Abstract
We study historical correlations and lead-lag relationships between individual stock risk (volatility of daily stock returns) and market risk (volatility of daily returns of a market-representative portfolio) in the US stock market. We consider the cross-correlation functions averaged over all stocks, using 71 stock prices from the Standard & Poor's 500 index for 1994–2013. We focus on the behavior of the cross-correlations at the times of financial crises with significant jumps of market volatility. The observed historical dynamics showed that the dependence between the risks was almost linear during the US stock market downturn of 2002 and after the US housing bubble in 2007, remaining at that level until 2013. Moreover, the averaged cross-correlation function often had an asymmetric shape with respect to zero lag in the periods of high correlation. We develop the analysis by the application of the linear response formalism to study underlying causal relations. The calculated response functions suggest the presence of characteristic regimes near financial crashes, when the volatility of an individual stock follows the market volatility and vice versa.
Highlights
A financial market is a complex system demonstrating diverse phenomena and attracting attention from a whole spectrum of disciplines ranging from social to natural science [1]
We focus on lead-lag effects between individual and collective volatility behavior in the US stock market, which might be further discussed in the context of the systemic regulation problem [47]
We have studied average lead-lag relationships between individual stock and collective market risk in the US stock market using cross-correlation analysis
Summary
A financial market is a complex system demonstrating diverse phenomena and attracting attention from a whole spectrum of disciplines ranging from social to natural science [1]. Better understanding of the behavior of financial markets has become an integral part of the discussion on further sustainable economic development In this context, proper assessment of financial risks [2] plays a crucial role: Underestimated risks contribute to financial bubbles with eventual crashes while overestimation of risks might cause inefficiency of financial resource allocations and a slowdown in economic growth, giving rise to periods of stagnation. Proper assessment of financial risks [2] plays a crucial role: Underestimated risks contribute to financial bubbles with eventual crashes while overestimation of risks might cause inefficiency of financial resource allocations and a slowdown in economic growth, giving rise to periods of stagnation This multifaceted problem, lying at the core of finance, draws significant interest from the physical and mathematical communities [3,4]. Related phenomena, being a result of collective behavior, involve such aspects as estimation of correlation [18,19,20] and cross-correlation [21,22,23,24] matrices, study of their dynamics [25,26], asymmetric correlations [27], nonlinear correlations [28,29,30] and detrending [31,32], financial networks and clustering [33,34,35,36,37,38,39,40,41,42], multivariate stochastic models [43,44], critical phenomena [45,46], etc
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