RCo Behavior Modeling


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  • The US debt market is the largest credit market in the worldThe U.S. mortgage market is among the largest debt market in the U.S. and in the WorldOf the total $111.5 trillion in outstanding global debt as of 2008 (See Appendix A, B):17.43% or 19.429 trillion were in U.S. residential real estate10.10% or 11.25 trillion were in U.S. mortgage debtOf the total $19.429 residential real estate outstanding as of 2008 (See Appendix A, B):58% or $11.25 trillion were in U.S. mortgage debt36.5% or $7.1 trillion were in Agency and Non-Agency mortgage debt
  • For first two months, the CPR is a slightly higher, which implies the possible bridge or temporary loans effects.From the 3rd to the 30th month, the ramp speed is about .6 per month until it reaches 30 CPR.From the 30th to 60th month. The average CPR is 24.5. On average, there are at least 100 loans for each age less than 50, at least 42 loans for each age less than 60. After 60th month, the CPR is volatile and loans have low frequencies
  • The S-shape relationship can be observed. When the refinance spread goes up, the CPR goes up at a decreasing speed.When spread becomes zero or negative, the CPR becomes relatively flat, not sensitive to refinance spread.
  • RCo Behavior Modeling

    1. 1. RCo Behavior ModelingJuly 2011Robert J. Wyle, CFA
    2. 2. Agenda» Introduction– What is behavior– Why is behavior Important» Mortgage Prepayments– How are mortgage prepayments measured?– How are prepayment modeled?– Demo2
    4. 4. What is Behavior“Where Contractual Terms May Be Varied By Custom or Implication”» Prepayment Due To Unscheduled, Part Or Full, Principle Repayments» The Variability and Lack of Sensitivity of Non Maturity Liabilities in Terms of:– Maturity– Coupon or Interest Rate Repricing, or Rate Repricing Lag To Market Rates,Or The Rate Off-set Due To High Account Servicing Cost» Call Options, Put Options» Caps, Floors» Changing Credit Card Balances4
    5. 5. U.S. Mortgage Debt Outstanding as of 20085Residential Real-Estate$19,429 Billion$8,790 Billion $11,254 BillionOn-balance Sheet Non-Agency MBS$3,880 Billion $5,068 Billion $282 Billion $2,025 BillionREITs, FinanceBanks & Thrifts Companies, Insurance$3,375 Billion Companies, etc.$505 Billion1st Liens 2nd Liens$2,247 Billion $1,128 BillionPrime / Jumbo Alt-A Subprime Total$530 $530 Billion $880 $880 Billion $770$770 Billion $2,180 Billion$2,344 Billion AAA AAA AAA AAA96% $509 95% $836 78% $601 89% $1,9451st Lien$1,600 Billion $744 Billion1.5% AA 3% AA 10% AA 5% AA$8.0 $26 $77 $1111% A 1% A 5% A 2% A$5.3 $8.8 $39 $530.5% BBB 0.7% BBB 4% BBB 2% BBB$2.7 $6.2 $31 $401.0% Equity 0.3% Equity 3% Equity 1% Equity$5.3 $2.6 $23 $31Tranche proportions are estimates, based on a sampling of securitizationsSome numbers do not sum exactly, given different data sources.(1) Financial system debt includes financing for $626 billion of debt financing nonfinancial corporate businessand nonfarm noncorporate business mortgages. Total household mortgages total $10.6 trillion.(2) Other includes private and government funded mortgages.Other (2)2nd LienPublicly Traded, US Banks & ThriftsHomeownersEquityMortgage DebtOutstanding (1)Agency17.4 of global debt are inU.S. residential real estate!
    6. 6. Why is Modeling Behavior Important?Understanding correlated behavior is important because it allows risk managers to reflectthe impact of market volatility on embedded options.6-10%0%10%20%30%40%50%60%70%-2.0% -1.5% -1.0% -0.5% 0.0% 0.5% 1.0% 1.5%Refi CPRRefi SpreadActual refinancing vs. S-like curve: 5/1 ARMsObservationsModel
    7. 7. 7Term Structure Modeling-2.00%0.00%2.00%4.00%6.00%8.00%10.00%12.00%0481216202472120168216264312360
    8. 8. 8Effective DurationEffective Duration Recognizes that Changes in Yield will Change the Cash Flows ofInstruments with Embedded OptionsPriceDuration Actual PricePositive ConvexityNegative ConvexityYieldΔi ΔiV0 = initial priceV- = price if yield changes by -yV+ = price if yield changes by +yΔi = change in yieldDe =V- - V+2(V0)(Δi)
    9. 9. EVEExposures-60.00%-50.00%-40.00%-30.00%-20.00%-10.00%0.00%10.00%-300 -200 -100 +100 +200 +300Parallel Change in Rates%ChangeinEVEDec-00Jun-01Dec-01Limits
    11. 11. How are Mortgage Prepayments Measured?» Single Monthly Mortality (SMM)» Constant Prepayment Rate (CPR)» PSA Standard Prepayment Benchmark11PrepaymentSMMBegBalance ScheduledPrinciple121121 11 1CPR SMMSMM CPR6%* ; 30306%; 306%*min 1,30nnCPR nCPR nnCPR
    12. 12. How are Mortgage Prepayments Modeled?» The purpose of a prepayment model is to define a relationship between projectedmortgage rates and the resulting rates of prepayment activity, given all availableinformation regarding the mortgage, the mortgage holder, the current state of theeconomy, etc. If this relationship were well modeled, it would in turn allow one to answerall of the questions that one may ask as a holder of a mortgage-backed security.» Questions like: the value of the option to refinance, the average advantage of owning a mortgagevs. owning other instruments, how one can compare a mortgage to a collection of bonds and shortpositions in interest rate derivatives, etc.» A well constructed model should capture the differences between short-term projectionsand long-term projections.» A well-constructed model should incorporate all known factors that effect a mortgageholders inclination to move or to refinance, as well as the overall state of the US housingmarket.» Typical prepayment factors include: Refinance spread, seasoning, seasonality, burnout, loan size, FICO score, etc.12
    13. 13. Proposed Model» The prepayment model we are about to build in the slides that follow is the product of aCPR based seasoning ramp and seasonality and refinance multipliers:13actorrefinanceFyIndexSeasonalitPRSeasoningCCPR **
    14. 14. Seasoning (Age)Quantification of seasoning (age) factor:» Remove any sold loans from the bank data» For each month, calculate the age of the loans at prepayment» For each month, calculate the Single Monthly Mortality (SMM) and CPR. The CPR is theannualized percentage of the existing mortgage balances expected to be prepaid in ayear.» Finally, calculate the monthly average CPR for each age.14
    15. 15. Seasoning Analysis15010203040MonthlyAverageCPR,%0 20 40 60 80Age (in month)CPR and Age
    16. 16. Proposed Seasoning Curve160102030400 20 40 60 80Age (in month)Monthly Average CPR, % Existing Seasoning CurveProposed Seasoning Curve
    17. 17. Seasonality Index170.000.200.400.600.801.001.201.401 2 3 4 5 6 7 8 9 10 11 12SeasonalityIndexMonth
    18. 18. Refinance Incentive» Refinance incentive/spread (RS) is defined as gross weighted average coupon rateminus the current offer rate, which is the sum of 3 year swap rate and 150 basis pointspricing spread. If the three year swap rate becomes lower, more people are going torefinance.» Quantifying refinance incentive:» In each month, group deal level loans by age and refinance spread cohorts.» The market rate for the loans is assumed to be the three year US swap rate and the 150 basispoints are assumed to be the average pricing spread.» Calculate the monthly average CPR.» Adjust for other behavior factors i.e. de-season and de-seasonalize the CPR/refi-incentive18%5.13 YearUSttt SwapGWACRS
    19. 19. De-Seasoned / De-Seasonalized CPR and RefinanceSpread19010203040-4 -2 0 2 4 6Refinance Spread
    20. 20. Refinance Factor20spread refinance factor-6 0.7626-5 0.7963-4 0.8328-3 0.8720-2.75 0.8821-2 0.9133-1.75 0.9239-1.5 0.9346-1.25 0.9454-1 0.9562-0.75 0.9671-0.5 0.9781-0.25 0.98900 10.125 1.00550.25 1.01100.5 1.02191 1.04381.5 1.06542.5 1.10763.5 1.14794.5 1.18585 1.20375.5 1.22096 1.23746.20/}*1.0arctan*05.96.20{ preadrefinancesactorrefinancef%5.13 YearUSttt SwapGWACRS
    21. 21. Conclusion» “Every aspect of a “good” prepayment model must be designed to reflect people’sbehavior. History should be used, but only as an indication of what the parametersshould be. And, if there is not enough history to set the value of certain parameters thatwe know exist in the real world, it is better to set them to some reasonable value than notset them at all, and have them implied by other parameters, since the implied value maynot be a reasonable one.» The quality of a model depends ONLY on the accuracy and completeness of therepresentation of the underlying phenomenon that we know exists in the real world.”21
    22. 22. Appendix A• “Bond Markets, Analysis, and Strategies”; Frank Fabozzi; 1989• “The Handbook of Fixed Income Securities”; Frank Fabozzi; 2001• “Mortgage Backed Securities”; Frank Fabozzi; 2001; 199222