Portfolio Optimization Model of Mean-Standard Deviation using Non-Singular Covariance Matrix and Singular Covariance Matrix Methods

Abstract

Investing in the stock sector, investors often face risk problems. Usually to minimize risk, it is done by forming an investment portfolio. In this study aims to optimize the investment portfolio. The data analysed are 8 shares traded on the capital market in Indonesia through the Indonesia Stock Exchange (IDX). Optimization is done by using the Mean-Standard Deviation model with the singular covariance matrix and non-singular covariance matrices to determine the optimal weights of both methods. The results of the portfolio optimization of the Mean-Standard Deviation model with the non-singular covariance matrix method obtained optimum portfolio weights for each share, namely 17.19% for BBCA shares; 26.2% for TKIM shares; 19.97% for BBRI shares; 8.69% for BMRI shares; 3.79% for ADRO shares; 6.50% for GGRM shares; and 17.24% for UNTR shares. Where the optimal portfolio composition is obtained the expected rate of return is 0.18% with a portfolio risk level of 0.07%. While the results of portfolio optimization with the Mean-Standard Deviation model with the singular covariance matrix method, the optimum portfolio weight for each share is 17.22% for BBCA shares; 26.64% for TKIM shares; 9.96% for BBRI shares; 9.96% for BBNI shares; 8.70% for BMRI shares; 3.75% for ADRO shares; 6.52% for GGRM shares; and 17.25% for UNTR shares. Where the optimal portfolio composition is obtained the expected rate of return is 0.18% with a portfolio risk level of 0.07%.