A closed-form solution to the risk-taking motivation of subordinated debtholders

TL;DR

This paper derives a closed-form solution revealing that the value of subordinated debt is hump-shaped with respect to asset risk, impacting understanding of banks' market discipline mechanisms.

Contribution

It provides a novel closed-form analytical model showing the non-monotonic relationship between junior debt value and asset risk.

Findings

Junior debt value is hump-shaped with asset risk.

Implications for market discipline of banks' junior debt.

Contrasts with previous claims of monotonic increase.

Abstract

Black and Cox (1976) claim that the value of junior debt is increasing in asset risk when the firm's value is low. We show, using closed-form solution, that the junior debt's value is hump-shaped. This has interesting implications for the market-discipline role of banks' junior debt.