PERBANDINGAN OPTIMISASI PORTOFOLIO METODE MEAN- VARIANCE DENGAN METODE MEAN-SEMIVARIANCE

SEPTI WAHYUNI, Yunita Wulansari, S.Si., M.Sc.

2013 | Skripsi | STATISTIKA

Pada tahun 1952 Markowitz memelopori penggunaan metode Mean-Variance untuk permasalahan optimisasi portofolio, yang hingga saat ini metode Mean- Variance sangat populer untuk digunakan. Namun, metode Mean-Variance ini memiliki kekurangan bahwa data return harus berdistribusi normal. Faktanya, sangat sulit mendapatkan data saham yang memiliki return berdistribusi normal. Markowitz (1959) berpendapat bahwa “analisis berdasarkan semivariansi cenderung menghasilkan portofolio yang lebih baik dibandingkan portofolio berdasarkan variansi”. Walaupun begitu, mengapa analisis portofolio dengan Mean-Variance lebih sering digunakan daripada Mean-Semivariance? Hal ini dikarenakan, tidak seperti matriks variansi-kovariansi yang bersifat simetrik dan eksogen, matriks semivariansi-semikovariansi bersifat tidak simetrik dan endogen. Sehingga dalam penghitungan bobot harus digunakan algoritma numerik yang jarang digunakan oleh para praktisi dan akademisi. Oleh karena itu, digunakanlah pendekatan heuristik yang berfungsi untuk mengubah matriks semivarian-semikovarian menjadi simetrik dan eksogen. Sehingga penghitungan bobot portofolio Mean-Semivariance bisa menggunakan metode yang sama dengan Mean-Variance. Optimisasi portofolio menggunakan Mean-Semivariance tidak memerlukan asumsi distribusi apapun, sehingga lebih mudah penggunaannya dibandingkan Mean-Variance. Penghitungannya pun mudah dan dengan pendekatan heuristik dihasilkan matriks semivarian-semikovarian yang memiliki bentuk dan penyelesaian yang sama dengan matriks varian-kovarian milik metode Mean- Variance. Pada skripsi ini akan dilakukan perbandingan empiris antara optimisasi portofolio Mean-Semivariance dengan optimisasi portofolio Mean-Variance. Lalu dalam studi kasus dilakukan pembentukan portofolio Mean-Variance dan juga portofolio Mean-Semivariance dengan kombinasi dari beberapa aset finansial yang berupa saham.

In 1952 Markowitz pioneered the use of Mean-Variance method for portfolio optimization problems, for which Mean-Variance method is very popular to use. However, Mean-Variance method has drawbacks that the return data should be normal distributed. In fact, it is very difficult to get data that has normal distributed return. Markowitz (1959) argued that “analysis based on semivariance tend to produce better portfolios than those based on variance”. However, why is the analysis of the portfolio with Mean-Variance more often used than Mean-Semivariance? This is because, unlike covariance matrix that is symmetric and exogenous, semicovariance matrix is asymmetric and endogenous. Thus in calculating the weights, numerical algorithms must be used that is rarely used by practitioners and academics. Therefore, heuristic approach used which fuction to change semicovariance matrix to be symmetric and exogenous. So calculating the weights of Mean-Semivariance portfolio could use the same with Mean-Variance portfolio. Portfolio optimization using Mean-Semivariance does not require any distribution assumptions, making it much easier to use than Mean-Variance. The calculations are easy and with heuristic approach obtained semicovariance matrix which has the same form and finishing with covariance matrix of Mean-Variance. In this thesis the empirical comparison will be made between Mean-Semivariance portfolio optimization with Mean-Variance portfolio optimization. Then in case studies portfolio formation carried out Mean-Variance portfolio and Mean- Semivariance portfolio with combination of multiple financial assets.

Kata Kunci : portofolio, Mean-Semivariance, pendekatan heuristik