# Fixed Income, Mortgage Backed Sector, Extension Risk

\$200 million of mortgage pass-throughs will be used as collateral for three tranches. The first two tranches are planned amortization class tranches: \$110 million of bonds of tranche U and \$50 million of bonds of tranche V. The third tranche consists of the holders of the \$40 million of bonds in tranche W, which is a support tranche. Which of the following statements regarding the contraction risk and extension risk of the U bonds versus the V bonds is most accurate? The U bonds: A) have less extension risk but not less contraction risk than the V bonds. B) have less contraction risk but not less extension risk than the V bonds. C) have less contraction risk and less extension risk than the V bonds. Your answer: C was correct! The planned amortization portion of the tranches allows for the lower support tranches to absorb the prepayments first with the upper tranches having the least amount of prepayment risk with tranche V having more prepayment risk than tranche U because U is more senior than V. Because U has the least amount of prepayment risk it also has the least amount of contraction risk once again because all the lower subordinate tranches and support tranches absorb the prepayments first. ***** MY QUESTION ***** WHY WOULD THE U BONDS HAVE LESS EXTENSION RISK THAN THE V BONDS?

U is senior to V. W is the support tranche. When any prepayments occur - first W absorbs the prepayments, after that V absorbs the prepayments. So U has the least Contraction risk. Now say both V and W are gone - any prepayments that occur after that, will ensure that U does not extend [only 1 way is DOWN, it can only CONTRACT]. So it has the least extension risk as well.

First, thanks for responding. Regarding the contraction risk: I understand that U is senior to V. W is the support tranche. When any prepayments occur - first W absorbs the prepayments, after that V absorbs the prepayments. So U has the least Contraction risk. Regarding extension risk: I understand your theory: “Now say both V and W are gone.” But, the question doesn’t say anything about V and W being gone. I think I understand that if V and W are gone, then, U has less extension risk and more contraction risk. Could there be another explanation for why U has less extension risk (without making the assumption that V and W are gone)? Thanks

Yes. There is an explanation. Again, because U is senior to V, if the interest rates rise (which creates an extension), all the principals received will be used to pay that tranche first. Then if more principals are received it will be used to pay V and then W. Due to that U has less extension risk.

…and finally, the trick here is that this question is on a PAC not a Sequential Pay CMO. A PAC has a support bond that absorbs all prepayment and extension risk beyound a certain limit! This limit is what defines the reduced risk of Bond U than the rest bonds. If interest rate rises, and (which creates extension), Bond U still get first the few principal received (therefore a lower extension risk). If interest rate lowers, (and prepayment occur) Bond U will not take more than the defined limit and the excess is passed to the Others (W first, and then V), still reducing the risk of prepayment.