Chapter

McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

20 Mortgage-Backed Securities

20-2

Mortgage-Backed Securities

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

• Mortgage pools are simply sets of home mortgages, which are "bonds" issued by home owners.

20-3

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, a mortgage originator usually sells the mortgage to a mortgage repackager, who accumulates them into mortgage pools.

20-4

A Brief History of Mortgage-Backed Securities, Cont.

• 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 from the home-owners and then passes the cash flows through to the bondholders.

• The transformation from mortgages to mortgage-backed securities (MBSs) is called mortgage securitization.

20-5

Fixed-Rate Mortgages

• A Fixed-Rate Mortgage is a loan that specifies constant monthly payments at a fixed interest rate over the life of the mortgage.

• 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.

20-6

Fixed-Rate Mortgage, Monthly Payments

• The equation to calculate the payment required to “retire” a fixed rate mortgage is:

• In the equation, r is the annual mortgage financing rate, and T is the number of years in the mortgage term.

12T

12r1

11

12ramount loan

payment Monthly

20-7

Mortgage Payments Using a Spreadsheet

A 30-year mortage specifies an annual interest rate of 8 percentand a loan amount of $100,000. What are the monthly payments?Hint: Use the Excel function PMT.

-$733.76 =PMT(0.08/12,360,100000,0,0)

Monthly interest is 8% / 12 = 0.667%Number of monthly payments is 12 x 30 = 360.Initial principal is $100,000.First zero indicates complete repayment after last monthly payment.Second zero indicates end-of-month payments.

For a 15-year mortgage, we get a bigger monthly payment.

-$955.65 =PMT(0.08/12,360,100000,0,0)

Monthly Payments for a 30-Year Mortgage

20-8

Mortgage Payments, by Rate and Time

20-9

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.

20-10

Example: Fixed-Rate Mortgage Amortization

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

• In the first month:Interest payment = $100,000 .08/12 = $666.67Principal payment = $733.76 – $666.67 = $67.09New principal = $100,000 – $67.09 = $99,932.91

• In the second month:Interest payment = $99,932.91 .08/12 = $666.22Principal payment = $733.76 – $666.22 = $67.54New principal = $99,932.91 – $67.54 = $99,865.37

$733.76

12.08111

12.08$100,000Payment Monthly

1230

20-11

Fixed-Rate Mortgage Amortization

• Mortgage amortization can be described by an amortization schedule.

• An amortization schedule states the scheduled principal payment, interest payment, and remaining principal owed in any month.

20-12

Fixed-Rate Mortgage Amortization, Using a Spreadsheet

A 30-year mortage specifies an annual interest rate of 8 percentand a loan amount of $100,000. What are the monthly interest and principal payments?Hint: Use the Excel functions IPMT and PPMT.

After 10 years, i.e., for the 120th payment interest and principal payments are:

-$585.82 =IPMT(0.08/12,120,360,100000,0)

-$147.95 =PPMT(0.08/12,120,360,100000,0)

After 20 years, i.e., for the 240th payment interest and principal payments are:

-$405.38 =IPMT(0.08/12,240,360,100000,0)

-$328.39 =PPMT(0.08/12,240,360,100000,0)

A 30-year mortage specifies an annual interest rate of 8 percentand a loan amount of $100,000. What is the remaining balance?Hint: Use the Excel function CUMPRINC.

After 8 years and 4 months, the remaining balance is the present value of paymentnumber 101 through payment number 360.

#NAME? =CUMPRINC(0.08/12,360,100000,101,360,0)

Amortization Schedule for a 30-Year Mortgage

Remaining Balance for a 30-Year Mortgage

20-13

Mortgage Payments, by Rate and Time

20-14

Mortgage Interest and Principal, by Age of Mortgage

20-15

Fixed-Rate Mortgage Prepayment and 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.

• This means that mortgage investors face the risk of a reduced rate of return.

20-16

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 Veteran’s Administration (VA), and – The Farmer’s Home Administration (FmHA).

20-17

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.

• 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.

20-18

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.

20-19

GNMA Clones, Cont.

• Like GNMA, both FHLMC and FNMA operate with qualified underwriters who accumulate mortgages into pools financed by an issue of bonds.

• However, because FHLMC and FNMA are only GSEs, their fully modified pass-throughs do not carry the same default protection as GNMA fully modified pass-throughs.

• That is, Congress may or may not be willing to rescue a financially strapped GSE.

20-20

PSA Mortgage Prepayment Model, I.

• 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.

20-21

PSA Mortgage Prepayment Model, II.

• 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 ( > 30 months old) mortgages, the CPR is constant at 6% annually for 100% of the PSA benchmark (100 PSA).

• For unseasoned (< 30 months old) mortgages, the CPR rises steadily in each month until it reaches an annual rate of 6% in month 30 (for 100 PSA).

20-22

PSA Mortgage Prepayment Model, III.

20-23

PSA Mortgage Prepayment Model, SMM

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

• The SMM is based on the conditional prepayment rate, CPR.

• The equation for an SMM is:

SMM = 1 – (1 – CPR)1/12

20-24

PSA Mortgage Prepayment Model, Average Life

• 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 14.68200 PSA 8.87400 PSA 4.88

20-25

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.

20-26

Principal and Cash Flows for a GNMA Bond

20-27

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.

20-28

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.

20-29

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).

• Collateralized mortgage obligations (CMOs) are securities created by splitting mortgage pool cash flows according to specific allocation rules.

20-30

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.

20-31

Cash Flows for GNMA IO and PO Strips

20-32

Sequential CMOs, I.

• 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, because cash flows are distributed sequentially, this creates securities with a range of maturities.

20-33

Sequential CMOs, II.

• Cash flows are passed through as follows:– All principal payments goes to the topmost tranche (in

alphabetical order), until all the principal in that tranche has been paid off.

– Except for the Z-tranche, all tranches receive proportionate interest payments, which are passed through immediately.

– Until all the principal in the topmost tranche has been fully paid off, interest on Z-tranche principal is paid as cash to the topmost tranche in exchange for an equal amount of principal.

20-34

Sequential CMO Principal and Cash Flows

20-35

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.

20-36

Protected Amortization Class Bonds, Cont.

• 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 .

20-37

PAC Cash Flows and Total Cash Flows

20-38

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.

20-39

MBS Yields

20-40

Useful Websites

• www.investinginbonds.com (for information on bonds, bonds, bonds)

• www.ginniemae.gov (GNMA)

• www.hud.gov (HUD)

• www.fanniemae.com (FNMA)

• www.freddiemac.com (FHLMC)

• www.bondmarkets.com (Visit the Public Securities Association)

20-41

Chapter Review, I.

• 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

20-42

Chapter Review, II.

• 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