Interior Point Algorithm in Multi-objective Portfolio Optimization: GlueVaR Approach

Investors, in their pursuit to maximize expected returns, minimize risks in their stock portfolios, and achieve the desired benefits, require suitable methods and criteria to select stocks for their portfolios and allocate capital. One of the most important things in stock portfolio optimization is the use of a suitable optimization algorithm. The function of the multi-objective portfolio optimization model is quadratic. Quadratic functions are a special class of nonlinear programming problems in which the objective function is quadratic and the constraints are linear. Common algorithms for quadratic programming require certain parameters with fixed values. Such algorithms are extensively employed for solving real-world problems, particularly in financial contexts. The major objective of this research is to apply the inner point mathematical algorithm to optimize the stock portfolio and to use this algorithm to address the multi-objective portfolio optimization problem. With the GlueVaR risk measurement criterion, the problem of portfolio optimization takes into account the two objectives of maximizing returns during the research period and reducing investment risk, reassuring investors to make better and more accurate decisions about the final object of this research.

The necessary information for this study was provided by 50 active companies listed on the Tehran Stock Exchange. However, due to the availability of their daily prices during the study period, the final number of companies considered was reduced to 33. The inner point mathematical approach was utilized to optimize the model with the dual objectives of increasing efficiency and reducing risk. To demonstrate the effectiveness and capability of the algorithm in solving the problem of two-objective optimization, its output was compared with other risk measurement criteria such as variance, and value at risk (VaR). The investment risk in the stock portfolio was also calculated using the GlueVaR criterion. Comparing conditional (CVaR) was also done. The GlueVaR criterion has the advantage over the other criteria since it takes the investor's attitude toward risk into account. This advantage formed the basis of the calculation method in this research according to the mentioned algorithm.

According to the research, value at risk (VaR) and conditional value at risk (CVaR) perform better than other variance risk measures in the portfolio optimization model with the GlueVaR risk measure and the internal point optimization method for determining the most effective border. Additionally, when applied to optimization problems, the internal point method discovers the optimal point with fewer iterations, providing strong evidence of the algorithm's effectiveness.

Based on the current findings, it is evident that the internal point algorithm is effective in resolving stock portfolio optimization issues. Additionally, the GlueVaR risk measurement criterion outperforms VaR, variance, and CVaR for most investors with diverse risk and return preferences