Analysis of portfolio optimization with inequality constraints

Abstract

In investing, generally an investor wants an optimum portfolio. This means that the forming portfolio has minimum risk, maximum return or can also be a combination of both with other constraints determined by the investor. These constraints could be in the form of short selling, amount of owning funds, return target, risk target or other constraints. Short selling constraints are inequality in the mathematical model, while other constraints can be in the form of equalities or inequalities. This paper discusses the portfolio optimization with these inequality constraints. In addition, we will provide an example for this portfolio optimization application by analysing portfolio that consists of shares in the LQ45 index. We do this analysis with Solver that is available in Microsoft Excel.