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1 IV2008#004.nb MBS (Mortgage-Backed Securities) à ü
2 IV2008#004.nb 2 MBS MBS GNMA,FHLMC,FNMA MBS CMO( )
3 IV2008#004.nb 3 ü Bloomberg
4 IV2008#004.nb 4
5 IV2008#004.nb 5 ü Adjustable Rate Mortgage Mortgage Obligation Interest Only) (Principal Only) ü
6 IV2008#004.nb 6 ü Government National Mortgage Association Federal National Mortgage Association (Government Sponsored Enterprise) Federal Home Loan Mortgage Corporation à MBS ü h ü
7 IV2008#004.nb 7 ü MBS monthly amortization uncertainty of cashflow Cashflows are dependent on interest rate trajectories. full prepayment partial prepayment (curtailment) delinquency default à concept and terminology ü pool factor the remaining balance of the pool as a ratio of its original balance ü weighted average coupon (WAC) the average interest rate on the mortgages in the pool weighted by the principal amount of the mortgages ü weighted average maturity (WAM) the average remaining maturity of the underling mortgages in the pool weighted by the remaining balance of the mortgages ü weighted average life (WAL) the measurement of mortgage backed securities time horizon other than maturity. It considers the impact of all principal payments both scheduled and prepaid. à prepayment speed ü Single Month Mortality (SMM) SF n : scheduled factor at the end of month n AF n : actual factor at the end of month n SAF n : scheduled amortization factor (without prepayment at the end of month n) SMM n := HSF n - AF n LêSF n SF n := AF n µ SAF n ê SAF n-1 ü Constant Prepayment Rate (CPR) The monthly SMM can be converted and annualized in terms of a constant prepayment rate (CPR). CPR := 1 - H 1 - SMM L 12
8 IV2008#004.nb 8 ü Public Securities Association (PSA) Standard percent PSA (1) at a 0.2% CPR in the first month (2) at a faster rate of incrementally 0.2% CPR per month during the fist 30 months (3) at a constant 6.0% CPR per month at the 31st month and thereafter % PSA year à cashflow of mortgage with prepayment ü setup the original pool balance = 1 ü four scenarios PSA = 0 (green) 50 (cyan) 100 (blue) 200 (red)
9 IV2008#004.nb 9 ü mortgage balance mortgage balance principal PSA year mortgage balance year
10 IV2008#004.nb 10 ü principal prepayment principal prepayment prepayment PSA year principal prepayment year
11 IV2008#004.nb 11 ü total principal payment total principal payment payment PSA year total principal prepayment year ü WAL year 20 Weighted Average Life PSA
12 IV2008#004.nb 12 ü animation PSA = 0 ~ 400 principal prepayment year à mortgage ü cashflow uncertainty mortgagor's option full prepayment turnover refinance partial prepayment (curtailment) low for newer loans, but increase with age delinquency default ü negative convexity prepayment r PSA
13 IV2008#004.nb green red : without prepayment : with prepayment MBS/CMO negative convexity ü prepayment prepayment ï average life ï yield-to-maturity bond average life ï yield-to-maturity bond average life ï yield-to-maturity prepayment à ü % 10 S&P R&I AAA AAA
14 IV2008#004.nb 14 ü ü ,125,921,555 10% 2001/01 100% ü 55,563,300,000 19,626,740 55,125,921,555 2,831 4, LTV 78.47% 18.95% 6,984, % 38.4 ü
15 IV2008#004.nb 15 ü bonus paymentsemi-annual monthly bonus payment bonus payment month ü prepayment 2001/05/25 55,125,921, /02 54,843,588, /03 54,650,023, /04 54,462,622, mortgage
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