Wednesday, March 08, 2006

What an X% default rate should mean to you, part 1


Note from 3/30/06: We users have gotten mixed answers to questions addressed to Prosper.com re: default rate horizons -- that is, we've been told 3 years, but then a 2 year horizon was confirmed as correct. Throughout this exercise, I'm assuming 1 year horizons (as the most pessimistic possible). Clearly, if 19% of HR borrowers default every year, that's very different from saying that over 3 years, only 19% of HR borrowers default.

In fact, I do believe the 2 year horizon is the correct one (it seems consistent w/the 2-year horizon delinquency rates I got from Fair Isaac, inventors of FICO scores), but it doesn't hurt to double expected risk as a rule of thumb when dealing with uncharted territory. (end of note)



Note 2 from 3/31/06: Looks like I was right -- the 2 year terms were for annualized numbers, so my worst-case-scenario, is actually the correct one.(end of note)


All the following notwithstanding, I'm blown away by the coolness of the idea of Prosper as a whole, and the potential beneficial-to-default-rate social effects. And, I swear I'm not trying to improve my lending rates by scaring anyone off :) However, as a lender, I'm worried about risk, and I also want to make sure that others are lending rationally. I'd welcome additional comments on tenable risk-reduction strategies in lending...

Various necessary mental adjustments to default rates for calculating expected value of loans:

In a nutshell, my first (awful) approximation of expected value (ignoring taxes) is the following:

1.E borrower, $100 loan, <20% DTI ratio, experian-cited default rate of 19%, offering 36% returns.
2.I assume default occurring means I get paid back $0, otherwise, I get paid back everything.
3.Probability of default x $0 + Probability of not defaulting x $100 x (1.36)=
0.19 x $0 + 0.81 x $136 =1.1016
so, I expect 10.16% returns on average.

Obviously, this is really wrong -- chances are that even if the borrower defaults, s/he won't do so before even the first payment is made. I partially ignore time value of money. Furthermore, if default occurs, you can still recover some money on average, and even if not, prosper is set up so that you can sell the loan (at a huge discount) -- or to quote prosper's site: "Loans that are written off as uncollectable are offered for sale at an auction to a selected group of debt collection companies that are in the business of purchasing defaulted loans."

This is a partial list of factors still in the air (for my retail-sized purposes, I don't care if there is a formal Experian-calculated number out there somewhere or not -- if the info isn't public/costs a lot of money to get, it is the same to me):

a)technical definition of default -- strictly speaking, in the corporate finance world, historical default statistics don't typically distinguish between being a day late on an interest payment once, from a complete Enron style bankruptcy. [Or more precisely, if you see a single number being offered for "default rate for BBB firms," that's the case -- clearly Experian or Moody's records and distinguishes between various types of default, etc, and will provide such data -- for a price]

b)recovery rates on defaults -- even if the definition of consumer default is more lenient than the corporate one, it still will be an objective line, and anything beyond the line will be counted equally, despite differences in severity of default (the guy who misses a payment because he deosn't use auto-debit, vs the internet ID thief who steals all the money immediately).

c)are the sample of E borrowers all from the same cohort (all E loans opened last year, say), or is it randomly chosen E loans that existed at the time of sampling? This definitely makes a difference w/respect to default rates -- there are well known differences between an E-rated borrower who has made 50 payments already, and a brand new E-rated borrower.

d)even if we ignore whether loans are seasoned or unseasoned, we need transition probabilities because we're looking at 3 year loans, not 1 year -- ie, you have an E loan in year one. say it doesn't default this year. Next year, what's the chance that the person borrowing becomes A rated? B rated? stays the same?

e)loan weights -- I'm nearly certain that default frequency is unweighted -- so some guy who borrows $10,000 and defaults, and one guy who runs w/$1,000, are both going to increase default probabilities equally in the pool.

f)The pool of consumers that determine default rates, are already professionally modelled, for the most part -- prosper lenders are unlikely to have complex models available, and definitely have a big informational disadvantage -- we see scores and self-reported (w/some checking) income -- professional lenders see everything.

g)vintage year of loans -- experian default rates are calculated across lots of historical data. Say you put $50 into thousands of loans -- unless you commit to putting similar amounts into prosper every year for many many years, you still may not be properly diversified. After all, are you investing in the equivalent of March 2000, at the peak of the internet boom, or are you investing at the beginning of a long economic boom?

And, of course, the big, exciting, unknown:
h)systematic differences between prosper lending and generic consumer lending...does the max $25k loan limit skew default down? does internet familiarity skew defaults down, because of marginally better education/income/opportunities? does internet familiarity increase the chance that a borrower is younger, and perhaps more spendthrift? does the knowledge that a lender is a person, not a big corporation, make defaults less likely out of sympathy -- more likely out of jealousy -- more likely because of reduced fear? do borrowers willingly pay a premium for the straightforward, user-friendly, easy-to-get-a-loan interface of Prosper?

i)true realized return:
What if my nondefaulting loans also tend to prepay, as nondefaulting borrowers are the ones who actually stay on track, improve credit grades -- and voila -- refi my loan out of existence? Hello, reinvestment risk!

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