The research entitled “Developing of Mean-Variance Portfolio Modeling Using Robust Estimation and Robust Optimization Method” was conducted by Epha Diana Supandi under the guidance of Prof.Dr. rer. nat. Dedi Rosadi, S.Si., M.Sc. and Dr. Abdurakhman, S.Si., M.Si in 2018.
The following is the abstract of this research.
The person who pioneered the basic theory of portfolio selection was Markowitz (1952) who shed light on the concept of mean-variance (MV) in allocating the asset and management of active portfolio. Mean vector and variance-covariance matrix must be discovered at hand as an entry in the procedure of developing optimum portfolio of MV model requiring estimation. There are a number of estimation techniques to apply parameter estimation, all of which are not free from estimation error. As a pivotal input in the making of mean-variance portfolio model, estimation error will impinge on the output of optimum portfolio formation. Some researchers have built robust portfolio, ie the portfolio that can reduce the estimation error of the mean vector and variance-covariance matrix of the portfolio MV’s model. There are two standard approaches in the formation of the optimal robust portfolio through robust estimation and robust optimization approaches The formation of optimum portfolio through robust estimation can be carried out in two stages. The first stage, the estimation of mean vector and covariance matrix constructed by using robust estimators. After the robust estimator came to light, it is being input to the MV portfolio model to attain robust estimation portfolio of MV model. This research selects two robust estimators with high breakdown namely S estimator, Constrained-M (CM) and Fast Minimum Covariance Determinant (FMCD). Unlike robust statistic approach, the theoretical basis of robust optimization is to reduce the sensitivity of optimum portfolio due to uncertain estimation of mean vector and variance-covariance matrix. The parameter input of robust portfolio optimization is considered uncertain situated in the uncertainty set. Afterwards, the optimum solution of this model which is accomplished for the worst solution occurs at the minimum expected return and maximum risk. In the robust optimization, the uncertainty set has a pivotal role for determining parameter. Until now there is no fixed certainty as how to determine uncertainty set accurately. In this study, a new approach is carried out to construct the set of uncertainty for the mean vector and variance-covariance matrix ie using block Bootstrap percentile method. This method is appropriately used because the resampling is performed on return data, therefore the structure of dependencies between data is not lost. The determination of optimum portfolio in the value of the worst cases of the robust optimization becomes one drawback of this method. One of the potential consequences of this approach is a decision strongly influenced by the extreme observations (outlier) in the set of uncertainty. As a result, the portfolio will tend to be too pessimistic and unable to attain optimum result. To overcome these obstacles, then this research also attempts to develop MV portfolio by combining robust optimization with robust estimator. The research leads to unbiased formulation for optimum portfolio of MV model, portfolio model formulation for robust estimation, and development of portfolio model of robust optimization. The research also builds computation program to ease the end-user in utilizing the resulted theory. Afterwards, the resulted portfolio models will be applied in the registered share data as a blue chip share. The last stage of the research is the performance comparison of those portfolios by using in-samples and out-samples analysis.
Keywords: portofolio mean-variance, penduga robust, optimasi robust, Bootstrap