### PEMBENTUKAN PORTOFOLIO SAHAM OPTIMAL DENGAN MEAN ABSOLUTE DEVIATION PADA DATA SAHAM JAKARTA ISLAMIC INDEX

*Alifia Hana Linda Rachmawati  -  Departemen Statistika, Fakultas Sains dan Matematika, Universitas Diponegoro, Indonesia
Mustafid Mustafid  -  Departemen Statistika, Fakultas Sains dan Matematika, Universitas Diponegoro, Indonesia
Di Asih I Maruddani  -  Departemen Statistika, Fakultas Sains dan Matematika, Universitas Diponegoro, Indonesia

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Abstract
In 2017 to 2020 the Jakarta Islamic Index (JII) showed a positive trend and was quite stable compared to the LQ45 index. The selection of the JII stock index in this study is intended to obtain maximum profits. Investors are expected to create a series of portfolios to get maximum profit. One of the ways to identify stocks for portfolio formation is to use factor analysis. Factor analysis is used to summarize a large number of variables into new, smaller factors. This new factor is called the portfolio. The Mean Absolute Deviation (MAD) method is used for the formation of an optimal portfolio as well as an improvement on the Markowitz method in terms of non-linear (quadratic) mathematical models. The MAD method is the mean of the absolute value of the deviation between the realized return and the expected return. The optimization technique used in the MAD portfolio is the simplex method. Optimizing the objective function by constraining the set of constraints on the simplex method is done by forming a simplex table. Based on the processing using the simplex method, the investment weight for each of the stocks that make up the first portfolio is 30% CPIN shares; 29.23% of JPFA's shares; 10.77% shares of SMGR; and 30% shares in UNVR. Meanwhile, the investment weight of the constituent stocks for the second portfolio is 30% ACES shares; 10% of ERAA's shares; 30% of INCO's shares; 30% of PGAS shares; and 0% WIKA shares. The results of portfolio performance evaluation show that portfolio 2 is better than portfolio 1, by looking at the Sharpe Index for portfolio 2 of 0.0135629 and portfolio 1 of -0.0281177.
Keywords: Factor Analysis; Mean Absolute Deviation; Simplex Method; Sharpe Index

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