Does Limited Liability Reduce Leveraged Risk?: The Case of Loan Portfolio Management

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 which are maximizing the expected return with risk constraint, including and excluding limited liability, and other two of which are minimizing 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. More specifically, the portfolios that included limited liability are less risky as compared to the portfolios that did not include limited liability. Finally, an illustrative example is presented to support the theoretical results obtained.