Bond Math, + Website (2^nd Ed.)
The Theory Behind the Formulas
Wiley Finance Series

Bond Math is a quick and easy resource that puts the intricacies of bond calculations into a clear and logical order. This simple, readable guide provides a handy reference, teaching the reader how to think about the essentials of bond math. Much more than just a book of formulas, the emphasis is on how to think about bonds and the associated math, with plenty of examples, anecdotes, and thought-provoking insights that sometimes run counter to conventional wisdom. This updated second edition includes popular Bloomberg pages used in fixed-income analysis, including the Yield and Spread Analysis page, plus a companion website complete with an Online Workbook of multiple choice questions and answers and spreadsheet exercises. Detailed coverage of key calculations, including thorough explanations, provide practical guidance to working bond professionals.

The bond market is the largest and most liquid in the world, encompassing everything from Treasuries and investment grade corporate paper to municipals and junk bonds, trading over $900 billion daily in the U.S. alone. Bond Math is a guide to the inevitable calculations involved in managing bonds, with expert insight on the portfolios and investment strategies that puts the math in perspective. Clear and concise without sacrificing detail, this book helps readers to:

• Delineate the characteristics of different types of debt securities
• Calculate implied forward and spot rates and discount factors
• Work with rates of return, yield statistics, and interest rate swaps
• Understand duration-based risk measures, and more

Memorizing formulas is one thing, but really learning how to mentally approach the math behind bonds is something else entirely. This approach places calculations in context, and enables easier transition from theory to application. For the bond professional seeking a quick math reference, Bond Math provides that and so much more.

Preface to the Second Edition xi

Preface to the First Edition xiii

Chapter 1 Money Market Interest Rates 1

Interest Rates in Textbook Theory 2

Money Market Add-On Rates 3

Money Market Discount Rates 6

Two Cash Flows, Many Money Market Rates 9

A History Lesson on Money Market Certificates 12

Periodicity Conversions 13

Treasury Bill Auction Results 15

The Future: Hourly Interest Rates? 19

Conclusion 21

Chapter 2 Zero-Coupon Bonds 23

The Story of TIGRS, CATS, LIONS, and STRIPS 24

Yields to Maturity on Zero-Coupon Bonds 27

Horizon Yields and Holding-Period Rates of Return 30

Changes in Bond Prices and Yields 32

Credit Spreads and the Implied Probability of Default 34

Conclusion 38

Chapter 3 Prices and Yields on Coupon Bonds 39

Market Demand and Supply 40

Bond Prices and Yields to Maturity in a World of No Arbitrage 44

Some Other Yield Statistics 48

Horizon Yields 52

Some Uses of Yield-to-Maturity Statistics 53

Implied Probability of Default on Coupon Bonds 55

Bond Pricing between Coupon Dates 56

A Real Corporate Bond 59

Conclusion 63

Chapter 4 Bond Taxation 65

Basic Bond Taxation 66

Market Discount Bonds 68

A Real Market Discount Corporate Bond 70

Premium Bonds 74

Original Issue Discount Bonds 77

Municipal Bonds 79

Conclusion 82

Chapter 5 Yield Curves 83

An Intuitive Forward Curve 84

Classic Theories of the Term Structure of Interest Rates 87

Accurate Implied Forward Rates 91

Money Market Implied Forward Rates 93

Calculating and Using Implied Spot (Zero-Coupon) Rates 96

More Applications for the Implied Spot and Forward Curves 99

Discount Factors 105

Conclusion 109

Chapter 6 Duration and Convexity 111

Yield Duration and Convexity Relationships 112

Yield Duration 115

The Relationship between Yield Duration and Maturity 118

Yield Convexity 121

Bloomberg Yield Duration and Convexity 125

Curve Duration and Convexity 129

Conclusion 138

Chapter 7 Floaters and Linkers 139

Floating-Rate Notes in General 140

A Simple Floater Valuation Model 141

A Somewhat More Complex Floater Valuation Model 146

An Actual Floater 149

Inflation-Indexed Bonds: C-Linkers and P-Linkers 157

Linker Taxation 162

Linker Duration 165

Conclusion 171

Chapter 8 Interest Rate Swaps 173

Pricing an Interest Rate Swap 174

Interest Rate Forwards and Futures 178

Inferring the Forward Curve 181

Valuing an Interest Rate Swap 185

Interest Rate Swap Duration 188

Collateralized Swaps 192

Traditional LIBOR Discounting 193

OIS Discounting 196

The LIBOR Forward Curve for OIS Discounting 198

Conclusion 202

Chapter 9 Bond Portfolios 205

Bond Portfolio Statistics in Theory 205

Bond Portfolio Statistics in Practice 208

A Real Bond Portfolio 213

Thoughts on Bond Portfolio Statistics 223

Conclusion 225

Chapter 10 Bond Strategies 227

Acting on a Rate View 228

An Interest Rate Swap Overlay Strategy 233

Classic Immunization Theory 237

Immunization Implementation Issues 242

Liability-Driven Investing 245

Closing Thoughts: Target-Duration Bond Funds 246

Technical Appendix 249

Acronyms 267

Bibliographic Notes 269

About the Author 275

Acknowledgments 277

About the Companion Website 279

Index 281

DONALD J. SMITH is an associate professor of finance at the School of Management, Boston University. Smith specializes in teaching fixed-income markets and risk management courses and has published widely in academic and trade journals, including the Financial Analysts Journal; Journal of Finance; Journal of Money, Credit, and Banking; Journal of Fixed Income; Journal of Financial Engineering; and many others.