# Initial Collar change

According to the CFAI: the PAC schedule may not be satisfied even if the actual prepayments never fall outside the intial collar. It gives an example (page 365) where initial collar is 90-300PSA, and the PSA for the first 2 years is 300. It claims that the effective collar shifts to 115-300PSA. I just don’t get it how this can be. Any explanation?

let me try to take a crack at that. the “initial” PAC Collar is calculated using a constant PSA speed FOR THE LIFE OF THE STRUCTURE. So as long as the PSA speed remains within the collar band FOR THE LIFE OF THE STRUCTURE, the initial PAC will equal the effective PAC. In the example you site above, the PSA speed starts within the initial PAC collar, but after 24 months, it shifts to another PSA speed. This makes the initial PAC collar shift (up or down depending on what the new PSA speed is), resulting in a slightly different PAC collar – the “effective” collar. Does that make sense?

ylager Wrote: ------------------------------------------------------- > let me try to take a crack at that. > > the “initial” PAC Collar is calculated using a > constant PSA speed FOR THE LIFE OF THE STRUCTURE. > So as long as the PSA speed remains within the > collar band FOR THE LIFE OF THE STRUCTURE, the > initial PAC will equal the effective PAC. In the > example you site above, the PSA speed starts > within the initial PAC collar, but after 24 > months, it shifts to another PSA speed. This > makes the initial PAC collar shift (up or down > depending on what the new PSA speed is), resulting > in a slightly different PAC collar – the > “effective” collar. > > Does that make sense? That’s what the CFAI book claim, but I don’t get. Another try?

I dont have the book now. But say you assumed a prepayement of 200PSA for the life of the structure and then you calculate that initial collar as 100PSA to 300PSA. The average life of the structure will not change if the prepayment for the life were at the rate of 200PSA (since that is what you assumed while designing the strucute). Now once you the actual prepayements come in and you see that the prepayment rate keeps varying and the current prepayment rate is 290PSA (a bit towards the upper end of the initial collar), means that the effective collar is shrink as the actual prepayments (280PSA) are greater than assumed prepayments (200PSA). So though the actual prepayements (280PSA) are still in the range of the initial collar bountries, the effective collar shrinks/windens to explain the real prepayment rate.

Collars are a mathematical calculation of the average life of a given tranch using an assumption that a particular PSA speed within the collar will be sustained throught the life of the CMO (if you start with an assumption of 100PSA, that 100PSA must not change for the duration of the life of the CMO in order for the initial collar and its average life to stay equal to the effective collar and average life. Once that assumption is broken, and the PSA speed moves around during the life the CMO, that initial calculation of the average life is no longer valid – it shifts depending on what the new PSA speed is. So for example, you have a 20 year CMO with an initial PAC collar of PSA 100 PSA to 300 PSA, with an average life of let’s say 4 years. The way that this average life of the PAC was calculated, was using an assumption that no matter what PSA speed you choose within the collar AS LONG AS THAT PSA ASSUMPTION REMAINS CONSTANT OVER THE ENTIRE 20 YEARS, the average life of the effective collar would be equal to the initial collar of 4 years. So if you assume any PSA between 100 - 300 over the entire 20 years (in other words 100 PSA for 20 yrs, or 110 PSA for 20 yrs, or 120 PSA for 20 yrs, … or 300 PSA for 20 yrs), the average life of that PAC will remain 4 years. HOWEVER, if at any time during the life of the CMO, the PSA is changed from the original PSA assumption, the effective collar will shift, such that the effective collar will be either wider or narrower (depending on what direction the PSA change took place). In other words if you start with a PSA of 150 for the first 5 years, and then change to PSA 200 for the remaining 15 years of the CMO, your original average life of 4 years in the PAC collar tranch will shift to let’s say 3.8 years, and the effective collar will be slightly different from the original PSA 100 - PSA 300 (it will probably look something like PSA 90 - PSA 280). Are you seeing the subtle difference? – the key is that a given PSA speed assumption within the collar MUST CONTINUE FOR THE ENITRE DURATION OF THE CMO LIFE – an assumption of 100 PSA must remain 100 PSA for the entire 20 years. If at any time during its life of the CMO that assumption is changed from 100 PSA to whater (lets say 150 PSA), the effective collar shifts, and the average life of the PAC collar changes.

I don’t even know if Schweser mentions this