Efficient Frontier Mean – Semivariance Menggunakan Metode Sequential Quadratic Programming (sqp)

Reiza Krisnaviardi, Deni Saepudin, Aniq Atiqi Rohmawati

Abstract


Abstrak

Pada tugas akhir ini dibahas mengenai penerapan metode SQP (Sequential Quadratic Programming) untuk mencari efficient frontier dari portofolio mean-semivariance. Portofolio mean-semivariance merupakan perbaikan dari portofolio mean-variance karena portofolio mean-variance hanya mengukur risiko berdasarkan variansinya. Artinya rata – rata penyimpangan nilai return dari nilai acuannya (ekspektasi return) dapat bernilai lebih besar atau pun lebih kecil. Efficient frontier yang dibentuk pada tugas akhir ini menggunakan saham – saham yang tergabung dalam LQ45 dengan mengambil data harga saham per minggu selama sepuluh tahun dari bulan November 2007 – Desember 2017. Kemudian dari data harga saham tersebut diperoleh nilai return saham secara time series sebagai informasi dasar untuk proses perhitungan selanjutnya. Kemudian metode SQP (Sequential Quadratic Programming) digunakan untuk menyelesaikan masalah optimasi dengan kendala. Hasil dari eksperimen pada tugas ini akhir ini menunjukkan efficient frontier yang terbentuk dari portofolio mean-semivariance sedikit berbeda dengan efficient frontier portofolio mean-variance, dimana nilai semivariance pada efficient frontier portofolio meansemivariance berada di bawah efficient frontier portofolio mean-variance.

Kata kunci : efficient frontier, SQP, semivariance, mean – variance, mean – semivariance

Abstract

In this final project, we discussed the application of SQP (Sequential Quadratic Programming) method to find efficient frontier of mean-semivariance portfolio. The mean-semivariance portfolio represents an improvement over the mean-variance portfolio because the mean-variance portfolio only measures risk by its variance. This means that the average deviation of the return value from the reference value (expectation return) can be worth bigger or even smaller. Efficient frontier formed in this final task using shares - shares that are incorporated in LQ45 by taking stock price data per week for ten years from November 2007 - December 2017. Then from the stock price data is obtained value of stock return in time series as basic information for further calculation process. Then the SQP (Sequential Quadratic Programming) method is used to solve the optimization problem with constraints. The results of experiments on this final task show that the efficient frontier formed from the mean-semivariance portfolio is slightly different from the efficient frontier portfolio mean-variance, in which the semivariance value of the efficient frontier portfolio mean-semivariance falls below the efficient frontier portfolio mean-variance.

Keywords: efficient frontier, SQP, semivariance, mean – variance, mean – semivariance

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