Family of K-Means Clustering for Robust Mean-Variance Portfolio Selection: A Comparison of K-Medoids, K-Means, and Fuzzy C-Means

This paper proposes a robust portfolio construction method based on cluster analysis. The fundamental data and the daily closing price of the LQ45 index listed on the Indonesia Stock Exchange were employed for the empirical study. Firstly, using fundamental data of LQ45, three clusters are formed using K-Medoids clustering. K-Means and fuzzy C-Means cluster analysis were also performed as a comparison. Secondly, two stocks with the highest Sharpe ratios from each cluster were chosen to form an optimum portfolio. The optimum portfolio was obtained using non-robust (classic) and robust estimate approaches. The robust estimations used are the Fast Minimum Covariance Determinant (FMCD) and the S estimation. A robust process allows for creating the best-performing portfolio from many stocks, especially as outliers largely impact the outcomes. This study revealed that the portfolio produced by combining K-Medoids clustering and robust FMCD estimation outperformed those created using other approaches.