019 - 192 Answers to Questions and Problems 1. Explain the...

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Unformatted text preview: 192 Answers to Questions and Problems 1. Explain the relationship among mortgage-backed securities, mortgage pass-throughs, and collateralized mortgage obligations. The mortgage-backed security (MBS) is a security that gives the security owner rights to cash flows from mortgages that underlie the MBS. The MBS comes in two basic types: mortgage pass-through securities and collateralized mortgage obligations. The owner of a pass-through owns a fractional share of the entire pool of mortgages that underlie the pass-through security. The owner of a pass-through participates in all the cash flows from the underlying mortgage pool. A collateralized mortgage obligation (CMO) is another type of MBS. A CMO is created by decomposing the cash flows from a pool of mortgages. For example, some CMOs are backed by interest-only payments from a pool of mortgages, while other CMOs might be backed by principal-only payments from the same mortgage pool. 2. Explain the similarities and differences between the zero-coupon yield curve and the implied forward yield curve. Both the zero-coupon yield curve and the forward yield curve show rates of interest that apply to single future payments. The rates from both curves can be used to discount a single payment from a distant future date to an earlier date. The zero-coupon yield curve gives discount rates for discounting a distant payment to the present. The rates from the forward curve are essentially rates for discounting a distant payment from its payment date to a time one period earlier. For example, if the forward curve has annual rates, the forward rate for a period from year 7 to year 8 could be used to discount a payment to be received at year 8 back to year 7. Together, the single-period forward rates that constitute the forward yield curve can be used to discount a distant payment back to any earlier time. 3. Given the zero-coupon yield curve, explain how to find the implied forward yield curve. The forward rate between any two periods is a function of the zero-coupon discount rates for a horizon from the present to the initiation point of the forward rate and the zero-coupon rates for a horizon from the present to the termination date of the forward rate. For example, consider a single-period forward rate from year 5 to year 6. This forward rate can be found by using the zero-coupon yield curve to find the zero-coupon factors for years 5 and 6, Z 0, 5 and Z 0, 6 . The forward rate factor for this period, FRF 5, 6 , is given by: FRF 5, 6 5 Z 0, 6 Z 0, 5 19 Interest Rate Options ANSWERS TO QUESTIONS AND PROBLEMS 193 Given the set of one-period FRF s, the elements of the forward yield curve can be found quite easily, because the one-period forward rate is simply the one-period FRF minus 1: In general, for any forward rate factor for a period beginning at time x and ending at time y , we have: 4. Given the implied forward yield curve, explain how to find the zero-coupon yield curve....
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019 - 192 Answers to Questions and Problems 1. Explain the...

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