# PAC bond - PSA

Suppose that a PAC bond is created using prepayment speeds of 90PSA and 240PSA and the average life is 5years. Will the average life for this PAC tranche be shorter than, longer than or equal to 5 years if the collateral pays at 140PSA over its life? Explain your answer. According to a long arithmetic proof, I concluded that the higher PSA the longer average life. Assuming equal weight for both PSA (90 & 240), the avg=165>140. Hence the avg life for this PAC tranche is longer over its life. But that’s incorrect. Can anyone point out the flaw in this way of thought? Thanks.

I will take a stab at this. it will equal to 5 yr becuase the PSA is within the PAC band, which means the supporting tranches will absorb prepayments risks. the long arithmetic proof you got there certainly confuses the hell outta me, care to elaborate?

Oh, let me correct myself: the higher PSA the shorter average life. Since it’s hard to type math functions here hence here is the flow: Higher PSA -> higher CPR -> higher SMM higher projected prepayment -> lower average life Avg life = sum |each t * {(scheduled principal pmt + (begining balance - scheduled pmt)*[1-(1-6%*PSA*n/30)]} ----------------------------------------------------------------------------------------- (12*Total principal) (actually it’s only need to think higher PSA -> higher projected prepayment for short, but since the question gave numeric PSA, I wanted to see the link in term of formula). Seriously, I think this chapter is a big crisis among all CFAII’s chapters, just as what the crisis now in the world.

I think \$tarving_banker’s logic is right. What is the right answer?

The right answer is equal to 5 years. It’s text book question btw.

Yes, higher PSA will mean higher prepayment and shorter avg life. But since the actual prepayment is within the PAC band, all additional prepayments will go to the supporting tranches and reduce the avg life of the supporting tranches. The life of the PAC tranche will not be affected as it is being “protected” by the supporting tranches. It is only the if the prepayment rate is consistently high for a prolonged period of time that the PAC will start absorbing the repayments. (Becuase the supporting tranches will eventully be killed off and retired) In which case, yes the avg life of the PAC bond will be shortened.

I’m not sure that’s exactly true, let me try and find the post on it…