Abstract
In risk management and portfolio optimization it is important to know which assets move individually or in certain groups to make a diversified portfolio. The statistical uncertainty of the correlation matrix is the main problem into the optimization of a financial portfolio. Indeed, estimates of correlations are often noisy particularly in stress period and unreliable as estimation horizons are always finite. Another drawback in the classical estimation of correlations is that time series are estimated on historical data and prediction based on past data is very difficult, since finding elementary structures in data which are valid and persistent in the future is not really easy. The Markowitz optimization approaches of portfolio suffer from theses estimation errors. From the perspective of machine learning, new approaches have been proposed in the literature of applied finance. Among these techniques, clustering has been considered as a significant method to capture the natural structure of data. The objective of this research is to use data mining approaches for identifying the best clustering indicators for building optimal portfolios. Clustering is an empirical procedure for grouping financial assets into homogeneous groups. The aim of cluster analysis is to maximize similarity within groups of assets and minimize similarity between groups. The similarities and dissimilarities are based on the attribute values and frequently involve distance measures. There are different techniques used for clustering, some are Partitioning based technique, Density based technique, Model based technique, Grid based technique. In this research we consider the symbolic approach based histogram-valued data and clusters as a new approach for investment funds portfolio optimization. Firstly, it is based on aggregating individual level data into group-based summarized by symbols. In our case, symbols are histogram-valued data taking into account variability inside groups. Secondly, for partitioning, we use dynamical clustering which is an extension of K-means where, instead of the means, we use other kinds of centers called ‘kernel’ distributions in our case. After clustering, stock samples are selected from these clusters to create funds of funds optimal portfolios which impose the lowest risk measured in terms of Conditional Value at Risk for a certain return. Funds’ Portfolios are compared during the period of 2008–2016 using the conditional Sharpe ratio and the 2017 year is used to validate our results out of sample. In this research we show that the use of symbolic data clustering algorithms can improve the reliability of the portfolio in terms of the risk adjusted performance.
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Appendix
Appendix
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Period 2010–2012
Intra-class inertia for a number of classes between 2 and 8
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Period 2013–2014
Intra-class inertia for a number of classes between 2 and 8
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Period 2015–2016
Intra-class inertia for a number of classes between 2 and 8
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Terraza, V., Toque, C. (2021). Cluster Analysis for Investment Funds Portfolio Optimisation: A Symbolic Data Approach. In: Zopounidis, C., Benkraiem, R., Kalaitzoglou, I. (eds) Financial Risk Management and Modeling. Risk, Systems and Decisions. Springer, Cham. https://doi.org/10.1007/978-3-030-66691-0_5
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