eprintid: 37242 rev_number: 7 eprint_status: archive userid: 12397 dir: disk0/00/03/72/42 datestamp: 2020-01-07 06:30:07 lastmod: 2020-01-07 06:30:07 status_changed: 2020-01-07 06:30:07 type: article metadata_visibility: show contact_email: epha.diana@uin-suka.ac.id creators_name: Supandi, Epha Diana creators_name: Rosadi, Dedi creators_name: Abdurakhman, Abdurakhman title: THE OPTIMAL PORTFOLIO WEIGHTS USING THE PROPORTIONAL TYPE ESTIMATORS ispublished: pub subjects: Matematika divisions: artkl full_text_status: public keywords: Portfolio, error estimation, loss function note: Prof Dedi Rosadi, Ph.D. UGM. Yogyakarta. Indonesia Dr. Abdurakhman, M.Si. UGM. Yogyakarta. Indonesia abstract: Error estimation in both the expected returns and the covariance matrix hamper the construction of optimal mean-variance portfolio model. In order to overcome this problem, we consider the class of proportional type estimators. The sensitivity of the proposed estimators to errors is measured by the expected loss function (the risk function). The simulation study is conducted when multivariate returns are normally distributed and serially independent. Furthermore, simulation study is complemented by an investigation of the ex post excess returns for empirical datasets, i.e., average, standard deviation, Sharpe ratio, and utility. It turns out that the unbiased proportional estimator and the maximum likelihood estimator are underperformed compared to “the dominant” estimator. date: 2017-07-01 date_type: published publication: Far East Journal of Mathematical Sciences volume: 101 number: 3 publisher: Pushpa Publishing House, Allahabad, India pagerange: 643-657 id_number: http://dx.doi.org/10.17654/MS101030643 refereed: TRUE issn: ISSN: 0972-0871 official_url: http://www.pphmj.com referencetext: [1] M. J. Best and R. R. Grauer, On the sensitivity of mean-variance efficient portfolios to changes in asset means: some analytical and computational results, Rev. Fin. Stud. 4(2) (1991), 315-342. [2] M. Broadie, Computing efficient frontiers using estimated parameters, Ann. Oper. Res. 45 (1993), 21-58. [3] S. Ceria and R. A. Stubbs, Incorporating estimation errors into port folio selection: robust portfolio construction, J. Asset Manage. 7 (2006), 109-127. [4] V. K. Chopra and W. T. Ziemba, The effects of errors in means, variances, and covariances on optimal portfolio choice, J. Portfolio Manage. 19(2) (1993), 6-11. [5] V. DeMiguel and F. J. Nogales, Portfolio selection with robust estimation, J. Oper. Res. 57(3) (2009), 560-577. [6] V. DeMiguel, A. Martin-Utrera and F. J. Nogales, Size matters: optimal calibration of shrinkage estimators for portfolio selection, J. Bank. Fin. 37 (2013), 3018-3034. [7] V. Golosnoy and Y. Okhrin, Multivariate shrinkage for optimal portfolio weights, European J. Fin. 13(5) (2007), 441-458. [8] J. D. Jobson and B. Korkie, Estimation of Markowitz efficient portfolios, J. Amer. Stat. Assoc. 75 (1980), 544-554. [9] R. Kan and G. Zhou, Optimal portfolio choice with parameter uncertainty, J. Fin. Quant. Anal. 42 (2007), 717-727. [10] T. Kinkawa, Estimation of optimal portfolio weights using shrinkage technique, Dissertation, School of Science and Technology, Keio University, 2010. [11] O. Ledoit, Essays on risk and return in the stock Market, Doctoral Theses, Massachusetts Institute of Technology, 1995. [12] H. Markowitz, Portfolio selection, J. Fin. 7(1) (1952), 77-91. [13] R. O. Michaud, The Markowitz optimization enigma: is optimized optimal?, Fin. Anal. J. 45(1) (1989), 31-42. [14] H. Mori, Finite sample properties of estimators for the optimal portfolio weight, J. Japan Stat. Soc. 34(1) (2004), 27-46. [15] Y. Okhrin and W. Schmid, Distributional properties of portfolio weights, J. Econ. 134(1) (2006), 235-256. [16] A. Palczewski and J. Palczewski, Theoretical and empirical estimates of meanvariance portfolio sensitivity, European J. Oper. Res. 234(2) (2014), 402-410 citation: Supandi, Epha Diana and Rosadi, Dedi and Abdurakhman, Abdurakhman (2017) THE OPTIMAL PORTFOLIO WEIGHTS USING THE PROPORTIONAL TYPE ESTIMATORS. Far East Journal of Mathematical Sciences, 101 (3). pp. 643-657. ISSN ISSN: 0972-0871 document_url: https://digilib.uin-suka.ac.id/id/eprint/37242/1/Far%20East%20Journal.pdf