Loan portfolio management and Liquidity Risk: The impact of limited liability and haircut

TL;DR

This paper develops a novel loan portfolio model considering liquidity risk and limited liability, demonstrating that imposing a haircut constraint reduces liquidity risk and providing numerical evidence for this benefit.

Contribution

The paper introduces a new loan portfolio model with limited liability and a haircut constraint, analyzing its impact on liquidity risk reduction.

Findings

Haircut constraints lead to lower liquidity risk.

The model shows reduced insolvency probability with haircut.

Numerical results support theoretical conclusions.

Abstract

In this article, we consider the problem of a bank's loan portfolio in the context of liquidity risk, while allowing for the limited liability protection enjoyed by the bank. Accordingly, we construct a novel loan portfolio model with limited liability, while maintaining a threshold level of haircut in the portfolio. For the constructed three-time step loan portfolio, at the initial time, the bank raises capital via debt and equity, investing the same in several classes of loans, while at the final time, the bank either meets its liabilities or becomes insolvent. At the intermediate time step, a fraction of the deposits are withdrawn, resulting in liquidation of some of the bank's assets. The liquidated portfolio is designed with the goal of minimizing the liquidation cost. Our theoretical results show that model with the haircut constraint leads to lesser liquidity risk, as compared to the scenario of no haircut constraint being imposed. Finally, we present numerical results to illustrate the theoretical results which were obtained.