported (0/1 for 0 and >0 delinquencies)

 has_delinq Pct Default nDefaults 0 6.48% 21,883 1 1.30% 4,402

If you look at the above table breaking down for each value in delinq_2yrs, you get a monotonically decreasing % defaults until you get to the point of only having a few hundred loans with that reported amount.

Anyone have a good "story" for why this could be?

#### Fred

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##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #1 on: December 17, 2015, 04:08:05 AM »
I think a few people in this forum has done extensive "factor analysis"-- https://en.wikipedia.org/wiki/Factor_analysis -- on all the attributes in LC historical data.  Not sure if delinq_2yrs really has a negative coefficient, and if it is statistically significant.

Good luck.

#### dompazz

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• Posts: 224
##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #2 on: December 17, 2015, 08:34:41 AM »
I've run some basic logistic regressions, sampled and not, and with other factors included, the coeficient is significantly negative.  As a modeler, anything that doesn't make economic sense, I would generally toss out.  Trying to understand if there is a world where this makes sense.

One thing I have come up with is LC's underwriting possibly rejects borrowers with higher delinquencies with a higher probability to default.  Those that make it through are better credit risks and have a lower probability to default.

#### jennrod12

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• Posts: 134
##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #3 on: December 17, 2015, 09:26:15 AM »
If I read that right, you are looking at loans that defaulted and what % of them were from borrowers with delinquincies?

Did you look at all loans from borrowers with delinquincies and what % of them defaulted?

Jenn

#### dompazz

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• Posts: 224
##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #4 on: December 17, 2015, 11:00:46 AM »
Did you look at all loans from borrowers with delinquincies and what % of them defaulted?

Jenn

7.38% of borrows with delinquencies eventually default (4,400/59,600) versus 7.86% of borrowers without delinquencies (21,900/278,300).  That is a significant difference and is what is getting picked up in the logistic regressions.

#### jennrod12

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• Posts: 134
##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #5 on: December 17, 2015, 09:21:08 PM »
Interesting info,

Is there a difference when looked at by the borrower's number of delinquencies or how many months since the last delinquency?

Jenn

#### AnilG

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##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #6 on: December 17, 2015, 11:41:25 PM »
7.38% of borrows with delinquencies eventually default (4,400/59,600) versus 7.86% of borrowers without delinquencies (21,900/278,300).  That is a significant difference and is what is getting picked up in the logistic regressions.

How did you determine default difference is significant?

Your borrower count with delinquencies and without delinquencies has large difference. Have you investigated why is that?

Are there any characteristics that are very different between the two groups that might influence your findings? What is the vintage, grade, and interest rate profile for these groups?

Have your checked the fully paid, delinquencies, and current stats for same group of borrowers?

Lending Club Past Loan Performance by Delinquencies in Last 2 Years
https://www.peercube.com/histperf/perfbyattr/dq_2yrs
---
Anil Gupta
PeerCube Thoughts blog https://www.peercube.com/blog
PeerCube https://www.peercube.com

#### dompazz

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##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #7 on: December 21, 2015, 09:19:37 AM »
Have your checked the fully paid, delinquencies, and current stats for same group of borrowers?
I have not and will do so.  Off the top of my head, I'm betting this will "fix" it.

*Jeopardy Theme*

Adding a filter for loan_status="Fully Paid" or default the proportions reverse, more like I expected.  15.53% of borrowers without delinquencies eventually default vs. 17.43% with delinquencies.

Are there any characteristics that are very different between the two groups that might influence your findings? What is the vintage, grade, and interest rate profile for these groups?

However, if I add other variables (dti, grade, and purpose) into a logistic regression, the effect is negative.  That is, having a past delinquency reduces default probability.  The effect is marginal -- just barely significant at the 10% level.

This result seems to hold for the full sample as well as a sampled subsets.

#### lascott

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##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #8 on: December 21, 2015, 10:58:41 AM »
That is, having a past delinquency reduces default probability.
So in layman's terms more people learned their lesson from past "irresponsible" (some circumstantial) behavior more so than people falling into the same trap of debt incurred over income to cover it. Interesting.
Tools I use: (main) BlueVestment: https://www.bluevestment.com/app/pricing + https://www.interestradar.com/ , (others) Lending Robot referral link: https://www.lendingrobot.com/ref/scott473/  & Peercube referral code: DFVA9Y

#### hoggy1

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• Posts: 401
##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #9 on: December 21, 2015, 01:55:16 PM »
As I understand it, a Delinquency is 30 or more days late and I don't count one in the last two years against the borrower. By contrast a major derogatory is more than 120 days late and I don't buy notes with any.
Steve

#### Fred93

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##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #10 on: December 21, 2015, 06:05:53 PM »
However, if I add other variables (dti, grade, and purpose) into a logistic regression, the effect is negative.  That is, having a past delinquency reduces default probability.  The effect is marginal -- just barely significant at the 10% level.

This is not an easy variable to understand.  Having zero delinquencies does not necessarily mean you are a "responsible" borrower who has paid back loans in the past.  It can also mean you are an inexperienced borrower who has never borrowed, so never had anything to pay back.  So zero has two meanings, with very different implications.  This distinction can be made apparent when you include other variables.  Perhaps variables such as total accounts or first credit date will help.  (First credit date isn't easy either, as it has to be transformed.)

#### brycemason

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• Posts: 801
##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #11 on: December 23, 2015, 04:32:15 AM »
Being stumped by covariance is so 2011 on this forum, but you caught me in a good mood after a pleasant 16-hour day of building loan servicing logic. Data: LC 9/30/2015 extract, matured policy code 1 36-month loans between 3 and 5 years old (out of convenience); various other exclusions I'll cite later.

Define prior_delinq to be 1 just in case delinq_2yrs is greater than 0. Useful practice because of the few data points past 1 anyway. Avoids estimation issues.

. tab delinq_2yrs

delinq_2yrs |      Freq.     Percent        Cum.
------------+-----------------------------------
0 |     39,617       89.42       89.42
1 |      3,493        7.88       97.31
2 |        779        1.76       99.07
3 |        243        0.55       99.62
4 |         73        0.16       99.78
5 |         47        0.11       99.89
6 |         23        0.05       99.94
7 |         12        0.03       99.97
8 |          3        0.01       99.97
9 |          4        0.01       99.98
10 |          3        0.01       99.99
11 |          4        0.01      100.00
18 |          1        0.00      100.00
------------+-----------------------------------
Total |     44,302      100.00

Observation (single-variable analysis): Having a prior delinquency increases the chance of a charge off event.

Logistic regression                               Number of obs   =      44302
LR chi2(1)      =      27.03
Prob > chi2     =     0.0000
Log likelihood = -16924.115                       Pseudo R2       =     0.0008

------------------------------------------------------------------------------
chargeoff |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
prior_delinq |   .2302795    .043396     5.31   0.000      .145225    .3153341
_cons |   -1.94617    .015193  -128.10   0.000    -1.975947   -1.916392
------------------------------------------------------------------------------

Observation (Multi-variate analysis): This relationship vanishes when controlling for the four horsemen of the consumer credit scoring apocalypse.

Logistic regression                               Number of obs   =      44302
LR chi2(5)      =    1575.80
Prob > chi2     =     0.0000
Log likelihood = -16149.729                       Pseudo R2       =     0.0465

--------------------------------------------------------------------------------
chargeoff |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
prior_delinq |  -.0021604    .044922    -0.05   0.962    -.0902059    .0858851
fico_range_low |  -.0153585   .0005158   -29.78   0.000    -.0163695   -.0143476
inq_last_6mths |   .1900362    .013459    14.12   0.000      .163657    .2164155
emp_na_slf_ret |   .4404685   .0522608     8.43   0.000     .3380393    .5428978
loan2inc |   2.286919   .1299917    17.59   0.000      2.03214    2.541698
_cons |   8.213554   .3604598    22.79   0.000     7.507065    8.920042
--------------------------------------------------------------------------------

« Last Edit: December 23, 2015, 04:34:01 AM by brycemason »

#### dompazz

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• Posts: 224
##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #12 on: December 23, 2015, 09:38:39 AM »

Being stumped by covariance is so 2011 on this forum, but you caught me in a good mood after a pleasant 16-hour day of building loan servicing logic. Data: LC 9/30/2015 extract, matured policy code 1 36-month loans between 3 and 5 years old (out of convenience); various other exclusions I'll cite later.

Gee, glad I caught you in a less passive aggressive a-hole-ish mood.  Lucky me!

Define prior_delinq to be 1 just in case delinq_2yrs is greater than 0. Useful practice because of the few data points past 1 anyway. Avoids estimation issues.
If you read the first post, you will see I did just that.  Not my first time at the modeling rodeo, just the first time in this context.

Observation (Multi-variate analysis): This relationship vanishes when controlling for the four horsemen of the consumer credit scoring apocalypse.
Pretty much what I said in my last post.  Once controlling for other variables, the effect reverses and is only barely significant.  I have no doubt that adding the variables you had, I would see the same thing.

So at the end of the day, thanks for providing backhanded help.  Your regression output actually does help me move along as I search for variables.  And I'm glad I provided you a place to vent your frustration at the the end of the day.

#### brycemason

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• Posts: 801
##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #13 on: December 23, 2015, 10:05:29 AM »
You are super welcome! Don't take my snark personally .

#### nonattender

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##### Re: Effect of Previous Delinquencies on Probability of Default
« Reply #14 on: December 23, 2015, 04:12:32 PM »
*giggle*  Welcome, Dompazz.  Stick around, I think you're gonna fit in just fine!
A little nonsense now and then is relished by the wisest men.