Abstract:
Researchers from the field of econophysics have favoured the idea that financial markets are a complex adaptive system, consisting of entities that behave and interact in a diverse manner, leading to non-linear, emergent behaviour of the system. In the last twenty years, there has been an increasing focus on modelling complex adaptive systems using network theory. Correlation-based networks, where stocks are represented as entities in the network, and the relationships amongst the stocks are based on the strength of the co-movements of the stocks, have been widely studied. Network filtering tools, such as the Minimal Spanning Tree (MST), and the Planar Maximally Filtered Graph (PMFG), have been useful to attenuate the impact of noise in these networks, thereby allowing important macroscopic and mesoscopic structures to emerge. One of the main benefits of the PMFG is that it is accompanied by a hierarchical clustering algorithm called the Directed Bubble Hierarchical Tree (DBHT). This method has the benefit of being fully unsupervised in that it does not require the user to decide a priori on the number of clusters that the data should be split into.
These techniques have been applied here to analyse the complex interactions amongst stocks on the Johannesburg Stock Exchange. A structure emerged in which shares from similar ICB sectors tended to cluster together. However, the so-called Rand Hedge shares, and shares which exhibited low liquidity, tended to override the sector effect and clustered together. From a dynamic perspective, the MST and PMFG seemed to shrink during market crashes, while the Basic Materials sector was typically the most important or central sector over time. Over the long-term, the DBHT divided the stocks in the South African stock market into six clusters. This technique was compared to other popular hierarchical clustering algorithms, and the amount of economic information that each method extracted was quantified. The most recent PMFG and DBHT showed a changed structure as compared to the long-term data, highlighting that the way that market participants view South African shares can change over time.
