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CPS1863 La Gubu et al.
portfolio Sharpe ratio with FMCD estimation is 0.2248905 and the classic MV
portfolio ratio Sharpe is 0.1464506. So for risk aversion = 0.5, the
performance of the MV portfolio with robust FMCD estimation is better than
the classic MV portfolio. If we look further, it turns out that for all risk aversion
values γ, FMCD's estimated portfolio return is higher than the classic MV
portfolio return. Unlike risk, for all values of , the classic MV portfolio risk is
better than FMCD's portfolio. However, the Sharpe ratio of FMCD's portfolio
ratio is higher than the classic MV portfolio for all values . Therefore, we can
concluded that the performance of the MV portfolio with robust FMCD
estimation was better than the classic MV portfolio.

4.2 Conclusions
This paper shows how to integrate clustering techniques into portfolio
management and building systems to get an efficient portfolio. The clustering
process can reduce very significantly the time required to select the best stocks
for the portfolio because stocks from similar categories can be easily grouped
into one cluster. The best performing stocks from each cluster are then chosen
as representations of the cluster to build the portfolio. The results showed that
45 stocks included in the LQ-45 group was into 7 clusters. Stock as a
representation of each cluster then used to form a portfolio using the MV
model with FMCD estimation. The portfolio performance formed by using the
MV portfolio model with robust FMCD estimation is then compared with the
portfolio performance formed using the classic MV portfolio model. The
results showed that the performance of the MV portfolio with robust FMCD
estimation was better than the classic MV portfolio for all risk aversion values
γ.
For future research, it will be interesting to use other robust estimates and
compare portfolio performance that builds up using these estimates.

Acknowledgments
I thank to Indonesia Endownment Fun for Education (Lembaga Pengelola
Dana Pendidikan, LPDP) Ministry of Finance of the Republic of Indonesia for
the scholarship funds given for my Doctoral program at the Mathematics
Department of Gadjah Mada University.

References
1. Chen, L.H., and Huang, L. (2009). Portfolio optimization of equity mutual
funds with fuzzy return rates and risks, Expert Systems with Applications,
36, 3720-3727.

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