PPT PDF FIXED INCOME

Fixed Income

Foued Ayari, PhD

TOPICS

Features of Debt Securities

Risks Associated with Investing in Bonds

Overview of Bond Sectors and Instruments

Understand Yield Spreads

Monetary Policy in an Environment of Global Financial Markets

Introduction to the Valuation of Debt Securities

Yield Measures, Spot Rates, and Forward Rates

Introduction to the measurement of Interest Rate Risk

Coverage

• Describe the basic features of a bond (maturity, coupon, par, provisions for

retirement, currency denomination)

• Identify the different range of coupon structures (zeros, step-up, deferred, FRNs)

• Describe the structure of FRNs

• Describe the various forms of FRNs (inverse floaters, dual indexed, ratchet,

stepped)

• Define and understand accrued interest

• Describe the provisions for paying off bonds (including amortising and non-

amortising securities)

• Explain the provisions for early retirement (call and refunding provisions

prepayments and sinking funds)

• Explain the difference between standard redemption and special redemption price

• Explain the importance of embedded options

• Describe a repo agreement

• Describe the usual methods used by institutional investors to finance bond

purchasing (margin vs. repos)

Overview of Debt Capital Markets

The differences between equity and debt products

The differences between loans and bonds

Hybrid securities

Securitisation

Differences Between Equity and DebtDebt Equity

Return to

Investors

Interest terms contractually agreed in advance

(e.g. fixed coupon)

Dividends at discretion of management and

performance-dependent

Timing Fixed maturity date contractually agreed in

advance

No fixed redemption, perpetual

Payout Priority High (debt interest ranks ahead of dividend

payments to equityholders)

Low (last in queue once debtors have been

paid)

Control Only in event of debt restructuring or bankruptcy Voting rights (for ordinary shares)

Tax Interest costs deductible against income in

many jurisdictions worldwide

Differences Between Loans and Bonds

Loans

Can be tradeable, but rare

Can be listed, but rare

Illiquid market

Investor: banks (in some

circumstances also insurance

companies, pension funds)

Bonds

Tradeable instruments

Usually listed

Liquid market

Investor: anyone

Difference used to be clear cut: bonds were tradeable loans.

However, loans are now becoming more tradeable

Banks trade loan books

For the vast majority of the market the distinction still stands

Hybrid securities

Combine debt and equity characteristics

CONVERTIBLE bond: Legally a fixed income instrument - investor can

convert it into equity at future option date(s)

Preference shares: provide a fixed return like bonds

Uses of hybrids include:

Capital raising but avoid diluting equity issuance

Generally tax-deductible, i.e. treated like debt

Can provide insulation from predators

Securitisation

The pooling of loans or other receivables as a security. Such packaging can

create liquid assets from illiquid ones with enhanced credit rating

Typically many illiquid loans are pooled together through an SPV (Special

Purpose Vehicle) whereby they can be traded as an “asset backed security”

de-coupled from the individual loans

Structures often amortise rather than pay back only at redemption – this tends

to match better the individual re-payments and balance pre-payment risk

which can cause such structures to pay off early

Examples include:

• Mortgages

• Auto loans

• Student loans

Introduction

WHAT IS A BOND?

A bond represents a loan to a company or government.

If an investor lends money to a company the company gives the investor a promise,

or bond, to repay the debt.

XYZ plc

$1000 nominal

6%

2030

XYZ plcInvestor

$$$

THE BASIC FEATURES OF A BOND

A bond will have three fundamental features:

The maturity or redemption date of the bond is the date when the loan is

repaid:

The par or nominal (a.k.a. principal or capital) value is the amount repaid at

redemption. It is not necessarily the price of the bond:

The coupon is the income from the bond:

Quoted as an annual % of par

Usually paid semi-annually, for example 100 nominal of a 4-year 4%

coupon bond:

2 2 2 2 2 2 2 102

THE STATUS OF A BOND HOLDER

Bond holders are creditors of the company. They rank above the shareholders in

terms of distributions and the winding up process.

Companies normally issue more than one class of bonds; there will be ranking, or

seniority, within these different classes:

Senior secured debt

Unsecured debt

Subordinated debt

Debt versus equity

Debtholders receive the promise of a known cash flow at

specific dates.

Sectors:

Treasury

Agency

Municipal

Corporate

Bonds

Loans

Debt can be senior or subordinate.

Debt can be investment or speculative grade.

Price Paid is called “Dirty Price”, which is

Dirty Price=Clean Price + Accrued Interest

Foued Ayari, PhD 12

Money Market Instruments

Maturity less than 1 year, highly liquid, little risk, such as:

Treasury bills

Certificates of deposit

Commercial Paper

Eurodollars

Federal Funds

Repurchase Agreements (Repos)

Foued Ayari, PhD 13

Treasury Bill

Issued by the US Treasury

Negotiable, zero-coupon obligations of the US Treasury

Issued with maturities of 1, 3, 6, and 12 months

Very low risk. Often taken as Risk Free

Issued at a discount and redeemed at par

Repos

• REPO AGREEMENTS

• Definition

• A transaction in which one party sells another a security. At the same time, as part

of the same agreement the party agrees to repurchase identical securities on a

specified date at a specified price.

– There are two legs to a classic repo

– The seller delivers securities and receives cash from the buyer

– The difference between the cash received by the seller in leg 1 and returned

in leg 2 is known as the repo rate

Foued Ayari, PhD 14

Types of Bond

Federal Government, local ,state authorities and corporations; all issue bonds. These leads to a great deal of variation in bond features. An ordinary bond is known as a vanilla bond:

Government bonds

UK Gilts

French OATs

German Bunds

US T-bonds

Index-linked

Treasury Inflation-Protected Securities (known as TIPS)

Index-linked gilts

Zero–coupon

Foued Ayari, PhD 15

Bonds and Fixed Income


The maturity or redemption date of the bond is the date

when the loan is repaid:

The par or nominal value is the amount repaid at


The coupon is the income from the bond: Quoted as an

annual % of par, Usually paid semi-annually

Revenue or return from Bond is : Income + Capital Gain

(loss)

Rating will impact the cost of borrowing and an

upgrade/downgrade will affect price.

Rating: Investment Grade and Non-Investment Grade

Foued Ayari, PhD 16

$$$

Types of Bonds

Callable & Putable Bonds

Accrual Bonds

Similar to zeros except issued at par and earns interest

Step-up bonds

Coupons increase over time at a pre-determined rate

Deferred coupon bonds

Defer initial coupon payments for a given time

Floating Rate Coupon

Caps (disadvantage to holder) and floors (disadvantage to issuer)

If both cap and floor present you have a collar

Bullet maturity

All principal cash flows paid at once at redemption

Amortizing bonds

Periodic principal payments fully amortize the principal amount over the life of the bond

Balloon maturity

Principal is partially amortized over the life of the bond with a larger principal payment due at maturity

Serial bonds

Series of similar bonds with different maturities

Foued Ayari, PhD 17

Convertible Bonds

Convertible bonds

These are corporate bonds that may be swapped for shares. They are more

expensive than an ordinary vanilla bond. The extra value you pay for a

convertible is the conversion premium.

Foued Ayari, PhD 18

International Bonds

Domestic: A bond issued by a company in its own currency and on its own domestic markets

Foreign bonds: A bond issued by a foreign company via another country‟s debt markets and currency

Yankee

Bulldog

Samurai

International / Eurobonds: bonds issued by a company in a Eurocurrency:

A Eurocurrency is a currency on deposit outside its own country i.e. Japanese yen on deposit in the US would be referred to as Euroyen

Companies wishing to raise USD, but do not want to issue Japanese foreign bonds (Samurais) could target Euroyen deposits.

Foued Ayari, PhD 19

Yield Curves and Term Structure

CONSTRUCTIING A YIELD CURVE

Yield curves are a chart of yields against maturity or term.

Yield curves are sometimes called the term structure of

interest rates.

Shapes of Yield Curve: Upward sloping, downward sloping and

flat/humped.

Theories: Expectation/Liquidity/Market Segmentation

Foued Ayari, PhD 20

Securitization

MORTGAGE-BACKED SECURITIES

Bonds issued in the US by agencies(and other financial institutions)

such as:

Federal Home Loan Mortgage Corporation (FHLMC), Freddie Mac

Government National Mortgage Association (GNMA), Ginnie Mae

Federal National Mortgage Association (FNMA), Fannie Mae

ASSET BACKED SECURITIES

Foued Ayari, PhD 21

22

On-the-Run Treasury Notes and Bonds

Recently issued or current

bonds

Prices and yields close to par

Notes issued with maturities

of 2, 5, and 10 years

Bonds issued with maturity of

30 years

23

Benchmark Japanese Government Bonds

24

5Y OTR Treasury Note

25

Market Price

Price shown as 100-5+

Quoted in thirty-seconds

A 64th can be added to the price with a plus sign, so 100-5+

means 100 and 5/32 and 1/64:

171875.100

015625.064

1

156250.032

5

000000.100100

26

Accrued Interest

Date Days Days

Last coupon date (or issue date)

30 Apr 2008

Settlement date 19 May 2008 19

Next coupon date 31 October 2008 165 184

30/4/08 19/5/08 31/10/08

103261.0184

19 896739.0

184

165

27

Accrued Interest

Accrued interest is for the period

From the last coupon date (or the issue date)

To the settlement date

%161345.0%5625.10.1032612

%125.3

184

19

28

Dirty Price vs. Clean Price

The “market price” of the bond is 100.181775%

Note that this is NOT the PV of the bond‟s cash flows

The “dirty price” is the PV of the bond‟s cash flows

The market price is:

Dirty price – accrued interest = Market price

29

Summary

Issuer: U.S. Treasury

Settlement: 19-May-08

Coupon: 3.125%

Issue Date: 30-Apr-08

Maturity: 30-Apr-13

Previous Coupon (or issue date): 30-Apr-08

Market Price: 100.171875%

Accrued Interest: 0.161345%

“Dirty” Price: 100.333220%

Market YTM: 3.087%

Types of Bond

Governments, local authorities and corporates all issue bonds. These leads to a

great deal of variation in bond features. An ordinary bond is known as a vanilla

bond:

Government bonds

UK Gilts

French OATs

German Bunds

US T-bonds

Index-linked

Treasury Inflation-indexed Securities (known as TIPS)

Index-linked gilts

Zero–coupon

Discount = „interest earned‟

Types of Bond

Accrual Bonds

Similar to zeros except issued at par and earning interest on top

Step-up bonds

Coupons increase over time at a pre-determined rate

Deferred coupon bonds

Defer initial coupon payments for a given time

Floating Rate Coupon

Coupon formula: Coupon rate = reference rate +/- margin (the reference rate

is usually 6m LIBOR)

Margin usually quoted in BASIS POINTS

Caps (max coupon paid) and floors (min coupon paid)

If both cap and floor present you have a collar

Types of Bond

Bullet maturity

All principal cash flows paid at once at redemption

Amortizing bonds

Periodic principal payments fully amortize the principal amount over the live of

the bond

Balloon maturity

Principal is partially amortized over the life of the bond with a larger principal

payment due at maturity

Serial bonds

Series of similar bonds with different maturities

Types of Bond

Callable and put-able bonds

Embedded Options

Call

1. Issuer has right to redeem early at

pre-determined price (strike)

2. Usually deferred call period

3. Strike usually above par

4. Enables borrower to redeem

expensive bonds if interest rates fall

5. Favours issuers

Put

1. Investor / lender has right to redeem

early at pre-determined price)

2. Strike usually at, or close to, par

3. Benefits holder if there is an increase

in interest rates

4. Favours holders

Types of Bond

Convertible bonds

These are corporate bonds that may be swapped for shares. They are more

expensive than an ordinary vanilla bond. The extra value you pay for a

convertible is the conversion premium.

Types of Bond

Domestic: A bond issued by a company in its own currency and on its own domestic

markets

Foreign bonds: A bond issued by a foreign company via another country‟s debt

markets and currency

Yankee

Bulldog

Samurai

International / Eurobonds: bonds issued by a company in a Eurocurrency:

A Eurocurrency is a currency on deposit outside its own country i.e. Japanese

yen on deposit in the US would be referred to as Euroyen

Companies wishing to raise USD, but do not want to issue Japanese foreign

bonds (Samurais) could target Euroyen deposits.

Types of Bond

MORTGAGE-BACKED SECURITIES

Bonds issued in the US by agencies such as:

Federal Home Loan Mortgage Corporation (FHLMC), Freddie Mac

Government National Mortgage Association (GNMA), Ginnie Mae

Federal National Mortgage Association (FNMA), Fannie Mae

Structure of a mortgage-backed security issue

Agency MBSs are PASSTHROUGH securities. This means the cash flows from the

mortgages are paid on a pro-rata basis:

Mortgage 1

Mortgage 2

Mortgage 3

Mortgage

Pool

Investors

Passthrough

securities

$

Each month: interest from

mortgages plus any principal

from early repayments

Types of Bond

Collateralised Debt Obligations (CDOs)

CDOs are securitised issues whereby an issuer bundles loans / bonds into a

portfolio and issues different tranches of bonds via an SPV:

1st loss / equity tranche

retained by originator

Originator

Senior Notes

AAA rated

LOANS

A ratedSPV

Mezzanine Notes

A rated

Equity / 1st loss tranche

Bond Markets

Bond Markets

There are two elements to bond markets;

The PRIMARY market

The market for new issues

The issuer raises funds

The SECONDARY market

The market for buying and selling second-hand bonds

PRIMARY MARKET

Bringing bonds to the market for the first time is an involved process that takes time

and a lot of organisation.

The Process

The initial stages take place a long time before the bond issue itself happens. A

company is courted by many banks lending money at low rates as a loss leader to

build a relationship.

This is followed by the banks being more aggressive, pitching for a full-blown bond

deal. This stage involves beauty parades by the banks, these:

give the banks an opportunity to talk about their expertise;

remind the company of its obligations; and

suggest what the company might use the money for

The company appoints one or more (joint) lead managers (a.k.a bookrunners).

The prospectus is created (a document containing the small print and conditions of

the up coming loan) and a launch / issue date is decided.

If one or more banks are involved in the issue a syndicate is formed:

BORROWER

(ISSUER)

LEAD MANAGER / BOOKRUNNER

Bank Bank Bank Bank Bank Bank

The Launch

For a big, well known issuer the bonds may be launched on the issue date with a

start time of, say, 7.00am. Up until this point knowledge of the issue is confined to

the capital markets team (a Chinese wall exists between investment banking and

markets).

T -1 day Launch

• Inform bond sales

team to prepare for

a launch early next

day (no details yet)

• Give details to

Reuters / Bloomberg

with an embargo.

7.00 am:

• Press release by Reuters

and Bloomberg etc

• Sales team make / receive

calls

• Bookrunner(s) monitor

demand at price on

„Bookrunner‟

SECONDARY MARKET

In addition to the three fundamental features a bond will also have a price. The price

or market value is what $100 (or £100, or YEN100) would cost you.

It is sometime easier to think of it as a percentage of the nominal value.

Values, Yields and Coupons

RETURNS

Bonds are transferable and negotiable. The value of a bond at any given time

depends fundamentally on the RETURN, or YIELD we expect from it.

Price depends on the required return

Returns or yields are expressed as an annual percentage of the amount invested:

Example: we invest $50 for a year and receive $5 this is a 10% p.a. return:

Bonds can generate return in the form of both income (coupons) and capital gains.

10%0.1$50

$5

THE RELATIONSHIP BETWEEN THE PRICE AND YIELD

What is the return (yield) we would receive on a $100 nominal of a two-year bond

with an annual 4% coupon if it is trading at 98?

This would equate to an extra $1 per year return meaning that overall the investor

make an average annual return of 5.1%. This is known as the redemption yield

or the yield to maturity (YTM):

.. and make a $2

profit at

redemption

$4 + $100

Buy the bond now

for

$98… $4

%150.051$98

$5

$98

$1$4.

Conclusion

If the required yield from a bond rises its price will fall. If the required yield from a

bond falls its price will rise.

Bond prices have an inverse relationship with their yields

The Simple Yield to Maturity

The bond return which takes into account the coupon and the capital gain or loss at

redemption is known as the SIMPLE YIELD TO MATURITY.

The simple yield does not take into account the time-value of money; receiving a

profit of $4 in four year‟s time is NOT the same as receiving $1 at the end of each

of the four years

Price = Par Coupon Yield

Clean & Dirty Pricing


n

n

tt

t

n

n

i

par

i

cpn

i

parcpn

i

cpn

i

cpnPV

)1()1(

)1()1()1(

1

2

2

1

1

cpnt Fixed coupon of bond at time t

par Redemption amount at maturity

i Yield-to-maturity of bond

n Number of coupon periods

The Dirty Price of a Bond

Equal to:

The Clean Price, plus

The Accrued Interest from the most recent coupon payment today

Bonds are traded on a „clean‟ basis, though at settlement the „dirty‟ price is invoiced

and paid


Bond prices in the market are calculated using the assumption that there is a whole number

of coupon payment periods remaining.

When the bond trade is settled the additional amount added for accrued interest is

calculated by dividing the coupon payment period as follows:

period coupon the in days .of No

date settlement to coupon last from days of No.

Interest earned by seller Interest earned by buyer

Last coupon

Next coupon

Fractional Period (w) = 1 - AI

Whole coupon period


Example:

A bond has a 8% coupon payable on 1 April and 1 October. An investor buys a

bond for settlement on 10 August.

Calculate the Accrued Interest period/fractional period

Calculate the dirty price assuming bond trading at par

Use the Actual/Actual day count convention

1st April

Last coupon

Next coupon

1st Oct10 Aug

Settlement Date

2nd April – 30 April 29

May 31

June 30

July 31

1st August – 10 August 10

131

11th Aug – 31st Aug 21

September 30

October 1

52

Repos

REPO AGREEMENTS

Definition

A transaction in which one party sells another a security. At the same time, as part

of the same agreement the party agrees to repurchase identical securities on a

specified date at a specified price.

There are two legs to a classic repo

The seller delivers securities and receives cash from the buyer

The difference between the cash received by the seller in leg 1 and returned

in leg 2 is known as the repo rate

Classic Repo

In a classic repo the sale and repurchase prices are the same, although

settlement values will differ because of addition of repo interest on termination

A sale and repurchase is a “repo”, whereas a purchase and sell back is a

“reverse repo”. Of course the counterparty is either one or the other, opposite

to your position!

If a coupon is paid during the term of the repo it will be handed over to the

seller

A classic repo is subject to a legal contract signed in advance by both parties

Leg 1: Today

Leg 2: Following Day

$10,000,000

BANK A BANK B

$10 MM Nom T-bond 5% ‟09

BANK A BANK B

$10 MM Nom T-bond 5% ‟09

$10,000,000 + $1,369.86 (a repo rate

of 5.0%)

Margin

An initial margin is given to the supplier of cash in the transaction. The market value

of the collateral is reduced (or given a “haircut”) by the amount of margin when

determining the value of cash lent out

Collateral

General collateral (“GC”)

Collateral that is not a specified security but of a defined homogenous credit

quality, for example UK gilts or AA-rated sterling Eurobonds. A repo in GC

does not specify any particular security, but the repo buyer must be informed

what stock is being passed over fairly shortly after the trade is agreed

Specific repo

Repo in a specific security, specified at time of trade. Equity repo is almost by

definition always specific repo. A specific is not necessarily a „special‟

Special repo

Repo using a bond that has gone „special‟

Repo Variations

Sell/Buy Back

Tri-party Repo

Term Repo

Repo-to-Maturity

Sell / Buy Back

A sell / buy back is a spot sale and forward repurchase of bonds transacted

simultaneously. The repo rate is not explicit but is implied in the forward price

Therefore the end clean price in the trade is different to the start clean price.

This simply reflects repo interest and has nothing to do with the actual market

price at the time

Coupon payments during the term of the trade are paid to the buyer, and may

be passed over at the time or handed over to the seller through incorporation

into the forward price (in which case a payment is not received immediately)

Tri-Party Repo

Market participants such as cash rich investors may prefer tri-party repo

because it eases admin (lower admin burden than “delivery” repo, but less

risky than HIC repo)

Collateral is held in an independent third-party account; service provided by

Euroclear and Clearstream Banking

The tri-party agent is also custodian, manages exchange of collateral and

cash internally

Tri-party agreement signed by all three parties

Other Repo Types

Term repo

Repo trades (of a maturity over one day) with a fixed end or maturity date

Repo/reverse repo to maturity

A repo or reverse repo where the security repo‟ed matures on the same

day as the closing leg

Financing a bond purchase via a repo

Repos are used by hedge funds to go long of bonds. The bond is purchased in the

market by the fund and then „repo‟d out‟ to replace the cash expenditure:

Hedge FundRepo

CounterpartyBond Market

BondBond

$$

Short Positions in Bonds Using Repos

In this instance the hedge fund obtains the bond via a repo and sells it on the bond

markets using the cash proceeds from the sale to pay to the repo counterparty:

Hedge FundRepo

CounterpartyBond Market

BondBond

$$

The Risk of Investing in Bonds

Module 3

Coverage

• Explain the risks associated with investing in bonds (interest rate risk, call and prepayment risk, yield curve risk, re-investment rate risk, credit risk, liquidity risk, exchange rate risk, volatility risk, inflation risk, event risk)

• Understand the inverse relationship between changes in interest rates and bond prices

• Identify the relationship between coupon and yield

• Explain how characteristics of a bond affect the bonds interest rate risk

• Identify the relationship between the price of a callable bond, an option free bond and the price of an embedded call option

• Explain how the market yield affects the interest rate risk of a bond

• Explain the interest rate risk of a FRN

• Explain the yield curve risk

• Explain key rate duration as a measure of yield curve risk

• Explain the disadvantages of a callable and prepayable security

• Identify the factors affecting reinvestment rate risk

• Explain why prepayable amortising securities are exposed to greater reinvestment rate risk

• Describe other risks associated with bonds (default risk, credit spread risk and downgrade risk)

• Compute the market bid-offer spread from the bid-offer spread provided by dealers

• Describe exchange rate risk

• Describe why inflation risks exists

• Explain why yield volatility affects prices of bonds with embedded options

• Describe the forms of event risk

Quick Recap of the Basics

Introduction

WHAT IS A BOND?




XYZ plc

$1000 nominal

6%

2030

XYZ plcInvestor

$$$

THE BASIC FEATURES OF A BOND

A bond will have three fundamental features:

The maturity or redemption date of the bond is the date when the loan is

repaid:

The par or nominal (a.k.a. principal or capital) value is the amount repaid at


The coupon is the income from the bond:

Quoted as an annual % of par

Usually paid semi-annually, for example 100 nominal of a 4-year 4%

coupon bond:

2 2 2 2 2 2 2 102

Bond Risks

Bond Risks

risks associated with

bonds?

Interest Rate Risk

Interest Rate Risk

The movement of a bond‟s price in response

to movements in interest rates/yield

Interest Rate Risk

FACTORS EFFECTING INTEREST RATE RISK

• Longer dated more volatile than shorter dated

•Lower coupons more volatile than higher coupons

•Lower yields more volatile than higher yields

Understanding Sensitivity Analysis

The determinants of sensitivity

Macaulay and modified duration

Using duration as a measure of sensitivity

Taking convexity into account

The determinants of sensitivity

The dirty bond price can be written as:

Looking at the price equation, is a function of both coupon and N, time to maturity

A low coupon bond will be more sensitive to changes in yield than a higher coupon bond, providing maturity is equal

A longer maturity bond with the same coupon will be more sensitive than a short maturity bond

To examine the combined scenario of coupon and time effects we use a concept called “duration”

Py

1 (1 )

Ni

d y ii n

CFP

Mathematics of Duration

1

( 1)1 1 1

1

mod

(1 )

1 1 1

(1 ) (1 ) (1 ) (1 )

(1 )

Ni

y ii n

N N Ni i

iy y y yi ii i in n n n

Ni

mac

i

mac

y

n

CFP

iCF iCFPiPV

y n n n

PViD

n P

DD

mod(1 )

mac

y

n

D PPD P

y

Hence:

Duration as a Measure of Sensitivity

Examining the equation for Dmac we can see that we have a weighted sum of cashflows which is a basic measure used to gauge bond sensitivity

1 2

3 4

Reference Bond for

comparison

Duration 3 years

Bond 1, but lower

coupon

Cashflows more

weighted in the future

Risk higher

Duration 3.5 years

Bond 1, but

longer maturity

Cashflows more

weighted in the

future

Risk higher

Duration 5 years

Zero coupon bond

Only one cashflow at

end of life

Duration = Maturity

Taking Convexity into Account

Macaulay duration provides a risk measure of bonds and allows them to be compared. So does modified duration.

Since duration is related to the price derivative it also provides to calculate price changes for small yield movements, i.e. for a 1% change in yields the price will change by approximately the modified duration of the instrument times its price

A second order effect known as convexity can be introduced to enhance the price sensitivity analysis further – this relationship becomes important for higher coupon and higher yielding bonds where the duration first order approximation is no longer sufficient

0 0 mod 0( ) ...P P y y D P

2

0 0 mod 0 0( ) ( ) ...P P y y D P y y C

Interest Rate Risk of an FRN

An FRN has a coupon that resets regularly to market rates – this means

that the bond‟s coupon reflects the return that investors require and so the

bond price does not need to change markedly to reflect this (unlike in a

fixed coupon bond where the price needs to change to reflect the new

required market return because the coupon cannot change)

This means that the Duration of an FRN is very low (close to zero)

Credit Risk

Credit Risk

Credit risk is the risk of default by the issuer

Credit Ratings

Credit rating agencies, such as S&P and Moodys, analyse the ability of bond issuers

to service an repay their debt. This analysis is expressed as a credit rating:

Standard and Poors Moodys

AAA Aaa

AA+ Aa1

AA Aa2

AA- Aa3

A+ A1

A A2

A- A3

BBB+ etc.. Baa1 etc..

Default

Credit rating agencies, such as S&P and Moodys, publish tables of default

probability.

Below is an example of Moody‟s cumulative default table, this is the % probability

that an issue is going to default within the following number of years:

Rating / Years 1 2 3 4 5 6 7 8 9 10Aaa 0.00 0.00 0.02 0.09 0.20 0.31 0.43 0.62 0.83 1.09Aa 0.08 0.25 0.41 0.61 0.97 1.37 1.81 2.26 2.67 3.10A 0.08 0.27 0.60 0.97 1.37 1.78 2.23 2.63 3.10 3.61

Baa 0.30 0.94 1.73 2.62 3.51 4.45 5.34 6.21 7.12 7.92Ba 1.42 3.45 5.57 7.80 10.04 12.09 13.90 15.73 17.21 19.05B 4.48 9.16 13.73 17.56 20.89 23.68 26.19 28.32 30.22 31.90

Cumulative default probabilities

Credit Migration

Credit ratings and default probabilities do not help with the idea of credit migration.

For this we use a transition matrix:

Rating

Now:

probability of rating at year end (percent)

AAA AA A BBB BB B CCC Default

AAA 93.66 5.83 0.40 0.08 0.03 0.00 0.00 0.00

AA 0.66 91.72 6.94 0.49 0.06 0.09 0.02 0.01

A 0.07 2.25 91.76 5.19 0.49 0.20 0.01 0.04

BBB 0.03 0.25 4.83 89.26 4.44 0.81 0.16 0.22

BB 0.03 0.07 0.44 6.67 83.31 7.47 1.05 0.98

B 0.00 0.10 0.33 0.46 5.77 84.19 3.87 5.30

CCC 0.16 0.00 0.31 0.93 2.00 10.74 63.96 21.94

Default 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100.00

The return to an asset may change due to an increase, or decrease, in the risk-free

rate:

..or a change in the credit risk premium:

What would you expect the credit risk premium to do if we increased the life of the

bond?

Risk Free Return Risk free Return

Credit Risk PremiumCredit Risk Premium

Risk Free Return

Credit Risk PremiumCredit Risk Premium

Risk Free Return

The term structure of credit premium

The probability of default will increase as the life of the bond increases.

Maturity

Yie

ld

Risk-free yields

Credit yields

Yield Curve Risk

Yield Curve Risk

Yield curve risk is the risk of a non-parallel movement in the yield curve

Duration assumes parallel shifts in the yield curve, so a different measure

known as key rate duration is necessary.

Key rate duration shows the bond portfolio‟s price sensitivity to yield curve

changes at various single maturity points – this gives an indication of

where the portfolio is most sensitive along the yield curve

Example

A bond portfolio has a 7 year key rate duration of 5.2 – this means that for a

1bp change in the 7 year yield the value of the portfolio will change by

approximately 5.2bp

Yield Curve Movements

Short Medium LongYield change

Upwards parallel shift

Short Medium Long

Yield change

Downwards parallel shift


Short Medium Long

Yield change

Flattening twist

Short Medium Long

Yield change

Steepening twist


Short Medium Long

Yield change

Positive butterfly

Short Medium Long

Yield change

Negative butterfly

Yield Curve Movements - Summary

Parallel

Flattening

Positive butterfly

Parallel

Steepening

Negative butterfly

Maturity Maturity

Yield Yield

Theories of the Yield Curve Shape

Expectations

Liquidity preference

Market segmentation

Preferred habitat

Supply/Demand (technical factors)

Expectations Theory

In equilibrium the long-term rate is a geometric average of today‟s short-

term rate and expected short term rates in the future

R annual yield on 2-year bond

R1 annual yield from a 1-year bond

R2 a 1-year forward rate beginning in one year‟s time

Therefore:

(1 + R)2 = (1+ R1) x (1+ R2)

Suppose that the yield on a 2-year government bond is 9%p.a. and that the

yield on an equivalent 1-year bond is 8% p.a. Assuming the pure

expectation theory holds, what is the implied yield on a 1-year bond held

during year two of the 2-year bond‟s life, i.e the implied 1-year forward

rate?

Expectations Theory: Examples

The current three-year rate is 9 percent, the current one-year rate is 6 percent, and

the one-year forward rate for one year is 8 percent. What is the two-year forward

rate for one year?

Suppose the current six-year rate is 5 percent while the one-year spot rate is 3

percent. What is the five-year forward rate one year from today?

Why would an analyst invest in a 12 month T-bill yielding 5.6% rather investing in a

6 month T-bill yielding 4.5% and rolling her investment forward for 6 months after

that?

Yield curve shapes - theories

Pure expectation theory

Economic crystal ball gazing

Liquidity Preference

Implies an upwards sloping yield curve

Market Segmentation

Different classes of investors

Number of separate markets

Different supply and demand conditions

Preferred Habitat

Supply/Demand

The Yield Curve and the Economy

Normal

Expectations of steady economy / liquidity preference

Associated with middle of economic cycle

Steep

Expectations of strong economic recovery

Typical at the beginning of an economic expansion, just after the end of a

recession

Inverted

Paradox? Less yield, more risk!

Long-term investors expect future short term rates to get even lower – lock in

rates now!

Indicates slowing economy – or even recession

Re-Investment Risk

RE-INVESTMENT RISK

If an investor buys a fixed coupon bond on a yield of (eg) 7%,

then the investor will only realise a return of 7% to maturity if

all the coupon cash flows can be re-invested at 7% over the

bond‟s life.

At the outset this cannot be guaranteed, hence the investor

has the risk of an unknown reinvestment rate at the outset of

the investment

Amortising bonds (those which repay principal and interest

each payment date) have higher reinvestment risk due to the

larger cash flows that must be reinvested

Call & Prepayment Risk

CALL & PREPAYMENT RISK

Callable bonds and quasi-callable bonds like MBS are subject

to the risk that the issuer may repay the bond early (either in

full or partially) – this creates additional risk for the bond

holder regarding the amounts and timings of the bond‟s cash

flows

A Callable bond can be analysed as a long position in a non-

callable bond and a short position in a call option

This risk gives rise to negative convexity, whereby yield falls do

not result in the bond price increase that a non-callable bond

would exhibit

Call Option

Value

Price of Straight Bond

Price of Callable Bond

Call Price

Bond Price

Pcall

r

Other Bond Risks

OTHER BOND RISKS

• Liquidity risk

Illiquidity will cause the bond spreads to widen and the price

to fall

• FX risk

Investment in a non-domestic currency bond

• Volatility risk

Embedded option bonds such as callables and putables have

exposure to option pricing influences, including volatility

• Inflation risk

Fixed coupon bonds cannot guarantee a real return (ie above

inflation) – unexpected changes in inflation cause additional

uncertainty for the investor as to what their real return will be

• Event risk

The risk of unforeseen events impacting on the bond price

Valuing Fixed Income Securities

Module 2

Coverage

Fundamentals of bond valuation

Compute the value of a zero-coupon bond

Compute the dirty price of a bond

Yield Measures

Construct, by bootstrapping, the spot rate yield curve

Construct forward rates

Illustrate the relationship between spot and forward rates

Introduction to Bond Valuation

Introduction

WHAT IS A BOND?




XYZ plc

$1000 nominal

6%

2030

XYZ plcInvestor

$$$

The Time Value of Money – Simple and Compound

Invest £100 in a savings account for 3 years at 10%

Scenario 1 – „Simple Interest‟

After year 1 take out the £10 you have earned, leave £100 there

Year 2: you earn £10 on £100, which you take out

Year 3: you earn £10 on £100

Total wealth: £100 + £10 + £10 + £10 = £130

Scenario 2 – „Compound Interest‟

Year 1: earn £10 interest on £100- leave the full £110 in account

Year 2: earn £11 interest (on £110) –leave the full £121 in

Year 3: earn £12.10 on £121

Total wealth: £100 + £10 + £11 + £12.10 = £133.10

Assuming you do not take income out of the investment cycle:

You receive interest on your interest

„The eighth wonder of the world‟

The Time Value of Money

T0 T1 T2 T3

£100

£110

£121

£133.10

At the end of each year the interest earned is re-invested together with the capital for a further year.

10%

10%

10%

£10 At the end of the 3 years the total is £133.10, which includes principal and compounded interest.

£11

£12.10


COMPOUNDING FORMULA

TV = PV (1+r)n

Where TV is the terminal value of an amount PV invested today for n periods at an

interest rate of r per period

EXAMPLES

£6,000 placed on deposit for 5 years at an interest rate of 6 1/2%. What is the final

sum assuming compound interest?

What is the future value of $10,000 received today, placed on deposit for 25 years

at 9%?


NON-ANNUAL COMPOUNDING

• So far we have assumed annual payment of interest

• Suppose instead the interest on the account is 5% p.a. but it is paid QUARTERLY (1.25% 4 times per year)

• How would this affect the final sum?

•£1,000 invested at 5% over 10 years

•Annual compounding: TV = £1,628.89•Quarterly compounding: TV = £1,643.62

•More frequent interest = more interest on your interest•You start earning the extra interest sooner•More time for compounding to have an effect


DISCOUNTING

We began by growing £100 to an amount in 1 year‟s time

If we can identify a payment of £100 paid in 1 year, what is this worth today?

i.e What amount today would make you INDIFFERENT?

We can calculate this using the DISCOUNT formula:

Where PV is the Present Value of a known Terminal Value TV to be received

after n periods at an interest rate of r per period.

nr1

TVPV


DISCOUNTING EXAMPLES

What is the value of £6,000,000 paid in 5 years using a discount rate of 5 ½ %?

What is the present value of $100,000 paid in 20 years at a discount rate of 9%?

Bond Pricing - Zeros

A Zero Coupon Bond will repay €10,000 in 5 years time. Interest rates are 7%.

What is the value of the bond?

Bond Pricing – Coupon Bonds

So far we have looked at discounting single future cashflows back to today‟s value

A bond is a series of cashflows e.g.

• 3 year, £100 bond, paying an annual coupon of 5%

• Future cashflows are:

?

?

?

• Interest rate is 4%.

How much would you pay for each of those separately today?

How much would you pay for the bond?

Using Your Calculator

Future Value Of A Single Cash Flow

Tell the calculator everything you know, and ask it to calculate the unknown

£100 nominal bond, 5% coupons, 4% interest rate, 3 year maturity

BEFORE YOU START CLEAR THE CALCULATOR: 2nd CLR TVM

N

I/Y

PV

PMT

CPT FV

Ans:NB : Signs

Question:

Calculate the price of a 6% annual coupon bond, with a $1,000 face value, which

matures in 3 years?

using a required return of 5%.

using a required return of 8%?

using a required return of 15%?

Plot your results on the graph paper

Price yield relationship

Yield/%

Price/$

BOND YIELDS

The yield to maturity (YTM):

this is the total return the investor receives if they:

buy the bond at its current price and hold it until redemption

invest all of the coupons at the same rate

Quick and dirty calculation (ignore investment income on coupons):

4 year bond priced at £92, 5% coupon. What is the yield?

What if the price falls to £88?

BOND YIELDS

The interest / flat / income yield:

this is the return the holder receives on their investment in terms of COUPONS only:

Nominal yield: the nominal yield is the coupon

price Clean

amount Couponyield Flat

Yield Measures

RELATIONSHIP BETWEEN YIELDS

Par Nominal yield = Flat yield = YTM

Discount (below par) Nominal yield < Flat yield < YTM

Premium (below par) Nominal yield > Flat yield > YTM

Other Yields

Yield to call

Who has call option?

Yield to put

Who has put option?

Yield to worst

Case Study – Investment Decisions

We are running an International Government Bond Fund

We read in a piece of sellside research

Fedwatch – Interest rates to rise tomorrow in the US

What do we do with our US bonds?

Problem – we are a bond fund…

All interest rates to rise

5 year rates up 5bp

30 year rates up 12bp

Now what can we do?

Valuing Fixed Income

MATURITY AND PRICE CONVERGENCE

Par

Bond at a premium: e.g. 8% coupon bond with a YTM of 4%

Bond at a discount: e.g. 4% coupon bond with a YTM of 8%

Time

Price

Price becomes less volatile later in the bond‟s life

One day before maturity- would you pay £110 for £100 nominal?

Would you sell at £90?

Case Study – Price a New Bond Issue

You work on the Telecoms fixed income fund

Today: launch of a new bond for Deutsche Telekom

Benchmark issue – get this right

Structural requirements

6 years maturity

Currency: USD

Coupon to be paid semi-annual

Par / Par structure

Call structure – 4 year HNC (cost – 14bp per year)

Put – none

$6bn required

Market Inputs

USD 6 year T-Bond yield – 4.23%

What should be the coupon / yield of the new bond?

If DT wish to fix the coupon at 6%, what price should we buy the bond at?

Issuer

Maturity

(years) Spread (bp)

Deutsche Telekom 4 45



France Telecom 1.5 39

France Telecom 6.2 56

France Telecom 8 62

Vodafone 6 61

Vodafone 14 71

Vimpelcom 6 243

British Telecom 3.4 40

British Telecom 5.8 51

British Telecom 11 56

Reference Credit Spreads

Further Bond Valuation

Arbitrage Free Approach

Different Interest Rates

• Bond Yields

Annual total rate of return on a bond investment

Used to discount cashflows within a bond to get a price

PROBLEM: uses same interest rate for cashflows at different times

So it‟s a kind of average

How can this be right?

• Spot rates

Single interest rate starting today for each time period

• Forward rates

Interest rates available today for a period starting in the future

Forward Rates

Today is January 1st 2007. 12m interest rates (spot rates) are 6%.

• We believe the 12 month spot rates starting on January 1st 2008 will be 7%

12v24 forward

• The 24v36 forward is 9%

• If you invest £100 today, how much is it worth at the end of 2007?

• If today you fix the 12v24 forward, how much is you £100 worth at the end of

2008?

• What single interest rate, applied during 2007 and 2008, gets you to the same

number?

This is the 24m spot rate

• What is the 36m spot rate?

Spots and Forwards

£100

How can we get Spots and Forwards from Bond Prices?

The discount rate of needed for the one-year cash-flow is known as the one

year SPOT rate. It is the discount rate used for a zero coupon bond for that

period.

Bonds will be priced according to the individual spot rates for each cash-flow

and the YTM calculated from the price retrospectively.

To do this a SPOT RATE YIELD CURVE is required.

A spot yield curve is constructed using the US Treasury Yield curve (using

YTM) and a process known as BOOTSTRAPPING.

Stripping the Yield Curve to Price a Bond

The US Treasury yield curve is:

6m4.000% p.a.

12m 5.951% p.a.

A 1-year 10% semiannual bond with a YTM of 5.951% is therefore priced at $103.874:

103.874 = 5 / (1.029755) + 105 / (1.029755)2

If we treat the cash-flows individually – and assign them individual discount rates from the yield curve we can see that discounting the 1st coupon at 4.00% would result in a higher bond price.

So if the 6m spot rate is 4%, what is the 12m spot rate?


YTM Valuation

Coupon 1

$5Redemption

$105

6m

12m

103.874 = 5 / (1.029755) + 105 / (1.029755)2

103.874 = 5 / (1.02) + 105 / (1+?)2

YTM 5.9515 / 2

6m rate 4 / 2

Spot Valuation

Both Valuation methods should come to the same price


The value of the bond is 103.874. The 1 year spot rate may be calculated using the

6m spot rate as follows:

03.0

06090.11

1

105972.98

1

105902.4874.103

1

105

)02.1(

5874.103

12

2

12

2

12

2

12

2

12

m

m

m

m

m

z

z

z

z

z

Remember, this is one half of the

annualised spot rate of 6%


The 18 month spot rate could be calculated using the 6 and 12 month spot

rates and a 18 month Treasury bond:

8% 18 month T bond with YTM 6.455% p.a. priced at $102.176

6m spot is 4% p.a.

12m spot is 6% p.a

Calculate the 18 month spot rate


p.a. 6.5%or 0325.0

1007.11

)1(

104485.94

)1(

104770.3921.3176.102

)1(

104

03.1

4

)02.1(

4176.102

18

3

18

3

18

3

18

3

18

2

m

m

m

m

m

z

z

z

z

z

Yield and Spot Curves

We can now construct the yield a spot curves going out 18 months

Yield and Spot Curves

4.000%

4.500%

5.000%

5.500%

6.000%

6.500%

6m 12m 18m

Yield

Spot

Yield Spot

6m 4.000% 4.000%

12m 5.951% 6.000%

18m 6.455% 6.500%

Forwards

Fixing an interest rate today for a period in the future

What must the 6v12 Fwd rate be?

What about 12v18? 6v18?

What about 0v6?

If the price on the screen for 6v12 was 7%, how could GM make

profit?

6m spot: 4%

12m spot: 6%

18m spot: 6.5%

6v12 Forward

Relationship Between Spot Rates, Forward Rates & Yield

Relationship Between Spot Rates, Forward Rates & Yield

Spot Rates

SPOT RATE

• Rate used to discount a single cash flow received in the future

• Used to discount bonds – arbitrage free approach

• Therefore, bonds will always be priced at, or around, the arbitrage-free price

Z1 = 1-year spot

Z2 = 2-year spot

Z3 = 3-year spot

Zn = N-year spot

Spot Rates

SPOT RATE: EXAMPLE

• You observe the following data for 3 T-securities. Assume ANNUAL compounding

Maturity YTM Coupon Price

1 Year 5% 0% 95.24

2 Years 7% 7% 100

3 Years 14% 5% 79.11

NOTE: To calculate spot rates simply ‘strip’ each bond and value them as standalone instruments – known as bootstrapping

Spot Rates

Z1 = YTM on 1 year zero coupon bond = 5%

To calculate Z2:

22Z 1

107

1.05

7100

Solve for Z2 =

Spot Rates

Z1 = 5%

Z2 = 7.07%

To calculate Z3:

79.11 =

Solve for Z3 =

332 Z 1

105

1.0707

5

1.05

5

Forward Rates

Market expectations of future spot rates

Calculate the 1 year & 2 year forward rates, based on

the preceding spot rate info

Forward vs Spot vs Yield

Next Page :

Plot the Spot rate, Forward rate & YTM for the 3 year

bond

Yield, spot and forward curves

Yield/%

Price/$

The Interest Rate Risk within Bonds

Sensitivity Analysis

Bond risk and bond price sensitivity

Factors influencing bond price sensitivity to interest rates

A bond‟s price is derived from 3 factors:

Maturity

Coupons

Required return (interest rate + credit spread)

These factors also determine price volatility (risk) due to interest moves

The effect of maturity on price volatility

You are analysing the price movements of two bonds

10% 3 year bond; and

10% 6 year bond

Calculate the prices of the two bonds assuming yields of:

2%

5%

15%

Maturity – Effect on Price Volatility

Longer dated bond: more sensitive to interest rate changes

Discounting over longer period

More pronounced volatility

3 Year BondYear Cashflow 2% 5% 15%

1 10.00 9.80 9.52 8.70

2 10.00 9.61 9.07 7.56

3 110.00 103.66 95.02 72.33

123.07 113.62 88.58

6 Year BondYear Cashflow 2% 5% 15%

1 10.00 9.80 9.52 8.70

2 10.00 9.61 9.07 7.56

3 10.00 9.42 8.64 6.58

4 10.00 9.24 8.23 5.72

5 10.00 9.06 7.84 4.97

6 110.00 97.68 82.08 47.56

144.81 125.38 81.08

PV of bond

cashflows in

today's terms

Investors' Required Yields


Bond Valuation

Bond Valuation

+8.3% -22.0%

+15.5% -33.3%


Price yield relat ionship

80.00

90.00

100.00

110.00

120.00

130.00

140.00

150.00

160.00

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00

Yield

Pri

ce 3yr 10%

6yr 10%


Longer maturity – more volatility

…but we can see this intuitively anyway

Bond price must be less volatile closer to maturity

Par



Time

Price

Par



Time

Price

Coupon – Effect on Price Volatility

The effect of coupons

You are analysing the price movements of two bonds

15% 3 year bond; and

5% 3 year bond

Calculate the prices of the two bonds assuming yields of:

2%

5%

15%


Higher coupon : less sensitive to interest rate changes

Receive more of the cashflows earlier – less discounting

Higher coupons: protection against interest rate risk

Coupon: impact on volatility less pronounced than with maturity differential

3% CouponYear Cashflow 2% 5% 15%

1 3.00 2.94 2.86 2.61

2 3.00 2.88 2.72 2.27

3 103.00 97.06 88.98 67.72

102.88 94.55 72.60

15% CouponYear Cashflow 2% 5% 15%

1 15.00 14.71 14.29 13.04

2 15.00 14.42 13.61 11.34

3 115.00 108.37 99.34 75.61

137.49 127.23 100.00Bond Valuation

PV of bond

cashflows in

today's terms



Bond Valuation

+8.8% -23.2%

+8.1% -21.4%


Price yield relat ionship

40.00

60.00

80.00

100.00

120.00

140.00

160.00

180.00

200.00

0.00 5.00 10.00 15.00

Yield

Pri

ce 2% 6yr

15% 6yr

Macaulay Duration

Duration is the (PV) weighted average maturity of a bond‟s cash-flows

It serves to measure bond risk, higher duration bonds are more risky than lower

duration bonds

MACAULAY DURATION

Cashflows further in the future: more interest rate risk

The average period to discount back each £ invested

Macaulay Duration

1 2

3 4

Reference Bond for

comparison

Duration 3 years

Bond 1, but lower

coupon

Cashflows more

weighted in the future

Risk higher

Duration 3.5 years

Bond 1, but

longer maturity

Cashflows more

weighted in the

future

Risk higher

Duration 5 years

Zero coupon bond

Only one cashflow at

end of life

Duration = Maturity

Macaulay and Modified Duration

Next step of duration analysis.

Adjust from Macaulay to Modified Duration through simple formula

Modified Duration is a measure of the sensitivity of a bond‟s price to

changes in yield. It is the slope of the price / yield chart.

Higher Macaulay Duration – higher Modified Duration

Higher Modified Duration – more sensitivity – steeper curve

ytm1

Duration MacualayDuration Modified

Modified Duration- Price Movement Prediction

Modified Duration: slope of the price / yield curve at any point

Can therefore use MD to predict bond price for any new yield

Good approximation, but not quite accurate

Straight line: bond prices predicted by Modified Duration

Actual bond prices: curved relationship with yield

30-year maturity, 8% coupon straight bond

Bond Price (P)

Bond Yield or Interest Rate (r)

P

P r

r

r0 r r

Convexity

0.67

0.87

1.07

1.27

1.47

1.67

1.87

2%2.

2%2.

4%2.

6%2.

8%3.

0%3.

2%3.

4%3.

6%3.

8%4.

0%4.

2%4.

4%4.

6%4.

8%5.

0%5.

2%5.

4%5.

6%5.

8%6.

0%6.

2%6.

4%6.

6%6.

8%7.

0%7.

2%7.

4%7.

6%7.

8%8.

0%

Yield

Pri

ce Bond Price Line

Duration Line

Convexity is the difference between the price / yield relationship

as predicted by MD, and the actual observed relationship

More complex calculation– But allows investment manager to predict accurate price movements for

changes in interest rates or credit spreads

Convexity adjustment

Duration – A Summary

Duration is the investment manager‟s key measure of non-credit risk

Exposure to interest movements, but not to investment quality

Macaulay Duration

Length of time each £ or $ is discounted back by

Relative interest risk metric

Modified Duration

Calculated from Macaulay figure

A risk indicator, just like Macaulay…

…but also an approximate indicator of future price movements

Made more exact when combined with convexity calculation

If in doubt: „duration‟ refers to Modified Duration

“Risk” = price volatility: not the risk you lose your investment

Only subject to this risk if you trade in and out of the bond

If you hold bond to maturity

Bond price in the market changes, but irrelevant to your P/L

Interest rate changes have no effect (on you)

Unless issuer defaults- credit risk, not interest rate risk

SPREAD

Corporate Bonds- Additional Risk, Additional Return

Corporate Spreads

There are yield curves for different sorts of issuers

E.g. all Treasuries, or all BBB bonds, or all Utilities bonds

The difference between the corporate curve and treasuries at any point is the „spread‟ -

might not be constant at all maturities

Spread is the additional yield on top of treasury yields (interest rates) to compensate

investors for extra risk in the corporate

Corporate yield therefore = interest rate + spread

3m 2Y 5Y 10Y 20Y

5.5

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

AAA

Treasuries

BBB

Corporate Spreads

Example: evolution over time of the spread between

5 year Government bonds („treasuries‟) and

5 year bonds issued by „BBB‟ rated corporates

5yr BBB Credit Spreads

0

100

200

300

400

Date

Sp

read

over

T

Corporate Spreads

Case study

You are the lead manager of a corporate bond issue. Use the information below, to

determine a possible issue price:

Name: Thin Air Plc

Maturity Dec 31 2010

Annual coupon 6%

5 year GBP Government bond yield 4.16%

S&P rating BBB+

BBB+ 5 years spreads 115bp

Corporate Spreads

Why are spreads important?

Relationship between yield and value of bond in the portfolio

Yields up, portfolio down

Yields are interest rates plus spreads- moving independently

Bond portfolio stock selection

Each bond issuer has a different credit profile (risk) and therefore a different

credit spread

Investment manager‟s skill: „To beat the market I choose bonds with credit

spreads which I think will …… [rise or fall?]‟

Credit spread: indicator of financial health of the corporate

(Market‟s view of it, anyway)

Combining Yield Curve and Spreads

Bond prices driven by interest rates and credit spread

Investment managers make decisions on both

Example:

Investment manager expects the yield curve to steepen, and believes

telecoms will outperform tech companies

A) Sell 5 year IBM, buy 30 year British Telecom?

B) Sell 30 year IBM, buy 5 year British Telecom?

C) Sell 5 year British Telecom, buy 30 year IBM?

D) Sell 30 year British Telecom, buy 5 year IBM?

Switching, or pair trading, is a common investment method

Self funding trade- the sale provides the cash for the purchase

UNDERSTANDING REPO

Classic Repo

First Leg

Bank A Bank B

sells 100 worth of stock

pays 100 cash for stock

Second leg

Bank A Bank B

pays 100 cash plus interest

sells 100 worth of stock

Classic Repo

In a classic repo the sale and repurchase prices are the same, although settlement

values will differ because of addition of repo interest on termination

A sale and repurchase is a “repo”, whereas a purchase and sell back is a “reverse

repo”. Of course the counterparty is either one or the other, opposite to your

position!

If a coupon is paid during the term of the repo it will be handed over to the seller

A classic repo is subject to a legal contract signed in advance by both parties

Classic Repo - Example

On 6 September 1997 Bank A agrees to sell £1m nominal of a UK gilt, the 8%

Treasury 2000, which is trading at a dirty price of 104.30

Trade value date is 7 September, term 30 days, matures 7 October and agreed repo

rate is 6.75%

The first leg of the trade Bank A passes over the stock and receives £1.043m

On 7 October Bank B returns the gilt and Bank A pays over the original monies plus

repo interest of £5786.50

Classic Repo - Example

First Leg

Bank A Bank B

sells £1m nominal UKT 8% 2000

pays £1.043m

Second leg

Bank A Bank B

returns £1.043m plus £5786.5 interest

returns £1m nominal UKT 8% 2000

Margin

An initial margin is given to the supplier of cash in the transaction. The market value

of the collateral is reduced (or given a “haircut”) by the amount of margin when

determining the value of cash lent out

Two methods used to calculate the margin, assume a 2% level :

dirty price of bonds x 0.98

dirty price of bonds / 1.02

Bloomberg uses the second method

Repo Strategies

Transfer of cash and collateral is temporary

Economic benefits of bonds remain with the seller

Seller marks to market the bond position, and receives coupon (despite not

legally owning bonds)

Method of getting the cash today, but keeping participation in the P/L

Rationale (i): Yield enhancement

Keep bond P/L

Use bonds as collateral to raise cheap funding

Invest funding at better returns

Fund bond position:

Buy bonds and immediately repo them out

Cash back straight away

Repo counterparty effectively funds your trading position

Margin

Size of margin required in any transaction is a function of

credit quality of counterparty

term of the repo

duration (price volatility) of collateral

existence of any legal agreement

quality of collateral

A provision for variation margin is contained in repo agreements, to allow for the

level of collateral to be say, increased if its market value has fallen significantly

during the term of the trade

Collateral

General collateral (“GC”)

Collateral that is not a specified security but of a defined homogenous credit

quality, for example UK gilts or AA-rated sterling Eurobonds. A repo in GC

does not specify any particular security, but the repo buyer must be informed

what stock is being passed over fairly shortly after the trade is agreed

Specific repo

Repo in a specific security, specified at time of trade. Equity repo is almost by

definition always specific repo. A specific is not necessarily a „special‟

Special repo

Repo using a bond that has gone „special‟

PPT PDF FIXED INCOME

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