View Full Version : Why full prepayment won't reduce avg maturity?

bracta

05-01-2008, 12:29 PM

From Handbook page 527:

Full prepayment of loans within a pool serve to reduce the outstanding balance but not reduce the average maturity of the underlying loan pool.

I can't see the reasoning here. Suppose a pool consisting of only 2 loans. one 1 yr to maturity, the other 10 yr. The avg maturity of the pool is about 4.5yr. With the full prepayment of the 2nd loan, the pool has only one loan and has a maturity of 1yr.

Am I right? I'm confused.

Laurelinda

05-01-2008, 12:40 PM

I don't have the Handbook in front of me. What are the characteristics of the security they're talking about? It makes a difference how the pools are constructed, I think.

The Smokin' Cracktuary

05-01-2008, 01:35 PM

From Handbook page 527:

Full prepayment of loans within a pool serve to reduce the outstanding balance but not reduce the average maturity of the underlying loan pool.

I can't see the reasoning here. Suppose a pool consisting of only 2 loans. one 1 yr to maturity, the other 10 yr. The avg maturity of the pool is about 4.5yr. With the full prepayment of the 2nd loan, the pool has only one loan and has a maturity of 1yr.

Am I right? I'm confused.

I wondered the same thing.

Here is how I reasoned it.

The example you gave is correct, but you have to think on a larger scale. Say you have 1,000 mtgs with an average life of 15 yrs. On average your prepayments are going to have a 15 yr. life, the same as the underlying pool. Therefore, the average life of the pool won't change.

Now you may have a bunch of prepayments of longer maturities, but then a greater proportion of what is left is shorter maturities. So going forward you expect more prepayments by shorter maturities countering the earlier prepayments by longer maturities. Over time the average life on a large pool will fluctuate slighty around the mean, but it will always stay close. It won't fluctuate by much. Maybe period to period, but not overall. The avearage life will be mean reverting, if you will. The mean maturity should be reducing on average by one per year.

Of course, this isn't accounting for differences in tendencies to prepay based on loan maturity (if there are any), but then you get into modeling the actual distribution of prepayments by relative maturity. I think that is a little more complicated and I think outside the scope of what was trying to be explained there.

Also, remember you are talking about the weighted average loan maturity. That's just the term left on the loan assuming no prepayment. It's not talking about the expected life of the security (or collateral pool) which will be less due to factoring prepayments.

bracta

05-01-2008, 04:14 PM

I wondered the same thing.

Here is how I reasoned it.

The example you gave is correct, but you have to think on a larger scale. Say you have 1,000 mtgs with an average life of 15 yrs. On average your prepayments are going to have a 15 yr. life, the same as the underlying pool. Therefore, the average life of the pool won't change.

Thanks! I need to think further about every word of yours.

Actually my thinking (after I post here) leads to the same explanation as yours. That is, it is a pool consisting of thousands of loans with an AVERAGE maturity of say 20yr. I guess the maturity dispersion within the pool will not be too wide around 20yr.

And when we talk about full prepayment, on an AVERAGE basis, we may assume among those loans that are fully prepaid, the number of loans with maturity longer than 20yr is the same as the number of loans less than 20yr. In this way, the remaining pool still has an avg maturity of 20yr.

In short, this is a large pool and we are talking about "average".

The Smokin' Cracktuary

05-01-2008, 04:18 PM

In short, this is a large pool and we are talking about "average".

Right on. The average life of prepaid mtgs can't vary from the average life of the remaining pool. At least not consistently.

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