Investment affairs is one of the most important factors affecting the economics of countries. Investors have always been looking for optimal investment choices. Investors use one of two active or passive management methods to manage their portfolios. In an active way, the investor tries to find stocks that have higher returns in future moments than other stocks. In order to find such stocks, the investor must well predict stock performance in the coming moments. But passive investment does not require market prediction. The great benefits of the passive investment strategy, including less risk, less managment costs, and the lack of market forecasting, have led to special attention in this way in the world’s capital markets in recent years. In this thesis, in addition to introducing the basic financial concepts and being familiar with the active investment method, we focus mainly on index tracking as one of the most important passive investment methods. The purpose of index tracking is creating a portfolio, which has a similar performance to that of the benchmark index. Sparse tracking is one of the tracking methods. The aim of sparse index tracking is creating a portfolio with small number of stocks, to track a benchmark index. The smaller the number of portfolio components, the less money the investor will need to pay. We also consider diversity in sparse index tracking for the first time for error reduction. In this thesis two different problems are considered for index tracking. In the first problem, the goal is to minimize a multi-objective function (in terms of the total weight of the tracking error, the degree of sparsity, and diversity of the portfolio), taking into account the long only and the capital budget constraints. Then, we deal with the first problem via MaMi technique. In the second problem, in addition to the constraints considered for the first problem, the holding constraint is also considered. This problem has also been dealt with MaMi technique. The simulation results show that with considering the diversity property for portfolio, a portfolio can be designed that track a benchmark index with less error. Key Words: Portfolio, Passive Investment, Index Tracking, MaMi Algorithm.
