Portfolio Optimization and Random Matrix Theory in Stock Exchange

The purpose of this study was to optimize the stock portfolio based on stochastic matrix theory in the stock market. and igenvalues to answer the question of whether the relevant information will exist using the Marčenko – Pastur distribution.

The data of 31 shares in Tehran Stock Exchange in the period 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 has been done by descriptive-correlation method and is of applied research type.

The results showed: a) Observing the largest distribution of eigenvectors components, it can be seen that there is a strong 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, by identifying and removing non-valuable stocks from the portfolio of portfolio, the risk is reduced. c) Stochastic stock matrix can significantly predict the realized return and risk of the market and therefore has a great ability to explain the risk of market information. d) The inverse participation ratio determines the stocks affecting the special vectors and the main analysis of random matrices is based on adjusting this ratio using random matrix clearance.

Stochastic matrix theory, unlike other portfolio formation methods that determine the weight of each asset in the portfolio, identifies unused stocks and removes them from the stock portfolio, thereby improving portfolio return and risk.