Securitization

1
Securitization
2
I.1 Secondary Mortgage Market

• Primary Mortgage Market Lender deals directly
  with the borrower for underwriting (risk analysis
  to determine if the loan should be made), and
  origination of the loan (direct interaction with
  the borrower).
• Secondary Mortgage Market Mortgage loans and
  securities backed by mortgage loans are sold to
  investors, typically through intermediaries, for
  inclusion as part of the investors portfolio of
  assets.

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I.1 Secondary Mortgage Market

• Evolution of the Secondary Mortgage Market
• 1. Early Market Development 1930 1969
• 2. Introduction of Mortgage-backed Securities
  1970 1980
  
• 3. Initial reaction to interest rate volatility,
  and prepayment risk 1980 1986
  
• 4. Growth in derivative mortgage-backed
  securities and opening new market areas 1987
  the present

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I.1 Secondary Mortgage Market

• Early Development
• Prior to the 1930s there was no organized
  secondary mortgage market.
  
• Development was part of President Roosevelts
  New Deal program to lift the U.S. economy out
  of the Great Depression. It was one element of
  a multi-faceted plan to encourage homeownership
  and stimulate mortgage lending.
• Aside Other elements of the plan
• 1. Development of Federal Home-Loan Bank system
• 2. Inception of government mortgage insurance
  programs (VA and FHA)
  
• 3. Insurance of Savings Deposits (FDIC, FSLIC)
• 4. Fixed payment fully amortized mortgage
  introduced.

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I.1 Secondary Mortgage Market

• Federal National Mortgage Association (Fannie
  Mae)
  
• Created in 1938 first federal government
  secondary market agency
  
• Goals for Fannie Mae and the Secondary Mortgage
  Market
  
• 1. To provide liquidity for mortgage originators
  and investors
  
• 2. Integrate local mortgage markets with national
  capital markets
  
• 3. Transfer funds from capital surplus to capital
  shortage areas
  
• 4. To provide special assistance to the federal
  government in implementing housing and mortgage
  market policies

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I.1 Secondary Mortgage Market

• Surge of Growth in secondary market after WWII
  for two reasons
  
• 1. Great demand for VA guaranteed loans
• 2. Growth in demand for long-term investments by
  pension funds and life insurance companies.
  
• Grow makes problems of secondary market apparent
• 1. No secondary market for privately insured
  loans, so integration of local mortgage and
  national capital markets ineffective
  
• 2. Many potential investors not interested in
  direct mortgage investment

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I.1 Secondary Mortgage Market

• Monumental Changes in the Mortgage-backed
  Securities Market
  
• 1. 1968 Government National Mortgage
  Association (Ginnie Mae) created
  
• a. First mortgage-backed securities issued under
  Ginnie Mae guarantee program
  
• b. Takes over special assistance function from
  Fannie Mae
  
• 2. 1970 Act of Congress creates Federal Home
  Loan Mortgage Corporation (Freddie Mac)
  
• For the first time privately insured mortgages
  are traded in the secondary mortgage market

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I.2 Mortgage-Backed Securities

• Mortgage-backed securities or "MBS" are a type of
  fixed income investment. The main feature that
  distinguishes MBS from other fixed income
  investments is prepayment risk.
• Because of prepayment risk, MBS usually offer
  higher yields than otherwise-comparable fixed
  income securities.

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I.2 Mortgage-Backed Securities
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I.2 Mortgage-Backed Securities

• A simple "pass-through" security that represents
  ownership of an underlying "pool" of mortgage
  loans. An investor who owns the MBS is entitled
  to receive collections of interest and principal,
  including prepayments. In MBS jargon, the
  payments on the loans are "passed-through" to the
  investors.
• A small portion of the interest collections is
  not passed through to cover expenses. Thus, an
  MBS has a "pass-through rate, which is the net
  rate at which investors receive interest on the
  balance of the mortgage loans backing the
  security.
• For example, if the mortgage loans backing an MBS
  have interest rates of 6.5, the MBS might have a
  pass-through rate of 6. The difference, 0.5,
  covers expenses.

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I.2 Mortgage-Backed Securities

• Most MBS are issued or guaranteed by one of the
  three mortgage-related "agencies" or "government
  sponsored enterprises" (GSEs) (1) Ginnie Mae,
  (2) Fannie Mae, and (3) Freddie Mac.
• Each "agency MBS" has the benefits of a credit
  guarantee from its related agency. Those
  guarantees insulate MBS investors from credit
  risk on the underlying loans.
• The federal government backs Ginnie Mae's
  guarantee. The guarantees of the other two
  agencies do not have federal backing, but
  professionals generally view those agencies as
  having extremely high credit quality.

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I.2 Mortgage-Backed Securities

• Private sector entities also issue MBS. Those are
  called "private label MBS. Private label MBS do
  not carry guarantees from the GSEs and,
  therefore, use other forms of credit enhancement
  to counter-balance the credit risk of their
  underlying mortgage loans.

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I.2 Mortgage-Backed Securities

• The loans backing an agency MBS are similar to
  each other.
  
• For example, a given agency MBS could be backed
  either by fixed-rate mortgage loans (FRMs) or by
  ARMs, but not by both.
  
• In the case of agency MBS composed of FRMs, all
  the loans would have interest rates close
  together.
  
• For some kinds of agency MBS, all the FRMs must
  have exactly the same interest rate. In other
  agency MBS, the interest rates on the FRMs can
  vary by as much as 1.75.

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I.2 Mortgage-Backed Securities

• In the case of an agency MBS backed by ARMs, the
  interest rate adjustment mechanism in all the
  loans must be based on the same index.
  
• For example, all the ARMs backing an agency MBS
  could have adjustment formulas tied to LIBOR.
  
• Alternatively, all the ARMs could have formulas
  tied to the one-year Treasury constant maturity
  index (CMT). However, an agency MBS could not be
  backed by a mixture of LIBOR-based and CMT-based
  ARMs.
• A given agency MBS would have roughly similar
  maturities.
  
• An agency MBS would not be backed by a mixture of
  loans having both 30-year and 15-year final
  maturities.

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I.2 Mortgage-Backed Securities

• Professionals tend to group agency MBS into large
  categories and often treat the securities as
  fungible within each category.
  
• For example, one category would be all the Fannie
  Mae MBS with pass-through rates of 6 and backed
  by 30-year FRMs. Another category would be all
  Ginnie Mae MBS with 5½ pass-through rates and
  backed by 15-year FRMs.

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II.1 Mortgage-Backed Securities

• Mortgage-Backed Securities
• Definition A financial instrument whose interest
  and principal payments are either derived
  directly from the cash flows of an underlying
  pool of mortgages (e.g., pass throughs) or are
  collateralized by such a pool (e.g.,
  mortgage-backed bonds).

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II.1 Mortgage-Backed Securities

• Why investors prefer mortgage-backed securities
  to investment in whole mortgage loans?
  
• 1. Separates ownership of cash flows from
  origination and servicing functions
  
• 2. Provides small investor with the ability to
  diversify across a pool of loans
  
• 3. Provides an extra layer of security from
  default
  
• a. government guarantees
• b. private pool insurance
• c. over collateralization of the pool
• 4. Good information about the characteristics of
  the mortgages in the pool
  
• 5. Ability to restructure cash flows from the
  pool
  
• 6. Increases liquidity through standardization
  and good information

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II.1 Mortgage-Backed Securities

• Three Major of Mortgage-backed securities
• Pass-through securitization
• Collateralized mortgage obligations
• Mortgage-backed bonds

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II.2 Pass-Through Securities

• The pass through or participation certification
  (PCs) is the most common structure for
  mortgage-backed securities.
  
• The MBS acquires mortgages from original mortgage
  lenders.
  
• The agency then examines mortgage at to ensure
  that they meet the credit-quality guidelines.
  
• Loans with similar characteristics and maturity)
  are pooled together and the servicer passes
  through a pro rata share of all interest and
  principal payments to the investors.
• For example if an investor owns 2 of the pool,
  she would receive 2 of all the payments of
  interest and principal received by e pool less
  fees.

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II.2 Pass-Through Securities

• The actual packaging or pooling can be done by
  the government sponsored enterprises Ginnie Mae,
  Fannie Mae and Freddie Mac, or by private
  enterprises.
• Payments to investors are made on a monthly
  basis. Since not all the mortgages in a pool have
  the exact same mortgage rate and maturity, a
  weighted-average coupon (WAC) is calculated for
  the pool of mortgages backing the pass-through.
  However, investors receive what is called net
  coupon which is the WAC less the fees that the
  MBS issuer charges for guaranteeing

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II.2 Pass-Through Securities

• Credit Risk
• Like any debt instrument, mortgages involve
  credit risk. Credit risk arises from uncertainty
  over whether the borrower will perform as
  required to fulfill interest and principal
  payments. In order to reduce that risk on
  mortgages, the conventional mortgage contract,
  which was developed by Fannie Mae in the 1930s,
  requires borrowers to put down 20 of the house
  price as down payment. This is expressed as 80
  loan-to-value ratio when value refers to the
  market price of the home. Thus the collateral for
  the mortgage, the value of home, amounts to 125
  of the debt principal.
• Mortgage insurance is provided by several federal
  government programs as well as by private
  mortgage insurance companies
  

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II.2 Pass-Through Securities

• Credit Risk
• The The Federal Housing Administration (FHA) was
  created under the National Housing Act of 1934.
  It insures mortgages of low- and moderate-income
  families to promote ownership for those people.
  The FHA insurance covers the whole amount of the
  loan, but there is a limit to what the size of
  the loan could be. If the borrower with FHA
  insurance defaults insurance, the FHA has two
  options. It can pay the lender the insured amount
  and let the lender take the title of the house.
  The FHA can reimburse the lender for the entire
  loan amount and take the title of the house.
• The Department of Veterans Affairs (VA) offers
  insurance on mortgages for veterans. Unlike the
  FHA, the VA insurance covers only a certain
  percentage of the loan, up to 25.

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II.2 Pass-Through Securities

• Credit Risk
• Most loans are not insured by the government
  agencies like FHA, VA, or RHS. These are called
  conventional mortgages. Private lenders
  investing in these mortgages often require
  private mortgage insurance (PMI) if the
  loan-to-value ratio exceeds 80 (that is, if the
  home buyer puts down less than 20). Such
  insurance can be obtained from a mortgage
  insurance company (MIC). The MIC industry was
  created in 1920s but collapsed in the 1930s. It
  gained popularity again in the 1950s. Recently,
  private insurers have been accused of abuses such
  as repeated sale of PMI insurance policies to
  borrowers with enough equity to not require
  mortgage insurance.

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II.2 Pass-Through Securities

• Credit Risk
• Most Investors in MBSs do not want to hold credit
  risk on the underlying mortgages, so MBS issuers
  provide guarantees. When Fannie Mae and Freddie
  Mac issue MBSa, they charge a guarantee fee that
  is currently between 20-30 basis points. This is
  taken from the gross yield on the loan so it is
  netted to the investor. These corporations are
  able reduce their risk of mortgage default by
  diversifying their large portfolios across the
  nation. Investors in these MBS thus have not the
  individual borrower, but Fannie Mae and Freddie
  Mac as a counter party to their credit risk.
  Therefore the credit risk of mortgage-backed
  securities issued by Fannie Mae and Freddie Mac
  reflects the credit rating of those corporations.

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II.2 Pass-Through Securities

• Ginnie Mae Pass-through programs
• Ginnie Mae offers three pass-through programs
  Ginnie Mae I, Ginnie Mae II and Ginnie Mae
  Platinum.
  
• These programs are backed by the full faith and
  credit of the US government. Therefore, they have
  virtually the same risk as US treasury securities
  except for the prepayment risk.
• Ginnie Mae pass-throughs are backed by newly
  originated FHA and VA insured mortgages and their
  credit is further enhanced by Ginnie Maes
  guarantee.

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II.2 Pass-Through Securities

• Ginnie Mae I has the lowest servicing spread with
  6 basis points for guarantee fee and 44 basis
  points for servicing fees. The majority of Ginnie
  Mae pass-throughs are issued under Ginnie Mae I,
  where the securities are backed by single-family
  fixed-rate 30- or 15-year mortgages and one-year
  adjustable rate mortgages.

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II.2 Pass-Through Securities

• Freddie Mac
• Freddie Mac offers a pass-through program that
  offers full and timely payment of interest and
  principal.
  
• Like Freddie Mac notes and bonds, these
  pass-throughs are not guaranteed by the full
  faith and credit of the US government. However,
  some market participants view them as similar in
  credit worthiness to Ginnie Mae pass-throughs.
• Freddie Macs pass-through pools consist of
  conventional mortgages as well as those from FHA
  and VA mortgages. Freddie Mac charges guarantee
  fee under 25 basis points and a servicing fee
  between 25-37 basis points. Freddie Mac has
  implemented a contract feature that adjusts the
  guarantee fee up or down relative to the current
  level of security price spreads.

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II.2 Pass-Through Securities

• Fannie Mae
• Fannie Mae offers a pass-through program which,
  like Fannie Mae notes and bonds, is not backed by
  the full faith and credit of the US government.
  
• Fannie Maes pass-through pools consist of
  conventional mortgages as well as those from FHA
  and VA mortgages.
  
• Fannie Maes have similar fees as Freddie Macs
  guarantee fee 25 basis points and servicing fee
  of 25 to 37 basis points. In 2003, the average
  effective guarantee fee that Fannie Mae reported
  was 20.2 basis points

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II.3 Incentives and Mechanics of Pass-Through
Security Creation

• 1. To Reduce Regulatory Taxes
• Create a mortgage pool from one-thousand,
  100,000 mortgages (for a 100 m mortgage pool)
  with 30 years in maturity and 12 percent interest
  rate.
• Each mortgage receives credit risk protection
  from FHA.
  
• Capital requirement 100m .05 .08 4
  million (the risk-adjusted value of residential
  mortgages is 50 of face value and the risk-based
  capital requirement is 8).
• Must issue more than 96 million in liabilities
  due to a 10 reserve requirements. ( FDIC
  premia).

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II.3 Incentives and Mechanics of Pass-Through
Security Creation

• Reserve requirement 10 106.6 10.66m,
  leaves 96m to fund the mortgages.
  
• FDIC insurance premium 106.66m .0027
  287,982
  
• The three levels of regulatory taxes
• 1. Capital requirements
• 2. Reserve requirements
• 3. FDIC insurance premiums.

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II.3 Incentives and Mechanics of Pass-Through
Security Creation

• Bank Balance Sheet Before Securitization
• Assets Liabilities
• __________________________________________________
  ______
  
• Cash reserves 10.66 Demand Deposits 106.6
• Long-term mortgage 100.00 Capital 4.00
• __________________________________________________
  ______
  
• Bank Balance Sheet After Securitization
• __________________________________________________
  ______
  
• Cash reserves 10.66 Demand Deposits 106.6
• Cash proceeds from 100.00 Capital 4.00
• mortgage securitization
• __________________________________________________
  ______

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II.3 Further Incentives

• 2. To Reduce Gap exposure The FI funds the
  30-year mortgages out of short-term deposits
  thus has a duration mismatch.
  
• 3. To Reduce Illiquidity exposure illiquid
  portfolio of long term mortgages.
  
• Creating GNMA pass-through securities can largely
  resolve the duration and illiquidity risk
  problems on the one hand and reduce the burden of
  regulatory taxes on the other.

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II.3 Further Incentives

• Investors of GNMA securities are protected
  against two levels of default risks
  
• 1. Default Risk by the Mortgages
• Phoenix, AZ in 1980s.
• Through FHA/VA housing insurance, government
  agencies bear the risk of default.
  
• 2. Default Risk by Bank/Trustee GNMA would bear
  the cost of making the promising payments in full
  and on time to GNMA bondholders.
  

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II.3 Further Incentives

• Given the default protection, the returns to GNMA
  bondholders
  
• _______________________________________
• Mortgage coupon rate 12
• - Service fee (to the bank) 0.44
• - GNMA insurance fee 0.06
• GNMA pass-through bond coupon 11.50
• ________________________________________

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II.3 Further Incentives

• Bank Balance Sheet after Securitization
• Assets Liabilities
• __________________________________________________
  ______
  
• Cash reserves 10.66 Demand Deposits 106.6
• Cash proceeds from 100.00 Capital 4.00
• mortgage securitization
• __________________________________________________
  ______
  
• A dramatic change in the balance sheet exposure
  of the bank
  
• 1. 100m illiquid mortgage loans have been
  replaced by 100m cash
  
• 2. The duration mismatch has been reduced
• 3. The bank has an enhanced ability to deal with
  and reduce its regulatory taxes.

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III. Effects of Prepayments

• Prepayment Risk Makes Mortgage-Backed Securities
  Unique
  
• Prepayment gives mortgage holders a very valuable
  call option on the mortgage when this option is
  in the money.
  
• The effect is to lower dramatically the principal
  and interest cash flows received in the later
  months of the pools life.
  
• There are two reasons for prepayment by
  borrowers
  
• 1. Adjustment in housing consumption
• 2. Changes in market interest rates

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III. Effects of Prepayments

• Effects of prepayments
• 1. Good news effects
• Lower market yields increase present value of
  cash flows.
  
• Principal received sooner.
• 2. Bad news effects
• Fewer interest payments in total.
• Reinvestment at lower rates.

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III. Effects of Prepayments

• Measuring Prepayments
• A specialized vocabulary for describing and
  measuring prepayments A "prepayment speed" or
  "prepayment rate" describes the pace at which
  borrowers prepay their mortgage loans.
• Professionals often use two standardized models.
  The first, called "constant prepayment rate" or
  CPR, expresses the pace of prepayments in terms
  of a constant annual rate of prepayment.
• For example, 10 CPR refers to a constant annual
  rate of prepayment such that borrowers prepay 10
  of the balance of a pool of loans each year.

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III. Effects of Prepayments

• A prepayment rate of "10 CPR" corresponds to a
  monthly prepayment rate (i.e., single monthly
  mortality or SMM) of approximately 0.8742,
  calculated as follows

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III. Effects of Prepayments

• Exhibit 5 shows the monthly level of principal
  cash flow on the pool of mortgage loans (100
  million, 30-year, 7, fixed rate). The shaded
  portions of the four panels have different
  shapes, but all have the same area. That is
  because the total amount of principal cash flows
  remains the same under all prepayment scenarios
  only the timing of the principal cash flows
  changes. At higher CPR prepayment speeds, more of
  the principal cash flow comes in the early years
  of the life of the pool. For example, at a
  prepayment speed of 6 CPR, the weighted average
  life or "WAL" of the pool is 10.8 years.25 At a
  slower prepayment speed of 3 CPR, the WAL is
  somewhat longer 14.4 years. Conversely, at a
  fast prepayment rate of 24, the WAL is just 3.5
  years. In graphical terms, the WAL corresponding
  to given CPR is roughly the point along the
  x-axis that divides the shaded area in half.

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III. Effects of Prepayments
42
III. Effects of Prepayments

• The second commonly used prepayment model is
  called PSA. The PSA model is based on the CPR
  model. It's like the CPR model except that
  prepayments start slowly and rise to their
  ultimate rate over a period of 2½ years (30
  months). More precisely, the base case of the PSA
  model (i.e., "100 PSA") is defined as follows
  prepayments are 0.2 CPR in the first month
  following origination of a pool of mortgage loans
  and increase by 0.2 CPR per month until they
  reach a steady-state rate of 6 CPR in the 30th
  month. Multiples of the base case, such as 200
  PSA, refer to situations where prepayments in
  each month are at a level corresponding to a
  multiple of the 100 PSA scenario.

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III. Effects of Prepayments

• Exhibit 7 shows the principal cash flows on our
  hypothetical pool of mortgage loans at various
  PSA prepayment speeds. Each panel in Exhibit 7
  shows the cash flows at a PSA prepayment speed
  that relates to the corresponding CPR speed in
  Exhibit 6. For example, the top left panel in
  Exhibit 7 shows the 100 PSA scenario, which
  corresponds to the 6 CPR scenario in Exhibit 6.
  Likewise, the 400 PSA scenario in Exhibit 7
  corresponds to the 24 CPR scenario in Exhibit
  6.

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III. Effects of Prepayments
45
III. Effects of Prepayments

• Prepayment in the Real World
• Prepayments in the real world do not adhere to
  steady patterns like those embodied in the CPR
  and PSA models. Instead, prepayments are erratic
  and jumpy. All other things being equal, an
  environment of low interest rates motivates more
  borrowers to refinance their loans, producing
  higher prepayment speeds. Similarly, loans with
  higher interest rates tend to experience faster
  prepayments because the borrowers get favorable
  refinancing opportunities more frequently.

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III. Effects of Prepayments

• Exhibit 8 shows the reported prepayment speeds on
  loans backing two cohorts of Fannie Mae MBS
  those with pass-through rates of 5 and 6.5,
  respectively. The chart shows that the prepayment
  speed on the 6.5 MBS is consistently faster than
  the prepayment speed on the 5 MBS. In addition,
  the chart shows that the prepayment speeds of
  both cohorts rise and fall over time as interest
  rates fluctuate.

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III. Effects of Prepayments
48
III. Effects of Prepayments

• Prepayments result of sales or refinancing.
• Since prepayment affects the cash flows to MBS,
  pricing models require estimates of the
  prepayment rates.
  
• Methods
• Option pricing approach.
• Public Securities Association approach.
• Empirical approach.

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III. Effects of Prepayments PSA Model

• The PSA (Public Securities Association) model
  assumes that the prepayment rate starts at 0.2
  per annum in the first month, increasing by 0.2
  per month for the first 30 months, until
  prepayment rate then levels off at a 6
  annualized rate for the remaining life of the
  pool.
• Issuers or investors who assume that their
  mortgage pool prepayment exactly match this
  pattern are said to assume 100 percent PSA
  behavior.

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III. Effects of Prepayments PSA Model

• Actual prepayment rate may differ from PSAs
  assumed pattern
  
• The level of the pools coupon relative to the
  current mortgage coupon rate
  
• The age of the mortgage pool
• Whether the payments are fully amortized
• Assumability of mortgages in the pool.
• Size of the pool
• Conventional or nonconventional mortgages
• Geographical location
• Age and job status of mortgagees in the pool.

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III. Effects of Prepayments PSA Model

• On approach to control these factors is by
  assuming some fixed deviation of any specific
  pool from PSAs assumed average or benchmark
  pattern. E.g., one pool may be assumed to be 75
  PSA, and another 125 PSA. The formal has a
  lower prepayment rate than historically
  experienced the latter, a faster rate.

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III. Effects of Prepayments PSA Model
Prepayment rate ()
125 PSA
7.5
100 PSA
6.0
4.5
75 PSA
Months
30
360
53
III. Effects of Prepayments Other Empirical
Models

• Most empirical models are proprietary versions of
  the PSA model in which FIs make their own
  estimates of the pattern on monthly prepayments.
  
• FIs begin by estimating a prepayment function
  from observing the experience of mortgage holders
  prepaying during any particular period on
  mortgage pools.

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III. Effects of Prepayments Other Empirical
Models

• The conditional prepayment rates in month i for
  similar pools would be modeled as functions of
  economic variables driving prepayment e.g.,
  
• pi f(mortgage rate spread, age,
  collateral,
  
• geographic factors, burn-out
  factor).
  
• Once the frequency distribution of the pis is
  estimated, the bank can calculate the expected
  cash flows on the mortgage pool under
  consideration and estimate its fair yield given
  the current market price of the pool.

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III. Effects of Prepayments Option Model Approach

• Fair price on pass-through decomposable into two
  parts
  
• PGNMA PTBOND - PPREPAYMENT OPTION
• Option-adjusted spread between GNMAs and T-bonds
  reflects value of a call option. Specifically,
  the ability of the mortgage holder to prepay is
  equivalent to the bond investor writing a call
  option on the bond and the mortgagee owning or
  buying the option. If interest rates fall, the
  option becomes more valuable as it moves into the
  money and more mortgages are prepaid early by
  having the bond called or the prepayment option
  exercised.

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III. Effects of Prepayments Option Model Approach

• In the yield dimension
• YGNMA YTBOND YPREPAYMENT OPTION
• That is, the fair yield spread or option-adjusted
  spread (OAS) between GNMAs and T-bonds plus an
  additional yield for writing the valuable call
  option.

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III. Effects of Prepayments Option Model Approach

• Example Smiths Model
• Assumptions
• 1. The only reasons for prepayment are due to
  refinancing mortgage at lower rates
  
• 2. The current discount (zero-coupon) yield curve
  for T-bonds is flat
  
• 3. The mortgage coupon rate is 10 on an
  outstanding pool of mortgages with an outstanding
  principal balance of 1,000,000
  
• 4. The mortgages have a 3-year maturity and pay
  principal and interest only once at the end of
  each year.
  
• 5. Mortgage loans are fully amortized, and there
  is no service fee.

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III. Effects of Prepayments Option Model Approach

• Thus the annually fully amortized payment under
  no prepayment conditions is
  
• R 1,000,000/(PVIFA 10, 3 yrs) 402,114.
• At the current mortgage rate of 9, the GNMA
  bond would be selling at
  
• P 402,114 (PVIFA 9, 3 yrs) 1,017,869.

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III. Effects of Prepayments Option Model Approach

• 6. Because of prepayment penalties and
  refinancing costs, mortgagees do not begin to
  prepay until mortgage rates fall 3 or more below
  the mortgage coupon rat
• 7. Interest rate movements over time change a
  maximum of 1 up or down each year. The time
  path of interest rates follows a binomial
  process.
• 8. With prepayment present, cash flows in any
  year can be the promised payment R 402,411,
  the promised payment (R) plus repayment of any
  outstanding principal, or zero in all mortgages
  have been prepaid or paid off in the previous
  year.

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III. Effects of Prepayments Option Model Approach

• End of Year 1 since interest rates can change up
  or down by 1 per annum, mortgages are not
  prepaid. GNMA bondholders receive the promised
  payment R401,114 with certainty.

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III. Effects of Prepayments Option Model Approach

• End of Year 2There are three possible mortgage
  rates 11, 9, and 7 with 25, 50, and 25 of
  probability.
  
• If prepayment occurs, the investor receives
• R principal balance remaining at the end of yr
  2
  
• 402,114 365,561 767,675
• Thus CF2 .25(767,675) .75(402,114)
  493,504.15
  

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III. Effects of Prepayments Option Model Approach

• End of Year 3 since there is a 25 probability
  that mortgages are prepaid in yr 2, the investor
  will receive no cash flows at the end of yr 3.
  However, there is also a 75 probability that
  mortgages will not be prepaid in yr 2, the
  investor will receive the promised payment R
  402,114.
• CF3 .25(0) .75(402,114) 301,586

63
III. Effects of Prepayments Option Model Approach

• Deviation of the Option-Adjusted Spread
• The required yield on a GNMA with prepayment risk
  is divided into the required yield on T-bond plus
  a required spread for the prepayment call option
  given to the mortgage holders
• E(CF1) E(CF2) E(CF3)
• P ------------ -------------
  --------------
  
• (1d1Os) (1d2Os)2 (1d3Os)3

64
III. Effects of Prepayments Option Model Approach

• Assume that the T-bond yield curve is flat, so
  that d1 d2 d3 8 then
  
• 401,114 493,504 301,585
• P ------------ -------------
  --------------
  
• (1.08Os) (1.08 Os)2 (1.08 Os)3
• Os 0.96 and
• YGNMA YTBOND Os
• 8 0.96 8.96

65
IV. Collateralized Mortgage Obligation (CMO)

• Definition A mortgage-backed pay-through Bond
  that categorized investors into groups
  (traunches) who were designated to receive
  repayment of principal in the pool in a
  sequential manner, rather than the traditional
  pro-rata share.
• Initial CMO was issued by Freddie Mac in 1983
  note that prepayment risk was a big concern at
  this time because interest rates had been
  relatively volatile, moving up very rapidly to
  unanticipated heights during the preceding decade.

66
IV. Collateralized Mortgage Obligation (CMO)

• CMO structure
• CMOs can be created either by packaging and
  securitizing whole mortgage loans or by placing
  existing pass-throughs in a trust.
  
• The investment bank or issuer creates the CMO to
  make a profit. The sum of the prices at which the
  CMO bond classes can be sold normally exceeds
  that of the original pass-throughs.
• Prepayment effects differ across tranches.
• Improves marketability of the bonds.

67
IV. Collateralized Mortgage Obligation (CMO)
68
IV. Collateralized Mortgage Obligation (CMO)

• Other classes
• Class Z is the last regular class. After the
  other classes have been retired, Z-class
  bondholder receives the promised coupon and
  principal payments
• Class R Garbage class is the residual class
  giving the owner the right to any remaining
  collateral in the trust after all other bond
  classes have been retired any reinvestment
  income earned by the trust.

69
IV. Collateralized Mortgage Obligation (CMO)

• The Value Additivity of CMOs
• Suppose an investment bank buys a 150m issue of
  GNMAs and places them in trust as collateral. It
  then issues a CMO with
  
• Class A Annual fixed coupon 7, class size 50m
• Class B Annual fixed coupon 8, class size 50m
• Class C Annual fixed coupon 9, class size 50m

70
IV. Collateralized Mortgage Obligation (CMO)

• Assume that in month 1 the promised amortized
  cash flows on the mortgages are 1m but there is
  an additional 1.5m cash flows as a result of
  early prepayment. These are distributed to CMO
  holders as
• Coupon payments
• Class A (7) 291,667
• Class B (8) 333,333
• Class C (9) 375,000

71
IV. Collateralized Mortgage Obligation (CMO)

• Principal Payments
• The 1.5m cash flows remaining will be paid to
  Class A holders to reduce its principal
  outstanding to 50m-1.5m48.5m.
  
• Between 1.5 to 3 years after issue, Class A will
  be fully retired. The trust will continue to pay
  Class B and C holders the promised coupon
  payments of 333,333 and 375,000 monthly. Any
  cash flows over the promised coupons will be paid
  to retire Class B CMOs.

72
IV. Collateralized Mortgage Obligation (CMO)

• Class Z This class has a stated coupon, such as
  10, and accrues interest for the bondholders on
  a monthly basis at this rate. The trust does not
  pay this interest, however, until all other
  classes are fully retired. Then Z-class holders
  received coupon and principal payments plus
  accrued interest payments. Thus, Z-class has
  characteristics of both a zero-coupon bond and a
  regular bond.

73
IV. Collateralized Mortgage Obligation (CMO)

• Class R CMOs tend to be over-collaterized
• CMO issuers normally uses very conservative
  prepayment assumptions. If prepayments are
  slower than expected, there is often excess
  collateral left over when all regular classes are
  retired.
• Trustees often reinvest cash flows in the period
  prior to paying interest on the CMOs. The higher
  the interest rate and the timing of coupon
  intervals is semiannual rather than monthly, the
  larger the excess collateral.

74
IV. Collateralized Mortgage Obligation (CMO)

• This residual R-class is a high-risk investment
  class that gives the investor the rights to the
  overcollateralization and reinvestment income on
  the cash flows in the CMO trust.
• Because the value of the returns in this bond
  increases when interest rates rise, while normal
  bond values fall with interest rate increases,
  Class R often has a negative duration.

75
V. Mortgage-Backed Bonds (MBBs)

• Definition This security represents a general
  obligation of the issuing entity. The payments
  are collateralized by and derived from an
  underlying pool of mortgages.
• Ways that the bond differs from the pass-through
  security
  
• 1. Prepayment risk is absorbed by the issuer
• This is handled through over collateralization of
  the pool
  
• (range 120 to 240 of the mortgages needed to
  handle
  
• the cash flows)

76
V. Mortgage-Backed Bonds (MBBs)

• 2. Typically issued by private mortgage
  originators. Therefore government guarantees are
  replaced with private pool insurance and/or
  ratings by bond rating agencies (e.g., Standard
  and Poors or Moodys)
• 3. Sale of securities not treated as an asset
  sale to the issuer.
  
• 4. Cash flows can be restructured to meet the
  needs of the investor because mortgage payments
  are not being directly passed through.

77
V. Mortgage-Backed Bonds (MBBs)

• Differs from pass-throughs and CMOs in two key
  dimensions
  
• 1. While pass-throughs and CMOs remove mortgages
  from balance sheets, MBBs normally remain on the
  balance sheet.
  
• 2. Pass-throughs and CMOs have a direct link
  between the cash flow on the underlying
  mortgages, with MBBs the relationship is one of
  collateralization.

78
V. Mortgage-Backed Bonds (MBBs)

• Normally remain on the balance sheet and
  over-collaterized to reduce funding costs.
  
• __________________________________________________
  ________________
  
• Assets Liabilities
• __________________________________________________
  ________________
  
• Long-term Mortgages 20 Insurance
  Deposits 10
  
• Uninsured Deposits 10
• __________________________________________________
  ________________
  
• Collateral 12 MBB 10
• Other Mortgages 8 Insured Deposits
  10
  
• __________________________________________________
  ________________

79
V. Mortgage-Backed Bonds (MBBs)

• Regulatory concerns the bank gains only because
  the FDIC is willing to bear enhanced credit risk
  through its insurance guarantees to depositors.

80
V. Mortgage-Backed Bonds (MBBs)

• Other drawbacks to MBBs
• MBB ties up mortgages on the balance sheet.
• The need to overcollaterize to ensure a
  high-quality credit risk rating.
  
• By keeping mortgages on the balance sheet, the
  bank continues to be liable for capital adequacy
  and reserve requirement taxes.
  

81
VI. Innovations in Securitization

• IO/PO Stripped Securities
• Definition Mortgage-backed securities in which
  the payments from a mortgage are split (stripped)
  into two securities.
  
• Investors in the interest only portion (IO)
  receive only the interest payments from the pool
  of mortgages. Investors in the principal only
  portion (PO) receive all principal repaid
  including amortization and prepayment.
• The change in the value of these two components
  is very different when interest rates change.

82
VI. Innovations in Securitization

• For a decline in interest rates
• 1. The price of the PO strip security increases
  there is rapid prepayment of most principal and
  discount rates drop. The combined effect is to
  increase the value of these securities
• 2. The price of an IO strip security decreases
  the rapid prepayment rate truncates the interest
  payment stream so severely that the value goes
  almost to zero.

83
VI. Innovations in Securitization

• For an increase in interest rates
• 1. The price of the PO strip security decreases
  the repayment of principal further in the future
  and the increasing discount rate causes this
  securitys value to decrease.
• 2. The price of the IO strip may increase or
  decrease the payment stream is increasing as
  the prepayment rate is reduced, thereby
  increasing value. However, increases in the
  discount rate will decrease the value.
• These two effects would offset one another and we
  would expect there to be relatively little impact
  on value.

84
VI. Innovations in Securitization

• Pass-through strips
• IO strips The owner of an IO strip has a claim
  to the present value of interest payments by the
  mortgagees. When interest rates change, they
  affect the cash flows received on mortgages
• Discount Effect As interest rates fall, the
  present value of any cash flows received on the
  strip rises, increasing the value of the IO
  strips.
• Prepayment Effect As interest rates fall,
  mortgagees prepay their mortgages. The number of
  IO payments the investor receives is likely to
  shrink, which reduces the value of IO bonds.

85
VI. Innovations in Securitization

• IO Strip (continued)
• Specifically, one can expect that as interest
  rates fall below the mortgage coupon rate, the
  prepayment effect gradually dominates the
  discount effect, so that over some range of the
  price or value of IO bond falls as interest rates
  fall (negative duration).
• The negative duration IO bond is a very valuable
  asset as a portfolio-hedging device.
  

86
VI. Innovations in Securitization

• PO strip the mortgage principal components of
  each monthly payment, which include the monthly
  amortized payment and any early prepayments.
  
• Discount Effect As yields fall, the present
  value of any principal payments must increase and
  the value of the PO strip rises.
  
• Prepayment Effect As yields fall, the mortgage
  holders pay off principal early. The PO bond
  holders received the fixed principal balance
  outstanding earlier than stated. This works to
  increase the value of the PO strip.

87
VI. Innovations in Securitization

• PO Strip (Continued)
• As interest rates fall, both the discount and
  prepayment effects point to a rise in the value
  of PO strip. The price-yield curve reflects an
  inverse relationship, but with a steeper slope
  than for normal bonds I.e., PO strip bond values
  are very interest rate sensitive, especially for
  yields below the stated mortgage coupon rate.

88
VI. Innovations in Securitization

• Securitization of other assets
• CARDs (Certificates of Amortized Revolving
  Debts)
  
• Various receivables, loans, junk bonds, ARMs.

89
VII. Can All Assets Be Securitized?

• Benefits Costs
• __________________________________________________
  _________
  
• 1 New funding source 1. Cost of public/private
  credit risk
  
• insurance and guarantees
• 2. Increased liquidity of bank loans 2. Cost of
  overcollateralization
  
• 3. Enhanced ability to manage the 3. Valuation
  and packaging costs
  
• duration gap (the cost of asset heterogeneity)
• 4. If offbalance-sheet, the issuer
• on reserve requirements, deposit
• insurance premiums, and capital
• adequacy requirements
• __________________________________________________
  _________