The MBS Market Continued

Many different types of investors buy MBS.

Mortgage- and asset-backed security holdings by investor type 2003 at year-end are as follows:

Mutual Funds 7%

Mutual Funds 7%

Mbs Market

Foreign Investors 5%

* Other consists of Private Individuals, Finance Companies, MBS deal Inventory, REITs, Federal Credit Unions, HedgeFunds/ Non-Profits/ 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/ Non-Profits/ State and Local Gov't
  • Mortgagors have the statutory right to re-finance 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 higher-than-expected 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 lower-than-expected prepayments:
  • This harms the holder of a discount MBS, as the lower prepayments prolong the period of below-market coupon payments.
  • This benefits the holder of a premium MBS, as the lower prepayments prolong the period of above-market 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 lower-than-market 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

Psa Prepayment

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% PSA-100% PSA-200% PSA-500% 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 built-in equity in their homes;
  • Have higher incomes.
  • As a result, for the same refinancing incentive, more-seasoned 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 sub-models 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, up-front 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.
Mortgage 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 S-curve.
  • 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 option-adjusted 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 base-case 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 non-random 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 =

Lessons From The Intelligent Investor

Lessons From The Intelligent Investor

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Responses

  • emogene
    Why oas of premium mortgage volatile?
    5 years ago
  • ULLA KNIHTIL
    How to price mbs "option adjusted spread"?
    5 years ago

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