As mentioned earlier in the book, prepayment is defined as only the paydown

Transcription

1 Asset Securitization: Theory and Practice by Joseph C. Hu Copyright 2011 John Wiley & Sons (Asia) Pte. Ltd. APPENDIX A Analysis of Prepayment and Prepayment Rate As mentioned earlier in the book, prepayment is defined as only the paydown of the outstanding balance of a mortgage pass-through that is in excess of its scheduled amortization. The speed of the excess paydown is measured by the prepayment rate. This appendix presents the measurement and discusses the fundamental reasons for prepayment. MEASUREMENTS OF PREPAYMENT RATE Prepayment is the paydown of principal of a mortgage pass-through in a given month that exceeds the amount of its scheduled amortization for that month. The rate of prepayment is, therefore, the excess paydown in a given month as a percentage of the outstanding principal balance at the beginning of the month. This paydown is always measured on a monthly basis. Like interest rates, however, it is often expressed as an annualized rate. The prepayment rate of a mortgage pool is low right after its formation, but it accelerates as the pool ages. In the initial years, therefore, the prepayment rate is often measured in conjunction with the aging of the pool. Single Month Mortality (SMM) SMM measures the percentage of a pool s outstanding balance at the beginning of the month that was prepaid during the month. Algebraically, the SMM of month N, SMM N, is calculated using the following formulas: SMM N ¼ðSF N AF N Þ=SF N SF N ¼ AF N 1 ðsaf N =SAF N 1 Þ 233

2 234 APPENDIX A Where: SF N ¼ scheduled factor at the end of month N AF N ¼ actual factor at the end of month N SAF N ¼ scheduled amortization factor at the end of month N For example, the actual factors of a pool of 30-year mortgages with a WAC of 6 percent at the end of the 39th and the 40th months are and , respectively. (The factor is a ratio of outstanding balance to the original balance of a pool.) The SMM for the 40th month can be calculated in the following steps: Step 1: Based on the WAC, the scheduled amortization factors of the 39th and the 40th month, SAF 39 and SAF 40, can be mathematically derived. They are and , respectively. (For detailed derivation of scheduled pool balances and factors, see PSA Standard Formulas, The Bond Market Association.) Step 2: Given the actual factor of the 39th month and the scheduled amortization factors of the 39th and the 40th months, if there was no prepayment during the month 40, the scheduled factor of the 40th month, SF 40, would have been: SF 40 ¼ AF 39 ðsaf 40 =SAF 39 Þ ¼ 0: ð0: =0: þ ¼ 0: Step 3: Prepayment in the 40th month therefore is: SF 40 AF 40 ¼ 0: : ¼ 0: Step 4: Single month mortality rate of the 40th month is: SMM 40 ¼ðSF 40 AF 40 Þ=SF 40 ¼ð0: =0: Þ ¼ 0: ¼ 0:78284% Constant Prepayment Rate (CPR) The monthly SMM can be converted and annualized in terms of CPR. (In the parlance of prepayment calculation, CPR sometimes has been interpreted as conditional prepayment rate because the prepayment rate of the current month is dependent on the prepayment factor up to the previous month.) In fact, like interest rates, the prepayment rate is more often expressed in an annualized rate rather than the monthly rate. The conversion

3 Appendix A 235 is based on the formula CPR ¼ 1 (1 SMM) 12, and consists of the following steps: Step 1: Given the single month mortality rate, the survival rate is simply (1 SMM). From the above example, the monthly survival rate is ( ) ¼ Step 2: Given the monthly survival rate of , the annualized survival rate is ( ) 12 ¼ ¼ 91%. Step 3: Since an annualized 91% of the pool survived in the 60th month, the annualized rate of prepayment of the pool in the 60th month is CPR ¼ [1 (1 SMM) 12 ] ¼ 1 ( ) 12 ¼ ¼ ¼ 9%. Public Securities Association Standard (PSA) To measure the paydown of a mortgage pool with respect to its age, the Public Securities Association (now the Securities Industry and Financial Markets Association, SIFMA) promulgated a new yardstick termed percent PSA. (Interestingly, the PSA has also been interpreted as being short for Prepayment Speed Assumption.) As shown in Figure A.1, a 100% PSA (the PSA curve) refers to a pool that prepays (1) at a 0.2 percent CPR in the first month, (2) at a faster rate of incrementally 0.2 percent CPR per month during the first 30 months, and (3) at a constant 6 percent CPR per month at the 31st month and thereafter. The first 30 months of the PSA curve is sometimes called the ramp period. For a given month, a pool may prepay CPR % Month FIGURE A.1 The PSA Prepayment Curve

4 236 APPENDIX A faster or slower than this standard. Its prepayment speed is expressed as a multiple or a fraction of PSA. (Colloquially, the prepayment rate is often called the prepayment speed, or simply the speed.) From the above example, given that the CPR for the 60th month is 9 percent, the PSA speed for that month is 9%/6% ¼ 150% PSA. However, if the 9 percent CPR occurs for the 20th month, then the speed would be 100 [9%/(0.2 20)] ¼ 225% PSA. For the same CPR, the reason that the PSA speed is faster for the 20th month than for the 60th month is that the PSA standard expects a 20-month-old pool to prepay only 6 percent CPR on a 150% PSA. Due to the fact that it already prepays at 9 percent CPR, the PSA standard adjusts the speed upward to 225% PSA. Given the age of a mortgage pool, the following formulas convert interchangeably between CPR and PSA: When the age of a mortgage pool is younger than 30 months: PSA ¼ 100 ½CPR=ð0:2 ageþš CPR ¼ðPSA 0:2 ageþ=100 When the age of a mortgage pool is 30 months or older: PSA ¼ 100 ðcpr=6þ CPR ¼ðPSA 6Þ=100 It should be noted that the basic assumption of the PSA curve is that mortgages underlying a newly issued pass-through are exclusively originated to facilitate housing transactions. In a low-interest-rate environment, such as when refinancing accounted for a more significant portion of prepayment, this assumption may no longer be valid. TWO FUNDAMENTAL REASONS FOR PREPAYMENT A mortgage is originated as a long-term finance instrument to finance the purchase of a house. However, for a variety of reasons the mortgagor rarely holds onto the mortgage until its maturity. There are two fundamental reasons that a mortgage is prepaid: refinancing and housing turnover. Refinancing In a declining interest rate environment, the mortgagor has a strong incentive to refinance. That is, the mortgagor would prepay the existing mortgage that carries an above-market interest rate and obtain a new mortgage at the prevailing market rate. By refinancing, the mortgagor reduces the monthly

5 Appendix A 237 payment. Thus, refinancing is an important reason for prepayment. In 2003, for example, when mortgage rates plunged to below 5.5 percent, their lowest level in 50 years, nearly two-thirds of that year s $4.2 trillion of mortgage originations were the result of refinancing. This refinancing amount in one year was 40 percent of the outstanding mortgages as of year-end of Housing Turnover Absent refinancing, a mortgage is prepaid as a result of a change in the ownership of its collateral the house. The ownership change may be the result of a home sale, default, disaster (such as fire, flood, or earthquake), or death of the mortgagor. Home Sale The primary reason for ownership change is the mortgagor selling the house for a variety of reasons. They include, but are not limited to, upgrading housing, changing job, or divorcing. A conventional mortgage (not insured or guaranteed by the government) normally has a due-on-sale clause, which requires the mortgagor to prepay when the house is sold. While an FHA/VA mortgage allows the buyer to take over the mortgage from the seller (termed mortgage assumption), the seller usually still prepays the mortgage. (It could be that the equity in the house is too large for the buyer to assume the mortgage.) The housing turnover component of prepayment due to home sale can be approximated on the basis of existing home sales and the size of the single-family housing stock. In 1995, for example, annual existing home sales totaled 3.8 million units and the stock of single-family owner-occupied housing units was estimated at 50.2 million units. By dividing the existing home sales into the housing stock, the housing turnover rate is calculated to be around 7.5 percent, or 125% PSA. This speed can be viewed as the demographic factor, or the core component of the prepayment rate. 1 Unlike the refinancing component, the core component is rather stable. It is influenced primarily by demographic forces, such as housing upgrading, marriage, divorce, changing jobs, and death. In 2003, however, the historically low mortgage rates tremendously stimulated existing home sales to nearly 7 million units. With the housing stock estimated at around 57.5 million units, the housing turnover rate accelerated to 12 percent, or 200% PSA. In recent years, the turnover rate has decelerated to about 160% PSA, as the annual existing home sales have been depressed to around 5.5 million units.

6 238 APPENDIX A Default The financial condition of the mortgagor may deteriorate as a result of unemployment, making him or her unable to carry the obligation of making the monthly payment. If the condition is temporary, the mortgagor could be in arrears for a month or two. This behavior is called delinquency. However, if the delinquency persists for more than three months the mortgagor would be considered in default. In this case, the originator can initiate a foreclosure proceeding, which eventually will force the mortgagor to move out of the house. The originator then would liquidate the house and pay off the mortgage. It is important to note, however, that residential mortgages traditionally have a very low incidence of default. In recent years (prior to the subprime mortgage debacle) the average annual rate of default has been less than 0.5 percent. Disaster A mortgage may also be prepaid as a result of severe damage to the house because of fire, flood, or earthquake. Since the house is the collateral that secures the mortgage, severe damage to the collateral eliminates the very existence of the mortgage. If the house has casualty insurance, the mortgage will be prepaid. If not, the mortgage usually ends up in default. Death In case of death of the mortgagor, the executor usually sells the house and prepays the mortgage. Otherwise, if the mortgage becomes defaulted the originator will foreclose the house and prepay the mortgage. NOTE 1. Beginning in the mid-1980s, when mortgage pass-throughs were experiencing rapid growth, Wall Street securities dealers devoted great research efforts to analyzing determinants of prepayments. In 1987, this author when head of mortgage research at Shearson Lehman Hutton (which later on became Lehman Brothers) suggested the concept of using housing turnover rate as the core prepayment factor of current-coupon agency-guaranteed pass-throughs. See Joseph Hu, An Alternative Prepayment Projection Based on Housing Activity, The Handbook of Mortgage-Backed Securities, Frank J. Fabozzi, editor, revised edition, Probus Publishing, 1988.