فاطمه لکزایی

Stocks are fundamental instruments in capital markets, and understanding their interdependencies is crucial for effective investment and risk management. This study adopts a network-based framework to examine the structure and dynamics of the U.S. stock market by constructing correlation networks through analytical methods rather than purely data-driven approaches. Specifically, the Minimum Spanning Tree (MST) and Planar Maximally Filtered Graph (PMFG) techniques are employed to model the relationships among 371 constituent stocks of the S&P 500 index, using daily closing prices from January 11, 2013, to December 12, 2022. The key empirical findings indicate that MST and PMFG effectively capture the hierarchical organization of financial markets. These network structures facilitate the identification of stock clusters and central nodes, providing insights into systemic risk and potential contagion during periods of financial turbulence. Furthermore, the identified network topology supports enhanced portfolio diversification by enabling the selection of stocks across different clusters or based on centrality metrics. Temporal analysis of the network evolution also reveals shifts in market conditions and sectoral rotations. Additionally, the study integrates Markowitz’s portfolio optimization framework by applying the Sharpe ratio as the performance criterion. The resulting optimized portfolio achieves an expected annual return of 37.61%, with a volatility of 14.15%, yielding a Sharpe ratio of 2.6581 demonstrating robust risk-adjusted performance. In conclusion, MST and PMFG offer valuable tools for capturing market structure, informing portfolio construction, and enhancing risk assessment, thereby contributing to more resilient investment strategies.

An investment portfolio is a collection of financial assets consisting of investment tools such as stocks, bonds, and bank deposits, among others, which are held by a person or a group of persons. In this research, we use the Markowitz model to optimize the stock portfolio and identify the minimum spanning tree (MST) structure in the portfolio consisting of 50 stocks traded in the TSE. The observable which is used to detect the minimum spanning tree (MST) of the stocks of a given portfolio is the synchronous correlation coefficient of the daily difference of logarithm of closure price of stocks. The correlation coefficient is calculated between all the possible pairs of stocks present in the portfolio in a given time course. The goal of the present study is to obtain the taxonomy of a portfolio of stocks traded in the TSE by using the information of time series of stock prices only. In this research, report results obtained by investigating the portfolio of the stocks used to compute 50 stocks of the Iran Stock Exchange in the time period from January 2012 to October 2022.