ConvertibleArbitrageInsights and Techniques for Successful Hedging

NICK P. CALAMOS

John Wiley & Sons, Inc.

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ConvertibleArbitrage

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ConvertibleArbitrageInsights and Techniques for Successful Hedging

NICK P. CALAMOS

John Wiley & Sons, Inc.

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Copyright 2003 by Nick P. Calamos. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New JerseyPublished simultaneously in Canada

No part of this publication may be reproduced, stored in a retrieval system, ortransmitted in any form or by any means, electronic, mechanical, photocopying,recording, scanning, or otherwise, except as permitted under Section 107 or 108 ofthe 1976 United States Copyright Act, without either the prior written permissionof the Publisher, or authorization through payment of the appropriate per-copy feeto the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA01923, 978-750-8400, fax 978-750-4470, or on the web at www.copyright.com.Requests to the Publisher for permission should be addressed to the PermissionsDepartment, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008, e-mail: permcoordinator@wiley.com.

Limit of Liability/Disclaimer of Warranty: While the publisher and author haveused their best efforts in preparing this book, they make no representations orwarranties with respect to the accuracy or completeness of the contents of thisbook and specifically disclaim any implied warranties of merchantability of fitnessfor a particular purpose. No warranty may be created or extended by salesrepresentatives or written sales materials. The advice and strategies containedherein may not be suitable for your situation. You should consult with aprofessional where appropriate. Neither the publisher nor author shall be liable forany loss of profit or any other commercial damages, including but not limited tospecial, incidental, consequential, or other damages.

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Quotations of Warren E. Buffett are excerpted with permission from previouslycopyrighted material.

Library of Congress Cataloging-in-Publication Data

Calamos, Nick, P. 1961Convertible arbitrage: insights and techniques for successful hedging/Nick P.

Calamos.p. cm. (Wiley finance series)

Includes index.ISBN 0-471-42361-0 (CLOTH)

1. Hedging (Finance) 2. Arbitrage. I. Title. II. Series.HG6024.A3C345 2003332.645dc212003000580

Printed in the United States of America10 9 8 7 6 5 4 3 2 1

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http://www.copyright.comhttp://www.wiley.com

To my wife Kim, my parents Joan and Angelo, and my children, Zach, Katie, Kristie, and Cole

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This books target audience includes beginner and intermediate convertiblespecialists, hedge fund consultants, and convertible securities traders. Itshould also be a useful handbook for retirement and endowment plan spon-sors that invest in hedge funds and individual investors who would like tounderstand more about what their convertible hedge manager is doing andwhat the risks may be.

I want to thank John Calamos, Sr. for the opportunity he provided me20 years ago to join Calamos Asset Management, which was then a smallspecialist convertible securities investment shop managing $35 million inclient assets. Today, the firm has grown to become Calamos Investments,one of the largest convertible managers in the country as well as a respectedgrowth-equity, convertible-arbitrage, and high-yield manager with morethan $13 billion in assets under management. Over the years John has beena mentor and consultant to me in business as well as in my personal life. Hehas offered me many opportunities and challenges to grow professionallyand his commitment to constant improvement and lifetime learning hasbeen an example that I hope to pass on to my children. Put simply, Johnsguidance has been instrumental in my career and provided the foundationfor this book.

I also want to thank my wife Kim, as in all things over the past 22 years,for her love, patience, and support during the many weekends, evenings, andvacations spent in my office writing this book.

A number of colleagues at Calamos Investments have had a hand in thecompletion of this book. I want to thank Jeff Kelley who spent many hoursediting and improving my rough draft. His hard work and talent allowedthis book to progress quickly and provided much better flow than wouldotherwise have been the case. I also want to thank Marilyn Dale, who coor-dinated most of the communication and scheduling with the publisher, andkept me on schedule. Finally, I want to thank Tony Onorati and Chris Hart-man who helped with many of the graphs and charts in the book and JeffScudieri who reviewed drafts and provided valuable feedback.

Acknowledgments

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CHAPTER 1Convertible Arbitrage: An Overview 1Convertible Arbitrage: A Brief History 1Why Hedge with Convertibles? 6Convertible Arbitrage Performance 7What About Risks? 12Basics of Convertible Securities 15Risk-Reward Analysis 18Methods of Valuation 18Convertible Profile Graph 22Basics of Convertible Arbitrage 23Multiple Convertible Structures 26Appendix 1.1 32

CHAPTER 2Valuation 34Convertible Valuation Models 34Binomial Option Model 34

CHAPTER 3The Greeks 48Measures of Risk 48Delta () 48Gamma () 51Vega (v) 55Theta () 57Rho () 59More on Volatility 61Chi () 64Omicron () 65Upsilon (u) 67Phi (f) 69Mandatory Convertible Greeks 70

Contents

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CHAPTER 4Credit and Equity Considerations 74Credit Evaluation 74Credit Analysis and Equity Market Feedback 76Asset Value Credit Evaluation 79Cash Flow and Valuing a Business 85Business Valuation Model 85I. Cash Inflows: Capital Employed 87II. Cash Outflows: Economic Profit 94III. Cash-Inflow Model 100IV. Intrinsic Business Value 106

CHAPTER 5Convertible Arbitrage TechniquesDelta Hedging 110Delta Neutral Hedge (Long Volatility) 112Delta Estimates versus Theoretical Deltas 117Dynamic Rebalancing of the Delta Neutral Hedge 117Delta Neutral Hedge on Leverage 120Delta HedgeCurrency Hedge Overlay 122Appendix 5.1 128Appendix 5.2 131

CHAPTER 6Gamma Capture Hedging 134Capturing the Gamma in a Convertible Hedge 134Bearish Tilt Gamma Convertible Hedge 141Bearish Gamma Hedge on Leverage 143The Gamma Tilt Hedges Role in a Market Neutral Portfolio 145

CHAPTER 7Convertible Option Hedge Techniques 148Covered or Partially Covered Convertible Call Option Hedge 151Long Convertible Stock Hedge with Call Write Overlay 154Synthetic BondLong Busted Convertible with Call Write

and Long Out-of-the-Money Call for Protection 157Convertible Stock HedgePut Purchase Provides Additional

Downside Protection 161Convertible Hedge Call Write with Protective Long Put 165Mandatory Convertible PreferredStock Hedge with

Call Write Overlay 169

2 Contents

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CHAPTER 8Convertible Asset Swaps and Credit Default Swaps 172Convertible Asset SwapsExtracting Cheap Options from

Investment-Grade Convertibles 172The Mechanics of Convertible Asset Swapping 173Swap Hedge Setup 176Convertible Bond Credit Default SwapTransfer Credit Risk

in a Hedge 179Appendix 8.1 185

CHAPTER 9Non-traditional Hedges 194The Reverse Hedge 194Call Option Hedge: Monetization of a Cheap Embedded Call

Option 199Stock Hedge to Capture Cheap or Free Put Options 200Convergence Hedges 210Merger and Acquisition Risk Arbitrage Trades 217Reset Convertibles (or Death Spiral Convertibles) 218Capital Structure Hedge 218Distressed Convertible Hedge or Negative Gamma Hedge

Opportunities 220Basket Hedging Equity Delta 231Synthetic Worksheet Hedge 234Dividend Reduction Convertible Hedge 236Trading Desk Value Added 239Trade Execution 240Appendix 9.1 242Appendix 9.2 244Take-Over RisksAn Example 244

CHAPTER 10Portfolio Risk Management 248Balance Sheet Leverage 250Scenario Analysis 252Hedging Systematic Risks with Index Options 255Hedging Interest Rate RiskYield Curve Shifts 257Hedging Volatility with Volatility Swaps 258Hedging Omicron with Volatility Swaps 263Hedging Omicron with Credit Default Swap Basket or Short

Closed End Funds 265

Contents 3

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Rough Spots for Convertible Arbitrage 266Managing the Convertible Arbitrage Manager 271

Glossary 273

Index 289

4 Contents

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There was a time when the word arbitrage brought to mind apicture of a mysterious realm in finance which few people seemedto be inclined or at least to have the knowledge to discuss. I knewin a general way that profits depended upon price differences, butI believed that it was with lightning speed at a nerve-racking pacethat computations, purchases, and sales must be executed in orderto reap a profit.

Meyer H. Weinstein, Arbitrage in Securities

CONVERTIBLE ARBITRAGE: A BRIEF HISTORY

The practice of convertible arbitrage includes the traditional purchase of aconvertible while shorting its underlying stock, but also includes warranthedging, reverse hedging, capital structure arbitrage, and various other tech-niques that exploit the unique nature of the global convertible and warrantmarketplace. While the quantitative modeling, arcane mathematics, andhedge fund strategies affiliated with such techniques may make the practiceseem a symbol of the latest in financial innovation, it has actually beenaround for more than a century, practically since the launch of convertiblesecurities. Convertible securities came into being as a way to make securitiesmore attractive to investors. Convertible bonds are not new; issuers and in-vestors have been using them since the 1800s. During the nineteenth century,the United States was what we would now classify as an emerging market.It was not easy to gain access to capital in a rapidly growing country. Theconvertible clause was added first to mortgage bonds to entice investors tofinance the building of the railroads. The Chicago, Milwaukee & St. PaulRailway, for example, used many convertible issues for financing between

CHAPTER 1Convertible Arbitrage:

An Overview

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