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2004 | Book

Introduction Read chapter Read first chapter

Valuation of Convertible Bonds when Investors Act Strategically

Author: Christian Koziol

Publisher: Deutscher Universitätsverlag

Book Series : Beiträge zur betriebswirtschaftlichen Forschung

Included in: Professional Book Archive

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About this book

The large volume of literature on convertible bonds addresses two basic complexes of problems: • Why and under which conditions do firms issue convertible bonds? • What is the fair value of a convertible bond? Christian Koziol's dissertation deals with the second problem. His dissertation differs from the predominant part of the literature in two aspects. First, he explicitly considers the strategic character of the conversion decision, as the timing and the volume of con­ version affect the wealth of the stockholders and the remaining convertible bond holders. Second, he deals with a more general capital structure, where the firm has subordinated debt outstanding in addition to convertible bonds and stocks. Within this setting, he characterizes and analyzes the optimal conversion strategy and the endogenous prices of convertible bonds, stocks, and the additional debt for three cases: all convertible bonds are held by a monopolist, the convertible bond holders act competitively, and the compet­ itive bond holders are constrained to convert their bonds in one block. The third variant is typical for the option-theoretic valuation of convertible bonds that uses the typical high contact condition for American options.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
A convertible bond is like a corporate bond but with the added feature of being convertible into a specified number of stocks on the notice of its holder. Therefore, convertible bonds represent a complex instrument of corporate finance, as they contain elements of two different financing instruments, namely equity and debt. If the stock price is low and a conversion is unlikely, a convertible bond has the character of a straight bond, but it behaves like stocks when a conversion is very probable.
Christian Koziol
Chapter 2. Convertible Bonds: Markets, Motives, and Traditional Valuation
Abstract
Before we analyze convertible bonds in detail, it is useful to first gain an overview of the convertible bond market and the corresponding market usance. Therefore, the main focus of this section is to consider both the development of the German convertible bond market and the prevalent characteristics of the traded bonds. For this purpose, we consider 61 convertible bonds which were issued in the German convertible bond market in the period from 1952 to 2000. The data set consists of all those convertible bonds which are contained in the “Mannheimer Anleihedatenbank”1 which is part of the Deutsche Finanz-Datenbank.
Christian Koziol
Chapter 3. General Framework for the Analysis of Convertible Bonds
Abstract
To achieve our goal of valuing convertible bonds with a special focus on the conversion behavior, we now describe the considered model framework. Since convertible bonds have numerous complex characteristics, as presented in the previous chapter, we must select the components of the model set up carefully. Our purpose is to build a framework that accounts for all major parameters, on the one hand, but that also abstracts from minor ones obstructing the view on the essential points, on the other hand. Therefore, we regard a typical firm with convertible bonds outstanding, which also has stocks and debt in its capital structure. The reason to deal with both stock and debt is that a conversion might have a different effect on the stock value than on the debt value. Thus, the conversion strategy and the values of both convertible bonds and stocks may show fundamentally different properties caused by the existence of additional debt.
Christian Koziol
Chapter 4. Optimal Conversion Strategies and Valuation of Convertible Bonds at Maturity
Abstract
In this chapter, we examine the optimal conversion strategies at maturity of the convertible bond for the three conversion variants introduced in section 3.1: block conversion, unrestricted conversion, and monopolistic conversion. Additionally, we determine the related values of both the convertible bond and the stock resulting from the corresponding conversion strategy. In the succeeding chapter, we conduct the analogous analysis for a premature conversion date. The reason why we analyze both cases at maturity and prior to maturity is that the conversion decisions at maturity and at a prior conversion date are driven by different determinants. At maturity T, the fact that a later conversion is no longer possible might force a conversion in several cases. Prior to maturity, the investors have to weigh up the advantages of a prompt and a deferred conversion. The analysis is conducted by the following three steps.
Christian Koziol
Chapter 5. Optimal Conversion Strategies and Valuation of Convertible Bonds before Maturity
Abstract
In this chapter, we conduct the corresponding analysis to the previous chapter, but for a conversion date before maturity As the effects at every premature conversion date are basically the same, it is reasonable to employ a two conversion date model to emphasize the basic properties of the conversion strategy and the related asset values. In chapter 7, we will explicitly discuss the differences between the properties at the last and an arbitrary premature conversion date. For the ease of notation, we set the last premature conversion date t N equal to zero throughout this chapter. Since the total conversion volume before time t = 0, which is denoted by K0, is zero if only two conversion dates are considered, we can write for the values W0 (V 0 - , r0, k0), W 0 + (V 0 - , r0, k0), S0 (V 0 - , r0, k0), and D0 (V 0 - , r0, k0) instead of the more sophisticated notation.1
Christian Koziol
Chapter 6. Comparison of the Results for the three Conversion Variants
Abstract
According to the findings in the previous chapters, the properties of the optimal conversion volume and the values of a convertible bond and a stock primarily depend on the underlying conversion variant. As a consequence, the magnitude of the conversion volume and the corresponding values can differ substantially if another conversion variant is assumed. In this section, we first qualitatively compare the different properties of both the conversion volume and the values of a convertible bond and a stock resulting from the three conversion variants block, unrestricted, and monopolistic conversion. This comparison allows us to identify fundamental differences in the behavior of the conversion volume and the asset values, which arise from the underlying conversion variant. Then, we focus on the magnitude of the conversion volume and the asset values to ascertain whether the conversion volume and the asset values are higher for a particular conversion variant than for another one. As for the previous analysis, we distinguish between the point in time at maturity of the convertible bond and before maturity.
Christian Koziol
Chapter 7. Optimal Conversion Strategies and Valuation of Convertible Bonds in a Multi Period Framework
Abstract
The analysis of the previous chapters provided us with the basic properties of the conversion strategy and the asset values at maturity and at the last premature conversion date. In this chapter, we employ the general multi period framework presented in chapter 3 to analyze the properties of the conversion strategy and the values of a convertible bond and a stock for the three conversion variants. This extension will not only allow us to analyze convertible bonds in a static way but also dynamically in the course of the convertible bond’s maturity.
Christian Koziol
Chapter 8. Conclusion
Abstract
In this dissertation, we address two classical and closely related problems in corporate finance: the valuation of convertible bonds and the structure of optimal conversion strategies. In the literature convertible bonds are primarily considered as a portfolio of a straight bond and an American call option with the firm value as the underlying. Its arbitrage- free value is determined under the assumption of a block conversion, i.e. all convertible bond holders convert all their bonds simultaneously. Technically, the valuation problem is solved as a free boundary problem with a high contact condition where applicable.
Christian Koziol
Backmatter
Metadata
Title
Valuation of Convertible Bonds when Investors Act Strategically
Author
Christian Koziol
Copyright Year
2004
Publisher
Deutscher Universitätsverlag
Electronic ISBN
978-3-322-82016-7
Print ISBN
978-3-8244-9132-2
DOI
https://doi.org/10.1007/978-3-322-82016-7