Fundamentals of Investments

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Fundamentalsof Investments
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C h a p t e r
Mortgage-Backed Securities
Valuation Management
second edition
Charles J. Corrado Bradford D. Jordan
McGraw Hill / Irwin
Slides by Yee-Tien (Ted) Fu
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Mortgage-Backed Securities

• Our goal in this chapter is to examine the
  investment characteristics of mortgage pools.

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A Brief History of Mortgage-Backed Securities

• Traditionally, local banks wrote most home
  mortgages and then held the mortgages in their
  portfolios of interest-earning assets.
• Then, when market interest rates climbed to near
  20 in the early 1980s, bank customers flocked to
  withdraw funds from their savings deposits to
  invest in money market funds.
• Today, an originator usually sells the mortgage
  to a mortgage repackager, who accumulates them
  into mortgage pools.

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A Brief History of Mortgage-Backed Securities

• Financed by mortgage-backed bonds (also called
  mortgage pass-throughs), each mortgage pool is
  set up as a trust fund. A servicing agent
  collects the mortgage payments and then passes
  the cash flows through to the bondholders.
• The transformation from mortgages to
  mortgage-backed securities (MBSs) is called
  mortgage securitization.

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Work the Web

• For more information on mortgage-backed
  securities, visit
• http//www.investinginbonds.com

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Fixed-Rate Mortgages

• The size of the monthly payment is determined by
  the requirement that the present value of all
  monthly payments, based on the financing rate
  specified in the mortgage contract, be equal to
  the original loan amount.

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Fixed-Rate Mortgages

• where r annual mortgage financing rate
• T mortgage term in years

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Fixed-Rate Mortgages
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rights reserved.
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Fixed-Rate Mortgage Amortization

• Each monthly mortgage payment has two separate
  components
• payment of interest on outstanding mortgage
  principal
• pay-down, or amortization, of mortgage principal
• The relative amounts of each component change
  throughout the life of the mortgage.

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Fixed-Rate Mortgage Amortization

• Suppose a 30-year 100,000 mortgage loan is
  financed at a fixed interest rate of 8.
• Monthly payment

• In the first month,
• Interest payment 100,000 ? .08/12 666.67
• Principal payment 733.76 666.67 67.09
• New principal 100,000 67.09 99,932.91
• In the second month,
• Interest payment 99,932.91 ? .08/12 666.22
• Principal payment 733.76 666.22 67.54
• New principal 99,932.91 67.54 99,865.37

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Fixed-Rate Mortgage Amortization

• Mortgage amortization can be described by an
  amortization schedule, which states the scheduled
  principal payment, interest payment, and
  remaining principal owed in any month.

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Fixed-Rate Mortgage Amortization
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Fixed-Rate Mortgage Amortization
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Fixed-Rate Mortgage Prepayment Refinancing

• A mortgage borrower has the right to pay off all
  or part of the mortgage ahead of its amortization
  schedule. This is similar to the call feature of
  corporate bonds and is known as mortgage
  prepayment.
• During periods of falling interest rates,
  mortgage refinancings are an important reason for
  mortgage prepayments.
• Hence, mortgage investors face the risk of a
  reduced rate of return.

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Government National Mortgage Association

• The Government National Mortgage Association
  (GNMA), or Ginnie Mae, is a government agency
  charged with the mission of promoting liquidity
  in the secondary market for home mortgages.
• GNMA mortgage pools are based on mortgages issued
  under programs administered by the Federal
  Housing Administration (FHA), the Veterans
  Administration (VA), and the Farmers Home
  Administration (FmHA).

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Government National Mortgage Association

• Mortgages in GNMA pools are said to be fully
  modified because GNMA guarantees bondholders full
  and timely payment of both principal and
  interest.
• Note that although investors in GNMA
  pass-throughs do not face default risk, they
  still face prepayment risk.
• Prepayments are passed through to bondholders.
• If a default occurs, GNMA fully prepays the
  bondholders.

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GNMA Clones

• Besides GNMA, there are two other significant
  mortgage repackaging sponsors
• Federal Home Loan Mortgage Corporation (FHLMC),
  or Freddie Mac, and
• Federal National Mortgage Association (FNMA), or
  Fannie Mae.
• Both are government-sponsored enterprises (GSEs)
  and trade on the New York Stock Exchange.

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GNMA Clones

• Like GNMA, both FHLMC and FNMA operate with
  qualified underwriters who accumulate mortgages
  into pools financed by an issue of bonds.
• However, since FHLMC and FNMA are only GSEs,
  their fully modified pass-throughs do not carry
  the same default protection as GNMA fully
  modified pass-throughs.

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Work the Web

• Visit the GNMA website at
• http//www.ginniemae.gov
• Check out the FNMA and FHLMC websites at
• http//www.fanniemae.com
• http//www.freddiemac.com

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PSA Mortgage Prepayment Model

• Mortgage prepayments are typically described by
  stating a prepayment rate, which is the
  probability that a mortgage will be prepaid in a
  given year.
• Conventional industry practice states prepayment
  rates using a model specified by the Public
  Securities Association (PSA).
• Prepayment rates are stated as a percentage of a
  PSA benchmark.

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PSA Mortgage Prepayment Model

• In the PSA model, the rates are conditional on
  the age of the mortgages in the pool. They are
  conditional prepayment rates (CPRs).
• For seasoned ( gt 30 months old) mortgages, the
  CPR is a constant (6 annually for 100 of the
  PSA benchmark (100 PSA)).
• For unseasoned (lt 30 months old) mortgages, the
  CPR rises steadily in each month until it reaches
  an annual rate of 6 (for 100 PSA) in month 30.

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PSA Mortgage Prepayment Model
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PSA Mortgage Prepayment Model

• By convention, the probability of prepayment in a
  given month is stated as a single monthly
  mortality (SMM).

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PSA Mortgage Prepayment Model

• The average life of a mortgage in a pool is the
  average time for a single mortgage in the pool to
  be paid off, either by prepayment or by making
  scheduled payments until maturity.
• For a pool of 30-year mortgages,

Prepayment Schedule Average Mortgage Life
(years) 50 PSA 20.40 100 PSA 14.68 200 PSA 8.87
400 PSA 4.88
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Work the Web

• Visit the Public Securities Association at
• http//www.psa.com

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Cash Flow AnalysisGNMA Fully Modified Mortgage
Pools

• Each month, GNMA mortgage-backed bond investors
  receive pro rata shares of cash flows derived
  from fully modified mortgage pools.
• Each monthly cash flow has three components (less
  the servicing and guarantee fees)
• Payment of interest on outstanding mortgage
  principal.
• Scheduled amortization of mortgage principal.
• Mortgage principal prepayments.

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Cash Flow AnalysisGNMA Fully Modified Mortgage
Pools
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Macaulay Durationsfor GNMA Mortgage-Backed Bonds

• The interest rate risk for a bond is often
  measured by Macaulay duration, which assumes a
  fixed schedule of cash flow payments.
• However, the schedule of cash flow payments for
  mortgage-backed bonds is not fixed.
• With falling interest rates, prepayments speed
  up, and vice versa.

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Macaulay Durationsfor GNMA Mortgage-Backed Bonds

• Historical experience indicates that interest
  rates significantly affect prepayment rates, and
  that Macaulay duration is a very conservative
  measure of interest rate risk.
• In practice, effective duration is used to
  calculate predicted prices for mortgage-backed
  securities based on hypothetical interest rate
  and prepayment scenarios.

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Collateralized Mortgage Obligations

• The three best-known types of CMOs are
• interest-only (IOs) and principal-only (POs)
  strips,
• sequential CMOs, and
• protected amortization class securities (PACs).

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Interest-Only and Principal-Only Strips

• Interest-only strips (IOs) pay only the interest
  cash flows to investors, while principal-only
  strips (POs) pay only the principal cash flows to
  investors.
• IO strips and PO strips behave quite differently
  in response to changes in prepayment rates and
  interest rates.
• Faster prepayments imply lower IO strip values
  and higher PO strip values, and vice versa.

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Interest-Only and Principal-Only Strips
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Sequential CMOs

• Sequential CMOs carve a mortgage pool into a
  number of tranches (slices).
• For example, A, B, C, and Z-tranches.
• Each tranche is entitled to a share of mortgage
  pool principal and interest on that share of
  principal.
• However, cash flows are distributed sequentially,
  so as to create securities with a range of
  maturities.

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Sequential CMOs

• Cash flows are passed through as follows
• All payments of principal will go to the topmost
  tranche (in alphabetical order), until all the
  principal in that tranche has been paid off.
• All tranches receive proportionate interest
  payments. These are passed through immediately,
  except for the Z-tranche. Interest on Z-tranche
  principal is paid as cash to the topmost tranche
  in exchange for a transfer of an equal amount of
  principal, until all the principal in the topmost
  tranche has been fully paid off.

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Sequential CMOs
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Protected Amortization Class Bonds

• Protected amortization class (PAC) bonds take
  priority for scheduled payments of principal. The
  residual cash flows are paid to PAC support (or
  companion) bonds.
• PAC cash flows are predictable as long as
  prepayments remain within a specified band.

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Protected Amortization Class Bonds

• Creating a PAC bond entails three steps.
• Specify two PSA prepayment schedules that form
  the upper and lower prepayment bounds of the PAC
  bond. These bounds define a PAC collar.
• Calculate principal-only (PO) cash flows for the
  two prepayment schedules specified in ?.
• On a priority basis, at any point in time, PAC
  bondholders receive payments of principal
  according to the PSA prepayment schedule with the
  lower PO cash flow as calculated in ?.

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Protected Amortization Class Bonds
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Work the Web

• Check out the CMO section at
• http//www.bondresources.com

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Yields for MBSs and CMOs

• The yield to maturity for a mortgage-backed
  security conditional on an assumed prepayment
  pattern is called the cash flow yield.
• Essentially, cash flow yield is the interest rate
  that equates the present value of all future cash
  flows on the mortgage pool to the current price
  of the pool, assuming a particular prepayment
  rate.

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Chapter Review

• A Brief History of Mortgage-Backed Securities
• Fixed-Rate Mortgages
• Fixed-Rate Mortgage Amortization
• Fixed-Rate Mortgage Prepayment and Refinancing
• Government National Mortgage Association
• GNMA Clones
• Public Securities Association Mortgage Prepayment
  Model

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Chapter Review

• Cash Flow Analysis of GNMA Fully Modified
  Mortgage Pools
• Macaulay Durations for GNMA Mortgage-Backed Bonds
• Collateralized Mortgage Obligations
• Interest-Only and Principal-Only Mortgage Strips
• Sequential Collateralized Mortgage Obligations
• Protected Amortization Class Bonds
• Yields for Mortgage-Backed Securities and
  Collateralized Mortgage Obligations