  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.
