Portfolio Optimization and Random Matrix Theory in Stock Exchange

Abstract

Purpose: This study aimed to optimize the stock portfolio based on stochastic matrix theory in the stock market and to answer whether the relevant information will exist using the Marčenko–Pastur distribution.Methodology: The data of 31 shares in the Tehran Stock Exchange in 2016 - 2019 will be examined for cross-correlation between shares. So, there will be 749 end-of-day prices and 748 logarithms of returns. This research was done using the descriptive-correlation method and is of an applied research type.Findings: The results showed: a) Observing the most extensive distribution of eigenvector components, it can be seen that there is a solid asymmetry to the left of the distribution, meaning that the market responds more to bad events than good events. b) By clearing the correlation matrix, the difference between the predicted and realized risk can be slightly reduced. In other words, the risk is reduced by identifying and removing non-valuable stocks from the portfolio portfolio. c) A stochastic stock matrix can significantly predict the realized return and risk of the market and, therefore, explain the risk of market information. d) The inverse participation ratio determines the stocks affecting the particular vectors, and the primary analysis of random matrices is based on adjusting this ratio using random matrix clearance.Originality/Value: Unlike other portfolio formation methods determining the weight of each asset in the portfolio, stochastic matrix theory identifies unused stocks and removes them from the stock portfolio, thereby improving portfolio return and risk.

Keywords

• portfolio optimization
• random matrix theory
• cross-correlation
• inverse participation ratio
• eigenvectors