Given the preference stated in the last sentence of the quotation, what issuers is he likely to prefer? What issuers would he reject?

What will be an ideal response?

Given the last sentence, one would conclude that Pollard wants tranches backed by agency CMOs. In particular, he would want Ginny Mae, Freddie Mae, and Fannie Mae. He would reject any tranches backed by nonagency CMOs which are not (implicitly or explicitly) guaranteed by the government. More details as to what Pollard would prefer are given below.

Pollard wants to replace (or sell) adjustable-rate mortgage pass-throughs. The type of security he no longer wants and the implications of this desire can include a mortgage pass-through security, or simply a pass-through. This is a security that results when one or more mortgage holders form a collection (pool) of mortgages and sell shares or participation certificates in the pool. The cash flow of a mortgage pass-through security depends on the cash flow of the underlying mortgages. The cash flow consists of monthly mortgage payments representing interest, the scheduled repayment of principal, and any prepayments. Payments are made to security holders each month. Neither the amount nor the timing, however, of the cash flow from the pool of mortgages is identical to that of the cash flow passed through to investors. Because Pollard owns adjustable-rate pass-throughs, he is currently free from inflation rate risk. This implies he thinks that interest rates may be falling and adjustable rate securities will pay lower cash flows in the future.

Pollard wants to buy various types of CMO tranches. In particular, he wants "short companion" and "planned amortization" tranches. He prefers these tranches to be government guaranteed securities or those with implied guarantees. In particular, it appears that Pollard wants collateralized mortgage obligations (CMOs), which are bond classes created by redirecting the cash flows of mortgage-related products so as to mitigate prepayment risk for at least some classes. An accrual tranche can help overcome reinvestment rate risk if that is Pollard's main concern. While Pollard appears to be concerned with interest rates falling, he may be more concerned with mitigating prepayment risk, in particular contraction risk. For example, when interest rates fall there is greater prepayment risk because borrowers will want to retire their debt quicker. Thus, he wants to avoid contraction risk.
The mere creation of a CMO cannot eliminate prepayment risk; it can only transfer the various forms of this risk among different classes of bondholders. Pollard wants a "short companion" which indicates he wants a tranche where the principal is paid off early. This is not consistent with the notion that he believes interest rates are falling because the early pay-off means he would have to reinvest funds at a lower rate. Thus, we can eliminate this choice.

Pollard's other choice is "planned amortization" tranches (referred to as PAC tranches). PAC tranches can reduce prepayment risk in a manner desired by an investor's preference. However, despite the redistribution of prepayment risk with sequential-pay and accrual CMOs, there is still considerable prepayment risk. That is, there is still considerable average life variability for a given tranche. This problem is mitigated by the PAC tranche. The greater predictability of the cash flow for PAC bonds occurs because there is a principal repayment schedule that must be satisfied. PAC bondholders have priority over all other classes in the CMO issue in receiving principal payments from the underlying collateral. The greater certainty of the cash flow for the PAC bonds comes at the expense of the non-PAC classes, called support bonds. It is these bonds that absorb the prepayment risk. Because PAC bonds have protection against both extension risk and contraction risk, they are said to provide two-sided prepayment protection.

Given all of the above details and Pollard's assumed desire to reduce prepayment risk, it appears that Pollard would choose a "planned amortization" tranche. In particular, he would want a PAC class that avoids contraction risk. If alleviating reinvestment rate risk is also a major concern, then Pollard could also choose some accrual tranches. Whatever his choice, Pollard would want a tranche backed by an agency CMO.