# Bond Math: The Theory Behind the Formulas

ISBN: 978-1-57660-306-2
288 pages
July 2011
A guide to the theory behind bond math formulas

Bond Math explores the ideas and assumptions behind commonly used statistics on risk and return for individual bonds and on fixed income portfolios. But this book is much more than a series of formulas and calculations; the emphasis is on how to think about and use bond math.

Author Donald J. Smith, a professor at Boston University and an experienced executive trainer, covers in detail money market rates, periodicity conversions, bond yields to maturity and horizon yields, the implied probability of default, after-tax rates of return, implied forward and spot rates, and duration and convexity. These calculations are used on traditional fixed-rate and zero-coupon bonds, as well as floating-rate notes, inflation-indexed securities, and interest rate swaps.

• Puts bond math in perspective through discussions of bond portfolios and investment strategies.
• Critiques the Bloomberg Yield Analysis (YA) page, indicating which numbers provide reliable information for making decisions about bonds, which are meaningless data, and which can be very misleading to investors
• Filled with thought-provoking insights and practical advice, this book puts the intricacies of bond math into a clear and logical order.
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Preface xi

CHAPTER 1: MoneyMarket Interest Rates 1

Interest Rates in Textbook Theory 2

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? 20

Conclusion 22

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 33

Credit Spreads and the Implied Probability of Default 35

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 49

Horizon Yields 53

Some Uses of Yield-to-Maturity Statistics 55

Implied Probability of Default on Coupon Bonds 56

Bond Pricing between Coupon Dates 57

A Real Corporate Bond 60

Conclusion 63

CHAPTER 4: Bond Taxation 65

Basic Bond Taxation 66

Market Discount Bonds 68

A Real Market Discount Corporate Bond 70

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 86

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

Conclusion 105

CHAPTER 6: Duration and Convexity 107

Yield Duration and Convexity Relationships 108

Yield Duration 111

The Relationship between Yield Duration and Maturity 115

Yield Convexity 118

Bloomberg Yield Duration and Convexity 122

Curve Duration and Convexity 127

Conclusion 135

CHAPTER 7: Floaters and Linkers 137

Floating-Rate Notes in General 138

A Simple Floater Valuation Model 139

An Actual Floater 143

Conclusion 161

CHAPTER 8: Interest Rate Swaps 163

Pricing an Interest Rate Swap 164

Interest Rate Forwards and Futures 168

Inferring the Forward Curve 170

Valuing an Interest Rate Swap 174

Interest Rate Swap Duration and Convexity 179

Conclusion 184

CHAPTER 9: Bond Portfolios 185

Bond Portfolio Statistics in Theory 185

Bond Portfolio Statistics in Practice 189

A Real Bond Portfolio 194

Thoughts on Bond Portfolio Statistics 206

Conclusion 207

CHAPTER 10: Bond Strategies 209

Acting on a Rate View 211

An Interest Rate Swap Overlay Strategy 215

Classic Immunization Theory 218

Immunization Implementation Issues 224

Liability-Driven Investing 226

Closing Thoughts: Target-Duration Bond Funds 227

Technical Appendix 231

Acronyms 249

Bibliographic Notes 251