Dear Dr Fids,

Can you please help these questions? It is about MBS cash flow.

R Generating MBS cash flows can be messy so we are going to write some functions in R that allows us to generate the cash flows to structure and price the asset. 1. Using the MBScf function, generate cash flows for the following pool Balance = 25,000,000 - WAC = 4.5% - WAM = 355 - WALA (Age) = 5 - Net = 4% Assuming the following prepayment speeds: 100% PSA, 300% PSA, 500% PSA and 900% PSA. What is the average life of the pool for each speed? Excel sheet 2. Consider a pool with a $75,000,000 balance, a WAC of 3.45% and a WAM of 325. (a) What is the scheduled balance the next month? (b) Suppose the actual balance next month is 741,250,000, what is the CPR? (c) If the loan is 28 months old, what is the PSA? Excel sheet 3. Suppose you purchase a Fannie Mae 30 YR 3.5% MBS (3.5% net coupon) with a $75,000,000 balance on March 17. The current WALA = 10, WAM = 350, and WAC = 4.15% (a) What is the accrued interest? (b) The MBS is priced as 135 bps off the 10-year Treasury at 275 PSA. What is the yield you will use to price the MBS if the 10-year is currently yielding 1.86%? (c) Using the yield from (b), what is the price of the MBS taking the actual delay into account? (See slide 5-33, round price to nearest 1/4 tick) (d) What is the invoice amount paid for the purchase of the bond? Fixed Income: MBS Mechanics Lecture Set V Professor John P. Miller Professor John P. Miller Fixed Income: MBS Mechanics 1 / 47 How Important Is the MBS Market? Size: currently $10.74 trillion mortgage balance outstanding Second in size only to U.S. Treasury securities (recent development) Experienced a 13.5% growth rate from 2001 to 2007 ($5.6 - $12.0 billion) Held in most xed-income portfolios (25-45%) Diverse investor base: banks, money managers, pension funds, insurance companies, mortgage originators, GSEs and hedge funds Year 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Home Mortgages 10,063.8 11,185.0 12,012.1 11,976.1 11,765.5 11,269.5 11,034.8 10,851.5 10,796.7 10,782.9 U.S. Treasuries 4,678.0 4,861.7 5,099.2 6,338.2 7,781.9 9,361.5 10,428.3 11,568.9 12,328.3 12,544.4 Billions of dollars Source: Flow of Funds Accounts of the U.S., Table L.2, September 18, 2014 Complexity of products Professor John P. Miller Fixed Income: MBS Mechanics 2 / 47 Denitions and Terms Mortgage Loan secured by a specied real estate property Lender has right to repossess property in case of default Lien status Most mortgages are rst lien: Mortgage holder has rst rights to foreclosure and liquidation proceeds In some cases, borrowers add second mortgages (such as a home equity loans, HEL) to keep the loan-to-value (LTV) below a certain level which is typically 80%. These loans have rights to any proceeds after rst lien obligations are satised Loan Terms 30-year xed-rate, level pay, amortized on a monthly basis Terms of 10, 15 and 20 years are also popular Most loans amortize over loan term, however, some loans require a balloon payment before 30 years (typically 5 or 7 years) Professor John P. Miller Fixed Income: MBS Mechanics 3 / 47 Interest Rate Type Fixed-rate Level payment Majority of payment is interest at beginning of term and principal at the end of term Adjustable Rate (ARMs) Rate indexed to benchmark rate (LIBOR, or constant maturity treasury, CMT) LIBOR (London Interbank Oered Rate) Historically determined by using the BBA Method (British Bankers Association) where the oer rates from 16 BBA banks are ordered, the highest four and the lowest four rates of discarded, and the remaining 8 rates averaged. In February 1, 2014, ICE Benchmark Administration (IBA) took control, and is transitioning from bank submissions to tradable quotes. Hybrid ARMs: Rate is initially xed for a period of 3, 5, 7 or 10 years, then reset annually like a traditional ARM Professor John P. Miller Fixed Income: MBS Mechanics 4 / 47 Credit Guarantees Government Loans Backed by the \"full faith and credit\" of the U.S. government Originating federal agencies FHA (Federal Housing Authority): Provides loans to low income borrowers who can only aord low down payments VA: Provides loans to veterans Both agencies require borrowers to purchase mortgage insurance provided by the federal government Conventional conforming Loans Originated by government sponsored enterprises (GSEs): Fannie Mae and Freddie Mac Originators paid an average of 38 bps in 2012 GSEs introduced loan level price adjustments (LLPAs) in 2008: Upfront fees paid by lenders based on LTV and other risk factors Loans securitized on a non-recourse basis Private label loans Also termed jumbo or whole loans Loan sizes tend to be large Originator does not oer credit enhancements Professor John P. Miller Fixed Income: MBS Mechanics 5 / 47 Loan Characteristics: 2014 Loan Limits FHA Loan Limits Limit High-Cost Limit Single Family $271,050 $729,750 Two Unit $374,000 $934,200 Three Unit $419,425 $1,129,250 Four Unit $521,250 $1,403,400 VA $417,000 Fannie Mae/Freddie Mac Single Family $417,000 Two Unit $533,850 Three Unit $645,000 Four Unit $801,950 Loan sizes above the conventional limits are sold under a \"private label\" Professor John P. Miller Fixed Income: MBS Mechanics 6 / 47 Mechanics of Mortgage Loans: Determining Monthly Payments Loan amount = T M t=1 (1+i)t M = Loan Amount i 1(1+i)T Where i = mortgage rate divided by 12 M = monthly mortgage payment T = number of years times 12 Example: $250,000 30-year xed-rate mortgage at 6% i = 0.06/12 = 0.005 0.005 M = 250, 000 11.005360 = $1, 498.88 In Excel = pmt(0.06/12, 360, 250000) Professor John P. Miller Fixed Income: MBS Mechanics 7 / 47 Mechanics of Mortgage Loans: Cash Flows Example: 30-year xed-rate mortgage at 6% Pmt 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 Int 1,250.00 1,248.76 1,247.51 1,246.25 1,244.99 1,243.72 1,242.44 1,241.16 1,239.87 1,238.57 1,237.27 1,235.96 Princ 248.88 250.12 251.37 252.63 253.89 255.16 256.44 257.72 259.01 260.30 261.60 262.91 Bal 249,751.12 249,501.00 249,249.63 248,997.00 248,743.11 248,487.95 248,231.51 247,973.80 247,714.79 247,454.49 247,192.88 246,929.97 Month 349 350 351 352 353 354 355 356 357 358 359 360 Pmt 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 1,498.88 Bal 16,003.54 14,584.68 13,158.73 11,725.65 10,285.40 8,837.95 7,383.26 5,921.30 4,452.03 2,975.42 1,491.42 0.00 1200 1000 Amount ($) 800 600 400 Then, It = i Bt1 and Pt = M It Princ 1,411.80 1,418.86 1,425.95 1,433.08 1,440.25 1,447.45 1,454.69 1,461.96 1,469.27 1,476.62 1,484.00 1,491.42 200 Let Bt be the mortgage balance at time t, It be the interest at time t, and Pt be the principal paid at time t Int 87.08 80.02 72.92 65.79 58.63 51.43 44.19 36.92 29.61 22.26 14.88 7.46 Interest Principal 1400 Month 1 2 3 4 5 6 7 8 9 10 11 12 0 50 100 150 200 250 300 350 Month Professor John P. Miller Fixed Income: MBS Mechanics 8 / 47 Mechanics of Mortgage Loans: Amortization 1 (1 + i)nT 1 (1 + i)T where n is the payment month 100,000 Current balance = Original Balance 60,000 40,000 20,000 Principal Balance ($) 80,000 30Year 20Year 15Year 0 50 100 150 200 250 300 350 Month Professor John P. Miller Fixed Income: MBS Mechanics 9 / 47 Mechanics of Mortgage Loans: Components of Adjustable-Rate Mortgages Initial Rate: Usually ARMs are \"teased\" at a low initial rate and reset each period (usually annually) subject to periodic caps, life cap and oor Margin: Amount added to the index Example: 1-yr CMT is 4.5% and the margin is 200 bps, then the rate will be 4.5% + 2% = 6.5% Floor: Minimum rate Periodic Cap: Maximum change in the rate during any reset Life Cap: Maximum rate When the rate changes, the loan is recast such that it fully amortizes by the maturity date Professor John P. Miller Fixed Income: MBS Mechanics 10 / 47 The Mortgage Industry Origination channel Retail: Originators work directly with borrower Wholesale: Originators work indirectly with borrower through mortgage brokers Type of institution Depository (banks, savings and loans, and credit unions): loan originations either held on balance sheet or sold to market Nondepository (mortgage banks): loans are accumulated and sold to capital markets Originators underwrite and fund the loan Servicers collect the monthly payments, deal with delinquencies, and sometimes also collect property taxes and insurance Originators and servicers can be dierent entities Professor John P. Miller Fixed Income: MBS Mechanics 11 / 47 Loan Underwriting Process Determine the borrowers ability to repay the loan Credit scores: Fair Isaac Corporation (FICO) credit scores Scores range from 350 to 850 with 660 being the \"prime\"/\"subprime\" cuto Income ratios Front ratio: total monthly mortgage payments, including insurance and property taxes, divided by borrowers pretax monthly income Back ratio: total of mortgage payments plus any other debt including auto loans, school loans and credit card debt General front and back ratio limits are 29% and 41% Documentation: pay stubs, bank statements and tax returns and credit report from either Experian, Transunion or Equifax Determine the value of the property Property inspection Real estate appraisal Loan-to-value (LTV): borrowers may be required to purchase private mortgage insurance if the LTV is above 80% Professor John P. Miller Fixed Income: MBS Mechanics 12 / 47 The Mortgage Origination Process Application \u000f Underwriting / Commitment h \u000f Loan Closed o 7 Warehousing Risk: Interest rate changes Pipeline Risk 1. Interest Rate changes 2. Fallout \u000f w / Loan Sold ( \u000f Settlement Professor John P. Miller Fixed Income: MBS Mechanics 13 / 47 Originator Risks Lender/Originator assumes \"fallout\" and interest rate risks for time between mortgage commitment and loan is closed. Lender assumes interest rate risk while loan is warehoused between the time closing and loan sale settles. To reduce the interest rate risks, the market has developed what is known as the To-Be-Announced (TBA) market. Professor John P. Miller Fixed Income: MBS Mechanics 14 / 47 Creating a 30-Year Mortgage Pass-through Loan #1 - 30Yr Mortgage $250,000 balance 6.25% 358 remaining term Pass-through: $1 million face value Loan #2 - 30Yr Mortgage $150,000 balance 6.50% 360 remaining term Loan #3 - 30Yr Mortgage $200,000 balance 6.50% 360 remaining term \u001e + Pooled monthly cash ow / 3 Interest Scheduled principal payments Prepayments 7 \u000f Loan #4 - 30Yr Mortgage $100,000 balance 6.25% 355 remaining term Rule for distribution of cash ow Pro rata basis Loan #5 - 30Yr Mortgage $300,000 balance 7.00% 360 remaining term Mortgage servicer and securitizing agency receive a portion of interest rate paid by the borrower Professor John P. Miller \u000f Fixed Income: MBS Mechanics 15 / 47 Pool Characteristics Pool Balance = $250,000 + 150,000 + 200,000 + 100,000 + 300,000 = $1,000,000 Weighted average coupon (WAC) is current balance-weighted-average mortgage rate on loans in pool: WAC = 5 i=1 bi ri 5 i=1 bi = 6,562,500 = 6.5625 1,000,000 Weighted average maturity (WAM) is the current balance-weighted-average of remaining term of loans in pool: W AM = 5 i=1 bi Ti 5 i=1 bi = 359,000,000 = 359 1,000,000 WAC and WAM, along with the current pool balance will be used to generate cash ows for the pool. Professor John P. Miller Fixed Income: MBS Mechanics 16 / 47 Agency Mortgage Rate Components Net coupon is paid the holder of the MBS: generally traded on whole and half coupons Required servicing is portion of interest rate required to be held by servicer - generally 25 bps Guarantee fee is fee paid to the agencies to insure loan in the event of a default and loss Ginnie Mae g-fees are typically 6 bps Fannie Mae and Freddie MAC g-fees depend on the loan type, borrower characteristics, and securitizing institution Excess servicing is amount of servicing above the required amount and is sometimes sold Net coupon = gross rate - required servicing - g-fee - excess servicing Professor John P. Miller Fixed Income: MBS Mechanics 17 / 47 Development of MBS Market Federal Housing Administration (FHA) was established through the National Housing Act of 1934. FHA developed and promoted long-term, self-amortizing mortgage loans. It also provided for mortgage insurance to protect lenders from default risks. After WWII (1948), the Veterans Administration also had a standardized mortgage loan program. FNMA was established in 1938 to provide liquidity by purchasing qualied loans from lenders. FNMA was also responsible for establishing a secondary market for mortgages. In 1968 Congress split FNMA into two organizations: FNMA GNMA issued rst mortgage-backed pass-through (MBS) In 1970 Congress created FHLMC. In 1971, FHLMC issued its rst participation certicate (PC) which pooled conventional mortgages. Professor John P. Miller Fixed Income: MBS Mechanics 18 / 47 Development of MBS Market (cont) FNMA created rst x-rate mortgage pass-through in 1981, and was rst agency to create adjustable-rate mortgage pass-throughs in 1984. By the mid-1970s, depository institutions held 64% of loans, of which S&Ls held 37%. A sharp rise in short-term interest rates at the end of the 1970s led to an asset-liability mismatch for holders of mortgage loans. In response to market demands for assets that matched liabilities, FHLMC created the rst collateralized mortgage obligation (CMO). Professor John P. Miller Fixed Income: MBS Mechanics 19 / 47 Credit Characteristics of Agency Mortgages GNMA guarantees full timely payment of principal and interest. GNMA's guarantee is backed by \"full faith and credit of the U.S.\" FNMA and FHLMC also oer guaranteed timely payment of principal and interest payments, however, their guarantee is NOT backed by the \"full faith and credit of the U.S.\" - Until September 6, 2008 when GSEs were placed in conservatorship by the Treasury (Lehman les for bankruptcy 9/15/2008) Professor John P. Miller Fixed Income: MBS Mechanics 20 / 47 To-Be-Announced (TBA) Market Newly issued pass-through MBS trade on a forward basis Settlement occurs once a month Each type of mortgage is assigned a particular settlement day At a particular point in the month, settlement rolls forward to the following month Forward settlement allows originators to sell pools prior to creation Originators can sell up to nine months forward in the TBA market allowing them to \"lock in\" the price for the mortgages Forward settlement also facilitates the creation of CMOs by allowing dealers to purchase collateral used to construct the CMO Current-month occurs two days before the settlement date Dealers in need of collateral to settle a CMO deal, as settlement approaches, bid aggressively to attract the necessary collateral Collateral demand may also impact the dollar roll market Professor John P. Miller Fixed Income: MBS Mechanics 21 / 47 Features of the TBA Market Lenders can sell forward up to nine months Purchaser does not know the characteristics of the pool until the \"call out\" date, however, the Bond Market Association sets good delivery standards Species delivery date Net coupon Maximum number of pools delivered Maximum seasoning Fannie Mae, Freddie Mac and Ginnie Mae permit a 0.01% variance in the amount delivered Example: If you purchased a $10 million FNMA 6s for October delivery, your actual delivery could be between $9,999,900 and $10,000,100 The Bond Market Association Uniform Practices Manual can be found www.sifma.org Professor John P. Miller Fixed Income: MBS Mechanics 22 / 47 FNMA 30Yr TBA Quotes1 1 Bloomberg command APX3 Professor John P. Miller Fixed Income: MBS Mechanics 23 / 47 Features of the Specied Pool Market Pools can also be traded in the specied pool market according to stipulations (or stips) agreed to by the parties Some tradable characteristics A minimum spread between the WAC and the net coupon Seasoning parameters Geographic parameters Average and maximum loan size The specied pool market has grown tremendously since 1995 Professor John P. Miller Fixed Income: MBS Mechanics 24 / 47 Agency Pass-Throughs: Payment Delays Normal delay: Monthly payments are made in arrears. Principal & interest for September 2013 is paid at beginning of October 2013 Actual delay: Number of days the agency uses to process the payments and forward the proceeds onto the MBS investors. For example, if the payment is made on February 15th, then the actual delay is 14 days. Stated delay. Normal delay + actual delay+1. For example, have 30 days of normal delay plus fourteen days of actual delay, so the stated delay is 45 days. Agency Stated Delay Actual Delay Ginnie Mae I 45 14 Ginnie II 50 19 Fannie Mae 55 24 Freddie Mac 45 14 Accrued interest and principal is paid to owner of record on last day of previous month and paid on the Actual Delay + 1 the following month MBS accrued interest is 30/360 Professor John P. Miller Fixed Income: MBS Mechanics 25 / 47 How Does the Actual Delay Impact Pricing? Using our pricing formula: W AM + P = t=1+ CFt 1 = (1 + y)t (1 + y) where = W AM t=1 CFt (1 + y)t Actual delay 12 360 Examples 14 day actual delay, 5% yield: $0.19 or 0-06 ticks 24 day actual delay, 5% yield: $0.33 or 0-10+ ticks 24 day actual delay, 4% yield: $0.27 or 0-08+ ticks Professor John P. Miller Fixed Income: MBS Mechanics 26 / 47 Pricing a MBS Pass-Through: No Prepayments Assuming that there are no prepayments: P = 100 Face W AM t=1 CFt (1 + y)t y = current periodic yield W AC/1200 CFt = CF = current face 1 (1 + W AC/1200)W AM Example: What is the price of a $100,000 MBS pool with a 6.5% WAC and 360 WAM, assuming a 6.20% yield? CF = P = = 100,000 6.5/1200 1 (1 + W AC/1200)360 = 632.07 100 1 (1 + 0.062/12)360 632.07 100,000 0.062/12 100 103,200.33 = 103.20033 or 103-06+ 100,000 Note: Can only solve this way because of no prepayment assumption; however, in practice, prepayments dramatically impact the monthly cash ows! Professor John P. Miller Fixed Income: MBS Mechanics 27 / 47 Prepayments: SMM Single Monthly Mortality: SM Mt = 100 1 Actual balancet Scheduled balancet Example: A 30-year 6% mortgage with a $200,000 original balance. Prior to month 60th, there were no prepayments, and at month 60th, the actual balance was 185,000. What is the SMM that month? Using our formula Schedule balance60 = P60 = $186,108.71 Actual balance60 = $185,000 SM M = 100 (1 185,000/185,108.71) = 0.596% How much was prepaid? $186, 108.71 185, 000 = $1,108.71 Professor John P. Miller Fixed Income: MBS Mechanics 28 / 47 Prepayments: CPR Constant prepayment rate (CPR): SMM's annualized prepayment rate CP R = 100 1 (1 SM M/100)12 Example: What is CPR when the SM M = 0.596%? CP R = 100 (1 (1 0.596/100)12 ) = 6.92% Interpretation: If pool prepaid at 0.596% SMM for 12 months then the actual remaining factor would be lower than the scheduled factor by 6.92% at the end. Use the following expression to go from CPR back to SMM SM M = 100 1 (1 CP R/100)1/12 Professor John P. Miller Fixed Income: MBS Mechanics 29 / 47 Prepayments: PSA Prepayment Standard 100% PSA is denes the CPR according the pool WALA (weighted-average loan age) as follows: 100% PSA = min(WALA 0.2, 6) Example: if the prepayment is 6.92% CPR when WALA is 60, what is the PSA? 6.92 100 = 115% min(60 0.2, 6) 100% PSA at 28 WALA: min(28 0.2, 6) = 5.6% CPR 300% PSA at 28 WALA: 3 min(28 0.2, 6) = 16.8% CPR 150% PSA at 60 WALA: 1.5 min(60 0.2, 6) = 9% CPR Professor John P. Miller Fixed Income: MBS Mechanics 30 / 47 Projecting Monthly Cash Flows ft = ft1 (1 SM Mt /100) Survival factor: Pool mortgage payment: Mt = ft1 M0 Net interest received by investor: It = Pt1 (r s) Monthly servicing: St = Pt1 s Scheduled monthly princ pmt: Scht = Mt It St Monthly prepayment: P Pt = SM Mt /100 [Pt1 Scht ] Monthly CF received by investor: CFt = It + Scht + P Pt Period-end principal balance: Professor John P. Miller Pt = Pt1 Scht P Pt Fixed Income: MBS Mechanics 31 / 47 Monthly Cash Flows at 300% and 800% PSA Original Balance PSA t 1 2 3 4 5 6 7 8 9 10 11 12 CPRt 0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 6.6 7.2 100,000 300% SMMt 0.0501% 0.1006% 0.1513% 0.2022% 0.2535% 0.3051% 0.3569% 0.4091% 0.4615% 0.5143% 0.5674% 0.6208% Original Balance PSA t 1 2 3 4 5 6 7 8 9 10 11 12 CPRt 1.6 3.2 4.8 6.4 8.0 9.6 11.2 12.8 14.4 16.0 17.6 19.2 Professor John P. Miller ft1 1.00000 0.99950 0.99849 0.99698 0.99497 0.99244 0.98942 0.98589 0.98185 0.97732 0.97229 0.96678 Mt 632 632 631 630 629 627 625 623 621 618 615 611 It 500 499 498 497 496 494 492 490 487 485 482 478 St 42 42 42 41 41 41 41 41 41 40 40 40 WAM WAC Serv. Scht 90 91 91 92 92 92 92 93 93 93 93 93 360 6.5% 0.5% PPt 50 100 151 201 251 301 351 400 449 498 546 593 CFt 640 690 740 790 839 887 935 983 1029 1075 1120 1165 Pt 99860 99668 99426 99134 98791 98398 97954 97462 96919 96329 95690 95004 St 42 42 41 41 41 41 40 40 39 39 38 38 WAM WAC Serv. Scht 90 91 91 91 91 91 91 90 90 89 88 87 360 6.5% 0.5% PPt 134 270 406 543 680 816 951 1084 1214 1341 1465 1585 CFt 725 859 994 1129 1262 1394 1524 1652 1776 1896 2012 2123 Pt 99775 99415 98917 98283 97512 96605 95564 94390 93086 91656 90102 88430 100,000 800% SMMt 0.1343% 0.2707% 0.4091% 0.5496% 0.6924% 0.8375% 0.9850% 1.1349% 1.2873% 1.4424% 1.6003% 1.7609% ft1 1.00000 0.99866 0.99595 0.99188 0.98643 0.97960 0.97139 0.96182 0.95091 0.93867 0.92513 0.91032 Mt 632 631 630 627 623 619 614 608 601 593 585 575 It 500 499 497 495 491 488 483 478 472 465 458 451 Fixed Income: MBS Mechanics 32 / 47 Pricing a MBS Pool with Prepayments Generation of monthly cash ows is required to compute the price of the pool: The net present value of the monthly cash ows divided by the original balance and multiplied by 100 to convert price into a percentage of par: P MBS = 100 Original Balance WAM+ t=1+ CFt (1 + y)t Need to account for payment delay, (see slide 26), which depends on the type of pool being priced Prepayment assumption changes impact pricing as cash ows change, with one exception being the case where the discount yield equals the net coupon Since prepayment rates depend on mortgage rates, changing interest rate assumptions impacts the discount rate and the structure of the underlying cash ows! Professor John P. Miller Fixed Income: MBS Mechanics 33 / 47 Impact of Prepayments on Principal Cash Flows W AM t=1 t (principal received at time t) total principal 100,000 1 Average Life = 12 60,000 40,000 Avg. Life (in yrs) 19.6 14.7 11.5 5.8 2.3 20,000 PSA 0% 50% 100% 300% 1000% Pool Balance ($) 80,000 0 PSA 50 PSA 100 PSA 300 PSA 1000 PSA 0 50 100 150 200 250 300 350 Month Professor John P. Miller Fixed Income: MBS Mechanics 34 / 47 Prepayments Are Volatile: FNMA 30-Year Prepayments CPN YR 3.0 2013 3.0 2012 3.5 3.5 3.5 3.5 Iss Amt $mm 150,439 161,500 Remaining $mm Pools WAC WAM Age 149,056 3890 3.589 355 3 153,412 4423 3.591 349 8 May 2.7 7.9 Apr 1.9 5.1 CPR Mar Feb 1.3 0.8 4.4 4.6 Jan 0.5 6.8 2013 2012 2011 2010 42,582 232,747 50,951 23,326 42,213 3152 4.028 199,822 9730 4.007 34,607 1272 4.029 14,311 658 4.122 354 344 335 322 3 12 20 31 3.1 15.4 22.0 25.3 2.2 11.0 17.6 22.0 1.4 11.8 19.0 23.9 1.1 13.7 24.7 26.4 0.5 17.7 30.9 30.7 4.0 2012 4.0 2011 4.0 2010 74,741 118,061 127,504 64,230 6105 4.472 77,394 4104 4.469 67,927 3191 4.494 341 332 322 13 23 32 16.6 26.0 30.5 13.7 24.1 27.7 13.3 25.0 29.6 12.8 25.8 30.3 14.5 30.5 33.8 4.5 4.5 4.5 4.5 2012 2011 2010 2009 8,443 101,877 138,481 292,664 7,304 65,491 67,294 99,108 1746 6025 4686 4403 4.962 4.934 4.941 4.935 340 330 317 304 15 24 36 47 16.9 27.2 32.6 40.3 15.2 26.0 32.4 39.2 13.4 25.7 31.7 39.3 11.0 23.3 29.9 37.7 12.3 25.6 32.0 40.6 5.0 5.0 5.0 5.0 5.0 2011 2010 2009 2008 2007 29,485 66,211 81,946 90,286 21,612 20,777 36,744 30,291 13,622 3,541 3356 2949 3401 2096 985 5.373 5.363 5.425 5.656 5.744 329 317 307 291 278 25 37 46 61 74 24.0 28.2 35.1 55.0 49.0 22.4 26.8 33.3 53.2 50.0 20.1 25.0 32.0 51.1 48.3 19.0 23.1 28.8 48.4 45.4 19.1 24.4 30.2 51.2 49.0 5.5 2009 5.5 2008 5.5 2007 10,502 150,993 155,984 4,528 1436 5.939 22,674 4411 6.044 21,064 4003 6.14 306 292 280 46 61 72 31.1 52.8 51.9 26.3 50.3 49.7 26.6 47.8 46.4 22.9 44.4 44.4 24.2 46.9 48.8 6.0 2008 6.0 2007 6.0 2006 81,036 188,828 160,327 12,850 4425 6.538 28,253 6000 6.573 21,625 6201 6.561 292 282 268 60 71 83 50.0 48.6 47.1 47.8 46.7 44.6 44.9 42.7 42.8 41.5 40.4 39.2 43.1 42.9 42.8 Professor John P. Miller Fixed Income: MBS Mechanics 35 / 47 Prepayments are Path Dependent Unlike stock prices, prepayments do not follow a Markov process Cannot use any closed-form methods or binomial trees for valuation purposes MBS valuation depends heavily on econometric prepayment models to forecast cash ows as a function of the future mortgage rates Prepayment from renancing is the greatest source of prepayment risk Professor John P. Miller Fixed Income: MBS Mechanics 36 / 47 Path Dependence: A Simple Prepayment Example Assume model with three classes of borrowers who initially are equally represented in the pool Prepayment rates when prevailing mortgage rate is 2% lower than current mortgage rate Fast: 90% CPR Medium: 50% CPR Slow: 30% Pool prepayment speed = (90% + 50% + 30%)/3 = 56.7% Prepayments after one year of rate exposure Fast now represents only 7.7% of pool, medium represents 38.5% of the pool and slow represents 53.8% of the pool Prepayment speed = 0.077 90% + 0.385 50% + 0.538 30% = 42.3% Professor John P. Miller Fixed Income: MBS Mechanics 37 / 47 Basic Structure of Prepayment Models SMM = Turnover + Renancing Turnover Factors Loan Age LockIn: Spread to current mortgage rate (WAC rt ) 0 Burnout Surge Eect Loan Size Credit Quality Geography Prepayment Penalties Professor John P. Miller Fixed Income: MBS Mechanics 38 / 47 Prepayment S-Curve Prepayment S-curve was generated using Bloomberg median forecasts for a FNMA 30Yr 3% coupon with 359 WAM and 3.7% WAC 1650 1500 1250 PSA 1000 750 500 250 100 50 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 Mortgage Yield (%) Professor John P. Miller Fixed Income: MBS Mechanics 39 / 47 MBS Price-Yield Curve with Prepayments 130 140 150 The price-yield relationship curves assuming 0 prepayments, a 3% 10-Yr Treasury and prepayments using the S-curve from previous slide 120 110 100 3% 10Yr Treasury SCurve Price 70 80 90 MBS 3% Coupon Price 0% CPR Price 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Mortgage Yield (%) Professor John P. Miller Fixed Income: MBS Mechanics 40 / 47 Mortgage Securities Lending Provides market participants liquidity and exibility Reason for MBS lending Cover short positions such as an investment bank collecting collateral for a CMO deal Increase leverage: hedge funds use collateral to leverage and increase returns (and risk!) Institutional investors can earn extra income and defray custodial fees by lending securities Types of MBS lending Repurchase agreements (or \"repos\"): immediate sale simultaneous future repurchase agreements Dollar rolls: A simultaneous sell and future buy order Security Financing Rate Principal & Interest Used to Cover Short Haircut Same Securities Returned Prepayment Risk Professor John P. Miller Repo Any Collateral dependent Original owner No Yes Yes No Fixed Income: MBS Mechanics Dollar Roll MBS pass-through spread to repo rate Holder of record Yes No No, but similar Yes 41 / 47 Repo Basics Collateral: Besides MBS pass-throughs can include CMOs, corporates, Treasuries, etc. Haircut: Determines the margin, generally range from 1% to 10%, higher the haircut less that can be nanced Term Overnight repo: 1 day Term repo: periods exceeding 1 day, but less than 3 months Open repo: rate reset each day Title: Loses title, but receives principal and interest payments Risks Credit: Either party may default Liquidity: Short squeezes lead to failed transactions as lenders can't replace securities Market: Price declines lead to margin calls with T+0 settlement Settlement: failure of either party (cash or collateral at settlement) Professor John P. Miller Fixed Income: MBS Mechanics 42 / 47 Repo Example Repo $5 million of FNMA 30-Yr 3.5% for 10 days at 0.45% with a 5% haircut Current price (bid side) and accrued interest: 9 = 100.775 $100 22 + 3.5 360 Bond value: 5,000,000 1.00775 = 5,038,750 Repo Principle: 5,038,750 (1 0.05) = 4,786,812.50 10 Repo interest: 4,786,812.50 0.0045 360 = 598.35 +3 Day 1: Seller (borrower) $5,038,750 FN 30Yr 3.5% ks Buyer (lender) $4,786,812.50 +3 Day 10: Seller (borrower) $4,786,812.50 + $598.35 ks Buyer (lender) $5,038,750 FN 30Yr 3.5% Professor John P. Miller Fixed Income: MBS Mechanics 43 / 47 Dollar Roll Basics Selling the roll: Sell \"front month\" and buy \"back month\" Seller gives up principal and interest to buyer of roll Securities returned are \"substantially similar\Question 2 a) WAC WAM Current Balance Aggregate mortgage payments Interest payment Principal payment Scheduled balance next month 3.45% ... weighted average coupon. 325 ... weighted average maturity (months). 75,000,000.00 .. Principal. $355,440.45 .... PMT(rate = WAC/12, nper = WAM, PV = Current Balance) $215,625.00 .... (WAC/12) * Current balance. $139,815.45 .... Aggregate mortgage payments - Interest payment. 74,860,184.55 .... Current balance - Principal payment. b) Actual balance SMM CPR 74,125,000.00 ... Note that this differs from the actual balance in the question of $741,250,000. 0.982% ... Single Monthly Mortality. SMM = 1 - (Actual balance/Scheduled balance). 11.17% ... Constant prepayment rate. CPR = 1 - (1- SMM)^12. c) WALA 100% PSA 28 ... months. 199% ... 100% PSA = (CPR*100)/(min{WALA*0.2,6}) 2,578.18 Original Balance PSA t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 Age 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 SMM(t) #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 500,000 250 f(t-1) 1.00000 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! M(t) 2,578 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! Net Age WAM WAC Servicing I(t) S(t) 1667 271 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 4.00% 1 360 4.65% 0.65% Sch(t) 641 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! Discount Rate 3.500% Prices PP(t) #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 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Fac #VALUE! 0.9971 #VALUE! 0.9942 #VALUE! 0.9913 #VALUE! 0.9884 #VALUE! 0.9855 #VALUE! 0.9827 #VALUE! 0.9798 #VALUE! 0.9770 #VALUE! 0.9741 #VALUE! 0.9713 #VALUE! 0.9685 #VALUE! 0.9657 #VALUE! 0.9628 #VALUE! 0.9600 #VALUE! 0.9573 #VALUE! 0.9545 #VALUE! 0.9517 #VALUE! 0.9489 #VALUE! 0.9462 #VALUE! 0.9434 #VALUE! 0.9407 #VALUE! 0.9379 #VALUE! 0.9352 #VALUE! 0.9325 #VALUE! 0.9298 #VALUE! 0.9271 #VALUE! 0.9244 #VALUE! 0.9217 #VALUE! 0.9190 #VALUE! 0.9163 #VALUE! 0.9137 #VALUE! 0.9110 #VALUE! 0.9084 #VALUE! 0.9057 #VALUE! 0.9031 #VALUE! 0.9005 #VALUE! 0.8978 #VALUE! 0.8952 #VALUE! 0.8926 #VALUE! 0.8900 #VALUE! 0.8874 #VALUE! 0.8849 #VALUE! 0.8823 #VALUE! 0.8797 #VALUE! 0.8772 #VALUE! 0.8746 #VALUE! 0.8721 #VALUE! 0.8695 #VALUE! 0.8670 #VALUE! 0.8645 #VALUE! 0.8620 #VALUE! 0.8595 #VALUE! 0.8570 #VALUE! 0.8545 #VALUE! 0.8520 #VALUE! 0.8495 #VALUE! 0.8470 #VALUE! 0.8446 #VALUE! 0.8421 #VALUE! 0.8397 #VALUE! 0.8372 #VALUE! 0.8348 #VALUE! 0.8324 #VALUE! 0.8299 #VALUE! 0.8275 #VALUE! 0.8251 #VALUE! 0.8227 #VALUE! 0.8203 #VALUE! 0.8179 #VALUE! 0.8156 #VALUE! 0.8132 #VALUE! 0.8108 #VALUE! 0.8085 #VALUE! 0.8061 #VALUE! 0.8038 #VALUE! 0.8014 #VALUE! 0.7991 #VALUE! 0.7968 #VALUE! 0.7945 #VALUE! 0.7922 #VALUE! 0.7899 #VALUE! 0.7876 #VALUE! 0.7853 #VALUE! 0.7830 #VALUE! 0.7807 #VALUE! 0.7784 #VALUE! 0.7762 #VALUE! 0.7739 ### PV Coll. #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 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