Fixed-Income securities
Outline

Mortgages
Types
 Mortgage Risk


The Mortgage Backed Securities Market
History
 Types of Securities

Introduction
A mortgage is a loan with real estate
as collateral. The lender, called the
mortgage originator, often charges
points as a fee for preparing and
placing the mortgage.
It is quite common for the lender to sell the
mortgage to another party.
Mortgages: Types

A fixed rate mortgage is one with payments
based on a set interest rate that does not
change.

An adjustable rate mortgage (ARM), also
called a variable rate mortgage, has an
interest rate that moves with some market
interest rate, such as the Treasury bill rate.

Most ARMS have an annual reset to the
interest rate. Many also have either a
cap or a floor on the interest rate.
Mortgage Risk

Default risk is the risk that the borrower is
unable or unwilling to repay the debt as
agreed.

Interest rate risk is the risk that the general
level of interest rates rises, such that the
value of the mortgage’s cash flow stream
declines.

Prepayment risk is the risk of an early
payment of the original mortgage, such as
when the home is sold or when the
mortgage is refinanced at a lower rate.
The Mortgage Backed Securities Market

The Federal National Mortgage Association
(Fannie Mae), the Government National
Mortgage Association (Ginnie Mae), & the
Federal Home Loan Mortgage Corporation
(Freddie Mac) support the US mortgage
market by providing liquidity, buying
conforming mortgages from banks across the
country for resale elsewhere.

The term mortgage-backed securities refers to
all products based on mortgage loans.
Types of Securities

A pass-through security is a share of a pool
of mortgages.
Individual
Mortgages
Individual
Mortgages
Individual
Mortgages
Mortgage Pool
Pass Through Security

The holders receive a monthly check for their
portion of the scheduled principal and
interest payments, plus their share of
any prepayments that may occur.
Types of Securities
 Pass-through securities may be issued and
guaranteed by a government agency, or
they may be private label.
 Two types of derivative securities that
spring from pass-through securities are
collateralized mortgage obligations and
stripped mortgage-backed securities.
Mortgage-Backed Bonds
A Mortgage-Backed Bond is a bond backed
by mortgages, with fixed interest rate and
specific maturity
 The bond is “overcollateralized” 125% or
higher to insure that the income from
mortgages will be sufficient to pay interest on
the bonds and to repay principal at maturity
Most bonds are rated and insured

Types of Securities



A collateralized mortgage obligation (CMO)
is a debt security backed by a pool of
mortgages and structured to transfer
prepayment or interest rate risk from one
group of security holders to another
Like Pass-Troughs it’s pay through security
in that all interest and prepayments flow to
investors
A given pool of mortgages backs two or
more classes of securities called tranches,
with different maturities and risk/rating
Types of Securities
Collateralized Mortgage Obligation
Individual
Mortgages
Individual
Mortgages
Individual
Mortgages
Mortgage Pool
A Tranche
B Tranche
C Tranche
Other Tranches
Types of Securities

With a sequential pay CMO, all the tranche
holders receive monthly interest payments
based on the principal amount outstanding
in their tranche.

All principal payments go to the A tranche
until the A tranche principal is completely
returned. Only then will the investors in the
next tranche begin to receive principal.
Types of Securities

There are two types of stripped mortgage
backed securities, or strips.
Individual
Mortgages
Individual
Mortgages
Individual
Mortgages
Mortgage Pool
Interest Only Security

Principal Only Security
All the interest goes to the interest only (IO)
security holders, while the entire principal
goes to the principal only (PO) holders.
Considerations in
Pricing Mortgage Backed Securities

The price risk of a MBS comes from the
uncertainty about the timing of cash flows.

Prepayments can affect the realized return on
a MBS substantially.

The offering memorandum for a MBS will
state the assumptions used in estimating
cash flows from the mortgage pool.

A benchmark assumption for the rate of
mortgage prepayment is offered by the
Public Securities Association (PSA).
The Risk of Collateralized Mortgage Obligations

Declining interest rates will increase the
value of a cash flow stream and will lead to
prepayments.

If a mortgage pool sells at a discount,
prepayments will increase the value of each
of the tranches, with the higher duration
tranches benefiting the most.

If the pool sells at a premium, then
prepayments will reduce everyone’s yield,
with the effect most pronounced for the
holders of the longer duration tranches.
The Risk of Stripped Mortgage Backed Securities

Prepayment has different consequences for
IO and PO strips. An extension of the
mortgage decreases the value of the
principal payments but increases the value
of the interest payments.

Declining interest rates will increase the
value of a series of known cash flows, as
well as the likelihood of prepayment.
Normally, the prepayment effect overwhelms
the interest rate effect.
FIXED INCOME CONCEPTS
Key Features of a Bond
 Par value – face amount of the bond, which
is paid at maturity (assume $1,000).
 Coupon interest rate – stated interest rate (generally fixed) paid
by the issuer. Multiply by par to get dollar payment of interest.
 Maturity date – years until the bond must be repaid.
 Issue date – when the bond was issued.
 Yield to maturity - rate of return earned on
a bond held until maturity (also called the “promised yield”)
 Some bonds are callable
 Call provision: Allows issuer to refund the bond issue if rates
decline (helps the issuer, but hurts the investor)
What is the value of a 10-year, 10% annual coupon bond, if rd (discount
rate)= 10%?
0
1
2
rd
VB = ?
n
...
100
100
100 + 1,000
$100
$100
$1,000
VB 
 ... 

1
10
10
(1.10)
(1.10)
(1.10)
VB  $90.91  ...  $38.55  $385.54
VB  $1,000
Fixed Income Security Risk
 Default risk, or credit risk, is the possibility
that a borrower will be unable to repay
principal and interest as agreed upon in the
loan document.
 Reinvestment rate risk refers to the
possibility that the cash coupons received
will be reinvested at a rate different from
the bond’s stated rate.
 Interest rate risk refers to the chance of
loss because of adverse movements in the
general level of interest rates.
What is the Yield-to-Maturity or cost of debt capital?
 A discount rate (rd )/cost of debt capital and the
expected return for the debt holder if the
investor holds the bond until the maturity
rd = r* + IP + MRP + DRP + LP
r* = real risk free rate
IP = inflation premium (rate)
MRP = maturity risk premium
DRP = credit risk premium
LP = liquidity premium
What is interest rate (or price) risk?
 Interest rate risk is the concern that rising rd will
cause the value of a bond to fall.
% change
+4.8%
-4.4%
1 yr
$1,048
$1,000
$956
rd
5%
10%
15%
10yr
$1,386
$1,000
$749
% change
+38.6%
-25.1%
The 10-year bond is more sensitive to interest rate
changes, and hence has more interest rate risk.
What is reinvestment rate risk?
 Reinvestment rate risk is the concern that kd will fall, and future CFs will
have to be reinvested at lower rates, hence reducing income.
EXAMPLE: Suppose you just won $1,000,000 playing the lottery. You
intend to invest the money and live off the interest.
 If you choose to invest in series of 1-year bonds, that pay a 8% coupon
you receive $80,000 in income and have $1,000,000 to reinvest.
But, if 1-year rates fall to 3%, your annual income would fall to $30,000.
 If you choose a 30-year bond that pay a 10 % coupon you receive
$100,000 in income; you can lock in a 10% interest rate, and $100,000
annual income for 30 years
Interest Rate Risk : Malkiel’s Theorems
 Malkiel’s theorems are a set of
relationships among bond prices, time to
maturity, and interest rates.
 Theorem One : Bond prices move inversely
with yields.
 Theorem Two : Long-term bonds have
more risk.
 Theorem Three : Higher coupon bonds
have less risk.
Interest Rate Risk : Malkiel’s Theorems
 Bond A : matures in 8 years, 9.5% coupon
Bond B : matures in 15 years, 11% coupon
Which price will rise more if interest rates
fall?
 Apparent contradictions can be reconciled
by computing a statistic called duration.
Duration

For a noncallable security, duration is
the weighted average time until a
bond’s cash flows are received.
 Duration is not limited to bond analysis. It
can be determined for any cash flow stream.
 Duration is a direct measure of interest rate
risk. The higher it is, the higher is the risk.
Duration Measures
 Macaulay duration is the time-value-of-moneyweighted, average number of years necessary
to recover the initial cost of the security.
N

D
Ct
t  11 
R
P
t
t
where D = duration
Ct = cast flow at time t
R = yield to maturity (per period)
P = current price of bond
N = number of periods until maturity
t = period in which cash flow is received
Duration Measures
 Modified duration measures the percentage
change in bond value associated with a
one-point change in interest rates.
dP 1
 1  C1
2C 2
NC N  1
 

 


1
2
N 
dR P 1  R   1  R  1  R 
1  R  P
DMacaulay
Dmodified 
1+ R
2


price
Problems with Duration

The bond price - bond yield
relationship is not linear.
yield to maturity
 Graphically, duration is the tangent to the
current point on the price-yield curve. Its
absolute value declines as yield to maturity
rises.
 Duration is a first derivative statistic.
Hence, when the change is large, estimates
made using the derivative alone will
contain errors.
Convexity
 Convexity measures the difference
between the actual price and that predicted
by duration, i.e. the inaccuracy of duration.
 The more convex the bond price-YTM
curve, the greater is the convexity.
1 N t t  1C t N  N  1F
Convexity  

t 2
N 2
P t 1 1  R 
1  R
bond price
Using Convexity
yield to maturity
 No matter what happens to interest rates,
the bond with the greater convexity fares
better. It dominates the competing
investment.