Modeling of Mortgage Prepayments and Defaults

Transcription

1 See the Disclosure Appendix for the Analyst Certification and Other Disclosures. Modeling of Mortgage Prepayments and Defaults Lakhbir Hayre Managing Director Fixed Income Quantitative Analysis September 25, 2006

2 Topics An Overview of the Mortgage Market Challenges in Prepayment and Default Modeling Implications for Valuation of Mortgage- Backed Securities 2

3 The US Mortgage Market -- Colossus of the Bond World All Mortgage Debt Single-Family Mortgage Debt Mortgage-Backed Securities Asset-Backed Securities $12.3 trillion $9.5 trillion $6.2 trillion $2.0 trillion US Treasuries $4.2 trillion Corporate Bonds $5.2 trillion Municipals $2.3 trillion Sources: Federal Reserve System, Bond Market Association. 3

4 What are Mortgage Securities? A number of mortgage loans - from a few dozen to more than 10,000 - are pooled; Each loan pays interest and principal until it matures, is prepaid, or goes into default; Cashflows from the loans are paid to investors, after subtraction of administrative (or servicing) fees; Cashflows are either simply passed on to investors (passthrough securities) or allocated according to specified rules (structured securities, such as Collateralized Mortgage Obligations (CMOs). 4

5 Basic Security Features Cashflows are monthly, unlike Treasures or corporate bonds, which pay semi-annually; Amortizing assets => principal paid out over a period of time; For pass-throughs, each monthly payment will tend to include some principal; For structured MBS/ABS, principal paid out over a principal window Prepayment of principal by borrowers Þ call risk key property of many MBS/ABS durations much shorter than similar maturity bullet security. 5

6 Basic MBS is the Pass-Through Issued by FHLMC, FNMA, GNMA and Private Entities Many mortgages with similar characteristics collected into a pool Investor receives pro-rata share of monthly payments Interest and principal payments are guaranteed by the issuing agency, or through credit enhancements (for private issuers) 6

7 Structure of a Pass-Through Borrower pays 6.5% + principal payments Loan servicer receives servicing fee of 0.35% Investor receives coupon payments of 6% + principal payments Fannie/Freddie/Ginnie receives a guarantee fee of 0.15% Source: Citigroup. Actual numbers may vary from pool to pool 7

8 Valuation of Mortgage Securities MBSs are bonds with embedded options; More complex than standard callable bonds: Each $1 is a separate option Option-exercise is inefficient High degree of path dependence Prepayment models key to valuation; Prepayment models combined with Term Structure Models to obtain option-adjusted spreads (OAS). 8

9 Basic Steps in Mortgage Valuation Generate a large number of interest rate paths, both for discounting and for cash flow generation; On each path, call a prepayment model/default model to calculate mortgage cash flows; Calculate average PV of cash flows, using benchmark rates plus a spread; Spread that equates average PV to market price is the option-adjusted spread (OAS). 9

10 Prepayment Rates Are Critical in Determining MBS Value A. Cashflows Assuming No Prepayments Cash Flow Per $100,000 10,000 8,000 6,000 4,000 2, Interest Principal Servicing B. Cashflows Assuming a More Realistic Prepayment Rate 20,000 Source: Citigroup. Cash Flow Per $100,000 15,000 10,000 5, Interest Principal Servicing 10

11 Some Difficulties in Developing Prepayment Models A large number of important variables Continual innovations in mortgage financing implies constantly changing regimes Diverse and changing range of mortgage loan types A high degree of path dependence Unpredictable and inefficient borrower behavior Limited historical prepayment data and incomplete information 11

12 A Large Number of Factors Impact Prepayment and Default Rates Economic: Mortgage Rates, Housing Inflation, Consumer Confidence, Unemployment, etc. Loan: Coupon rate, original term, remaining term, type (Fixed, ARM, Hybrid), loan size, geographical location, etc. Borrower: Credit, Socio-Economic Status, Personal Situation Other: Past exposure to refinancing opportunities, mortgage origination and servicing process, etc. 12

13 Changing Environment Key determinants change over time: closing costs, choice of loan types, mortgage lending industry, loan origination process,etc. Borrowers have become more savvy over the years Borrower sentiment (or psychology) plays an important role 13

14 Changes in the Mortgage Market over Time CPR (%) Speeds on 2001 Coupons in Jul 2003 Speeds on 1992 Coupons in Nov WAC - "No Point" Mtg Rate (bp) Speeds on 2000 Coupons in Dec 2001 Speeds on 1996 Coupons in Dec 1998 Sources: Fannie Mae, Freddie Mac and Citigroup.. 14

15 The Media Effect Measures Psychological Impact of Multi-Year Lows in Rates Rate (%) Rates drop 100bp from April to Year- End 97, but nothing happens Rates hit multi-year low Rates back to early 1998 lows but nothing happens 5.5 Rates fall significantly 5.0 below early 1998 lows 4 Apr 97 4 Jul 97 3 Oct 97 2 Jan 98 3 Apr 98 3 Jul 98 2 Oct Mortgage Rate (Left Axis) MBA Refinancing Index (Right Axis) Source: Mortgage Bankers Association, Freddie Mac, Citigroup 15

16 Loan Type Variation: Term 30-Year: Most common type in the US; 15-Year: Higher monthly payments, so few 1 st time home buyers => slower turnover and seasoning ramp. Also common refi vehicle for 30-year mortgages; 20-Year. Attracts borrowers who want a 15-year loan, but cannot afford the higher monthly payments; 10-Year. Mostly people refinancing out of a 15-year loan; 40-Year. A newer product, popular with borrowers stretching to buy a house and who want to minimize the monthly payment. Notes: 1. For a given difference between the coupons on the current and a new mortgage, the shorter the term, the lower the refinancing incentive; 2. Regardless of the shape of the yield curve, the shorter the term, the lower the mortgage rate. 16

17 Loan Type Variation: Coupon Fixed Rate. Basic mortgage in the US; Adjustable Rate. Coupon resets periodically at a stated margin over a specified index (typically 1-year Treasury or 6-month LIBOR). Initial coupon often teasered and much lower than on a fixed-rate loan, so ARMs attract lot of 1 st time buyers or other people with short time horizons; Hybrid. Coupon fixed for the first 3, 5, 7 or 10 years, then adjusts like a standard ARM. The shorter the fixed rate period, the shorter the typical borrower horizon, and the faster the speeds. 17

18 Loan Type Variation: Credit Jumbo. Prime quality loans that are too large for agency pools; Fannie May/Freddie Mac. Generally prime quality loans that fall below the conforming limit ; Ginnie Mae. Loans insured by the FHA or the VA. Relative to FN/FH, poorer credit and lower loan balances. Alternative (Alt) A. Borrowers are generally moderate to good credit (hence the A ), but lack full documentation Sub-Prime. Borrowers with poor credit histories. 18

19 Loan Type Variation: Other Features Loan Size. Has a big impact on speeds. Geographical Location. Ditto. Prepayment Penalties. Uncommon in prime loans, but prevalent fro sub-primes. Amortization Schedule. Traditional mortgages in the US have been fully amortizing. However, strong growth in recent years in loans which pay interest only for a number of years (eg 10/20), or can even have negative amortization (ie. loan balance can increase), such as Option ARMs. 19

20 Prepayment Speeds on Prime and Subprime Loans Prime Subprime December-02 June-03 January-04 July-04 February-05 August-05 March-06 October-06 20

21 Effect of Loan Balance Loan Loan Balance (LLB) pools are less reactive to refinancing opportunities, but little difference in turnover speeds Generic 6s of 2003 LLB 6s of CPR (%) Source: Citigroup. 21

22 Significant Differences in Speeds by State Factors include loan size, closing costs, taxes, home price appreciation, and local economic conditions CA IL TX FL NY US CPR (%) Apr '03 Jun '03 Aug '03 Oct '03 Dec '03 Feb '04 Apr '04 Jun '04 Aug '04 Oct '04 Source: Citigroup. 22

23 High Degree of Path Dependence Borrowers will differ in their propensity and ability to refinance As a pool of borrowers experiences refinancings, most able borrowers leave the pool at higher rates Remaining borrowers less responsive (burnout) Hence prepayment rates depend on complete history of interest rates 23

24 Burnout Freddie Mac 9s of 1991 Freddie Mac 8.5s of Year Mortgage Rate Aug-91 May-93 Feb-95 Nov-96 Aug-98 May-00 Feb-02 Nov-03 5 Sources: Freddie Mac and Citigroup. 24

25 Inefficient Exercise of the Prepayment Option 90 Burnout and Media Effect CPR (%) Speeds on 2001 Coupons in Jul Speeds on 2001 Coupons in Jan WAC "No Point" Mtg Rate (bp) 25

26 History of Prepayment Modeling First Generation Models (Salomon, 1985) - Standard Multiple Regression Models - Many Variables good historical fit, but not robust over time Diversity of Collateral and Borrowers and Continuing Changes in Prepayment Environment Suggests More Fundamental Approach (Salomon, 1995) - Sources of Prepayments (Modular Approach) - Flexible and Dynamic Inputs and Relationships 26

27 Why are Mortgages Prepaid? Housing Turnover - the sale of a home triggers a prepayment Refinancings - the loan is refinanced Defaults - foreclosure on the house leads to the loan being paid off Curtailments (or partial prepayments) - borrowers make more than their scheduled payment Full Payoffs - the loan is paid off: for example, due to a natural disaster This is true for all loans, regardless of type of loan, country/region etc. However, the magnitude of each component will depend on cultural, demographic, collateral and economic factors. 27

28 Structure and Key Features of the Model Modular Approach: Projected Speed = Sum of speeds due to 1. Housing Turnover 2. Refinancings - Rate, Cash-Outs and Credit Driven 3. Curtailments 4. Defaults 28

29 Overall Housing Turnover Rate 10.0% -200bp 7.5% Housing Turnover Rate (in%) 5.0% 2.5% Actual No shift +200bp Projected 0.0% Jul-78 Jul-81 Jul-84 Jul-87 Jul-90 Jul-93 Jul-96 Jul-99 Jul-02 Jul-05 Jul-08 Source: National Association of Realtors, US Census Bureau, Citigroup 6 29

30 Housing Turnover-Related Speeds Dominant in high-interestrate environment Strong seasonal component Seasoning: brand-new pools tend to prepay more slowly Lock-in: higher coupons typically have higher turnover rates CPR (%) Source: Citigroup Prepayment Rates Fannie Mae 6s of 1993 Oct-93 Feb-94 Jun-94 Oct-94 Feb-95 Jun-95 Oct-95 Feb-96 Jun-96 Oct-96 Feb-97 Jun-97 Oct-97 30

31 Seasoning Depends on Loan Age and Home Price Appreciation % PSA 12 CPR (%) 10 Age-related Seasoning is a critical dimension of Turnover Loan Age (Months) However, Seasoning is Modulated by Appreciation in Home Prices 31

32 Actual and Projected Home Price Appreciation 16% Annual US Home Price Appreciation (in %) 12% 8% 4% 0% Feb-71 Projected Actual Feb-74 Feb-77 Feb-80 Feb-83 Feb-86 Feb-89 Feb-92 Feb-95 Feb-98 Feb-01 Feb-04 Feb-07 Feb-10 Source: Fannie Mae, Freddie Mac, Citigroup 32

33 Basic Dynamics of Refinancing Model We assume that there are several classes of borrowers, ranging from slowest to fastest, each class having its own refi curve Refi Rate Source: Citigroup. Refi Incentive 33

34 Evolution of Population of Mortgagors The mix of borrowers changes each month, as faster refinancers leave the pool at a faster rate 60% % in Class 50% 40% 30% 20% 10% 0% Initial Distribution Post-Refi Distribution Slowest Slow Fast Fastest Source: Citigroup. The model keeps track of the population mix, and the overall refi rate for month is the aggregate over the remaining borrowers: Refi Rate = Fraction of pool in class 1 * Refi rate for class Fraction of pool in class k * Refi rate for class k 34

35 Other Aspects of the Refinancing Model No consensus on how to calculate the refinancing incentive - A common approach is to compare PVs of new and old mortgages - Another approach: # of months to recoup costs of refinancing Mortgage rates used to calculate refi incentive need to depend on loan type eg sub-prime rates much higher than prime rates Loan balance is an important factor in determining incentive A seasoning curve can be introduced using transient costs of refinancing; Reactivity to refinancing opportunities depends on FICO, LTV and other loan features. 35

36 A Simple Default Model Multiple of the SDA Curve 1.2 The Standard Default Assumption (SDA Curve) Pe CPR (%) Tail Mortgage Age (Months) 36

37 A Default Model Framework Probability of Default = Probability(LTV > Threshold) *Probability (Trigger Event) Likelihood of Trigger Events depends on FICO, Debt-to-Income ratio, unemployment rates, payment shock, etc. Default Probability 0.5% 0.4% 0.3% 0.2% 0.1% 0.0% AR with Affordability AR(1) Age (years) 37

38 Key Determinants of Trigger Events Unemployment or Curtailment of Income % Illness or Death of Mortgagor Excessive Obligation 9.70 Marital Difficulties 9.45 Illness or Death in Family 7.31 Extreme Hardship 4.06 Business Failure 2.68 Property Problem or Casualty Loss 2.00 Inability to Sell or Rent Properties 1.83 Employment Transfer or Military Service 0.97 All other Reasons 6.77 Source: Freddie Mac. 38

39 Historical Monthly Transition Rates for Sub-Prime Loans Fixed-Rate Loans To Non-delinq Delinqent Foreclosure REO Payoff From (%) (%) (%) (%) (%) Non-delinq Delinquent Foreclosure REO /28 Hybrids Non-delinq Delinquent Foreclosure REO Payoff From (%) (%) (%) (%) (%) Non-delinq Delinquent Foreclosure REO Source: Citigroup. To 39

40 Subprime Collateral Default Rates by LTV L,10x,75 L,75x,85 L,85x,+ 40

41 Summary and Implications for MBS Valuation Modeling of prepayments and defaults as much art as science; MBS cashflow generation depends on these models; Hence little consensus on valuations, especially for complex MBS derivatives; Work by non-practitioners of little value in deciding, say, how much more to pay for a $60,000 average balance Texas pool vs. a $80,000 Illinois pool; On a positive note, great employment opportunities for good prepayment modeler; A book from John Wiley & Sons, SSB Guide to Mortgage- and Asset- Backed Securities, edited by L. Hayre, provides a great introduction to this area. 41

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