One of the more appealing ideas in econophysics is that financial markets can be described along lines similar to successful descriptions of critical phenomena. Critical phenomena are physical phenomena that occur in space (real or abstract) and time. We have considered thus far only a single asset and its time evolution, but in this chapter we discuss an approach based on the simultaneous investigation of several stock-price time series belonging to a given portfolio. Indeed, the presence of cross-correlations (and anticorrelations) between pairs of stocks has long been known, and plays a key role in the theory of selecting the most efficient portfolio of financial goods [49, 115]. We show how relevant these correlations and anticorrelations are by discussing a study devoted to detect the amount of synchronization present in the dynamics of a pair of stocks traded in a financial market [107]. The specific properties of the covariance matrix of stock returns of a given portfolio of stocks have been investigated extensively. Also we briefly consider studies that aim (i) to detect the number of economic factors affecting the dynamics of stock prices in a given financial market [34, 154], and (ii) to evaluate the deviations observed between market data and the results expected from the theory of random matrices [63, 87, 134].

Simultaneous dynamics of pairs of stocks

In financial markets, many stocks are traded simultaneously.