Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan Dengan Keterbatasan Manusia Dalam Memprediksi Masa Depan Dalam Perspektif Al-Qur`an - Noor Saif Muhammad Mussafi (Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta, 2012)
Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ð‘„ð‘¥with constraintsðœ‡ ð‘‡ ð‘¥ â‰¥ ð‘…andð´ð‘¥ = ð‘. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis.