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13. Consider the following fixed-rate, level-payment mortgage: · maturity = 360 months · amount borrowed = $100,000 · annual mortgage rate = 10% a)Construct an amortization schedule for the first 10 months. b) What will the mortgage balance be at the end of the 360th month, assuming no prepayments? c)Without constructing an amortization schedule, what is the mortgage balance at the end of month 270 assuming no prepayments? d)Without constructing an amortization schedule, what is the scheduled principal payment at the end of month 270 assuming no prepayments? 14. Suppose that $1 billion of pass-throughs is used to create a CMO structure with a PAC bond with a par value of $700 million and a support bond with a par value of $300 million. a. Which of the following will have the greatest average life variability: (i) the collateral, (ii) the PAC bond, or (iii) the support bond? Why? b. Which of the following will have the least average life variability: (i) the collateral, (ii) the PAC bond, or (iii) the support bond? Why? 15. Suppose that the $1 billion of collateral in Question 14 was divided into a PAC bond with a par value of $800 million and a support bond with a par value of $200 million. Will the PAC bond in this CMO structure have more or less protection than the PAC bond in Question 14? 16. Suppose that $1 billion of pass-throughs is used to create a CMO structure with a PAC bond with a par value of $700 million (PAC I), a support bond with a schedule (PAC II) with a par value of $100 million, and a support bond without a schedule with a par value of $200 million. A.Will the PAC I or PAC II have the smaller average life variability? Why? b.Will the support bond without a schedule or the PAC II have the greater average life variability? Why? 19. Consider the following CMO structure backed by 8% collateral: Tranche Par Amount (in millions) Coupon Rate (%) A $300 6.50 B 250 6.75 C 200 7.25 D 250 7.75 Suppose that a client wants a notional IO with a coupon rate of 8%. Calculate the notional amount for this notional IO. 20. An issuer is considering the following two CMO structures: Structure I Tranche Par Amount (in millions) Coupon Rate (%) A $150 6.50 B 100 6.75 C 200 7.25 D 150 7.75 E 100 8.00 F 500 8.50 Tranches A to E are a sequence of PAC I’s and F is the support bond. Structure II Tranche Par Amount (in millions) Coupon Rate (%) A $150 6.50 B 100 6.75 C 200 7.25 D 150 7.75 E 100 8.00 F 200 8.25 G 300 ? Tranches A to E are a sequence of PAC I’s, F is a PAC II, and G is a support bond without a PAC schedule. a. In structure II, tranche G is created from tranche F in structure I. What is the coupon rate for tranche G assuming that the combined coupon rate for tranches F and G in structure II should be 8.5%? b. What is the effect on the value and average life of tranches A to E by including the PAC II in structure II? c. What is the difference in the average life variability of tranche G in structure II and tranche F in structure II? Chapter 12: Agency Mortgage Pass-Through Securities Copyright © 2016 Pearson Education, Inc. 12-1 Chapter 12 Agency Collateralized Mortgage Obligations and Stripped Mortgage-Backed Securities 1 Copyright © 2016 Pearson Education, Inc. 12-2 Agency Collateralized Mortgage Obligations Collateralized mortgage obligations (CMOs) are bond classes created by redirecting the cash flows of mortgage-related products so as to mitigate prepayment 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. The bond classes created are commonly referred to as tranches. The principal payments from the underlying collateral are used to retire the tranches on a priority basis according to terms specified in the prospectus. Entities that issue agency pass-through securities also issue CMOs Copyright © 2016 Pearson Education, Inc. 12-3 Agency Collateralized Mortgage Obligations (continued) Sequential-Pay Tranches The first CMO was created in 1983 and was structured so that each class of bond would be retired sequentially. Such structures are referred to as sequential-pay CMOs. A CMO is created by redistributing the cash flow (interest and principal) to the different tranches based on payment rules. There are separate rules for the payment of the coupon interest and the payment of principal, the principal being the total of the regularly scheduled principal payment and any prepayments. The payment rules at the bottom of Exhibit 12-1 (see Slide 12-6) describe how the cash flow from the pass-through (i.e., collateral) is to be distributed to the four tranches. Copyright © 2016 Pearson Education, Inc. 12-4 Exhibit 12-1 FJF-01: Hypothetical Four-Tranche Sequential-Pay Structurea TranchePar AmountCoupon Rate A$194,500,0007.5% B 36,000,0007.5% C 96,500,0007.5% D 73,000,0007.5% $400,000,000 aPayment rules: 1. For payment of periodic coupon interest: Disburse periodic coupon interest to each tranche on the basis of the amount of principal outstanding at the beginning of the period. 2. For disbursement of principal payments: Disburse principal payments to tranche A until it is paid off completely. After tranche A is paid off completely, disburse principal payments to tranche B until it is paid off completely. After tranche B is paid off completely, disburse principal payments to tranche C until it is paid off completely. After tranche C is paid off completely, disburse principal payments to tranche D until it is paid off completely. Copyright © 2016 Pearson Education, Inc. 12-5 Agency Collateralized Mortgage Obligations (continued) Sequential-Pay Tranches Each tranche receives periodic coupon interest payments based on the amount of the outstanding balance at the beginning of the month. The disbursement of the principal, however, is made in a special way. A tranche is not entitled to receive principal until the entire principal of the preceding tranche has been paid off. The principal pay-down window for a tranche is the time period between the beginning and the ending of the principal payments to that tranche. Tranches can have average lives that are both shorter and longer than the collateral, thereby attracting investors who have a preference for an average life different from that of the collateral. Copyright © 2016 Pearson Education, Inc. 12-6 Agency Collateralized Mortgage Obligations (continued) Accrual Bonds In many sequential-pay CMO structures, at least one tranche does not receive current interest. Instead, the interest for that tranche would accrue and be added to the principal balance. Such a bond class is commonly referred to as an accrual tranche or a Z bond (because the bond is similar to a zero-coupon bond). The interest that would have been paid to the accrual bond class is then used to speed up the pay down of the principal balance of earlier bond classes. To understand this, consider FJF-02 in Exhibit 12-4 (see Slide 12-11), which is a hypothetical CMO structure with the same collateral as FJF-01 and with four tranches, each with a coupon rate of 7.5%. The difference is in the last tranche, Z, which is an accrual. Copyright © 2016 Pearson Education, Inc. 12-7 Exhibit 12-4 FJF-02: Hypothetical Four-Tranche Sequential-Pay Structure with an Accrual Bond Classa TranchePar AmountCoupon Rate (%) A$194,500,0007.5 B 36,000,0007.5 C 96,500,0007.5 Z (accrual) 73,000,0007.5 $400,000,000 aPayment rules: 1. For payment of periodic coupon interest: Disburse periodic coupon interest to tranches A, B, and C on the basis of the amount of principal outstanding at the beginning of the period. For tranche Z, accrue the interest based on the principal plus accrued interest in the preceding period. The interest for tranche Z is to be paid to the earlier tranches as a principal pay down. 2. For disbursement of principal payments: Disburse principal payments to tranche A until it is completely paid off. After tranche A is paid off completely, disburse principal payments to tranche B until it is paid off completely. After tranche B is paid off completely, disburse principal payments to tranche C until it is paid off completely. After tranche C is paid off completely, disburse principal payments to tranche Z, until the original principal balance plus accrued interest is paid off completely. Copyright © 2016 Pearson Education, Inc. 12-8 Agency Collateralized Mortgage Obligations (continued) Floating-Rate Tranches Floating-rate tranches can be created from fixed-rate tranches by creating a floater and an inverse floater. We can select any of the tranches from which to create a floating-rate and an inverse-floating-rate tranche. We can even create these two securities for more than one of the four tranches or for only a portion of one tranche. Exhibit 12-6 (see Slide 12-14) describes FJF-03, which is Hypothetical Five-Tranche Sequential-Pay Structure with Floater, Inverse Floater, and Accrual Bond Classes. Any reference rate can be used to create a floater and the corresponding inverse floater. There is an infinite number of ways to cut up the monetary value between the floater and inverse floater, and final partitioning will be driven by the demands of investors. Copyright © 2016 Pearson Education, Inc. 12-9 Exhibit 12-6 FJF-03: Hypothetical Five-Tranche Sequential-Pay Structure with Floater, Inverse Floater, and Accrual Bond Class TranchePar AmountCoupon Rate (%) A$194,500,0007.5 B 36,000,0007.5 FL 72,375,0001-month LIBOR + 0.50 IFL 24,125,00028.50 – 3 × (1-month LIBOR) Z (accrual) 73,000,0007.5 $400,000,000 Copyright © 2016 Pearson Education, Inc. 12-10 Agency Collateralized Mortgage Obligations (continued) Floating-Rate Tranches Unlike a floating-rate note in the corporate bond market, whose principal is unchanged over the life of the instrument, the floater’s principal balance declines over time as principal payments are made. The principal payments to the floater are determined by the principal payments from the tranche from which the floater is created. Assume that the reference rate is the 1-month LIBOR of 3.75%, then the coupon rate on the inverse floater takes the following form: K – L × (1-month LIBOR) where K is the cap or maximum coupon rate for the inverse floater and L is the multiple that determine the coupon rate for the inverse floater (L is referred to as the coupon leverage) EXAMPLE. If K is set at 28.50% and L at 3, then the coupon rate for the month is: 28.50% – 3(3.75%) = 17.25%. The higher the coupon leverage, the more the inverse floater’s coupon rate changes for a given change in 1-month LIBOR. Copyright © 2016 Pearson Education, Inc