Random Matrix Approach for Analysis of the Johannesburg Stock Exchange

Abstract

Random Matrix Theory gives us the theatrical framework to analyze computational and statistical properties of cross-correlation matrix. Usually, the cross-correlation matrix is noisy because of the estimation's error for the length and the finite nature of the underlying time series. The present work studies the Johannesburg Stock Market and the effects of eigenvalues filtering techniques on portfolio optimization in the mean-variance framework. The data stock prices are scraped on the Yahoo Financial website from 1st January 2020 to 1st January 2024. Further, we applied the LCPB, PG+, and KR cleaning techniques and observed that the predicted risk was closer to the realized risk in the prediction period. We conclude that the KR method is the best technique. In addition, the Johannesburg Stock Exchange reacts more to bad events than to good ones. This result considerably improves the constructive approach often used by practitioners in this market.