Contingent capital with repeated interconversion between debt‐ and equity‐like instruments

• Published date: 01 March 2019
• Author: Yanping Cai,Zhiming Zhao,Zhaojun Yang
• Date: 01 March 2019
• DOI: http://doi.org/10.1111/eufm.12165

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358 © 2017 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/eufm Eur Financ Manag. 2019;25:358–379.

DOI: 10.1111/eufm.12165

ORIGINAL ARTICLE

Contingent capital with repeated interconversion

between debt- and equity-like instruments

Yanping Cai1Zhaojun Yang2Zhiming Zhao3

1School of Business Administration,

Hunan University, Changsha, China.

Email: caiyanping@hnu.edu.cn

2Department of Finance, Southern

University of Science and Technology,

Shenzhen 518055, China.

Email: yangzj@sustc.edu.cn

3Business School, Xiangtan University,

Xiangtan 411105, China.

Email: zmzhao@xtu.edu.cn

Funding information

The research reported in this paper was

supported by the National Natural

Science Foundation of China (Project

Nos. 71371068 and 71171078).

Abstract

This paper introduces a new form of contingent capital, con-

tingent convertible securities (CCSs), which might repeat-

edly convert between debt- and equity-like instruments de-

pending on financial conditions. We derive explicit prices of

corporate securities, assuming the cash flow is modeled as

a geometric Brownian motion. We present an explicit value

of the increased tax shields due to CCSs. We provide an ex-

plicit optimal capital structure when CCSs are issued and

interestingly, the ratio of the optimal straight bond coupon

to CCS coupon is constant and independent of the firm’s

financial conditions. All the conclusions hold true also for

contingent convertibles.

KEYWORDS

contingent capital, repeated interconversion, capital structure

JEL CLASSIFICATIONS

G12 , G32

1INTRODUCTION

In general, a firm will have both equity and debt in its capital structure. This is because there are two

market imperfections: a tax deduction on interest expense and bankruptcy costs so that, with default,

a fraction of the value of the firm is lost. Consequently, a firm may have a strict but limited incentive

to issue debt and the optimal capital structure must be based on the trade-off between the value of tax

shields and of bankruptcy costs.

With regard to firms (e.g., banks) that are ‘too important to fail’, however, we must give much more

weight to bankruptcy costs. In particular, after the global financial crisis of 2007/2009, the new global

The authors wish to thank Editor John Doukas, and an anonymous referee for the constructive comments, which greatly helped

in improving the paper. The authors are grateful for helpful comments from George Pennacchi, Pab Jotikasthira, Zhenyu Wang,

Xiaolin Wang and participants on the ‘Financial Intermediary Capital’ session at the CICF 2013 meetings and the ‘International

Workshop on Credit Risk Management’ at Beihang University 2015. The order of the authors is alphabetical in the surnames

and the contributions of the authors are the same. All remaining errors are the authors’ responsibility.

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CAI ET AL.3

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bank regulatory standard, Basel III, introduced stricter capital requirements for banks to reduce default

risk to an acceptable level. Naturally, excessive debt financing is prohibited and so the benefits of tax

shields are decreased. To increase tax shields while keeping default risk at a low level, a proposal that

has recently received much attention is to induce banks to have contingent convertible bonds (CoCos

or CCBs, henceforth).

CoCos, also known as contingent capital, are bonds that can automatically convert into equity if

the issuer’s financial health deteriorates to a pre-specified threshold or trigger. In China, for the first

time, Tianjin Binhai rural commercial bank issued RMB 1.5 billion yuan of the write-down contingent

capital in July 2013. In the first half year of 2016, 55 rural commercial banks in China issued 51.25

billion yuan of the write-down contingent capital, which triples the amount issued in 2015. According

to Securities Times in China, the total newly-issued volumes of the contingent capital in China are

344.85, 269.86 and 227.35 billion yuan in 2014, 2015 and 2016, respectively. European banks issued

a total of €7.7 billion in CoCo bonds during the first quarter of 2017.

All papers in the literature assume that once CoCos convert into equity, they keep the form of equity

all the time until the firm goes bankrupt, i.e., they will never convert back into debt. We think that this

assumption could be improved. Intuitively, if this form of contingent capital can convert repeatedly

between debt and equity, the firm will get much more tax shielding while default risk does not increase.

Motivated by this observation, we relax the assumption and develop a new type of contingent capital,

called contingent convertible security (CCS, henceforth), in a Leland (1994)-style model. CCSs are

like CoCos but differently the former can repeatedly and automatically convert between debt and

equity depending on two specified values of a financial situation index, say the level of the cash flow

generated by the issuing firm or the corresponding unlevered firm’s value.

We derive closed-form expressions of the equilibrium prices of all corporate securities and an ex-

plicit optimal capital structure when the cash flow of a firm is modeled as a geometric Brownian motion.

The ratio of the optimal straight bond coupon to CCS coupon is a constant independent of the firm’s

financial conditions. We show that while CCSs decrease default risk like CoCos, they significantly in-

crease the value of the issuing firm by dynamically adjusting capital structure without incurring extra

adjustment costs. All the conclusions hold true for CoCos since they are simply a special type of CCSs.

The rest of the paper is organized as follows. Section 2 reviews the literature and develops intuition

about why CCSs are good instruments. Section 3 sets up the model. Section 4 presents the pricing of

corporate securities. Section 5 derives optimal capital structure and fixes the value of the increased

tax shields due to CCSs. Section 6 provides numerical simulations and comparative statics. Section 7

concludes. Some expressions are relegated to Appendix A.

2LITERATURE REVIEW AND INTUITIVE ANALYSIS

In this section, we give a brief overview of the literature and provide intuitive justification for why

CCSs are feasible.

On the design of contingent capital, there are two crucial issues: one is how to specify its ownership

stake, i.e., the fraction of equity into which it converts from a debt-like instrument. Berg and Kaserer

(2015) and Tan and Yang (2017) analyze the effect of the ownership stake of CoCos on equity holders’

incentives. The other issue is how to determine the conversion threshold of contingent capital for

its activation, which is considered by many papers in the literature. For example, McDonald (2013)

evaluates a form of contingent capital for financial institutions that converts from debt into equity if

two conditions are met: the firm’s stock price is at or below a trigger value and the value of a financial

institution index is also at or below a trigger value. Sundaresan and Wang (2015) consider the design

of contingent capital with a stock price trigger for mandatory conversion and the problem on multiple