Sometimes when I'm reading things I don't understand, there's one defining sentence that I can point to and say "That one, I don't understand a single word of it."
For this discussion, this would be that line.
I had my money on mtnchick not understanding a single word of it. Shoulda guessed it would be "debits on the left credits on the right and life is good" guy. (Despite the fact that if your assets equal your liabilities, mathematically, it doesn't really matter what side they go on as long as you're consistent.)
Here's the excutive summary: The English version of that sentence you don't understand is, "Given our ability to predict next month's loan performance, shouldn't we be able to determine the long run % of loans that will bk, default, pay off early, or payoff on time?"
The explanation is as follows, for those who desire a more in-depth explanation:
A discrete-time (things change at specific time points) Markov chain is something that can be modeled where something is in a specific state and has constant probability of moving to another state. In this example, loans more or less change states on a monthly basis. You can figure out the odds of a loan staying current or going late. Then from going late to really late, and eventually default. The current and all forms of late states are called transient states, because over the long run, a loan will never stay there. Eventually, loans get paid off, default, or file bk.
An absorbing state is a state that once entered is never left. This would be the paid off state, defaults, or bk. See that chart I have above? See how all of the rows have a percentage that is less than 1 (or less than 100%) for each combination? Well, mathematically, I would extend the rows of the table so that everything in the columns appears in the rows. The rows with Early PIF, FT PIF, BK, and Default would have a "1" in the corresponding column. That means once a loan enters the payoff, bk, and default states it stays that way. You might say "well duh" but that does have some important mathematical properties.
Once we have that matrix filled out, we now have a square matrix (# of rows = # of columns). We can multiply square matrices together (excel has an mmult function). If I multiplied that matrix by itself, I could then find the odds of the third payment being in a given state (current/late/bk/whatever) given its initial state. Multiply the matrix by itself again, and I can find the odds that a fourth payment will be in a specific state given an initial state. I can also find the oddds that something that is <15 days late will become current on the 10th payment. Follow me so far?
Well, if you keep multiplying that matrix by itself enough times, you get to the point where two things happen. First, ALL loans will eventually bk, pay off, or default. The entries in all of the other columns will be 0. Second, the entries in each column are homogenous within the column -- that is, they're all the same. In the long run, we simply ask, "what are the odds of a loan going bk, default, early payoff or payoff on time?" It doesn't matter if we look at the loan being <15 , late, or even 4+ right now. All responses would be the same. When I get around to fine tuning my chart, I might be able to show you some of that. The problem right now is that we don't have any full term loans paid off, so I don't know how to incorporate that into the analysis.