Fig 6. Annual relative change in volatility for the period 1985–2010.

Top panel is the volatility of the S&P 500 index, from 1985 to 2010, averaged over the previous year. Bottom panel is the annual change of volatility as a fraction of its standard deviation computed over the previous year. Four year-long windows (shading) follow two standard deviation increases in volatility greater than twice the standard deviation from one year earlier, after periods of decline. One day crashes are as in Fig 3 (vertical red lines). This indicator generates 3 true positives, 2 false positives and 1 false negative.