Does limited liability reduce leveraged risk?: The case of loan portfolio management

TL;DR

This paper investigates how incorporating limited liability into loan portfolio models affects risk and return, showing that models with limited liability yield better, less risky investment solutions.

Contribution

It introduces and compares four portfolio models that include and exclude limited liability, demonstrating the benefits of considering limited liability in portfolio optimization.

Findings

Models with limited liability produce higher expected returns.

Limited-liability models result in less risky portfolios.

Theoretical results are supported by an illustrative example.

Abstract

Return-risk models are the two pillars of modern portfolio theory, which are widely used to make decisions in choosing the loan portfolio of a bank. Banks and other financial institutions are subjected to limited liability protection. However, in most of the model formulation, limited liability is not taken into consideration. Accordingly, to address this, we have, in this article, analyzed the effect of including it in the model formulation. We formulate four models, two of them are maximizing the expected return with risk constraint, including and excluding limited-liability, and other two are minimization of risk with threshold level of return with and without limited-liability. Our theoretical results show that the solutions of the models with limited-liability produce better results than the others, in both minimizing risk and maximizing expected return. It has less risky investment than the other portfolio that solves the other model. Finally, an illustrative example is presented to support the theoretical results obtained.