Mortgage Vox

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%

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

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.

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 =