The MBS Market Continued
Many different types of investors buy MBS.
Mortgage and assetbacked security holdings by investor type 2003 at yearend are as follows:
Mutual Funds 7%
Mutual Funds 7%
Foreign Investors 5%
* Other consists of Private Individuals, Finance Companies, MBS deal Inventory, REITs, Federal Credit Unions, HedgeFunds/ NonProfits/ State and Local Gov't
Foreign Investors 5%
Source: Inside MBS & ABS
 Other consists of Private Individuals, Finance Companies, MBS deal Inventory, REITs, Federal Credit Unions, HedgeFunds/ NonProfits/ State and Local Gov't
 Mortgagors have the statutory right to refinance at their discretion, notwithstanding prepayment penalty mortgages (PPMs). This is called the prepayment option.
 Prepayments are usually the most important factor in valuing MBS.
 Prepayments affect MBS through call risk and extension risk.
 Call risk occurs when monthly cash flows are earlier than expected and hence the weighted average life of the bond is shortened. This is caused by higherthanexpected prepayments:
 This benefits the holder of a discount MBS (i.e., the holder bought the MBS for less than face principal value  below par), as principal purchased below par is returned early at par.
 This harms the holder of a premium MBS (i.e., the holder bought the MBS for more than face principal value  above par), as principal purchased above par is returned early at par.
 Extension risk occurs when monthly cash flows are slower than expected and hence the weighted average life of the bond is extended. This is caused by lowerthanexpected prepayments:
 This harms the holder of a discount MBS, as the lower prepayments prolong the period of belowmarket coupon payments.
 This benefits the holder of a premium MBS, as the lower prepayments prolong the period of abovemarket coupon payments.
 Reinvestment risk
 Prepayments are greater when interest rates are low, causing cash from MBS to be returned faster from above market mortgages.
 This creates the problem of having unexpected cash to reinvest in securities with lower yields.
 The following are commonly used prepayment measurements:
 SMM (single monthly mortality rate):
 Percentage of mortgages outstanding at the beginning of the month that are prepaid during the month.
 CPR (conditional prepayment rate):
 SMM expressed at an annual rate: CPR = 1  (1  SMM)12
 PSA (Public Securities Association):
 A CPR ramp model that accounts for seasoning of the loans and is modeled off of prepayment relocation assumptions.
 This ramp is made up of annualized prepayment rates of 0.2% CPR in the first month, 0.2% increases in every month thereafter until the 30th month, when the rate reaches 6% and stays at this level.
 This model acknowledges that prepayment assumptions will change; hence PSA is thought of as a baseline and referenced with a % difference (i.e., 120% PSA assumes 20% higher prepayments than PSA alone).
 This baseline can be estimated by the prepayment history of deep discount coupons, as prepayments on such coupons primarily reflect housing turnover.
 At a lowerthanmarket coupon, home owners do not have an incentive to refinance.
 of PSA is used to reflect views on future changes in the refinancing incentive.
 On a pool of mortgages with a face value or $1,000,000, a 360 month weighted average maturity, a 6.0% weighted average interest rate, at 100% PSA, the payments can be diagramed as follows:
12,000
10,000
31 61 91 121 151 181 211 241 271 301 331
31 61 91 121 151 181 211 241 271 301 331
Month
 Principal
 Interest
 Based on this, PSA prepayments affect principal paydown:
g 0.1
 0.0
 0 30 60 90 120 150 180 210 240 270 300 330 360
month
0% PSA100% PSA200% PSA500% PSA
 Borrowers who are usually the first to refinance and drop out of a mortgage pool generally:
 Are more sophisticated financially (optimally exercising their option to refinance);
 Face lower refinancing costs;
 Have more builtin equity in their homes;
 Have higher incomes.
 As a result, for the same refinancing incentive, moreseasoned pools show slower prepayment speeds. This is generally referred to as Burnout.
 As seasoned premium mortgages accumulate more burnout and thus are less sensitive to declines in mortgage rates, prepayment risk is generally lower.
 Because of the perceived lower optionality, investors usually are willing to pay more for vintage premiums than for new origination of the same coupon.
 A large variety of mortgage and market data are available for study, including:
 Loan types; — Refinancing alternatives;
 Coupons; — Prepayment costs;
 Vintages; — Housing values;
 Dollar balances; — Tax rates;
 Mortgage rates; — Regulations; and
 Shape of the yield curve; — Others.
 A prepayment function is generally based on four submodels of homeowner prepayment decisions:
(1) + 
(2) + 
(3) 
+ (4) 
Refinancings 
Relocations 
Defaults 
Curtailments 
 Different types of mortgages (e.g. FNMA or GNMA) require different prepayment functions.
 Prepayment functions are generally estimated by fitting actual prepayment speeds to various key variables, including:
 Level of interest rates in various products;
 Shape of the yield curve;
 Mortgage spreads;
 Refinancing costs (fees, upfront points);
 Loan age, seasonal factors; and
 Macroeconomic factors such as housing prices, aggregate income, etc.
 Prepayment models should:
 Consistently track absolute prepayment rates;
 Consistently track relative prepayment rates (achieve consistent results across various mortgage types, coupons and vintages);
 Be robust in treating prepayment outliers; and
 Be able to update models to reflect structural changes in the mortgage market.
 In practice, prepayment models are less than perfect. Hence, the MBS valuation is always subject to prepayment model risk (the risk that prepayment predictions are systematically biased).
 One known area of possible prepayment model risk, is that mortgagors usually do not or cannot optimize their right to exercise their prepayment options.
 Borrowers have various thresholds for refinancing under different incentives.
 Refinancing speeds are determined by measuring the difference between a borrower's mortgage rate and the current market mortgage rate.
 The following curve was developed as a general guideline to when borrowers refinance; however, each different type of mortgage pool has its own curve.

 Homeowner Refinancing Incentive (bp)
 To value an MBS, you must estimate the cash flows in future months; however, cash flows depend on future interest rates  both on their levels and on the paths they took to reach those levels.
 One way to model these cash flows is to assume that future rates implied by the forward curve will be realized:
 At each payment date there will be a yield curve implied by forwards.
 By using this yield curve in combination with a separate model of how mortgage rates respond to the yield curve, future refinancing incentive can be calculated.
 Future prepayment rates can be found with the Scurve.
 This will yield cash flows, which can be discounted to value the MBS.
 Problem: What if the forward rates aren't realized?
 In order to take this volatility and uncertainty of rates into account, a model to simulate future rate paths is used.
 Mortgage rates are generated as a function of these simulated rates, using a separate model of mortgage spreads with respect to interest rates.
 Prepayment rates, along each interest rate path, are calculated using the prepayment function, and mortgage cash flows (both scheduled and prepayments) are projected along each interest rate path.
 These projected cash flows are then discounted at the spot rates along each interest rate path.
 The optionadjusted spread (OAS) is then calculated by equating the average present value of projected cash flows under all the simulations to the market price of the security.
 If two bonds are equal in many respects, then a high OAS implies relative cheapness and a low OAS implies relative richness.
 Note that every prepayment model is different; hence, OAS is different based on these calculations.
 Owing to interest rate volatility, the prepayment characteristics of the underlying mortgages can create (or decrease) value.
 We can assume that interest rates have zero volatility and value an MBS along the basecase scenario: the forward mortgage rates curve.
 The spread that results between valuing the MBS along the forward mortgage rates curve and valuing the MBS along a LIBOR/swaps curve is called a zero volatility option adjusted spread (ZVO).
 This is the excess return over swaps that an MBS investor would earn if interest rates were nonrandom and the embedded option had no value.
 OAS, on the other hand, reflects the expected return when interest rates are volatile and the embedded option has value.
 The implied cost of the option embedded in an MBS is the difference between the ZVO and OAS (ZVO = OAS + option cost).
 Convexity measures the sensitivity of a bond's price to larger changes in yield.
 Duration is the percentage change in the price of an MBS due to a 100 basis point change in yield. For example, the value of an MBS with a duration of 3 will decline about 3 points for each 100 basis point increase in interest rates.
 Therefore, convexity is the sensitivity of a bond's duration to changes in yield: AD = C x Ay
 When looking at the price function of an MBS changing across small variations in yield, remember that prepayments will also vary. Given P = price, and Ay = change in yield,
Duration =
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