Market Connectedness: Spillovers, Information Flow, and Relative Market Entropy

The degree of connectedness of equity markets on a given day can be assessed by decomposing the forecast error variance resulting from a vector autoregressive model, applied to daily returns on stock indices. This well-known procedure leads, for each day, to a spillover matrix which can be readily interpreted as a network structure and summarized into the so-called spillover index, to which much recent research work has been devoted. Taking a sequence of spillover matrices as starting point, we show how the scope of this concept can be broadened in several ways. Firstly, we develop a concept to quantify a market's potential to spread information, which is related to the eigenvector structure of spillover matrices. Secondly, a Markov chain approach allows the definition of relative market entropy, quantifying the amount of information gained from day to day. A further entropy concept can be related to the speed of shock digestion and network stability. As an empirical example, we analyze a system of five markets represented by stock indices Dow Jones Industrial Average (USA), FTSE (UK), Euro Stoxx 50 (euro area), Nikkei 225 (Japan), and SSE Composite (China). It is demonstrated that increasing trends in the spillover index as well as in speed of information digestion are an empirical fact but no logical necessity theoretical examples show that there can be opposite trends in these series.