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A Theoretical and Empirical Study of Stock Purchase Warrants and Convertible Bonds

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A Theoretical and Empirical Study of Stock Purchase Warrants and Convertible Bonds Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1970 A Theoretical and Empirical Study of Stock Purchase Warrants and Convertible Bonds. Jerry Don Miller Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Miller, Jerry Don, "A Theoretical and Empirical Study of Stock Purchase Warrants and Convertible Bonds." (1970). LSU Historical Dissertations and Theses. 1794. https://digitalcommons.lsu.edu/gradschool_disstheses/1794 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. 71-3426 HILLER, Jerry Don, 1939- A THEORETICAL AND EMPIRICAL STUDY OF STOCK PURCHASE WARRANTS AND CONVERTIBLE BONDS. The Louisiana State University and Agricultural and Mechanical College, Ph.D., 1970 Economics, finance University Microfilms, Inc., Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED A THEORETICAL AND EMPIRICAL STUDY OF STOCK PURCHASE WARRANTS AND CONVERTIBLE BONDS A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy m The Department of Business Finance and Statistics by Jerry Don Miller B.S., North Texas State University, 1962 M.B.A., North Texas State University, 1963 May, 19 70 ACKNOWLEDGEMENTS The author is greatly indebted to his committee mem­ bers# Professors Donald E. Vaughn, Stanley W. Preston# Robert A. Rentz, James W. Pattillo, and Edmund R. Gray for their con­ structive council and encouragement. Professor Vaughn offered many helpful suggestions throughout this research work. His succinct comments frequently exposed the kernel of the situa­ tion and led to vast improvements in the overall content of this work. Both Professors Preston and Rentz gave freely of their time in'reviewing and commenting on early drafts of this work. Professor Preston was instrumental in directing my attention to•the topic of this research......... A note of appreciation is extended to two special individuals, Martin E. Rooney and Donald E. Kirsopp. Profes­ sor Rooney's method of research set the goal for this disser­ tation. Mr. Kirsopp wrote the first computer program used in this research and punched the first'cards. Finally, my total gratitude is expressed to my family. My parents, Anton and Imogene, and my brother, Tom, supported by educational endeavors. My wife, Jeane, typed the first draft and provided a climate conducive to intel­ lectual pursuit in an otherwise tenuous environment. My ii three sons, Mark, Trent, and Shane made the largest sacrifice; .they gave up their father for a period of over one year. TABLE OF CONTENTS Page LIST OF TABLES........................................ ix LIST OF C H A R T S .................................... X Chapter I. INTRODUCTION ................................. 1 Historical Use of These Securities .... 2 Purpose of the Study .................... 5 Scope of the Study .................. 6 Methodology ........ .............. 7 Preview of the Study ......................10 II. THE NATURE OF WARRANTS AND CONVERTIBLES BONDS..................................... 12 Introduction .................. 12 Basic Elements of Stock Purchase Warrants* 13 Unique Features of Warrants ........... 14 The Theoretical Value of a Warrant. 16 L e v e r a g e ............................ 25 Leverage Indicator .................. 26 The Origin of Warrants................ .. 29 *» ’ iv i Chapter Page Basic Elements of Convertible Bonds .... 33 Premiums on Convertible Bonds .............. 33 Theoretical Valuation of Convertible Bonds • * • 36 Analysis of Debt V a l u e ...................39 Yield Curve Concept ....................... 39 Anti-Dilution Clause For Warrants and Convertible Bonds ............................ 43 Issue of Additional Common Stock .... 46 Stock Splits and Stock Dividends ........ 51 Merger and Acquisition of Assets .... Through Issuance of Common Stock . 52 Issuance of Additional Options ........... 54 Other Methods of Dilution................. 55 Accounting For Warrants and Convertible Bo nds .............. ........................ Straight Debt Value and Option Value ■ • 53 Straight Debt or Stock ..................... 5q Importance of Opinion No. 1 5 .............. ^ III. REVIEW OF SELECTED RESEARCH PROJECTS • • • 65 Introduction to Stock Purchase War­ rant Models .............................. v Chapter Page Paul Ilallingby's Approach tc Warrant V a l u a t i o n ..............................66 Russell Morrison's Basic Formulas . 68 Imputed Return.......... * ............. 68 Break-even Price .................... 69 GUynemer Giguere's Mathematical Model . 72 Kassouf's Norm Value Model ........... 75 Investment Bankers Study of Warrants. 80 John Shelton's Multiple Regression I S t u d y ....................................84 Introduction to Convertible Bond Models. 89 Eugene Brigham's Convertible Bond Model. 89 Probability Distribution Model for Con­ vertible Bonds ............................. 93 A Regression Model for Convertible Bond P r e m i u m s ....................................96 1 Concluding Remarks ............................ 100 IV. AN EVALUATION MODEL FOR STOCK PURCHASE WAR­ RANTS . Introduction ...................................103 Development of the M o d e l ..................... 103 Influence of Prior Research Projects * • *103 Structuring the Time to Expiration . 109 vi Chapter Page Normalization of the Dependent and In­ dependent Variables ...................... 113 Selecting the Proper Statistical Approach 115 The Final Model for Warrants............... 118 Testing the Empirical Warrant Model .... 123 Purpose of the Test ....................... 12 3 Structure of the Test ............. 124 Decision Rules for the Models ........... 12 5 Unique Characteristics of Each Model . 126 Return on Investment....................... .. Results of the Test ....................... .. Conclusion.................................... .. V. AN EVALUATION MODEL FOR CONVERTIBLE BONDS ■ 138 Introduction ................................ 138 Development of the M o d e l ............. 139 Value of the Conversion Feature ........... 139 Normalization of the Variables............. 140 Selection of the Observations ............. 141 Structure of the Model. ........... 144 The Final Model for Convertible Bonds . 146 Testing the Empirical Model . ............. 150 Selecting the Proper T e s t .................. 150 Results of the T e s t ................ 153 vii Chapter Page Conclusion VI. SPECIAL TRADING TACTICS FOR WARRANTS AND CONVERTIBLE BONDS .......................... 159 Introduction ................................. 159 Arbitrage Verses Hedging ................ Importance of Short Selling .............. 161 Various Types of Arbitrage-Hedges . .163 Use of the Empirical Warrant Model in Locating Arbitrage-Hedges ............... 168 Use of the Convertible Bond Model in Locating Arbitrage-Hedge Candidates * *174 C o n c l u s i o n .................................... 178 VII. SUMMARYt CONCLUSIONS, AND RECOMMENDATIONS • 180 S u m m a r y .........................................180 Conclusions .................................... 185 Recommendations................. * ............ 190 BIBLIOGRAPHY 19 2 APPENDICES ...................... 198 Appendix A ...................... 198 Appendix B .................................. 210 Appendix C ..................... 222 V I T A 23 3 viii LIST OF TABLES Table Page I. Volume of Public Debt Securities (1924- (1930)......................................... 3 II. Volume of Domestically Underwritten Public Financing (1964-1969) 3 III. Earnings Per Share Stimulus Through Tender O f f e r ............................................ 32 IV. Impact of Common Stock Price On Earnings Per S h a r e ....................................... 62 V. Kassouf's Norm Value and Normal Conditions. 78 VI. Normalized Warrant Values ..................... 82 VII. Shelton's Approach In Determining Warrant Values......................................... ... VIII. List of Warrants Used In Each Classification, 211 IX. Summary of Test Results For Warrants........... 130 X. Summary of Test Results for Convertible B o n d s ........................................... 254 XI. Simulated Double Arbitrage-IIedge................269 XII. Simulated Double and Reverse Double Arbitrage-Hedge .............................. 271 XIII. Illustration of Arbitrage-Hedge on Soon To Expire Warrants .............................. 273 XIV. Simulated Arbitrage-Hedge in Sperry Rand XV. Arbitrage-Hedge in Selected Convertible Bonds . ............... ix LIST OF CHARTS Chart Page 1. Speculative And Intrinsic Values of Warrants..................................... 18 2. Samuelson's Theoretical Values of Warrants..................................... 21 3. The Nature of Convertible Bond Premiums . 35 4. Theoretical Price Range For Convertible B o n d s .............................. 37 5. Flat and Down-Sloping Yield Curves. 41 6. Graphic Comparison of Kassouf and Giguere Models ....................................... 79 7. Brigham's Model For Convertible Bonds . 90 8. Graphic Representation of the Warrant M°de l ...................................
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