Mike at ProsperousLands responds to my exponential decay post.  I will be commenting/responding formally in the near future, but one quick comment… my 1 month late or worse curves are real and cumulative. Meaning they reflect what actually happened and if we have enough data they will never go down.  The exponential decay was an attempt to forecast defaults from month 11-36.  His response is unedited and starts in the next paragraph. 

RateLadder proposed an exponential decay model for predicting the 3 year default rates on Prosper loans in a post on his site rateladder.com. I was quite skeptical that this was a safe model to use since it baked in a pretty hefty assumption. After a little back in forth, he invited me to respond…

By modeling default rates using an exponential decay model, you’re assuming that X% of the remaining loans will go bad in a certain time period. Of the remaining good loans, the same percentage will go back after the next time period. For example,  if 10% of the loans will sour every year. If you started with 100, you’d expect 90 still good after 1 year, 81 still good after 2 years, and 73 still good after 3 years. But will the default rate be constant? I think not, and, by looking at the financial cycle of the borrower, we can think through why.

When the loan is funded, the Prosper borrower receives a big chunk of change – up to $25,000. They’re flush with cash and can easily make the loan payments even if things not handled well. I’d expect lower than typical default rates. The extreme case is someone who borrowed the money and didn’t do a thing with it. For one of my loans (picked at random), the borrower could make over 2 years worth of payments just by sitting on the cash. Not financially smart, but illustrative on how repayment can look good even when it’s not sustainable.

After some time, the borrower will either be successful in their loan use (pay-off credit cards, start business) or not (rack up new credit card bills, business fails). This is loan payment crunch-time. The financially weak borrowers will default. Compared to the cash-flush period, I expect defaults to run higher as financial Darwinism hits and the weaker loans go bad. Following this crunch period and financially weaker borrowers falling out, I would expect that the remaining loan pool would be stronger with fewer defaults. There will be defaults but the remaining loans are more responsible and financially stable with the weak ones already in default.

Thus far, we have some fabulous hand waving. It looks like common sense, but common sense is sometimes deceiving.  Moody’s has kindly provided some insight and investigation to help with the common sense. In section of their 1999 Global Credit Research report discusses techniques used to model uncollateralized bond default rates, they discuss an “aging effect” and how default rates vary with time in a way very similar to the one hand-waved above. If it’s good enough for them, there must be something to it.

The best test is to look at Prosper’s loan data. Does it show aging effects? For this, the loans were placed into age groups based on month and the 3-year default rate predicted using RateLadder’s exponential decay mode (ugly calculation: r = 1-e^(ln(pct_good_loans)/t). If the default rates change with age, there’s an indicator for caution in using the exponential model.

 

As we can see, there are large variations in the loan failure rates, even after ignoring the first few months. Equally, most loan grades show some “aging effect”. D is the most profound with a ramp up to a crunch followed by a slow decline. 

But is the exponential decay model good enough? For the AA space, predictions for the 3-year default rates range from 1.5% to 9% (and more) based on with age group is used. The D space shows variations from 15% to 38%. HR is ugly regardless of what we do – the lender is screwed regardless of how it’s modeled. From these curves, it is difficult to determine which predicted default rate should be used. This validates that the “aging effect” should be considered and makes it a dangerous model to use without a more careful understanding of the dynamics involved.

Related Posts

• Big Prosper Changes -- 2nd Loans, Authenticated API, 0% on AA, 36% Max Rate, and Portfolio Plans Big changes for Prosper today in new release... Borrowers can now have second loans Authenticated API for access to extended credit and a lender's loans for lenders 0% servicing fee on AA credit In states where rates aren't capped the new maximum is 36% Portfolio Plans might be the biggest change of......
• Best of RateLadder 3rd Quarter 2007 This is a time of year reflection and goal setting for the year to come.  I think it has been a very interesting and prosperous year. Here are some of my best and/or most popular posts from the 3rd quarter of 2007… July 2007: WSJ Features ProProsper in P2P Lending......
• What is my Internal Rate Of Return on Prosper? Why do I want to calculate my Internal Rate of Return (IRR)?  To make sure it is higher than my cost of money - ergo a good investment.  I claim that my cost of money is 5% which I can earn in an Internet savings account.  So my IRR needs......
• Default Rate: It's Not Just If a Loan Defaults, But When I had a very interesting email exchange with RGF.  (I emailed him after using his forum posts in articles last week). Here is a portion of that email exchange on default rates over time and their affect on yield. RGF: Default rate:  It's not just if a loan defaults, but......
• Best of RateLadder 2nd Quarter 2007 This is a time of year reflection and goal setting for the year to come.  I think it has been a very intertesting and prosperous year. Here are some of my best and/or most popular posts from the 1st 3 months of my blog… April 2007: Adam Nash Merged with......

Related Websites

• are American kids stupid about personal finance? American kids are stupid about financial matters. That's what a Federal Reserve study says. From the Washington Post: High school seniors, on average, answered correctly only 48.3 percent of questions about personal finance and economics, according to a nationwide survey released Wednesday by the Federal Reserve. That was even lower......
• Home Owners Getting Shafted With Nightmare Loans Here's a must read article from BusinessWeek on Nightmare Loans. Jennifer and Eric Hinz of Somerset, Wis., are feeling the squeeze. They refinanced out of a 5.25% fixed-rate, 30-year loan in June, 2005, and into an option ARM with a 1% teaser rate from Indymac Bank. The $1,483 payment for......
• Introduction to Mortgages pt 5 of 5 This is part five in a five part series on what you need to know about mortgages before you buy a home. The housing market is an interesting beast, because it comes and goes, rises and falls, allows some people to flourish and brings others to ruins. If you want......
• The Peer to Peer Lending Guide (P2P Lending) What is Peer to Peer Lending? Peer to peer lending (P2P Lending) simply refers to the process of individuals loaning each other money directly rather than through a third party institution such as a bank. In the context of the internet, peer to peer lending generally refers to the business......
• NFL Championship Games: Colts 30, Jets 17 ; Indy Miami-bound Greg Cote Two weeks until the Miami Super Bowl and here are the two games that provide our teams. After a summer of training camp, way-too-many preseason games, 256 regular-season games and eight playoff games, it's down to this. The ultimate reality-TV: The Survivors... COLTS 30, JETS 17 : Manning-to-Collie......

Online Stores

• Cash Registers Banks, Registers Vending Collectibles
• Urban Decay Lip Gloss Makeup Store
• New Year Holiday, Seasonal Collectibles
• Current Year, Next Year Calendars Paper Collectibles
• New Year Holidays Postcards Collectibles

If you liked this article, vote for it on del.icio.us and stumbleupon.


Categories:

Prosper.com, Statistics, Tools

Tags:

azerbaijan, mozambique