Page 292 - Contributed Paper Session (CPS) - Volume 2

CPS1863 La Gubu et al.

Portfolio selection using cluster analysis and fast
minimum covariance determinant estimation
method
1,2
1
1
La Gubu , Dedi Rosadi , and Abdurakhman
1 Mathematic Department Gadja Mada University, Yogyakarta Indonesia
2 Mathematic Department Halu Oleo University, Kendari Indonesia

Abstract
In this paper a robust and efficient portfolio selection method is presented.
The stocks is firstly grouped into several clusters. Here in this paper, in
particular we apply the hierarchy agglomerative complete linkage clustering
method. After the clustering process, stocks are chosen to represent each
cluster to build a portfolio. The selected stocks for each cluster are the stocks
which has the best Sharpe ratio. The optimum portfolio is determined using
the Fast Minimum Covariance Determinant (FMCD) estimation method. Using
this procedure, we may obtain the best portfolio efficiently when there are
large number of stocks involved in the formulation of the portfolio. On the
other hands, this procedure also robust against the possibility of outlier
existence in the data. For empirical study, we use the stocks from the
Indonesia Stock Exchange, which included in the LQ-45 indexed, contain 45
stocks, which will give relatively large portfolio combination. The results
showed that after the clustering, LQ-45 stocks can be grouped into 7 groups
of stocks. Furthermore, it was also found that portfolio performance built on
the robust FMCD estimation method was better than the portfolio
performance of the classic MV model for all risk aversion value.

Keywords
Portfolio; Cluster analysis ; FMCD; Markowitz model; Sharpe ratio.

1. Introduction
The strategy in utilizing statistical measures from historical return data,
namely the mean, variance and covariance, has become a basic principle in the
formation of the classic mean-variance (MV) portfolio model by Markowitz
(1952). Markowitz proposes a portfolio model that uses the mean and variance
of asset returns to express the trade-off between portfolio returns and risks.
This model is expressed as an optimization problem with two conflicting
objectives. That is, the expected return on results from the portfolio needs to
be maximized, on the other hand, portfolio risk represented by the variance of
returns from different assets, needs to be minimized.
Various studies have been carried out to solve and develop the Markowitz
portfolio model. All of that is done to adapt the existing model to the
conditions of financial market factors and the demands of capital market
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