The 1 month or worse curves that I published over the weekend have many potential uses in determining the interest rate required to make a certain return.

When the curves are complete we can simply solve the Markov Model since the vehicle is a fairly straight forward 3 year fully amortized loan. If we can assume the remainder of the Markov Model (we are missing months 11-37), we could also solve the Markov Model.

Solving the Markov Model is the holy grail of investing in Prosper, because having done so, one can simply fall back on the law of large numbers, by diversifying in many loans, and make a fairly consistent rate of return. Any large investors rigorously analytical that are going to come onto the platform will undoubtedly be solving the Markov Model.

As a first step to solving the Markov model I thought I would predict the 3 year cumulative default rate. At the moment there are 2 obvious options: linear and exponential decay. While the curves currently look linear it is not possible that they will remain so. In the HR category for example a linear trend would result in a cumulative 3 year default rate of a ridiculous 108%. The next obvious choice is exponential decay.

The thinking is: if 30% default in 10 months, 30% of the remaining good loans will default in the next 10 months, and 30% of the remaining good loans will default in the next 10 months. In other words, 70% of the HR loans survive 10 months; 70% of those (100*0.70*0.70) survive the following 10 months. Or, as a mathematical expression, pct_good_loans(p,r,t) = 100 * (1-r)^(t/p), where p is period, r is rate at period, t is time in months.

For HR = 100 * ( 1 – (1-0.30)^(36/10) ) = 72%.

Yikes! Clearly believable looking at the current curve; although it may turn out to be slightly high as most unsecured debt curves are actually S-shaped even though Prosper’s havn’t turned yet.

I averaged the exponential decay 3 year cumulative default rates for period 6-10. Here are the results:

AAABCDEHR3.9%12.7%20.8%21.2%32.8%53.8%73.7%*If you liked this article, vote for it on del.icio.us and stumbleupon.*

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