Please give the formula and answer in detail

A. [20 points total] 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. 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.

B. [10 points total] Answer the following questions (on a separate worksheet within your workbook)

[2] What is the initial principal and cash flow yield for each class? Compare the total price of the tranches to the principal value. Generally, why does the total market value of the deal exceed the initial pool balance?

[2] Compute the WAL, modified duration, and convexity for each tranche at base PPC/default. For simplicity, assume that a small y does not affect the effective prepayment speed.

[2] Compute the nominal- and Z-spread for each tranche. Does a positive spread automatically mean that the tranche is a better investment than a Treasury?

[2] Keeping the SDA fixed at its baseline value, plot the WAL of each principal-paying tranche vs the PPC (in the range 0 to 300%).

[2] Plot the cash flow yield of each tranche vs the SDA percentage, in the range 0 to 800%, for a PPC of 100%.

[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.