Giddy/ABS Mortgage-Backed Securities/1 Asset-Backed Securities Mortgage-Backed Securities Prof. Ian Giddy Stern School of Business New York University Mortgages and MBS l Mortgage Loans l Pass-throughs and Prepayments l CMOs l Analysis of MBS Pricing and Convexity Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 3 Giddy/ABS Mortgage-Backed Securities/2 Structure of the US MBS Market MortgageMortgage Loan Loan BankBank (mortgage (mortgage originator) originator) makes makes a a whole whole loan loan Ancillary:Ancillary: brokers, brokers,servicersservicers, ,insurers insurers MortgageMortgage Pass Pass-Through-Through FNMAFNMA or or GMAC GMAC (conduit) (conduit) pools pools mortgagemortgage loans loans with with similar similar characteristics characteristics CMOCMO or or REMIC REMIC MortgageMortgage Strips Strips TakesTakes a a mortgage mortgage pool pool and and makes makes the the InterestInterest-Only-Only and and Principal Principal-Only-Only cashcash flows flows more more predictable predictable by by assigning assigning prioritypriority of of claims claims to to the the cash cash flows flows MBSMBS Portfolio Portfolio InstitutionalInstitutional investor investor evaluates evaluates risk/return risk/return behaviorbehavior of of mortgage mortgage-backed-backed securities securities through through optionoption-adjusted-adjusted price price and and spread spread analysis analysis Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 4 US Mortgage-Backed Securities AGENCY PRIVATE-LABEL PASS-THROUGHS PASS-THROUGHS INTERESTINTEREST INTERESTINTEREST PRINCIPALPRINCIPAL PRINCIPALPRINCIPAL PREPAYMENTPREPAYMENT PREPAYMENTPREPAYMENT GRANTORGRANTOR TRUST TRUST GRANTORGRANTOR TRUST TRUST STRUCTURESTRUCTURE STRUCTURESTRUCTURE Credit enhancement: FHLMCFHLMC PC PC Credit enhancement: GNMA MBS n GNMA MBS FNMA MBS n Corp g'tee (US Govt g'tee) FNMA MBS Corp g'tee (US Govt g'tee) n L/C (US(US Agency Agencyg'teeg'tee)) n L/C n n InsuranceInsurance (FSA) (FSA) n n Senior/subSenior/sub debt debt Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 5 Giddy/ABS Mortgage-Backed Securities/3 Form of cash flow allocation Pay-through Different tranches obligation Pass-through obligation PAC (planned aamortization class) TAC (targeted amortization plan) IO/PO strips Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 6 Mortgage-Backed Securities GNMA mortgage pool security Mortgage Mortgage ... Mortgage 1 2 n Equal monthly payments prepayable n Mortgage-backed securities are prepayable, so one cannot measure returns or values easily n They tend to pay down early when rates fall, and later when rates rise. Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 7 Giddy/ABS Mortgage-Backed Securities/4 Mortgage Prepayments Complexity of the option - l Systematic risk: exercise of the interest rate option l Unsystematic risk: reasons unrelated to mortgage interest rates (eg demographic) Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 8 Mortgage Pool Prepayment Conventions Traditional method is to forecast prepayments by adjusting the PSA (Public Securities Association) benchmark of a prepayment rate that reaches 6% a year for 30 year mortgages. Annual prepayment rate (CPR): 100% PSA: If t<=30 CPR=6%t/30 If t>30 CPR=6% 170% PSA: If t<=30 CPR=170%[6%t/30] If t>30 CPR=170%[6%] Monthly prepayment rate (SMM): SMM=[1-(1-CPR)]/12 Prepayment amount in dollars: = (Beginning Principal Balance - Scheduled Principal Repayment)*SMM Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 9 Giddy/ABS Mortgage-Backed Securities/5 Prepayment Assignment l Consider a $100,000 10-year, 9% mortgage loan, with monthly equal payments. l Make the following calculations, using a computer spreadsheet or financial calculator: 1. What are the scheduled monthly payments? 2. After 1 month and 3 months, u What is the CPR and SMM, assuming 200% PSA? u What is scheduled principal payment? u If it pays down at 200% PSA, what is the prepayment amount? u What is the remaining principal balance? Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 10 CMOs and Strips The technique: l Allocate cash flows (interest & principal) of MBS to mitigate prepayment risk l Pay different returns based on risk l The sum of the part should be worth more than the whole alone. Example: MDC Series J CMO with underlying pool WAC 9.5%, 297 months final maturity Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 11 Giddy/ABS Mortgage-Backed Securities/6 CMOs and Strips l First-priority classes l Z-class: last to be paid off l Floating/inverse floating CMOs l Planned Amortization Class bonds (PACs) and TACs l Companions with priority schedules (PAC IIs) l VADM bonds (use early principal and interest to pay priority bondholders) l CMO residuals (collateral interest - CMO interest) l IOs and POs Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 12 The Negative Convexity of MBS Securities backed by fixed-rate mortgages have "negative convexity." This refers to the fact that when interest rates rise, the MBS behave like long-term bonds (their prices fall steeply); but when rates fall, their prices rise slowly or not at all. Price Price-yield curve of 20 year bond callable in 3 years 20-year 3-year Callable bond Yield Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 13 Giddy/ABS Mortgage-Backed Securities/7 Convexity of Callables Mortgage-backed securities and other callable bonds may have negative convexity which cushions a bond’s price rise and accelerates its fall! PRICE 102 100 YIELD Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 14 MBS: Fannie Mae REMIC Pass-Throughs l What are the underlying mortgage pools? l Look at different asset groups: l Yields on different classes l Price risks on each class l What do the seller & servicer gain? Group work Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 15 Giddy/ABS Mortgage-Backed Securities/8 Bond Valuation, Duration and Convexity Bond Valuation The formula for a bond’s price is B0 = Ix(PVIFAk ,n ) + Mx(PVIFn ) n I M B0 = å + t =1(1 + k) t (1 + k) n Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 17 Giddy/ABS Mortgage-Backed Securities/9 Treasuries Treasury Notes and Bonds as quoted in the Wall Street Journal Rate Maturity, Mo/Yr Bid Asked Ask Yld. 6 Dec 97 99:29 99:31 6.01 n When US Government bonds are stripped, the coupons and principal are separated out and sold as individual zero-coupon instruments n Investment banks create Strips when the total can be sold for more than the cost of the bond. Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 18 Price Risk of Treasuries Treasuries differ: l Liquidity - traders quote wider bid-ask spreads for illiquid bonds l Duration - sensitivity of price to a change in interest rates - is based on the bond’s coupon levels and maturity date (low duration means less risky) l Convexity - measures how duration changes with a change in rates (high convexity is desirable) Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 19 Giddy/ABS Mortgage-Backed Securities/10 The Price-Yield Relationship Bond prices and interest rates have an inverse relationship: PRICE 100 9% YIELD(RATE) Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 20 The Price-Yield Relationship l Selling at a discount is when a bond sells for less than its par value (i.e., the quote is <100) l Selling at premium is when a bond sells for more than its par value (i.e., the quote is >100) Price of a 9% bond 100 Copyright ©1999 Ian H. Giddy 9% Mortgage-Backed Securities 21 Giddy/ABS Mortgage-Backed Securities/11 Maturity In general, the longer the maturity, the more sensitive is a bond’s price to interest-rate changes, other things being equal: Price Required 9%, 9%, yield 5 year 25 year 8% 104.0554 110.7510 9% 100.0000 100.0000 10% 96.1391 90.8720 Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 22 The Coupon Effect... But three bonds with the same maturity can have very different sensitivities, depending on their coupon levels: Price Required 9%, 6%, 0%, yield 5 year 5 year 5 year 8% 104.05 91.88 67.56 9% 100.00 88.13 64.39 10% 96.13 84.56 61.39 Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 23 Giddy/ABS Mortgage-Backed Securities/12 Duration Duration measures the % price change for a given change in yield: PRICE The steeper the line, the more the price falls for a given rise 100 in yield 9% YIELD Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 24 Greater Duration, Greater Risk Duration is measured as the PV-weighted average life, so low-coupon bonds have greater duration PRICE 100 9% BOND 6% BOND 0% BOND 9% YIELD Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 25 Giddy/ABS Mortgage-Backed Securities/13 Calculating Duration: MacCauley and Modified tCFt n (1+ r)t DMAC = å t=1 P dP D D = %DP = = - MOD P (1+ r) Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 26 Assignment For a 2-year, semiannual bond with a coupon rate of 10% and a yield of 8%: l Find the price sensitivity for a 10bp rise and fall of the yield l Find the price sensitivity for a 100bp rise and fall of the yield l Find the duration. Copyright ©1999 Ian H. Giddy Mortgage-Backed Securities 27 Giddy/ABS Mortgage-Backed Securities/14 Duration: An Excel Spreadsheet Yield 8.0% Bond A Time (year) 0.5 1 1.5 2 Cash-Flows 5 5 5 105 PV of CFs 4.80769 4.6228 4.445 89.754 Price 103.63 Weighted CFs 5 10 15 420 PV of weighted CFs 4.80769 9.2456 13.335 359.02 Sum of weight. CFs 386.406 Semiannual duration 3.72871 Macaulay duration is1.86436 Modified 1.72626 Copyright ©1999 Ian H.