Consider the second last (12.7+ million) and last (76.7+ million) "mortgage loans" in loan group 1 in the Countrywide Alternative Trust 2005-J7 (p S-69).

1. Amortize both loans with a 100% PPC assumption as given on p. S-70, and a 100% SDA (this is now the base PP/D assumption; leave the factors open to change).[1] To simplify, assume that any default is realized instantaneously and that there is no recovery.[2] Also make the standard assumption that default happens before mortgage payment, prepayment after.

2. How do I create a WAC IO and PO tranche to give a 5.75% deal coupon. Assume that these two classes are paid first (before subs and seniors - see below). The WAC PO gets the aggregate (initial PO%) (total principal cash flow), the WAC IO the aggregate excess interest on outstanding, current premium loan balance.[3]

3. With the remaining assets, create a senior/sub structure with 5% subordination, and a shifting interest structure as given on p S-61, under "shift percentage." Take a percentage of, for example, 60% to mean that the sub receives only 60% of its prorated prepay principal (provided the sub still exists). The sub will be a single class (called "B") that absorbs all realized losses first. Once the sub is exhausted, all seniors (see below) are allocated losses on a prorated basis. Assume interest is paid to the aggregate senior classes at 5.75% and any remaining interest is distributed to the sub.

4. Use the senior class to create a sequential pay structure of two classes, with principal A1:A2 :: 3:1. Prorate potential senior losses to A1 and A2 based on pre-default principal; assign each class its interest payment prorated on post-default beginning balance.

5. Assume all classes sold under the base PP/D assumption at:A-1: 102:01; A-2: 99:20; B: 75:04; IO: 0:20 (notional); PO: 81:31. The notation ":nn" means "nn/32nds."

6. Assume a Treasury term structure given by

z(T) = 0.03 ln[0.038 (T+40)]

where T is measured in months.

7. Make reasonable assumptions for any missing information, and justify them. Take care that you may only think the information to be missing.

[1] Note that these loans are Alt-A, and their default behavior is different from prime mortgages. Nonetheless, we use SDA to simplify the discussion.

[2] A gross simplification.

[3]This means that the IO and PO trance are effectively sharing in losses with trance B (see next), which is uncommon. More typically they are senior tranches.