shorter PAC tranche, more protection

it says in the CFAI book, volume 5, p. 398, the degree of protection against contraction risk increases the shorter the pac tranche. i’m a little confused here, first of all it says that the pac B tranche has a par amount of 8 mio and then in the test it mentionts 93 mio. what is the par amount or why they add 85+ 8? because for trance C they don’t do that. sorry, im a little confused here. the question at the end is, why does the shorter PAC tranche have more protection. and what is defined as shoerter? Is PAC A tranche shorter than PAC-B tranche? does it also depend on the par amount? thanks

shorter vs. longer is based on the Avg life of the tranche. shorter PAC Tranche - gets regular principal payments - as scheduled. Any “unscheduled” payments/prepayments are directed to the Support tranches. There is thus prepayment protection for the shorter tranche, it is not likely to expand (payments do not come in on time) or contract (payments come in too early). Given the size of support tranches, it is more than likely to be protected.

if you have a tranche that finishes in a year, and one that finishes in 2 years, the 2 year tranche is a bit riskier as you may be fairly certain that prepayments will stay within the collar for the front year but the next year is more uncertain. also the more time there is left on the tranche the more likely high prepayments will break the tranche

Just as a quick follow up to this question-the wider the collar on the PAC tranche, this would imply relatively more stable payments and greater protection from prepayment?

That is correct, although make sure it’s the effective collar you’re looking at. Once a CMO has been paying for a few years, the current effective collar may be drastically different from the intial collar. I.E., if you have very low prepayments in the past, the higher end of the effective collar will be higher than that of the initial collar, as more of the support tranches will be available. However the bottom side of the collar will also rise as well, which narrows it.

The wider collar does not mean it remains constant. It could narrow too. So if it narrows then there is a greater chance the prepayment rate could fall out of range and cause fluctuation in the age of PAC Tranche.