Financial portfolio optimization

Abstract

In modern financial markets, the major problem faced by investors or fund managers is the allocation of portfolio. With thousands of stocks available on the stock exchanges, the combination of possible portfolio is endless and impossible for humans to process. This limitation can be overcome using Multi-Objective Evolutionary Algorithms. The purpose of these algorithms is to maximize the return while minimizing the risk involved. In this project, make used of Markowitz’s theory of portfolio selection and Non dominated Sorting Genetic Algorithm II (NSGA-II). Markowitz quantified return and risk of a stock using statistical measures of it expected return and standard deviation. He also suggested using return and risk together to determine the allocation of portfolio on basis of return-risk trade off. As risk and return are two conflicting objectives where one objective is greater than others. Hence, there will not exist a single solution but a set of optimal solution call efficient frontier. By using NSGA-II we will be able to sort out the best possible risk-return stock from the stock market. Once the best possible set of stock is selected, we will apply Markowitz’s theory of portfolio selection. Using its mathematical framework, we will use it to calculate the best portfolio allocation of a given return while minimaxing the risk.