Implementing Markowitz's portfolio theory using a two-step approach

Numerous studies have provided insight into the challenges that investors may confront when making investments, such as allocating resources across a variety of stocks and securities. In response to these challenges, various portfolio theories have been developed. Among them, Modern Portfolio Theory (MPT), developed by Harry Markowitz, is one of the most famous. The purpose of this project is to investigate if MPT can be optimized in a way to achieve a higher return by constructing a fewer number of portfolios. We propose a two-step approach, and we compare the results with the existing theory. Rather than trying to find the optimal portfolio in one step, our two-step approach breaks the optimization process down into two steps, each of which involves a group of randomized portfolios. We find an initial optimal portfolio from the first group and then, in the second step, the final optimal portfolio will be determined from the second group of randomized portfolios which are generated based on the initial optimal portfolio from the first step. Our simulation proves that our two-step approach is more efficient and gives a higher rate of return comparing to the existing approach.