Cluster fusion-fission dynamics in the Singapore stock exchange

In this paper, we investigate how the cross-correlations between stocks in the Singapore stock exchange (SGX) evolve over 2008 and 2009 within overlapping one-month time windows. In particular, we examine how these cross-correlations change before, during, and after the Sep–Oct 2008 Lehman Brothers Crisis. To do this, we extend the complete-linkage hierarchical clustering algorithm, to obtain robust clusters of stocks with stronger intracluster correlations, and weaker intercluster correlations. After we identify the robust clusters in all time windows, we visualize how these change in the form of a fusion-fission diagram. Such a diagram depicts graphically how the cluster sizes evolve, the exchange of stocks between clusters, as well as how strongly the clusters mix. From the fusion-fission diagram, we see a giant cluster growing and disintegrating in the SGX, up till the Lehman Brothers Crisis in September 2008 and the market crashes of October 2008. After the Lehman Brothers Crisis, clusters in the SGX remain small for few months before giant clusters emerge once again. In the aftermath of the crisis, we also find strong mixing of component stocks between clusters. As a result, the correlation between initially strongly-correlated pairs of stocks decay exponentially with average life time of about a month. These observations impact strongly how portfolios and trading strategies should be formulated.