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We study historical correlations and lead-lag relationships betweenindividual stock risk (volatility of daily stock returns) and market risk(volatility of daily returns of a market-representative portfolio) in the USstock market. We consider the cross-correlation functions averaged over allstocks, using 71 stock prices from the Standard \& Poor's 500 index for1994--2013. We focus on the behavior of the cross-correlations at the times offinancial crises with significant jumps of market volatility. The observedhistorical dynamics showed that the dependence between the risks was almostlinear during the US stock market downturn of 2002 and after the US housingbubble in 2007, remaining on that level until 2013. Moreover, the averagedcross-correlation function often had an asymmetric shape with respect to zerolag in the periods of high correlation. We develop the analysis by theapplication of the linear response formalism to study underlying causalrelations. The calculated response functions suggest the presence ofcharacteristic regimes near financial crashes, when the volatility of anindividual stock follows the market volatility and vice versa.

Cross-correlation asymmetries and causal relationships between stock and market risk