Convertible Debt: Financing Decisions and Voluntary Conversion under Ambiguity

• Date: 01 December 2015
• Author: Elettra Agliardi,Rossella Agliardi,Willem Spanjers
• DOI: http://doi.org/10.1111/irfi.12057
• Published date: 01 December 2015

Convertible Debt: Financing

Decisions and Voluntary

Conversion under Ambiguity

ELETTRA AGLIARDI†,ROSSELLA AGLIARDI‡AND WILLEM SPANJERS§

†Department of Economics, University of Bologna, Bologna, Italy

‡Department of Mathematics, University of Bologna, Bologna, Italy and

§Department of Economics, Kingston University, Kingston-upon-Thames, UK

ABSTRACT

This paper integrates ambiguity into a contingent claim model for convert-

ible debt. We study how convertible debt valuation is affected by the ambi-

guity biases of equity holders and debt holders and provide sensitivity

analysis of the bond value to changes in attitude toward ambiguity, firm and

bond parameters. Our results, which are summarized into five main predic-

tions, are consistent with recent empirical evidence and offer a possible

interpretation of some corporate finance puzzles.

Convertibles occupy an important place in the international financial market.1

A convertible debt contract gives the bond holder the option to convert the

bond into another security, usually the common stock of the issuing company.

It has been argued at length that appropriately designed convertible debt can

reduce classical risk-shifting agency problems (both asset substitution and debt

overhang) between equity holders and debt holders (see for example, Green

1984; Brennan and Schwartz 1988; Chakraborty and Yilmaz 2011; Dorion et al.

2014). Convertibles seem particularly well suited to control risk incentives

because of their relative insensitivity to the risk of the issuing firm value. In fact,

convertible bonds align the objectives of firm and equity value maximization,

being hybrid securities that, while retaining most of the characteristics of

straight debt, add the upside potential of the underlying common stock, which

is associated with the conversion or equity option. Thus, these claims impose a

1 The total size of convertibles was on average $US500 billion per year during 2008–2012 with

around 2500 issues. This was about 1.5 the size of the FTSE 250 Index and equated approxi-

mately the 2007–2011 US high yield bond market issuance ($US591 billion). In 2014, the total

size of convertibles of $US268 billion from 2346 issuers became only a small fraction of the

$US9.6 trillion corporate bonds outstanding from almost 7000 issuers (BofA Merrill Lynch,

2014; Fitch Ratings’ Report: CB Funds Dashboard 2014), but the available evidence shows a

growing global convertible market also in developing countries (issuance volumes in Asia

jumped fivefold in 2014, largely driven by China. Source: Thomson Reuters, 2015).

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International Review of Finance, 15:4, 2015: pp. 599–611

DOI: 10.1111/irfi.12057

© 2015 International Review of Finance Ltd. 2015