What an X% default rate should mean to you, part 2

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)

If we assume that
1.prosper loans are perfectly representative of loans that generate Experian default data (eg, ignore all effects of new vs old HR rated loans, etc)
2.Loans are 1 year in length, rather than 3 year (again, assuming default probabilities have 1 year time horizon)
3.All loans are paid off fully with a single huge balloon payment at the end of the year, rather than monthly, or else default completely w/no resale value or recovery
4.The default rate % is relatively low in comparison to APR

Then as a very good first-order approximation, subtracting default rate from APR will give expected return.

More generally, if #4 is not true (in particular, for HR borrowers, default is 19% vs APR of 36%, say), one can still get an accurate expected return by taking:
APR x (1-probability of default) - (probability of default).
or
36% x (1-19%) - 19% = 10.16%

As probability of default gets close to 0%, the "APR x (1-probability of default)" term becomes APR x (1-0)
or APR x 1
or just APR
leaving us with a decent approximation of expected return as
APR - probability of default.