The following exercise is based on a series of investments made in 1993 by City Colleges of Chicago (CCC), a system of community colleges. Its treasurer decided to invest up to 70% of its portfolio in the lower tranches of a Fannie Mae MBS: FNMA 1993-237.15 All payments within this trust were Principal-Only (PO); this particular type of security was called a Stripped Mortgage Backed Security (SMBS). The FNMA 1993-237 had a principal balance of $425 million with a WAM = 348 and WAC = 8.27%. Because all tranches were PO, the coupon rate of the underlying pass through is not needed. The security was divided in the tranches and types reported in Table 8.12, where PAC stands for Planned Amortization Class, TAC stands for Targeted Amortization Class, and SUP stands for Support Class.
In Table 8.12, UC and LC stand for the upper collar and the lower collar for the PACs. TAC are similar to PAC but, instead of using a range of PSA, use only a single value of PSA to create a schedule of payments. The prospectus for the security pointed out the following principal distribution plan:
Principal will be distributed monthly on the Certificates in an amount (the "Principal Distribution Amount") equal to the aggregate distributions of principal concurrently made on the SMBS. On each Distribution Date, the Principal Distribution Amount will be distributed as principal of the Classes in the following order of priority:
(a) Sequentially, to the A, B and C Classes [Planned Amortization Class (PAC)], in that order, until the principal balances thereof are reduced to their respective Planned Balances for such Distribution Date;
(b) sequentially, to the E and G Classes [Targeted Amortization Class (TAC)], in that order, until the principal balances thereof are reduced to their respective Targeted Balances for such Distribution Date;
(c) To the H Class [Support Class], until the principal balance thereof is reduced to zero;
(d) To the G and E Classes, in that order, without regard to their Targeted Balances and until the principal balances thereof are reduced to zero;
(e) To the A Class, without regard to its Planned Balance and until the principal balance thereof is reduced to zero; and
(f) Concurrently, to the B and C Classes, in proportion to their then current principal balances, without regard to the Planned Balances and until the principal balances thereof are reduced to zero.
On October 1, 1993 the market faced the yield curve summarized by the following Extended Nelson Siegel model parameters (see Chapter 2 and Equation 8.23 above): (0 = 6,278.30, (1 = -6,278.30, (2 = -6,291.28, (3 = 0.70906, (1 = 27,056.50, and (2 = 20.2312.
(a) According to industry experts you find out that the PSA is currently at 450%.
i. Assuming a constant PSA rate, value the tranches of FNMA 1993-237.
ii. What is the duration of each of the tranches? Are G and H the tranches with the highest duration?
(b) CCC decides to invest $100 million, divided equally into tranches G and H.
After 6 months you receive new data to compute the yield curve (it is now April 4, 1994) according to the Extended Nelson Siegel model: (0 = 6,278.30, (1 = -6,278.30, (2 = -6,291.28, (3 = 0.97584, (1 = 27,056.50, and (2 = 20.2249.
i. Have interest rates risen? Stayed the same? Or fallen?
ii. What will the value of the portfolio be on April 4, 1994 assuming that the PSA stays the same?
(c) You find out that on April 4, 1994 the PSA is actually 200%.
i. Is the change in the PSA a reflection of what happens to the yield curve? Why or why not?
ii. Will this change offset the P/L in the portfolio's value from the change in interest rates?
iii. Compute the price of each tranche at April 4, 1994. Do the changes reflect what you expected from the duration calculation?
iv. What is the gain / loss of the portfolio at this time?

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anche Principal LC 27.50 51.00 25.50 8.00 59.50 350 550% 5504 135% 135% 1359 ТАС TAC SL/P 42500