HW about (CMBS, SDA,PAS,CDR) loan

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timer Asked: Nov 20th, 2016

Question description

HW4

FOR ANY SPREADSHEET, YOU MUST HIDE REPETITIVE ROWS THAT DO NOT ILLUSTRATE ANYTHING SUBSTANTIALLY NEW. Do not make any one spreadsheet printout more than 2 pages max (you will generally need only one). Do not continue table columns across several pages (best to print in landscape mode). FAILURE TO DO ALL THIS WILL RESULT IN A LOSS OF FIVE (5) POINTS. 41 points total.

ANNOTATE any formulae that involve more than addition and subtraction (e.g., using a pen or Office’s comment feature - just one period will suffice, of course)

  • [22pts]
    • [20pts] Consider a 100,000,000 CMBS pass-through (PT) security consisting of fresh 15 year fixed rate loans that fully amortize over a period of 30 years, and have a WAC of 7% with fees amounting to 0.5%. For purposes of this HW, a CMBS is like a RMBS, except that all loans have a prepayment lock-out (assume for the entire term), but default occurs according to the standard SDA function. Additionally, since the loans do not fully amortize, there is generally a balloon loss - quoted as a fraction of the outstanding balance at mortgage maturity. To simplify, assume that there is no recovery (unrealistic, of course). Assume that the PT is sold at 94.345. Allow for loans to default at the PSA’s SDA CDR, and allow for balloon risk. The current (corresponding maturity) Treasury yield is 5%. Create a table and graph of the spread (in bps) of cash flow yield to Treasury versus SDA, for 0% and 10% balloon loss. In the spreadsheet that you hand-in, show the situation for 100 SDA and 10% balloon loss. Use par pricing. See notes below for further assumptions and hints.
    • [2pts] Why is there generally a large fraction of outstanding principal that defaults at maturity?
  • [8pts] Consider the following par yield curve for semiannual bonds, all quoted as BEY:
    • [6pts] What are the corresponding zero rates?
    • [2pts] What is today’s lockable rate for a 6 month loan 1 year from now?
  • [10pts] Stratify the following Agency mortgages at a deal coupon of 4%. What are the initial pool and PO principals, and what are the initial notional principal and coupon of the IO?

Maturity [yr]

Par Yield

0.5

1%

1

2%

1.5

3%

Gross

Net

Balance (mln $)

4.10%

3.852%

50.343

4.20%

3.934%

101.435

4.30%

4.071%

123.777

4.40%

4.153%

40.123

_____________________________________________________________________________

Notes for question 1:

  1. Note that there is no messy tranching going on here.
  2. Allow for a general SDA; see the graph and spreadsheet in your lecture notes.
  3. Here is one way to get the CDR (as there are better versions, feel free to use your own, extra points if you can show me that the formula below is wrong); “A13” refers to the month and “SDA” to the SDA factor: =(IF(A13<=30,A13*0.006/30,0)+IF(AND(A13>30,A13<=60),0.006,0)+IF(AND(A13>60,A13<=120),0.006-(0.006-0.0003)/(120-60)*(A13-60),0)+IF(A13>120,0.0003,0))*SDA/100
  4. Assume that loss recovery is zero – any loan that defaults is a completely written down.
  5. Defaults work much like prepayment, with one exception: the monthly default happens just before the payment (why pay interest and principal if you are defaulting anyway). So take default = beginning balance × MDR and then apply the appropriate pool survival factor to get the realized “mortgage payment.”
  6. Make sure you create a column of the PT cash flows, including the initial investment at par, so that you can calculate the CF yield.
  7. Balloon losses are quoted as a fraction of the final outstanding principal.
  8. In your graph, show a range of SDA’s of 0 to 1,000. You will find that you do not have to compute very many values in that range.
  9. Display all cash flows to the nearest dollar (use format → cell).

FRL 383 Fall 2016 LN 4: Overview MBS Market 1 LN04 OVERVIEW OF MBS MARKET FRL 383 Fall 2016 LN 4: Overview MBS Market 2 Material • FBB.2, also • Overlap is partial • F.11 (parts of) • S.(1,2),6 • BF.19 • Overview • Types of MBS (Mortgage-Backed Securities, aka MRS, or Mortgage-Related Securities) • Trading • Structuring FRL 383 Fall 2016 LN 4: Overview MBS Market 3 Introduction • MBS = mortgage backed security • Generic term for a debt-like security that is backed by mortgages (which are in turn backed by real property) • Primary market: Mortgages originated • Secondary market: Sold into capital markets; MBS, REITs FRL 383 Fall 2016 LN 4: Overview MBS Market Introduction • Creation of MBS is called (mortgage) securitization and involves • Pooling & Structuring • Pooling = collecting “similar” mortgages • Structuring = rearranging cash flows • Characteristics • Security backed by mortgages (sometimes also leases) • Credit enhancement • Alter duration, prepay exposure • Legal structure so as to avoid double taxation 4 FRL 383 Fall 2016 LN 4: Overview MBS Market Introduction • Types of MBS • Mortgage pass-through securities (MPT) • Proportional, direct ownership in underlying pool • Little, if any, structuring • Collateralized mortgage obligations (CMO) • Pool is collateral • Extensive structuring (“tranching”) • Aka REMICs – Real Estate Mortgage Investment Conduits • Strips: IO and PO • Interest-only and principal only cash flows • Mortgage-backed bonds • Mortgage pay-through bonds 5 FRL 383 Fall 2016 LN 4: Overview MBS Market 6 Rationale • Supply-side: Liquidity for originators • Fresh lending possible; A=E+D and E/A>x, E/AR>y • Moderates boom-bust cycles in housing • Historically: Regulation-Q • Demand-side: Asymmetric information issues • Standardization (mortgages not homogeneous) • Credit risk insurable • Scale • Capital markets better suited to deal with interest rate risk when compared to banks • Geographical need-of-funds matching FRL 383 Fall 2016 LN 4: Overview MBS Market 7 Rationale • Additionally, secondary market development is encouraged by: • Life insurance funds traditionally purchased whole loans, but began reducing exposure 70’s and 80’s • Mortgage bankers need to find fresh sources of capital • Pension funds growing and needed long-term investments • Why long-term? • Government begins removing obstacles (state blue-sky laws), and subsidizing its development (chartering FNMA and FHLMC, for example, and expanding the role of GNMA) FRL 383 Fall 2016 LN 4: Overview MBS Market 8 MBS Creation • Generic MBS • Structure (see diagram, over) • Owner sells mortgage receives cash • Short mortgage, long house • Originator (S&L, mortgage banker,..) • Buys mortgage from borrower, pays cash • Sells mortgage to secondary market agency or firm, receives cash • Ends up flat • Secondary market agency/firm • Buys whole loans and sells MBS to capital markets • Ends up flat or long mortgages, short MBS • Investors (capital markets) • Short cash, long MRS FRL 383 Fall 2016 LN 4: Overview MBS Market 9 Generic MBS Creation Flat Mortgage Flat Cash (+) Mortgage (-) MBS Buys Originator Mortgage Mort. Banker, S&L, Thrift, … Sells MBS Secondary market agency or firm Cash Cash Mortgage Borrowers Homeowners, investors (+) MBS (-) Cash (-) (Mortgage) (+) (Cash) (i.e., asset) Investor Pension fund, insurance co, Mutual fund, etc Cash FRL 383 Fall 2016 LN 4: Overview MBS Market MBS Creation • Fundamental unit = pool • Mortgages with more or less similar characteristics • Note rate, term, credit quality, balance, etc. • Pools are transformed into MBS either as • Agency deals • Fannie Mae, Freddie Mac and Ginnie Mae • Underwriting standards • Guarantee fee • Private label transactions • All others 10 FRL 383 Fall 2016 LN 4: Overview MBS Market 11 MBS Creation • Structuring (tranching) • Split up CFs (interest and principal) • Create tranches of different • Duration/average life • Credit quality • Reflects market segmentation • Duration: Banks vs. life insurance/pension funds • Risk tolerance: credit & interest rate risk • Structured MBS are broadly called collateralized mortgage obligations (CMO) FRL 383 Fall 2016 MBS Creation LN 4: Overview MBS Market 12 FRL 383 Fall 2016 LN 4: Overview MBS Market 13 MBS Creation: Private Label • Credit enhancement • Internal: Subordination (senior/sub) (see Exh 2.2) • First loss (unrated, residual) tranche • Junior tranches (AA-B), mezzanine • Senior tranches (AAA) • Shifting interest structure: • Prepay goes to senior tranches first (according to shifting interest % schedule) • Increases subordination level • And therefore enhances credit quality • Internal: Overcollateralization (O/C structure) • Loan collateral (sum mortgage principal) > deal total • External: Insurance FRL 383 Fall 2016 MBS Creation LN 4: Overview MBS Market 14 FRL 383 Fall 2016 LN 4: Overview MBS Market 15 MBS Creation: Stratification • Fixed rate: security coupon created by • Deciding on deal coupon • Splitting mortgages into • Premium (net note rate > security coupon) and • Discount (net note rate < security coupon) loans • Discount loan rates are “brought to deal coupon” by stripping off principal • This excess principal is sold as a WAC PO tranche • Premium loan excess interest is paid to a WAC IO tranche • Principal of this tranche is notional FRL 383 Fall 2016 LN 4: Overview MBS Market MBS Trading • Mortgage loan timeline • Hedging requirements for pipeline leads to a thriving forward market • Pre-identified pools • TBA trades • Stipulated trade • More info available than in TBA • Often an undeliverable TBA, or a pool with better characteristics than deliverable minimum • Dollar rolls • Securities trade in (typically up to 3) forward markets 16 FRL 383 Fall 2016 LN 4: Overview MBS Market 17 MBS Trading: Dollar Rolls • Dealers are often short MBS • Creating CMO’s, Depository Institutions receive favorable tax treatment for actual security rather than forward instrument, etc. • Need to borrow these from investors in the dollar roll market • Roll-in: dealers take security from investor (borrow), investor borrows cash • No margin requirement or OC • Roll-out: dealers return substantially similar security, receive cash • Same issuer and program, coupon, maturity, similar mortgage collateral, aggregate principal must be within 0.1% of original delivered, FRL 383 Fall 2016 LN 4: Overview MBS Market 18 MBS Trading: Dollar Rolls • Compare with a repo agreement • Like a spot sale plus a forward contract • Investor sells security in a front month and agrees to repurchase (substantially similar) security in a back month • Dealer only returns a “substantially similar” security • Not same mortgages, principal has been paid down • Keeps CF’s from pool • Therefore repurchase price < sales price (difference is called the forward drop) FRL 383 Fall 2016 LN 4: Overview MBS Market 19 MBS Trading: Dollar Rolls • Why would an investor loan security, rather than hold it? • Dealer is loaning investor cash at an implied rate • Call this the breakeven reinvestment rate • The investor acts as a borrower, the dealer as a lender • Like a secured loan (MBS is security) • If the actual reinvestment rate for the investor is greater, she has a (somewhat risky) arbitrage opportunity FRL 383 Fall 2016 LN 4: Overview MBS Market 20 MBS Trading: Dollar Rolls • Let’s see how this happens using the (Bloomberg) exhibits in FH.38 (p 931, also handout). • FBB.2 has a shorter discussion – less clear, though • Why “somewhat risky?” • Need an estimate of prepayment rate. The higher the realized rate, better for the investor (lower implied breakeven rate) • The dealer need only return substantially similar security – so adverse selection risk (dealer may deliver poorer-performing security, even though within delivery guidelines) FRL 383 Fall 2016 LN 4: Overview MBS Market 21 MBS Trading: Dollar Rolls • Breakeven rate depends on • Sales price less repurchase price = forward drop • MBS coupon payment • MBS scheduled principal payments • MBS unscheduled principal payments (projected) • Returned MBS attributes • Amount of under- over-delivery permitted • Compare to reinvestment rate available to investor FRL 383 Fall 2016 LN 4: Overview MBS Market MBS Trading: Dollar Roll Analysis • Exh.38-1: • Bloomberg Analysis Screen 1/2 (Discount PT) • Exh.38-2: • Bloomberg Analysis Screen 2/2 • Exh.38-3: • Bloomberg Analysis Screen 1/2 (Premium PT) • Exh.38-4: • Bloomberg Roll Matrix (Discount PT) • Exh.38-5: • Bloomberg Roll Matrix (Premium PT) 22
FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 1 MEASURING PREPAYMENT AND DEFAULT PREPAYMENT MODELLING LN.05&06: FRL 383 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling Measuring Prepayment and Default • FBB.3, also • Overlap is partial • F.11 (parts of) • S.8 (parts of) • Overview • Prepay and default conventions • Not a model of either, more like a benchmark • Construct MPT cash flows • CFY, spreads (Z-spread and OAS) 2 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling Modeling Prepayment • FBB.4, also F.9 • Move away from “benchmarks” • Consider empirical behavior; two broad categories • Empirical models • Short shelf-life • Logit model • Rational prepayment models • Cumbersome • Components of prepayment • Variables that contribute to prepayment 3 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 4 MPT: Prepayment • Start with agency deals – no defaults • Must project CFs (since prepayment unknown) in addition to future interest rates to value MPT • Conventions important • Pricing at origination • Relative value (to other MBS, also other FI) • Hedging, risk management • Ex-post performance FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 5 MPT: Prepayment Conventions • Originally: no prepayment, then all at year 12 • FHA prepayment experience • Prepayment depends on interest rate environment • FHA loans assumable, conventional not • Conditional prepayment rate (CPR) • Constant fraction of remaining pool prepays each month • Conditional on rate environment, pool characteristics, etc. • Public Securities Association (PSA) convention FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 6 Conditional Prepayment Rate • Let • Bt be the unpaid pool balance at date t • Pt be the unpaid pool balance at date t if no prepayments • St be the scheduled repayment for period t (i.e., date t to t+1) • CPRt is an annual rate • Convert to “Single Month Mortality,” SMMt = periodic rate at which pool prepays in period t • SMMt = 1 – (1-CPRt)1/12 • Convention is to compound survival rates • Prepayment in period t is (Bt-1-St)×SMMt • So new pool balance is Bt = Bt-1 - St - (Bt-1-St)×SMMt • Note that (1-SMM) is the monthly survival rate FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 7 Survival Factor Qt aka Bond Factors • The fraction of mortgages in pool that have not prepaid at date t is given by the survival factor, Qt • Qt = (1-SMM1)×(1-SMM2)×… ×(1-SMMt) • = Bt /Pt • Needed to construct MPT cash flows • See example, next FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 8 PSA Benchmark • Think of as way to quote MPT value • Not really a model, but • Based on FHA prepay experience • Monthly series of CPR • Function of age of pool only • Independent of underlying term, interest rate environment, etc. • For “100 PSA:” CPRt = 6% × min(t/30,1), where t is measured in months • See diagram over • So, t=1: CPR = 0.2% and for t≥30: CPR = 6% • Increasing portion called the ramp • For any other “n PSA” benchmark, e.g. n=200, multiply asymptotic CPR factor (=6%) by n/100, e.g., 200/100 × 6%=12% FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 9 PSA Annual Conditional Prepayment Rate 16% 100 PSA 14% 50 PSA 200 PSA 12% 10% 8% 6% 4% 2% 0% 0 20 40 60 80 100 120 Pool Age (Month) 140 160 180 200 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling Agency Pass-Through Cash Flows 10 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 11 Other Conventions • PPC: Prospectus prepayment curve • E.g., ALT-A or subprime different from conforming • Why? • So prospectus will often include language like “8-20% CPR over 12 months” • What does this mean? • HEP: home equity prepayment curves • Ramp is only 10 months • “20% HEP” means the asymptotic CPR is 20% • See Exh 3.6 • MHP: manufactured housing prepayment curve • 100% MHP is 3.6% CPR at t=0 and 6% CPR at t=24months • See Exh 3.7 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling Delinquency, Default & Loss • Now switch to credit sensitive MBS • Private label, CMBS • Terminology is not standard • OTS (MBA): • 0 days late; Current • 1-30 days late: Current (30 days delinquent) • Usually the cut-off for MBA is 15 days late • 30-60 days late: 30 days delinquent • 60-90 days late: 60 days delinquent • More than 90 days delinquent: 90+ days delinquent • Default • Legally, when borrower loses title • Rule of thumb: 90+ = defaulted • Roll rate that far delinquent to default is near 100% 12 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 13 Delinquency, Default & Loss • CDR: Conditional default rate • Again, convert to MDR via MDRt = 1 – (1 – CDRt)1/12 • Default rate for month t = (Default loan balance in month t)/(Beginning balance for month t less Scheduled principal payment in month t) • SDA: Standard default assumption • “100 SDA:” 0 to 0.6% in 30 month, 0.6% in months 30-60, 0.6% to 0.03% from month 60 to month 120, 0.03% thereafter • See diagram over • “n SDA” is, as before, n/100 times this curve • CDX: Cumulative default rate • Total face value defaulted/total face value of pool • COR: Charge off rate (annualized) • Liquidation rate for month t = (Liquidated loan balance in month t)/(Beginning balance in month t less Scheduled Principal payment in month t) • Convert to COR via usual compounding FRL 383 Fall 2016 14 Prepayment and Default Measurement & Modelling PSA SDA CDR Benchmarks 1.40% 1.20% 50 SDA 100 SDA 1.00% 200 SDA 0.80% 0.60% 0.40% 0.20% 0.00% 0 20 40 60 80 100 120 Mortgage Age Months 140 160 180 200 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling Delinquency, Default & Loss • SDA base benchmark often includes a 150 PSA prepayment • Example: See spreadsheet below • Loss-severity rate = (Liquidation balance month t less Liquidation proceeds month t)/(Liquidation balance month t) • Numerator is also loosely the “loss-given-default” 15 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 16 Prepayment Models • Two broad categories • Rational prepayment models • Assume pre-payable and no recourse • View prepayment (and default) as a call option (put option), i.e., • call the mortgage at a strike equal to the outstanding balance plus prepay penalty (put the asset at a strike equal to the outstanding balance) • Mt = Bt - Ct – Pt, • where M is the mortgage value, • B is the equivalent option-free (amortizing) bond value, • C is the call option value, • P is the put option value • When are C and P ITM, OTM? FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 17 Prepayment Models (cont.) • Rational prepayment models • Need interest rate and house price models • Generate “states-of-world” • Solve backward in time, along each path and time choose whether to • • • • • exercise immediately or wait, based on comparison of expected present values Exercising one option extinguishes the other Also need external hazard (mortgage termination due to non-financial reasons) and a refinance cost (prevents continual termination) Note that embedded options are path dependent, since their value at any time will depend not only on current rate and future rates, but also on how you got to the current interest rate Strengths: structural, independent of interest rate environment Weaknesses: many parameters – difficult to estimate, cobbling on of hazard FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 18 Yields and Spreads • A word about spreads…. FBB.10 • Yield = discount rate that sets projected cash flows equal to price (or market value); • Called cash flow yield. • Note that must be quoted with prepay/default assumptions, e.g., 100 PSA, 100 SDA, etc. • Realized CFY will depend on realized PSA/SDA • Convention: convert MEY to BEY • Ease of comparison to Treasuries • Reinvestment risk ignored! FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling Yields and Spreads • Yield spread to Treasuries • Somewhat meaningless (why?) • Must use comparable • Duration, or • WAL, weighted average life: t  principal received at time t  WAL   12  total principal  t 1 T 19 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling Yields and Spreads: Simple & Static • Simple aka nominal spread • Difference between MBS CF yield and the Treasury yield for maturity = average life of MBS • Ignores fact that some of this spread is extra return for taking on prepayment risk • Static (or zero volatility) spread • aka Z-spread • Single number that must be added to the entire Treasury spot rate curve (term structure) to set expected discounted MBS cash flows equal to its market price 20 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling Yields and Spreads: OAS • Option-adjusted spread (OAS) • Adds interest rate volatility • Write down an interest rate model, simulate paths • Compute cash flows, including effect of options • Need prepayment and default model • These two steps comprise a valuation model 21 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling Yields and Spreads: OAS • The single fixed spread that must added to all paths in the interest rate model to match model value and market price is called the OAS • If IR model is realistic, OAS reflects cheapness/richness of traded price relative to model • OAS “corrects” (“removes”) added value of options embedded in mortgages relative to the base index (e.g., Treasury) 22 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling Z-spread, OAS: Examples 23 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 24 Prepayment Models (resumed) • Empirical prepayment models • E.g., Bear Stern’s agency prepay model (pool level) • Identify critical factors, e.g. current market rate vs. WAC, house price appreciation etc. • Postulate a functional form based on observations • Fit parameters • Strengths: flexible, easy, accurate • Weaknesses: short shelf life • Bear Stern’s components • Turnover • Due-on-sale clause in almost all but government loans • External hazard (life-cycle reasons for termination) • CPR looks very much like the PSA prepay function • Why is this reasonable • Factors: mainly seasoning (PSA), add housing appreciation (LTV), seasonality (higher spring/summer) as “perturbations” FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling 25 Prepayment Models (cont.) • Typical components (cont.) • Cash-out Refinancing • Principal components are HPI and WAC vs. current rate (see below) • Rate/Term refinancing • Critical variable “refinancing ratio” = WAC/Current Rate, found to be better than difference • HPI also important • S-curve for prepayments (explain shape). Schematically: CPR HPA1 HPA2 ramp time • D = WAC – CC-2, and let • T = value of D at which prepay increases, and P = value of D at which prepay reaches max, then • I = min(D-T,P), and estimate • CPR = α + β1A + β2I + … + ε • Or, e.g., use atan function 31 FRL 383 Fall 2016 Prepayment and Default Measurement & Modelling Empirical Prepayment Modeling • Alternative: Logit transformation • SMM = 1/[1+ exp(-xβ)], so • y = -ln[(1/SMM) – 1] = xβ • Then run OLS/GLS on y • Example 32
HW4 FOR ANY SPREADSHEET, YOU MUST HIDE REPETITIVE ROWS THAT DO NOT ILLUSTRATE ANYTHING SUBSTANTIALLY NEW. Do not make any one spreadsheet printout more than 2 pages max (you will generally need only one). Do not continue table columns across several pages (best to print in landscape mode). FAILURE TO DO ALL THIS WILL RESULT IN A LOSS OF FIVE (5) POINTS. 41 points total. ANNOTATE any formulae that involve more than addition and subtraction (e.g., using a pen or Office’s comment feature - just one period will suffice, of course) 1. [22pts] a. [20pts] Consider a 100,000,000 CMBS pass-through (PT) security consisting of fresh 15 year fixed rate loans that fully amortize over a period of 30 years, and have a WAC of 7% with fees amounting to 0.5%. For purposes of this HW, a CMBS is like a RMBS, except that all loans have a prepayment lock-out (assume for the entire term), but default occurs according to the standard SDA function. Additionally, since the loans do not fully amortize, there is generally a balloon loss - quoted as a fraction of the outstanding balance at mortgage maturity. To simplify, assume that there is no recovery (unrealistic, of course). Assume that the PT is sold at 94.345. Allow for loans to default at the PSA’s SDA CDR, and allow for balloon risk. The current (corresponding maturity) Treasury yield is 5%. Create a table and graph of the spread (in bps) of cash flow yield to Treasury versus SDA, for 0% and 10% balloon loss. In the spreadsheet that you hand-in, show the situation for 100 SDA and 10% balloon loss. Use par pricing. See notes below for further assumptions and hints. b. [2pts] Why is there generally a large fraction of outstanding principal that defaults at maturity? 2. [8pts] Consider the following par yield curve for semiannual bonds, all quoted as BEY: Maturity [yr] 0.5 1 1.5 Par Yield 1% 2% 3% a. [6pts] What are the corresponding zero rates? b. [2pts] What is today’s lockable rate for a 6 month loan 1 year from now? 3. [10pts] Stratify the following Agency mortgages at a deal coupon of 4%. What are the initial pool and PO principals, and what are the initial notional principal and coupon of the IO? Gross Net Balance (mln $) 4.10% 4.20% 4.30% 4.40% 3.852% 3.934% 4.071% 4.153% 50.343 101.435 123.777 40.123 _____________________________________________________________________________ Notes for question 1: 1. Note that there is no messy tranching going on here. 2. Allow for a general SDA; see the graph and spreadsheet in your lecture notes. 3. Here is one way to get the CDR (as there are better versions, feel free to use your own, extra points if you can show me that the formula below is wrong); “A13” refers to the month and “SDA” to the SDA factor: =(IF(A13<=30,A13*0.006/30,0)+IF(AND(A13>30,A13<=60),0.006,0)+IF(AND(A13>60,A13 <=120),0.006-(0.006-0.0003)/(120-60)*(A13-60),0)+IF(A13>120,0.0003,0))*SDA/100 4. Assume that loss recovery is zero – any loan that defaults is a completely written down. 5. Defaults work much like prepayment, with one exception: the monthly default happens just before the payment (why pay interest and principal if you are defaulting anyway). So take default = beginning balance × MDR and then apply the appropriate pool survival factor to get the realized “mortgage payment.” 6. Make sure you create a column of the PT cash flows, including the initial investment at par, so that you can calculate the CF yield. 7. Balloon losses are quoted as a fraction of the final outstanding principal. 8. In your graph, show a range of SDA’s of 0 to 1,000. You will find that you do not have to compute very many values in that range. 9. Display all cash flows to the nearest dollar (use format → cell).

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