A New Attempt to Identify Long-term Precursors for Financial Crisis in the Market Correlation Structures

Abstract

Prediction of events in financial markets is every investor's dream and, usually, wishful thinking. From a more general, economic and societal viewpoint, the identification of indicators for large events is highly desirable to assess systemic risks. Unfortunately, the very nature of financial markets, particularly the predominantly non-Markovian character as well as non-stationarity, make this challenge a formidable one, leaving little hope for fully fledged answers. Nevertheless, it is called for to collect pieces of evidence in a variety of observables to be assembled like the pieces of a puzzle that eventually might help to catch a glimpse of long-term indicators or precursors for large events -if at all in a statistical sense. Here, we present a new piece for this puzzle. We use the quasistationary market states which exist in the time evolution of the correlation structure in financial markets. Recently, we identified such market states relative to the collective motion of the market as a whole. We study their precursor properties in the US stock markets over 16 years, including two crises, the dot-com bubble burst and the pre-phase of the Lehman Brothers crash. We identify certain interesting features and critically discuss their suitability as indicators.

New Collectivity Measures for Financial Covariances and Correlations

“…Moreover, we found [22] that the mean reduced-rank covariances are relatively large in crises periods in which we detected corresponding market states. In contrast to other market state definitions or so-called "regimes" in finance [27][28][29] those market states are determined by clustering correlation matrices [15,16,21,22,[30][31][32][33][34][35][36][37][38][39][40][41]. The market operates in a state for a certain time, then jumps to another one and also might return to a previous state.…”

“…In Ref. [22], we interpreted this signal and the corresponding signal in cov L as precursors for the Lehman Brother crash inducing a spill-over effect from the financial sector in the US stock markets to the entire US stock market.…”

“…In Refs. [21,22], we put forward a new type of analysis by setting up a method to remove the contributions specific for individual eigenvalues from the standard covariance and correlation matrices. If the market mode is removed, the remaining reduced-rank covariance and correlation matrices allow for a much clearer analysis of the collectivity in the industrial sectors.…”

“…We measured the average dynamical behavior of the reduced-rank covariance matrices by the mean value of the matrix elements [22]. They are small compared to the mean standard covariances and correlations but larger than noise.…”

“…The mean reduced-rank covariances are potential measures for the average sector collectivity as it represents a remaining collectivity to which each sector contributes as well as the collectivities induced by the relations between the sectors. In the analyzed time period from 1997 to 2012 [22], non-zero signals emerge almost exclusively at time periods of endogenous crises as in the vicinity of the Lehman Brother crash and the dot-com bubble burst. We identified these mean values as new measures for endogenous risk [23][24][25][26].…”