In an article titled "CUNA Mutual Looks for Noncallable Corporates" that appeared in the November 4, 1991, issue of BondWeek, p

6, Joe Goglia, a portfolio manager for CUNA Mutual Insurance Group, stated that he invests in "planned amortization class tranches, which have less exposure to prepayment risk and are more positively convex than other mortgage-backeds." Is this true?

As seen below there are a lot of factors to consider before we assume that a PAC tranche will absolutely have less exposure to prepayment risk and will be more positively convex that other mortgage-backed securities.

The creation of a mortgage-backed security cannot make prepayment risk disappear. This is true for both a pass-through and a CMO. Thus the reduction in prepayment risk (both extension risk and contraction risk) that a PAC offers must come from somewhere. It comes from the support bonds. If the support bonds are paid off quickly because of faster-than-expected prepayments, there is no longer any protection for the PAC bonds.

Planned amortization class tranches are structured to have less exposure to prepayment risk. For a security that is option-free and displays positive convexity, the price appreciation will be greater than the price depreciation for a large change in yield. Negative convexitymeans that the price appreciation will be less than the price depreciation for a large change in yield.

Generally, the market will take the greater convexity bonds into account in pricing them. How much should the market want investors to pay up for convexity? If investors expect that market yields will change by very little—that is, they expect low interest rate volatility—investors should not be willing to pay much for convexity. In fact, if the market prices convexity high, investors with expectations of low interest rate volatility will probably want to "sell convexity."

In the case of a CMO tranche the price depends on the characteristics of the tranche and the spread to Treasuries at the termination date. The key determinants are the "quality" of the tranche, its average life (or duration), and its convexity. Quality refers to the type of CMO tranche. Consider, for example, that an investor can purchase a CMO tranche that is a PAC bond but as a result of projected prepayments could become a sequential-pay tranche.

As another example, suppose that a PAC bond is the longest-average-life tranche in a reverse PAC structure. Projected prepayments in this case might occur in an amount to change the class from a long-average-life PAC tranche to a support tranche. The converse is that the quality of a tranche may improve as well as deteriorate. For example, the effective collar for a PAC tranche could widen at the horizon date when prepayment circumstances increase the par amount of support tranches outstanding as a proportion of the deal.

For a tranche, a standard convexity can indicate positive convexity, whereas the effective convexity can indicates negative convexity. The difference is even more dramatic for securities not trading near par. For a PO created from a tranche, the standard convexity can be close to zero whereas the effective convexity can be very large.