Bond Math: The Theory Behind the FormulasISBN: 978-1-57660-306-2
Hardcover
288 pages
July 2011
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CHAPTER 1: MoneyMarket 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? 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
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 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
Inflation-Indexed Bonds: C-Linkers and P-Linkers 149
Linker Taxation 153
Linker Duration 156
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
About the Author 257
Acknowledgments 259
Index 261
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