We study historical correlation 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 calculate corresponding cross-correlation functions averaged over all stocks for 71 historical stock prices from the Standard & Poor's 500 index for 1992--2013. The provided analysis suggests that cross-correlations maximum value increases near periods of crisis and remains close to 1 since the US housing bubble in 2007. Our analysis is based on the linear response theory approximation and uses asymmetries of cross-correlation function  with respect to zero lag. Characteristic regimes , when changes of individual stock risks on average follow changes of the total market risk and vice versa , are observed near market crashes. Corresponding historical dynamics suggests a particular pattern: Shortly before a crash individual stock risks start to influence market risk while after the crash the situation is reversed .
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 shows that the dependence between the risks becomes linear near such events and the maximum value of this averaged cross-correlation function is often shifted with respect to zero lag. 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 .
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maximum value increases near periods of crisis and remains close to 1 since the US housing bubble in 2007. Our analysis is based on the linear response theory approximation and uses asymmetries of
at the times of financial crises with significant jumps of market volatility. The observed historical dynamics shows that the dependence between the risks becomes linear near such events and the maximum value of this averaged
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Characteristic regimes , when changes of individual stock risks on average follow changes of the total market risk
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
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, are observed near market crashes. Corresponding historical dynamics suggests a particular pattern: Shortly before a crash individual stock risks start to influence market risk while after the crash the situation is reversed