Methods and models for index tracking optimization

In the ever-evolving landscape of finance, the quest for optimal portfolio management has been a continuous pursuit. The process of selecting the right mix of assets to maximize returns while minimizing risk has long been at the core of investment strategy. With the advent of computational tools and the availability of financial data, this endeavor has witnessed a paradigm shift. Today, investors and financial analysts have at their disposal a plethora of quantitative techniques and software applications for portfolio optimization, each with its own strengths and limitations. This thesis delves into the realm of portfolio optimization by exploring and comparing the efficacy of two distinct methodologies—Monte Carlo simulation and Sequential Least Squares Quadratic Programming (SLSQP)—in the context of stock portfolio management. By examining and contrasting these three approaches, we aim to shed light on the advantages, drawbacks, and real-world applicability of each. Furthermore, we will assess the performance of these optimization models by comparing them with the Italian stock index IT40. The primary objectives of this study are to assess the performance of these optimization models, analyze their outcomes, and provide insights into their practical implications for financial decision-makers. Additionally, we seek to determine how diversification, a fundamental concept in portfolio theory, influences the effectiveness of these models in constructing portfolios that achieve the delicate balance between risk and return.