美联储或有资本的优化设计 2024

Optimal Design of Contingent Capital

Abstract

This paper proposes a framework for designing contingent capital contracts (CoCos) that are either optimal or incentive-compatible for equity holders, implement a unique equilibrium, and result in an optimal capital structure for firms. The authors consider CoCos with equity conversion and write-down modalities. Equity conversion CoCos are optimal, while write-down CoCos are incentive-compatible. Both types of CoCos can be implemented by specifying a capital ratio rule that triggers conversion and qualifies as additional tier 1 (AT1) capital. A policymaker can use a normative criterion to determine the desired capital ratio rule. Implementing such CoCos increases the firm's optimal levered value and resilience to bankruptcy.

Introduction

The paper addresses the design of CoCos to ensure they act as a line of defense rather than exacerbate crises. It highlights the 2023 Credit Suisse acquisition by UBS, where CoCos were written down to zero, creating tension in the market and raising questions about CoCo design.

Key Design Aspects

1. Equity Conversion Modality: The CoCo design is optimal, maximizing the value of equity holders' claims. There exists an endogenously optimal conversion threshold ( A^*_{\text{c}} ) that maximizes equity value. The conversion threshold is unique and can be implemented by mapping the capital ratio rule to a dilution factor.
2. Write-Down Modality: The contract can be designed to implement a unique and incentive-compatible equilibrium. Unlike the equity conversion modality, the write-down modality does not admit a well-defined optimal trigger. The CoCo contract is triggered by a preset threshold in a capital ratio rule, ensuring AT1 eligibility and maintaining equity value.

Results

1. Equity Conversion Modality:

   • Endogenous Optimal Conversion Threshold: The optimal conversion threshold ( A^*_{\text{c}} ) maximizes equity holders' claims. Equity holders are indifferent to conversion due to smooth pasting.
   • Implementation: The optimal CoCo can be implemented by mapping the capital ratio rule to a dilution factor, ensuring the firm's asset level equals ( A^*_{\text{c}} ) upon conversion.

2. Write-Down Modality:

   • Unique and Incentive-Compatible Equilibrium: The contract is designed to be triggered by a preset threshold in a capital ratio rule, ensuring AT1 eligibility and maintaining equity value.
   • Behavior: Equity holders prefer immediate write-down, while CoCo holders prefer delayed conversion to benefit from coupon payments.

Conclusion

Implementing optimally designed CoCos in the firm's capital structure increases its optimal levered value and resilience to bankruptcy. These CoCos are time-consistent, alleviating stakeholder renegotiation risks and removing the uncertainty of discretionary triggers.

Keywords

• Contingent Convertible Debt
• Bail-in Debt
• Capital Structure
• Capital Requirements
• Bank Regulation
• Bank Capital

Figures

• Figure 1: The ICE BofA Contingent Capital (CoCo) index and the ICE BofA US High Yield Index diverged significantly after UBS's acquisition of Credit Suisse, highlighting the impact of CoCo design on market dynamics.

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This summary provides a clear overview of the key points and findings of the paper, focusing on the design and implementation of optimal CoCos.