Fixed income securities

The Simple Rules of Risk: Revisiting the Art of Risk Management Erik BanksMeasuring Market Risk Kevin Dowd An Introduction to Market Risk Management Kevin Dowd Behavioural Finance James

Lionel Martellini Philippe Priaulet

and St´ephane Priaulet

The Simple Rules of Risk: Revisiting the Art of Risk Management Erik Banks

Measuring Market Risk Kevin Dowd

An Introduction to Market Risk Management Kevin Dowd

Behavioural Finance James Montier

Asset Management: Equities Demystified Shanta Acharya

An Introduction to Capital Markets: Products, Strategies, Participants Andrew M Chisholm

Hedge Funds: Myths and Limits Francois-Serge Lhabitant

The Manager’s Concise Guide to Risk Jihad S Nader

Securities Operations: A guide to trade and position management Michael Simmons

Modeling, Measuring and Hedging Operational Risk Marcelo Cruz

Monte Carlo Methods in Finance Peter J¨ackel

Structured Equity Derivatives: The Definitive Guide to Exotic Options and Structured Notes Harry Kat

Advanced Modelling in Finance Using Excel and VBA Mary Jackson and Mike Staunton

Operational Risk: Measurement and Modelling Jack King

Advance Credit Risk Analysis: Financial Approaches and Mathematical Models to Assess, Price and Manage Credit Risk Didier Cossin and Hugues Pirotte

Interest Rate Modelling Jessica James and Nick Webber

Volatility and Correlation in the Pricing of Equity, FX and Interest-Rate Options Riccardo Rebonato

Risk Management and Analysis vol 1: Measuring and Modelling Financial Risk Carol Alexander (ed)

Risk Management and Analysis vol 2: New Markets and Products Carol Alexander (ed)

Interest-Rate Option Models: Understanding, Analysing and Using Models for Exotic Interest-Rate Options (second edition) Riccardo Rebonato

Lionel Martellini Philippe Priaulet

and St´ephane Priaulet

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The views, thoughts and opinions expressed in this book are those of the authors in their individual capacities and should not in any way be attributed to Philippe Priaulet as a representative, officer or employee of HSBC-CCF.

The views, thoughts and opinions expressed in this book are those of the authors in their individual capacities and should not in any way be attributed to St´ephane Priaulet as a representative, officer or employee of AXA.

Library of Congress Cataloging-in-Publication Data

Martellini, Lionel.

Fixed-income securities : valuation, risk management, and portfolio strategies / Lionel

Martellini, Philippe Priaulet, and St´ephane Priaulet

p cm.—(Wiley finance series)

Includes bibliographical references and index.

ISBN 0-470-85277-1 (pbk : alk paper)

1 Fixed-income securities —Mathematical models 2 Portfolio

management— Mathematical models 3 Bonds — Mathematical models 4 Hedging

(Finance)—Mathematical models I Priaulet, Philippe II Priaulet, St´ephane III Title IV.

Series.

HG4650.M367 2003

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN 0-470-85277-1

Typeset in 10/12.5pt Times by Laserwords Private Limited, Chennai, India

Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire

This book is printed on acid-free paper responsibly manufactured from sustainable forestry

in which at least two trees are planted for each one used for paper production.

To our friends

About the Authors xix

PART I INVESTMENT ENVIRONMENT

1.6 Appendix: Sector Breakdown of the Euro, the UK and the Japan

2.2.1 Time-Value of Money 43

2.2.4 Time Basis and Compounding

PART II TERM STRUCTURE OF INTEREST RATES

3.2.4 The Biased Expectations Theory:

3.4.1 On the Empirical Behavior of the Yield Curve 893.4.2 On the Principal Component Analysis

3.4.3 On the Classical Theories of the Term Structure

4.1 Deriving the Nondefault Treasury Zero-Coupon Yield Curve 96

4.2 Deriving the Interbank Zero-Coupon Rate Curve 130

4.2.1 How to Select the Basket of Instruments? 130

PART III HEDGING INTEREST-RATE RISK

5.1 Basics of Interest-Rate Risk: Qualitative Insights 163

5.2.2 Duration, $Duration and Modified Duration 170

6.2.2 Regrouping Risk Factors through

6.2.3 Hedging Using a Three-Factor Model

6.4 References and Further Reading 200

PART IV INVESTMENT STRATEGIES

8.1 Market Timing: Trading on Interest-Rate Predictions 2338.1.1 Timing Bets on No Change in the Yield Curve

8.1.3 Timing Bets on Specific Changes in the

8.1.5 Active Fixed-Income Style Allocation Decisions 255

8.2.1 Trading within a Given Market: The Bond

8.2.2 Trading across Markets: Spread

9.2 Risk-Adjusted Performance Evaluation 295

9.2.1 Absolute Risk-Adjusted Performance Evaluation 296

9.2.2 Relative Risk-Adjusted Performance Evaluation 299

9.3 Application of Style Analysis to Performance Evaluation

PART V SWAPS AND FUTURES

10.3.1 Optimizing the Financial Conditions of a Debt 335

10.3.2 Converting the Financial Conditions of a Debt 336

10.4.1 Accrediting, Amortizing and Roller Coaster Swaps 342

10.4.3 Constant Maturity Swap and Constant

11 Forwards and Futures 353

11.3 Margin Requirements and the Role of the Clearing House 35811.4 Conversion Factor and the Cheapest-to-Deliver Bond 35911.4.1 The Cheapest to Deliver on the Repartition Date 36011.4.2 The Cheapest to Deliver before

11.5.1 Forward-Spot Parity or How to Price

11.5.3 Relation between Forward and Futures Prices 365

11.6.2 Fixing Today the Financial Conditions of a Loan

11.6.3 Detecting Riskless Arbitrage Opportunities

11.6.4 Hedging Interest-Rate Risk Using Futures 368

11.8.2 Websites of Futures Markets and of the Futures

11.10 Appendix: Forward and Futures Prices Are Identical

PART VI MODELING THE TERM STRUCTURE OF INTEREST RATES AND CREDIT SPREADS

12.3.1 A Discrete-Time Example: Ho and Lee’s

12.7 Appendix 1: The Hull and White Trinomial Lattice 413

12.7.2 Calibrating the Lattice to the Current

12.8 Appendix 2: An Introduction to Stochastic

12.8.3 Stochastic Differential Equations (SDE) 425

12.8.8 Application to Equilibrium Models

PART VII PLAIN VANILLA OPTIONS AND MORE EXOTIC DERIVATIVES

14.7 Appendix: Bond Option Prices in the Hull

15.2.2 Pricing and Hedging Caps, Floors and Collars 510

15.7 Appendix 1: Proof of the Cap and Floor

15.8 Appendix 2: Proof of the Swaption Formula

15.9 Appendix 3: Forward and Futures Option Prices Written on T-Bond

and Libor in the Hull and White (1990) Model 536

15.10 Appendix 4: Cap, Floor and Swaption Prices in the Hull

15.11 Appendix 5: Market Models (BGM/Jamshidian Approach) 541

15.11.3 The Dynamics ofL(t, θ) and K(t, t + θ) 543

16.1.2 Bounded Caps, Floors, Barrier Caps and Floors 550

16.1.21 Pricing and Hedging Interest-Rate Exotic Options 565

16.2 Credit Derivatives 565

16.4.3 On Numerical Methods (See the Appendix 2) 576

16.6 Appendix 1: Pricing and Hedging Barrier Caps and Floors

PART VIII SECURITIZATION

18.2 Market Quotes and Pricing 610

Lionel Martellini is an Assistant Professor of Finance at the Marshall School

of Business, University of Southern California, where he teaches “fixed-income

securities” at the MBA level He is also a research associate at the EDHEC Risk

and Asset Management Research Center, and a member of the editorial boards

of The Journal of Bond Trading and Management and The Journal of Alternative

Investments He holds master’s degrees in business administration, economics,

statistics and mathematics, as well as a Ph.D in finance from the Haas School of

Business, University of California at Berkeley His expertise is in derivatives valuation and optimalportfolio strategies, and his research has been published in leading academic and practitioners’journals He has also served as a consultant for various international institutions on these subjects.Philippe Priaulet is a fixed-income strategist in charge of derivatives strategies for

HSBC His expertise is related to fixed-income asset management and derivatives

pricing and hedging, and his research has been published in leading academic

and practitioners’ journals Formerly, he was head of fixed-income research in the

Research and Innovation Department of HSBC-CCF He holds master’s degrees

in business administration and mathematics as well as a Ph.D in financial

eco-nomics from University Paris IX Dauphine Member of the editorial board of The

Journal of Bond Trading and Management, he is also an associate professor in the

Department of Mathematics of the University of Evry Val d’Essonne and a lecturer at ENSAE,where he teaches “fixed-income securities” and “interest rate modeling”

St´ephane Priaulet is senior index portfolio manager in the Structured Asset

Man-agement Department at AXA Investment Managers Previously, he was head

of quantitative engineering in The Fixed Income Research Department at AXA

Investment Managers He also teaches “fixed-income securities” as a part-time

lecturer at the University Paris Dauphine He is a member of the editorial board

of The Journal of Bond Trading and Management, where he has published

sev-eral research papers He holds a diploma from the HEC School of Management,

with specialization in economics and finance, and has completed postgraduate

studies in mathematics at the University Pierre et Marie Curie (Paris VI), with

specialization in stochastic calculus

Debt instruments have evolved beyond the straight bonds with simple cash-flow structures tosecurities with increasingly complex cash-flow structures that attract a wider range of investorsand enable borrowers to reduce their costs of raising funds In order to effectively employ portfoliostrategies that may control interest-rate risk and/or enhance returns, investors must understand theforces that drive bond markets and the valuation of these complex securities and their derivativeproducts.

What this Book is About

This book is about interest rates and risk management in bond markets It develops insights intodifferent bond portfolio strategies and illustrates how various types of derivative securities can

be used to shift the risks associated with investing in fixed-income securities It also providesextensive coverage on all sectors of the bond market and the techniques for valuing bonds.While there certainly exists an impressive list of books that cover in some detail the issues related

to bond and fixed-income derivative pricing and hedging, we just could not find, in existingtextbooks, the same level of depth in the analysis of active and passive bond portfolio strategies.This is perhaps unfortunate because we have learnt a lot about active and passive bond portfoliostrategies in the past thirty years or so While no financial economist or practitioner in the industrywould claim they have found a reliable model for the valuation of stocks, we indeed have reached

a fairly high level of understanding on how, why and when to invest in bonds

We have written this book in an attempt to achieve the following goal: provide the reader with

a detailed exposure to modern state-of-the-art techniques for bond portfolio management Wecover not only traditional techniques used by mutual fund managers in the fixed-income area butalso advanced techniques used by traders and hedge fund managers engaged in fixed-income orconvertible arbitrage strategies

More specifically, we attempt to achieve the following:

• Describe important financial instruments that have market values that are sensitive to rate movements Specifically, the course will survey the following fixed-income assets and related securities: zero-coupon government bonds, coupon-bearing government bonds, cor- porate bonds, exchange-traded bond options, bonds with embedded options, floating-rate notes, caps, collars and floors, floating-rate notes with embedded options, forward contracts, interest-rate swaps, bond futures and options on bond futures, swaptions, credit derivatives, mortgage-backed securities, and so on.

interest-• Develop tools to analyze interest-rate sensitivity and value fixed-income securities cally, the course will survey the following tools for active and passive bond management:

Specifi-construction of discount functions, duration, convexity, and immunization; binomial trees for analysis of options; hedging with bond futures, using models of the term structure for pricing and hedging fixed-income securities; models for performance evaluation; systematic approach

to timing; valuation of defaultable bonds; bonds with embedded options; interest-rate tives, and so on.

deriva-For the Reader

This book is original in that it aims at mixing theoretical and practical aspects of the question in

a systematic way This duality can be traced back to the professional orientations of the authors,who are active in both the academic and the industrial worlds As such, this book can be of interest

to both students and professionals from the banking industry To reach the goal of providing thereader with a practical real-world approach to the subject, we have ensured that the book containsdetailed presentations of each type of bond and includes a wide range of products Extensivediscussions include not only the instruments but also their investment characteristics, the state-of-the art technology for valuing them and portfolio strategies for using them We make a systematicuse of numerical examples to facilitate the understanding of these concepts

The level of mathematical sophistication required for a good understanding of most of the material

is relatively limited and essentially includes basic notions of calculus and statistics When moresophisticated mathematical tools are needed, they are introduced in a progressive way and mostreally advanced material has been placed in dedicated appendices As a result, the book is suited

to students and professionals with various exposure to, or appetite for, a more quantitative ment of financial concepts Generally speaking, the material devoted to the modeling of the termstructure and the pricing of interest-rate derivatives is more technical, even though we have con-sistently favored intuition and economic analysis over mathematical developments Appendix 2 toChapter 12, devoted to advanced mathematical tools for term-structure modeling, can be skipped bythe nonquantitatively oriented reader without impeding his/her ability to understand the remainingsix chapters

treat-For the Instructor

The book is complemented with a set of problems (more than 200 of them) and their solutions,posted on a dedicated website (www.wiley.co.uk/martellini), as well as a complete set of Excelillustrations and PowerPoint slides (more than 400 of them) This makes it ideally suited for

a typical MBA audience, in the context of a basic or more advanced “Fixed-Income Security”course It can also be used by undergraduate, graduate and doctoral students in finance

The first nine chapters offer a detailed analysis of all issues related to bond markets, includinginstitutional details, methods for constructing the yield curve and hedging interest-rate risk, as well

as a detailed overview of active and passive bond portfolio strategies and performance evaluation

As such, they form a coherent whole that can be used for a shorter quarter course on the subject.Chapters 10 to 18 cover a whole range of fixed-income securities, including swaps, futures, options,and so on This second half of the book provides a self-contained study of the modern approachfor pricing and hedging fixed-income securities and interest-rate options The text mostly focuses

on the binomial approach to the pricing of fixed-income derivatives, providing cutting-edge theory

and technique, but continuous-time models are also discussed and put in context This material

can be taught either in the context of an advanced fixed-income class or as the second half of a

general semester course on fixed-income securities

By the way, we are aware that “Martellini, Priaulet and Priaulet” is a long, funny-sounding

reference name Please feel free to refer our textbook to your students as MPP, or MP2 (MP

squared)

We would like to express our gratitude to a number of people who have provided invaluablefeedback at different stages of the manuscript or helped in the publication process We are par-ticularly grateful to Noel Amenc, Tarek Amyuni, Yoann Bourgeois, Vicent Altur Brines, MooradChoudhry, Christophe Huyghues-Despointes, Yonathan Ebguy, R´emy Lubeth, Victoria Moore,Moez Mrad, Daad Abou Saleh, Alexandre Van den Brande and Franck Viollet for their commentsand suggestions.

This glossary contains some standard definitions and notations that are used throughout the book.

• α is the risk-adjusted expected return on a bond portfolio.

• β 0 , β 1 and β 2 are the parameters measuring respectively the level, slope and curvature of the term structure in the Nelson and Siegel (1987) model.

• β 0 , β 1 , β 2 and β 3 are the parameters measuring respectively the level, slope and curvatures

of the term structure in the Svensson (1994) model.

•  (delta) is a measure of the first-order sensitivity of an option price with respect to small changes in the value of the underlying rate or asset.

• γ (gamma) is a measure of the second-order sensitivity of an option price with respect to small changes in the value of the underlying rate or asset.

• γ (t, T ) is the volatility at date t of the instantaneous forward rate f (t, T ).

• σ (t, T ) is the volatility at date t of the zero-coupon bond B(t, T ).

• (x) is the distribution function of a standardized Gaussian, that is, it is the probability that

a normally distributed variable with a mean of zero and a standard deviation of 1 is less than x

• 
(x) is the first derivative of  with respect to x.

• ν (vega) is a measure of the first-order sensitivity of an option price with respect to small changes in the volatility of the underlying rate or asset.

• ρ (rho) is a measure of the first-order sensitivity of an option price with respect to small changes in the interest rate.

• θ (theta) is a measure of the first-order sensitivity of an option price with respect to small changes in time to maturity.

• AC t is the accrued interest on a bond at date t

• BPV is the basis point value, which is the change in the bond (or bond portfolio) given a basis point change in the bond’s (or bond portfolio) yield.

• B(t, T ) is the price at date t of a zero-coupon bond (also called a pure discount bond) maturing at time T ≥ t, that is, the price of a bond paying $1 at date T and nothing before

(no intermediate coupon payment).

• c is the coupon rate.

• c(n) is the par yield for maturity n, that is, the annual coupon rate that should be paying an n-year maturity fixed bond with a $100 face value so that it quotes at par.

• CF t is the cash flow at date t on a fixed-income security.

• Cov(X, Y ) is the covariance between the two stochastic variables X and Y

• CPI t is the Consumer Price Index on date t

• $Conv is the dollar convexity of a bond or a bond portfolio; it is a measure of the

second-order absolute sensitivity of a bond or bond portfolio with respect to small changes in the yield to maturity.

• D is the (Macaulay) duration of a bond or bond portfolio, that is, a measure of its weighted average maturity, where the weights are proportional to the size of the cash flows.

• $Dur is the dollar duration of a bond or a bond portfolio; it is a measure of the first-order

absolute sensitivity of a bond or bond portfolio with respect to small changes in the yield

to maturity.

• E(X) is the mean of the stochastic variable X.

• F t is the price of a futures contract at date t

• f (t, s) is an instantaneous (continuously compounded) forward rate as seen from date t and starting at date s.

• F (t, s, T − s) is a forward zero-coupon rate as seen from date t, starting at date s and with residual maturity T − s (or equivalently with maturity date T ).

• F c (t, s, T − s) is a continuously compounded forward zero-coupon rate as seen from date t, starting at date s and with residual maturity T − s (or equivalently with maturity date T ).

• FV is the face value of a bond.

• IP is the invoice price, that is, the price that the buyer of a futures contract must pay to the seller when a bond is delivered.

• Mis the transpose of matrix M

• M −1 is the inverse matrix of matrix M

• MD is the modified duration of a bond or a bond portfolio; it is a measure of the relative first-order sensitivity of a bond or bond portfolio with respect to small changes in the yield

to maturity.

• p t is the instantaneous probability of default at date t on a corporate bond.

• P t is the market price of a bond or bond portfolio at date t

• P∧t is the theoretical price of a bond or bond portfolio at date t , that is, the price that is obtained from a model of the term structure.

• r t is a spot rate; it can be regarded as the continuously compounded internal rate of return

on a zero-coupon bond with infinitesimal residual maturity.

• R(t, θ) is a zero-coupon rate (pure discount rate), starting at date t for a residual maturity

of θ years (or equivalently maturing at date t + θ).

• R c (t, θ) is a continuously compounded zero-coupon rate, starting at date t with residual

maturity θ (or equivalently with maturity date t + θ).

• RC is the relative convexity of a bond or a bond portfolio; it is a measure of the relative

second-order sensitivity of a bond or bond portfolio with respect to small changes in the yield

to maturity.

• TE is the tracking error, that is, the standard deviation of the difference between the return

on the portfolio and that of the benchmark; it is a measure of the quality of replication in the

context of a bond indexing strategy.

• Var(X) is the variance of the stochastic variable X.

• V (t, θ) is the volatility at date t of the zero-coupon rate with maturity t + θ.

• W is a Brownian motion, a process with independent normally distributed increments.

• [X − K ]+= Max[X − K ; 0 ]

• y is the yield to maturity (YTM ), that is, the single rate that sets the present value of the cash

flows equal to the bond price.

• y c is the current yield, that is, the coupon payment divided by the bond price.

• y d is the yield on a discount basis.

• y m is the yield on a money-market basis.

PA

1 Bonds and Money-Market Instruments

Fixed-income markets are populated with a vast range of instruments In the present chapter, weprovide a typology of the most simple of these instruments, namely bonds and money-marketinstruments, and describe their general characteristics

1.1.1 General Characteristics of Bonds

Definition of a Standard Bond

A debt security, or a bond, is a financial claim by which the issuer, or the borrower, is committed

to paying back to the bondholder, or the lender, the cash amount borrowed, called principal, plus

periodic interests calculated on this amount during a given period of time It can have either astandard or a nonstandard structure A standard bond is a fixed-coupon bond without any embeddedoption, delivering its coupons on periodic dates and principal on the maturity date

For example, a US Treasury bond with coupon 3.5%, maturity date 11/15/2006 and a nominalissued amount of $18.8 billion pays a semiannual interest of $329 million($18.8 billion×3.5%/2)

every six months until 11/15/2006 included, as well as $18.8 billion on the maturity date Anotherexample would be a Euro Treasury bond with coupon 4%, maturity date 07/04/2009 and a nominalissued amount of Eur11 billion, which pays an annual interest of Eur440 million (Eur11 billion×4%) every year until 07/04/2009 included, as well as Eur11 billion on the maturity date

The purpose of a bond issuer (the Treasury Department, a government entity or a corporation)

is to finance its budget or investment projects (construction of roads, schools, development ofnew products, new plants) at an interest rate that is expected to be lower than the return rate ofinvestment (at least in the private sector) Through the issuance of bonds, it has a direct access tothe market, and so avoids borrowing from investment banks at higher interest rates In the context

of financial disintermediation, this practice tends to increase rapidly One point to underscore isthat the bondholder has the status of a creditor, unlike the equity holder who has the status of anowner of the issuing corporation This is by the way the reason why a bond is, generally speaking,less risky than an equity

Terminology and Convention

A bond issue is characterized by the following components:

• The issuer’s name For example, Bundesrepublik Deutschland for a Treasury bond issued in Germany.

• The issuer’s type This is mainly the sector it belongs to: for example, the oil sector, if Total Fina Elf is the bond issuer.

• The market in which the bond is issued It can be the US domestic market, the Euro zone domestic market, the domestic market of any country, the eurodollar market, which corresponds

to bonds denominated in USD and issued in any other country than the US.

• The issuer’s domicile

• The bond’s currency denomination An example is US$ for a US Treasury bond.

• The method used for the calculation of the bond price/yield The method depends on the bond category For US Treasury bonds, the method used is the street convention, which is the standard calculation method used by the market.

• The type of guarantee This is the type of underlying guarantee for the holder of the security The guarantee type can be a mortgage, an automobile loan, a government guarantee

• The maturity date This is the date on which the principal amount is due.

• The coupon type It can be fixed, floating, a multicoupon (a mix of fixed and floating or different fixed) For example, a step-up coupon bond is a kind of multicoupon bond with a coupon rate that increases at predetermined intervals.

• The coupon rate It is expressed in percentage of the principal amount.

• The coupon frequency The coupon frequency for Treasury bonds is semiannual in the United States, the United Kingdom and Japan, and annual in the Euro zone, except for Italy where it

is semiannual.

• The day-count type The most common types are Actual/Actual, Actual/365, Actual/360 and 30/360 Actual/Actual (Actual/365, Actual/360) means that the accrued interest between two given dates is calculated using the exact number of calendar days between the two dates divided

by the exact number of calendar days of the ongoing year (365, 360) 30/360 means that the number of calendar days between the two dates is computed assuming that each month counts

as 30 days For example, using the 30/360 day-count basis, there are 84 days (2 ×30 +24 ) from 01/01/2001 to 03/25/2001 and 335 (11 × 30 + 5 ) from 01/01/2001 to 12/06/2001 Using the Actual/Actual or Actual/365 day-count basis, there are 83 days from 01/01/2001 to 03/25/2001 and 339 days from 01/01/2001 to 12/06/2001 Using the Actual/Actual day-count basis, the period from 08/01/1999 to 09/03/2001 converted in years is 152 365 + 1 + 246

365 = 2 0904 Using

the Actual/365 day-count basis, the period from 08/01/1999 to 09/03/2001 converted in years

is 764 /365 = 2 0931 Using the Actual/360 day-count basis, the period from 08/01/1999 to 09/03/2001 converted in years is 764 /360 = 2 1222 Using the 30/360 day-count basis, the period from 08/01/1999 to 09/03/2001 converted in years is 752 /360 = 2 0888

• The announcement date This is the date on which the bond is announced and offered to the public.

• The interest accrual date This is the date when interest begins to accrue.

• The settlement date This is the date on which payment is due in exchange for the bond It is generally equal to the trade date plus a number of working days For example, in Japan, the settlement date for Treasury bonds and T-bills is equal to the trade date plus three working days On the other hand, in the United States, the settlement date for Treasury bonds and T-bills is equal to the trade date plus one working day In the United Kingdom, the settlement date for Treasury bonds and T-bills is equal to the trade date plus one and two working days,

respectively In the Euro zone, the settlement date for Treasury bonds is equal to the trade date

plus three working days, as it can be one, two or three workings days for T-bills, depending

on the country under consideration.

• The first coupon date This is the date of the first interest payment.

• The issuance price This is the percentage price paid at issuance.

• The spread at issuance This is the spread in basis points to the benchmark Treasury bond (see

the next section called “Market Quotes”).

• The identifying code The most popular ones are the ISIN (International Securities

Identifi-cation Number) and the CUSIP (Committee on Uniform Securities IdentifiIdentifi-cation Procedures)

numbers.

• The rating The task of rating agencies’ consists in assessing the default probability of

corpo-rations through what is known as rating A rating is a ranking of a bond’s quality, based on

criteria such as the issuer’s reputation, management, balance sheet, and its record in paying

interest and principal The two major ones are Moody’s and Standard and Poor’s (S&P) Their

rating scales are listed in Table 1.1 We get back to these issues in more details in Chapter 13.

Table 1.1 Moody’s and S&P’s Rating Scales

Investment Grade (High Creditworthiness)

Note: The modifiers 1, 2, 3 or+, − account for relative standing within the major rating categories.

• The total issued amount It appears in thousands of the issuance currency on Bloomberg.

• The outstanding amount This is the amount of the issue still outstanding, which appears in thousands of the issuance currency on Bloomberg.

• The minimum amount and minimum increment that can be purchased The minimum ment is the smallest additional amount of a security that can be bought above the minimum amount.

incre-• The par amount or nominal amount or principal amount This is the face value of the bond Note that the nominal amount is used to calculate the coupon bond For example, consider

a bond with a fixed 5% coupon rate and a $1,000 nominal amount The coupon is equal to

5 % × $1 ,000 = $50

• The redemption value Expressed in percentage of the nominal amount, it is the price at which the bond is redeemed on the maturity date In most cases, the redemption value is equal to 100%

of the bond nominal amount.

We give hereafter some examples of a Bloomberg bond description screen (DES function), forTreasury and corporate bonds

The T-bond (Figure 1.1), with coupon rate 3.5% and maturity date 11/15/2006, bears asemiannual coupon with an Actual/Actual day-count basis The issued amount is equal to

$18.8 billion; so is the outstanding amount The minimum amount that can be purchased

is equal to $1,000 The T-bond was issued on 11/15/01 on the US market, and interestsbegan to accrue from this date on The price at issuance was 99.469 The first coupon date

is 05/15/02, that is, 6 months after the interest accrual date (semiannual coupon) This bondhas a AAA rating

In comparison with the previous US T-bond, the German T-bond (called Bund ) (Figure 1.2)

with coupon rate 4% and maturity date 07/04/2009 has an annual coupon with an Actual/Actualday-count basis It was issued on the market of the Euro zone, for an amount of Eur11 billion,

on 03/26/1999 The price at issuance was 100.17 The minimum amount that can be purchased

is equal to Eur0.01 The first coupon date was 07/04/2000 The minimum amount that can bepurchased is equal to Eur0.01 This bond has a AAA rating

In comparison with the two previous bonds, the Elf Aquitaine (now Total Fina Elf) bond(Figure 1.3) has a Aa2 Moody’s rating It belongs to the oil sector The issued amount is

Figure 1.1
2003 Bloomberg L.P All rights reserved Reprinted with permission.c

Eur1 billion and the minimum purchasable amount is Eur1,000 The price at issuance was

98.666 It delivers an annual fixed 4.5% coupon rate Its maturity date is 03/23/09 Its spread

at issuance amounted to 39 basis points over the French T-bond (Obligation Assimilable du

Tr´esor (OAT)) with coupon 4% and maturity date 04/25/2009

Market Quotes

Bond securities are usually quoted in price, yield or spread over an underlying benchmark bond

Bond Quoted Price The quoted price (or market price) of a bond is usually its clean price, that

is, its gross price minus the accrued interest We give hereafter a definition of these words Note

first that the price of a bond is always expressed in percentage of its nominal amount.1 When an

investor purchases a bond, he is actually entitled to receive all the future cash flows of this bond,

until he no longer owns it If he buys the bond between two coupon payment dates, he logically

must pay it at a price reflecting the fraction of the next coupon that the seller of the bond is entitled

to receive for having held it until the sale This price is called the gross price (or dirty price or

1 When the bond price is given as a $ (or Eur or £ ) amount, it is directly the nominal amount of the bond multiplied

by the price in % of the nominal amount.