Correlation based clustering of the Stockholm Stock Exchange

Abstract: This thesis present a topological classification of stocks traded on the Stockholm Stock Exchange based solely on the co-movements between individual stocks. The working hypothesis is that an ultrametric space is an appropriate space for linking stocks together. The hierarchical structure is obtained from the matrix of correlation coefficient computed between all pairs of stocks included in the OMXS~30 portfolio by considering the daily logarithmic return. The dynamics of the system is investigated by studying the distribution and time dependence of the correlation coefficients. Average linkage clustering is proposed as an alternative to the conventional single linkage clustering. The empirical investigation show that the Minimum-Spanning Tree (the graphical representation of the clustering procedure) describe the reciprocal arrangement of the stocks included in the investigated portfolio in a way that also makes sense from an economical point of view. Average linkage clustering results in five main clusters, consisting of Machinery, Bank, Telecom, Paper & Forest and Security companies. Most groups are homogeneous with respect to their sector and also often with respect to their sub-industry, as specified by the GICS classification standard. E.g. the Bank cluster consists of the Commercial Bank companies FöreningsSparbanken, SEB, Handelsbanken and Nordea. However, there are also examples where companies form cluster without belonging to the same sector. One example of this is the Security cluster, consisting of ASSA (Building Products) and Securitas (Diversified Commercial \& Professional Services). Even if they belong to different industries, both are active in the security area. ASSA is a manufacturer and supplier of locking solutions and SECU focus on guarding solutions, security systems and cash handling. The empirical results show that it is possible to obtain a meaningful taxonomy based solely on the co-movements between individual stocks and the fundamental ultrametric assumption, without any presumptions of the companies business activity. The obtained clusters indicate that common economical factors can affect certain groups of stocks, irrespective of their GICS industry classification. The outcome of the investigation is of fundamental importance for e.g. asset classification and portfolio optimization, where the co-movement between assets is of vital importance.