IV2008#004.nb 1 13. MBS (Mortgage-Backed Securities) à http://www.sjam.co.jp/college/mbs.htm ü
IV2008#004.nb 2 MBS MBS GNMA,FHLMC,FNMA MBS CMO( ) 6193 2
IV2008#004.nb 3 ü Bloomberg
IV2008#004.nb 4
IV2008#004.nb 5 ü Adjustable Rate Mortgage Mortgage Obligation Interest Only) (Principal Only) ü
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
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
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 0.07 0.06 0.05 0.04 0.03 0.02 0.01 100% PSA 5 10 15 20 25 30 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)
IV2008#004.nb 9 ü mortgage balance mortgage balance 1 0.75 principal 0.5 0.25 0 0 5 10 15 100 200 PSA year 20 25 30 50 1 mortgage balance 0.8 0.6 0.4 0.2 0 5 10 15 20 25 30 year
IV2008#004.nb 10 ü principal prepayment principal prepayment 0.006 prepayment 0.004 0.002 0 0 5 10 15 100 200 PSA year 20 25 30 50 0.01 principal prepayment 0.008 0.006 0.004 0.002 0 5 10 15 20 25 30 year
IV2008#004.nb 11 ü total principal payment total principal payment 0.0075 payment 0.005 0.0025 0 0 5 10 15 100 200 PSA year 20 25 30 50 0.01 total principal prepayment 0.008 0.006 0.004 0.002 0 5 10 15 20 25 30 year ü WAL year 20 Weighted Average Life 15 10 5 0 50 100 200 PSA
IV2008#004.nb 12 ü animation PSA = 0 ~ 400 principal prepayment 0.02 0.0175 0.015 0.0125 0.01 0.0075 0.005 0.0025 0 5 10 15 20 25 30 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 5 4 3 2 1 0 1 2 3 4 5 PSA 720 400 240 160 120 100 80 70 65 62.5 61.175
IV2008#004.nb 13 2 1.75 1.5 1.25 1 0.75 0.5 0.25-5 -4-3 -2-1 0 1 2 3 4 5 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 500 1.750% 10 S&P R&I AAA AAA
IV2008#004.nb 14 ü ü 500 55,125,921,555 10% 2001/01 100% ü 55,563,300,000 19,626,740 55,125,921,555 2,831 4,108 29.9 29.6 0.3 LTV 78.47% 18.95% 6,984,442 2.88% 38.4 ü
IV2008#004.nb 15 ü bonus paymentsemi-annual monthly bonus payment bonus payment month ü prepayment 2001/05/25 55,125,921,555 2.903 30.4 2001/02 54,843,588,271 2.902 30.3 3.48 2001/03 54,650,023,022 2.902 30.3 2.28 2001/04 54,462,622,413 2.902 30.2 2.24 mortgage