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 poolof mortgages.

The holders receive a monthly check for theirportion of the scheduled principal and interest payments, plus their share of any prepayments that may occur.

Individual Individual Individual Mortgages Mortgages Mortgages

Mortgage Pool

Pass Through Security

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.

Types of Securities

Types of Securities

A collateralized mortgage obligation (CMO) isa security backed by a pool of mortgages and structured to transfer prepayment or interest rate risk from one group of security holders to another.

A given pool of mortgages backs two or moreclasses of securities called tranches.

Types of Securities

Individual Individual Individual Mortgages Mortgages Mortgages

Mortgage Pool

A Tranche B Tranche C Tranche Other Tranches

Collateralized Mortgage Obligation

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.

All the interest goes to the interest only (IO)security holders, while the entire principal goes to the principal only (PO) holders.

Individual Individual Individual Mortgages Mortgages Mortgages

Mortgage Pool

Interest Only Security Principal Only Security

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 M BS substantially.

The offering memorandum for a M BS 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).

Declining interest rates will increase thevalue 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, thenprepayments will reduce everyone’s yield, with the effect most pronounced for the holders of the longer duration tranches.

The Risk of Collateralized Mortgage Obligations

The Risk of Stripped Mortgage Backed Securities

Prepayment has different consequences forIO 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 thevalue 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%?

$1,000 V$385.54 $38.55 ... $90.91 V

(1.10)$1,000

(1.10)$100

... (1.10)$100

V

B

B

10101B

0 1 2 nrd

100 100 + 1,000100VB = ?

...

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 1 yr rd 10yr % change

+4.8% $1,048 5% $1,386 +38.6%

$1,000 10% $1,000

-4.4% $956 15% $749 -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 abond’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.

D

C t

1 R tt1

N

t

Pwhere 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

Macaulay duration is the time-value-of-money-weighted, average number of years necessary to recover the initial cost of the security.

Duration Measures

PR

NC

R

C

R

C

RPdR

dPN

N 1

11

2

11

112

21

1

21 R+

DD Macaulay

modified

Modified duration measures the percentage change in bond value associated with a one-point change in interest rates.

Problems with Duration

The bond price - bond yield relationship is not linear.p

rice

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

N

tNt

t

R

FNN

R

Ctt

PConvexity

122 1

1

1

11

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.

Using Convexity

yield to maturity

bo

nd

pri

ce

No matter what happens to interest rates, the bond with the greater convexity fares better. It dominates the competing investment.