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THE TREASURY BOND BASIS OTHER TITLES IN THE MCGRAW HILL LIBRARY OF INVESTMENT AND FINANCE Active Portfolio Management by Richard Grinold and Ronald Kahn Applied Equity Analysis by James English Asset Allocation by Roger Gibson Building Financial Models by John Tjia The Complete Arbitrage Deskbook by Stephane Reverre Convertible Securities by John P Calamos Dynamic Portfolio Theory and Management by Richard Oberuc Equity Management by Bruce Jacobs and Kenneth Levy The Eurodollar Futures and Options Handbook by Galen Burghardt Exchange Rate Determination by Michael Rosenberg Global Invstment Risk Management by Ezra Zask The Handbook of Advanced Business Valuation by Robert F Reilly and Robert P Schweihs The Handbook of Business Valuation and Intellectual Property Analysis by Robert Reilly and Robert Schweihs The Handbook of Credit Derivatives by Jack Clark Francis Joyce Frost and J Gregg Whittaker The Hedge Fund Handbook by Stefano Lavinio Hedging Instruments and Risk Management by Patrick Cusatis and Martin Thomas High Yield Bonds by Theodore Barnhill William Maxwell and Mark Shenkman Implementing Credit Derivatives by Israel Nelken Managing Financial Risk by Charles W Smithson Modeling Financial Markets by Benjamin Van Vliet and Robert Hendry Pricing Derivatives by Ambar Sengupta Pricing Hedging and Trading Exotic Options by Israel Nelken Pricing and Managing Exotic and Hybrid Options by Vineer Bhansali Quantitative Business Valuation by Jay Abrams Risk Management and Financial Derivatives by Satyajit Das Valuing a Business by Shannon P Pratt Robert F Reilly and Robert Schweihs Valuing Intangible Assets by Robert F Reilly and Robert P Schweihs Valuing Small Business and Professional Practices by Shannon Pratt Robert F Reilly and Robert P Schweihs THE TREASURY BOND BASIS An In Depth Analysis for Hedgers Speculators and Arbitrageurs Third Edition GAL EN D BURGHARD T T ERRENCE M B EL T O N MO R T O N LANE JO HN PAPA McGraw Hill New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright 2005 by Galen D Burghardt and Terrence M Belton All rights reserved Printed in the United States of America Except as permitted under the United States Copyright Act of 1976 no part of this publication may be reproduced or dis tributed in any form or by any means or stored in a data base or retrieval system without the prior written permission of the publisher 10 11 12 13 14 TBT IBT 1 9 8 7 6 5 4 3 2 1 ISBN 0 07 145610 4 Appendix to Chapter 5 was originally published January 28 1998 as a Carr Futures now Calyon Financial research note Chapter 7 is a reprint of a journal of Portfolio Management article 1993 by The oumal of Portfolio Management Spring 1993 Reprinted with permission Appendixes C and E are excerpted from JPMorgan Govemment Bond Outlines October 2001 Reprinted with permission of JPMorgan Appendixes D F and G are excerpted from JPMorgan Govemment Bond Outlines April 2005 Reprinted with permission of JPMorgan McGraw Hill books are available at special quantity discounts to use as premiums and sales promotions or for use in corporate training programs For more information please write to the Director of Special Sales Professional Publishing McGraw Hill Two Pem1 Plaza New York NY 10121 2298 Or contact your local bookstore This book is printed on recycled acid free paper containing a minimum of 50 recycled de inked fiber To Birch and Mary CONTENTS List of Exhibits xn1 Preface to the Third Edition XIX Preface to the Second Edition xxi Preface to the First Edition xxv Chapter 1 Basic Concepts 1 Treasury Bond and Note Futures Contract Specifications 2 Definition of the Bond Basis 4 Units 5 Conversion Factors 6 Characteristics of Conversion Factors 6 Futures Invoice Price 7 Carry Profit or Loss of Holding Bonds 11 Theoretical Bond Basis 13 Implied Repo Rate 15 Buying and Selling the Basis 17 Sources of Profit in a Basis Trade 20 Altemative Summary P L 22 RP versus Reverse RP Rates 24 2 What Drives the Basis 27 The Short s Alternatives 27 Search for the Cheapest Bond to De l iver 28 The Best Time to Deliver a Bond 34 Rules of Thumb 36 The Bond Basis Is Like an Option 38 Shifts in the Cheapest to Deliver 41 History of the Most Delivered Bond 46 Examples of Buying and Selling the Cheapest to Deliver Basis 48 The Importance of Embedded Options 50 vii 基本概念 债券基差 转换因子 期货票面价 值 等等 viii CONTENTS 3 The Short s Strategic Delivery Options 51 Structure of the Delivery Process 52 Delivery Process 52 Delivery Month 54 The Switch Option 54 Parallel Changes in Yield Levels 55 Changes in Yield Spreads 57 The End of Month Option 64 Timing Options 70 4 The Option Adjusted Basis 75 An Outline for Pricing the Short s Delivery Options 76 Option Structures 77 Valuing the Switch and End of Month Options 78 Expected Basis Net of Carry 79 A Word about the Value of Early Delivery 80 Practical Considerations 82 Volatility and Distribution of Yield Levels 82 Yield Betas 83 Volatility and Distribution of Yield Spreads 83 Consistency between Forward Prices and Expected Forward Prices 84 Consistency between Delivery Option Values and Futures Options Values 84 Term Repo Specials 84 Anticipated New Issues 84 The Option Adjusted Basis in Practice 85 If the Basis Is Cheap Futures Are Rich 86 The CTD s BNOC Is Pure Option Value 86 Chapter 5 Approaches to Hedging 87 DV01 Hedge Ratios and Competing Objectives 88 Standard Industry Rules of Thu1nb 88 Rule of Thumb 1 89 Rule of Thumb 2 90 Contents The Rules of Thumb in Practice 91 Shortcomings of the Rules of Thumb 95 Spot and Repo DV01s 96 Forward Prices as a Function of Spot Yields and Repo Rates 96 The Short Term Independence of Spot Yields and Term Repo Rates 98 Creating Synthetic Bonds with Forwards and Futures 102 Handling Repo Stub Risk 103 Option Adjusted DV01s 104 Yield Betas 108 Putting It All Together 109 Reckoning the P L of a Hedge 111 Evaluating Hedge Performance 112 Working with Durations 113 Duration of a Futures Contract 116 Appendix to Chapter 5 Better Hedges with Yield Betas 118 Using Yield Betas to Improve Hedges 119 Estimating Yield Betas for Treasury Bonds and Notes 120 Using Yield Betas to Improve Hedges 122 Hedging Something Other Than the Current Long Bond 123 When Yield Betas Can Get You into Trouble 124 Unstable Yield Betas 124 Competing Hedge Ratios When Correlations Are Less Than 1 0 125 Competing Hedge Ratios 125 Sample Calculations 127 6 Trading the Basis 129 Selling the Basis When It Is Expensive 129 Selling the CTD Basis 130 Selling the Basis of Non Cheap Bonds 135 Buying the Basis When It Is Cheap 136 Trading the Basis of Hot Run Bonds 138 Basis Trading When the CTD Is in Short Supply 140 Trading the Calendar Spread 142 Fair Values for Treasury Note Calendar Spreads 143 Profiting from Mispricings in Calendar Spreads 143 Patterns in Calendar Spreads 146 Practical Considerations in Trading the Basis 147 ix X RP Specials 147 Term Financing versus Overnight Financing 150 Short Squeezes 150 The Short Squeeze of 1986 151 Taking a Basis Trade into the Delivery Month 153 Chapter 7 Volatility Arbitrage in the Treasury Bond Basis 157 Overview 158 The Options Embedded in Bond Futures 158 Calls Puts and Straddles 159 Two Arenas for Trading Volatility 161 The Option Adjusted Bond Ba is 162 History of Mispricings 164 Volatility Arbitrage 165 Report Card 167 Examples of Yield Enhancement 169 Leverage 170 Words of Caution 170 Other Applications 171 Chapter 8 Nine Eras of the Bond Basis 173 The Birth and Maturation of Bond Futures 173 Volatility of Yields Since 1977 174 Nine Eras of Trading 174 First Era Cash and Carry 1977 and 1978 176 Second Era Negative Yield curve 1979 through 1981 177 Third Era Positive Carry 1982 through 1984 178 Fourth Era The Golden Age of Yield Enhancement 1985 through 1989 179 Fifth Era Volatility Arbitrage 1990 through 1991 181 CONTENTS Sixth Era The Death of Gamma June 1991 through June 1993 182 Seventh Era The Callables Last Hurrah July 1993 through 1994 186 Eighth Era The Long Dry Spell of the 11 1 4 o 1995 through 1999 188 Ninth Era 6 o Factors and the Rebirth of Bond Contents xi Basis Trading 2000 to 189 Changing of the Guard The Rise of Notes and Fall of Bonds 193 Where Do We Go from Here 195 Chapter9 Non Dollar Government Bond Futures 197 Active Non Dollar Government Bond and Note Futures 198 The Transition to Electronic Trading 200 Portfolio Equivalent Value 201 Contract Specifications 201 Maturities Settlement Windows and Last Trading Days 203 Cash Settlement of SFE s CGB Contracts 203 Up to Date Informdtion 204 Cash Futures Relationships 205 Key Cash Market Features 205 Auction Cycles and Deliverable Sets 207 Basis Reference Sheets for Germany Japan and the United Kingdom 208 Optionality and Futures Mispricings 209 Trading Themes in European Bond Bases 211 Squeezes of CTD Bonds 213 Bonds Exiting the Basket Trades 214 New Issuance 215 A Word of Caution 216 10 Applications for Portfolio Managers 217 Hedging and Asset Allocation 217 Advantages of Using Futures for Hedging and Asset Allocation 218 Managing a Portfolio s Duration with Futures 219 Calculating the Duration of a Portfolio That Contains Futures 220 Example of Targeting Portfolio Duration When Futures Are in the Mix 221 Example of Solving for Hedge Ratios Using Target Durations 221 Synthetic Assets 224 Trade Construction 225 xii How Well Has the Synthetic Asset Strategy Worked 227 Historical Record on Yield Enhancement 229 Variations on a Theme 229 Caveats 232 A Calculating Conversion Factors 233 Appendix B Calculating Carry 235 Conventions in Major Government Bond Markets 237 D German Federal Bonds and Notes Bubills Schatze Bobls and Bunds 243 Japanese Government Bonds JGBs 251 Appendix F CONTENTS Government Bonds of the United Kingdom of Great Britain and Northem Ireland Gilts 257 Appendix G Glossary 263 Index 271 L I S T OF EXHI B ITS Exhibit 1 1 Treasury Futures Contract Specifications 4 Exhibit 1 2 Deliverable Notes and Bonds June 2001 Future 8 Exhibit 1 3 Conversion Factors for Deliverable Bonds 10 Exhibit 1 4 Basis of Cheapest to Deliver with One Deliverable Bond 14 Exhibit 1 5 EFB Basis Quotes 19 Exhibit 2 1 Choosing the Cheapest to Deliver Bond and the Best Time to Deliver It 29 Exhibit 2 2 Supplies of Deliverable Treasury Bonds April 4 2001 30 Exhibit 2 3 Measures of Cheapness to Deliver Trade Date April S 2001 33 Exhibit 2 4 Treasury Deliveries March 2001 35 Exhibit 2 5 Relative Duration and Cheapest to Deliver 37 Exhibit 2 6 Cash Futures Price Relationships With Crossover Points on April 5 2001 39 Exhibit 2 7 Basis of 5 1 2 o Is Like a Call Option on Bond Futures 40 Exhibit 2 8 Basis of 8 7 8 o Is Like a Put Option on Bond Futures 41 Exhibit 2 9 Basis of 7 5 8 o Is Like a Straddle on Bond Futures 42 Exhibit 2 10 BNOC Scenario Analysis June 2001 Bond Futures 44 Exhibit 2 11 History of the Most Delivered Bond 47 Exhibit 3 1 CBOT Delivery Process Chicago Time 53 Exhibit 3 2 Contract Month in Chicago Actual Dates for March 2004 Contract 55 xiii xiv Exhibit 3 3 Cash Futures Price Relationships 56 Exhibit 3 4 Yield Spread Relationships September 2000 September 2001 58 UST OF EXHIBITS Exhibit 3 5 Effect of Yield Spread Changes on 6 3 8 o Basis 59 Exhibit 3 6 Nonsystematic Changes in Yield Spreads 61 Exhibit 3 7 Effect of Change in Yield Spreads on the Cheapest to Deliver 62 Exhibit 3 8 Basis Net of Carry of 11 18 and 8 27 Treasury 63 Exhibit 3 9 How the End of Month Option Works 65 Exhibit 3 10 Bond Price Less Invoice Price and Carry to Last Delivery Day 67 Exhibit 3 11 Projected End of Month Option Payoffs 69 Exhibit 4 1 Vc trious Views of the Basis 76 Exhibit 4 2 Option Time Line 77 Exhibit 4 3 Theoretical Delivery Option Value Equals Expected BNOC at Expiration 78 Exhibit 4 4 Negative Carry and Early Delivery 81 Exhibit 4 5 Volatility of the Treasury Yield Curve Slope 83 Exhibit 4 6 If the Basis Is Cheap Futures Are Rich 85 Exhibit 5 1 Futures Hedge Algebra 89 Exhibit 5 2 Price and Yield Sensitivity Measures Close 4 4 01 Trade 4 5 01 Settle 4 5 01 92 Exhibit 5 3 Bloomberg Illustration for Rule of Thumb Hedge Ratio 94 Exhibit 5 4 Getting from the Current Spot Price to the Forward Price 97 Exhibit 5 5 Treasury Yield Levels versus One Month Repo Rates Oanuary 1988 through October 2003 99 Exhibit 5 6 Weekly Changes in Treasury Yields and Repo Rates January 1988 through October 2003 100 List of Exhibits Exhibit 5 7 Option Adjusted DV01s 105 Exhibit 5 8 Calculating the Option Adjusted DV01 for the June 2001 Bond Futures Contract 107 Exhibit 5 9 Hedging a Portfolio of Bonds 109 XV Exhibit 5 10 Future RiskMeasures Close 4 4 01 Trade 4 5 01 Settle 4 6 01 110 Exhibit 5 11 A Futures Hedge Is Like a Long Straddle 113 Exhibit 5 12 Measuring Duration with Futures in a Bond Portfolio 117 Exhibit A5 1 Shifts in the Yield Curve 119 Exhibit A5 2 The Relationship between Yield Changes and Duration 120 Exhibit A5 3 Estimated Yield Betas 121 Exhibit A5 4 Yield Betas for Selected Deliverable Bonds March 98 Bond Futures Contract 1 12 98 Trade Date 122 Exhibit A5 5 Futures DV01s and Yield Betas March 98 Bond Futures Contract 1 12 98 Trade Date 123 Exhibit A5 6 Yield Betas by Year 124 Exhibit A5 7 Correlations and Standard Deviations of Weekly Yield Changes On the Run Treasury Issues 1990 through 1997 125 Exhibit A5 8 Competing Hedge Ratios 126 Exhibit A5 9 Different Hedges for 100 Million of the OTR 30 Year Treasury January 12 1998 127 Exhibit 6 1 Basis Net of Carry of the Cheapest to Deliver 132 Exhibit 6 2 Cheapest to Deliver 10 Year Basis June 1998 to June 2004 32nds 133 Exhibit 6 3 Projected Basis of 6 1 2 o of 2 10 at December 2001 Expiration Projections as of 9 20 01 135 Exhibit 6 4 Mispricing of Treasury Bond Futures Futures Price Fair Value 32nds 136 Exhibit 6 5 Treasury Bond CTD Switches 137 xvi LIST OF EXHIBITS Exhibit 6 6 High Duration Bond Bases Widen When the Curve Flattens 138 Exhibit 6 7 Yield Spread Patterns around 5 Year Treasury Auctions 139 Exhibit 6 8 Basis and Futures Mispricings April 4 2001 Closing Prices 144 Exhibit 6 9 Calendar Spread Mispricing April 4 2001 Closing Prices 145 Exhibit 6 10 Average Treasury Bond Calendar Spreads 146 Exhibit 6 11 September 1986 Bond Basis 152 Exhibit 7 1 Cash Futures Price Relationships 159 Exhibit 7 2 Basis of 8 1 8 o Is Like a Call Option on Bond Futures 160 Exhibit 7 3 Basis of 10 3 8o o Is Like a Put Option on Bond Futures 161 Exhibit 7 4 Basis of 10 5 8 o Is Like a Straddle on Bond Futures 162 Exhibit 7 5 Option Adjusted Basis Closing Price for Thursday April 23 1992 in 32nds June Futures Price 98 02 163 Exhibit 7 6 The Option Adjusted Bond Basis May 1989 to May 1992 164 Exhibit 7 7 Report Card on Bond Basis Recommendations 1990 166 Exhibit 7 8 Report Card on Proprietary Basis Trades December 1990 to January 1992 16 7 Exhibit 7 9 Simulated Performances of Bond Basis Arbitrage Cheapest to Deliver Issues May 1989 to August 1990 169 Exhibit 7 10 Simulated Rates of Return on a Bond Basis Arbitrage Fund 171 Exhibit 8 1 Bond Yield Yield Curve Slope and Bond Yield Volatility 175 Exhibit 8 2 Average Delivery Dates of Delivered Bonds 176 List of Exhibits Exhibit 8 3 Government Securities Dealer Positions in Bonds and Bond Futures 178 Exhibit 8 4 Average Yield Spread between 30 Year and 20 Year Treasuries 180 Exhibit 8 5 Option Adjusted Bond Basis Lead Contract 7 88 to 7 90 182 Exhibit 8 6 Treasury Bond Yield Spreads 183 xvii Exhibit 8 7 7 1 2 o of 11 16 Yield Less 12 o of 8 13 08 Yield 184 Exhibit 8 8 Delivery History June 1991 to June 1993 184 Exhibit 8 9 Effect of Yield Spread Changes on 7 1 I 2 o Basis 185 Exhibit 8 10 Option Premium in the Bond Basis 186 Exhibit 8 11 September 1993 Bond Futures and Bond Yield Spreads 187 Exhibit 8 12 September 1993 Futures Duration and CTD Switches 187 Exhibit 8 13 The 7 1 8 o of 2 23 Basis 188 Exhibit 8 14 Bond CTD Maturity and Delivery Option Value 189 Exhibit 8 15 Bond CTD Maturity and Delivery Option Value 190 Exhibit 8 16 Net Bases for Deliverable Bonds 191 Exhibit 8 17 Reemergence of Basis Trading Opportunities 192 Exhibit 8 18 Average Daily Trading Volume in Bond and Note Futures 193 Exhibit 8 19 Open Interest in Bond and Note Futures 194 Exhibit 9 1 Global Bond Futures Trading Year Ending September 30 2002 198 Exhibit 9 2 Growth of U S Treasury and German Government Futures Markets 199 Exhibit 9 3 Non Dollar Government Bond Futures Activity 201 xviii Exhibit 9 4 Key Contract Specifications As of September 1 2004 202 LIST OF EXHIBITS Exhibit 9 5 Change in Australian 10 Year CGB Contract Value for a 1 Basis Point Change in the Futures Rate 204 Exhibit 9 6 Exchange Web Addresses for Contract Specifications 205 Exhibit 9 7 Bond Market Characteristics 206 Exhibit 9 8 Basis Reference Sheet Eurobund Bobi and Schatz Futures Pricing January 3 2003 Settlement January 9 2003 208 Exhibit 9 9 Basis Reference Sheet JGB Futures Pricing January 6 2003 Settlement January 10 2003 210 Exhibit 9 10 Basis Reference Sheet U K Gilt Futures Pricing January 3 2003 Settlement January 9 2003 210 Exhibit 9 11 Delivery Option Values for German and U K Bond Contracts 1997 through June 2003 212 Exhibit 9 12 History of Mispricings in German and U K Bond Contracts June 15 1999 to June 13 2003 Units Are Cents 213 Exhibit 9 13 Effect of a CTD Squeeze on the Eurobund Calendar Spread 214 Exhibit 9 14 Moving Out of the Basket Trade 215 Exhibit 10 1 Bid Asked Spreads in Government Bond Markets 218 Exhibit 10 2 Futures Risk Measures Close 4 4 01 Trade 4 5 01 Settle 4 6 01 222 Exhibit 103 Basis Carry and Premium of cheapest to Deliver 6 o Coupon Bond 225 Exhibit 10 4 Examples of Yield Enhancement 228 Exhibit 10 5 Yield Enhancement on Cheapest to Deliver 10 Year June 1998 to June 2004 230 P R EF AC E T O T H E T HIRD EDI T IO N In 2000 when the Chicago Board of Trade adopted a 6 o coupon for calculating conversion factors Terry and I resolved to update The Treasury Bond Basis It has been our good fortune that the theory and insights were sound and that readers were able to make much of the leap from 8 o to 6 o conversion factors without our help Even so we are pleased with this version It has given us a chance to improve our discussions of several aspects of basis valu ation hedging trading and the uses of Treasury futures for portfolio managers Also we have greatly expanded our chapter on non dollar government bond futures and have included several new appendixes that provide useful information on bond markets in Germany Japan and the United Kingdom Several notable changes and innovations have taken place since we released the Revised Edition For one the most actively traded Treasury futures contracts are now the 10 year and 5 year contracts The shift has been so pronounced that this book would be more aptly named The Treasury Note Basis For another the emergence of the credit default swap market has greatly enriched the usefulness of Treasury futures for creating synthetic assets It is now possible by combining Treasury futures with high yielding term cash instru ments and credit default swaps to create synthetic corporate bonds with very desirable return characteristics Both Terry and I have a number of debts that we would like to acknowledge Terry would like to thank Hussein Malik Holly Huffman and Josh Brodie who were a great help in editing manu scripts and helping us bring this project to completion In addition we would like to acknowledge the support of JPMorgan Excerpts from their Government Bond Outlines publication are included in Appendixes C to G Moreover much of the empirical work in this edition makes use of JPMorgan s extensive historical data on bond bases which are available to their clients on their Web site via Data Query I would like to thank Bill Hoskins who greatly increased my understanding of interest rate markets and heightened my appreci ation for the importance of using forward prices for just about xix XX PREFACE TO TilE TI IIRD EDITION everything Also he and Niels Johnson pr

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