Fig. 4 extends Figs. 2 and 3 by performing a sensitivity analysis on the simple log-periodic formula (continuous lines in Figs. 2 and 3), in order to assess the reliability and range of uncertainty of the prediction. Using the fit shown in black solid lines in Fig. 3, we have generated 10 realizations of an artificial S&P 500 by adding GARCH noise to the black solid line. The innovations of the used GARCH noise have been drawn from a Student distribution with 3 degrees of freedom with a variance equal to that of the residuals of the fit of the real data. The fits are shown as the bundle of 10 curves in magenta. The typical width of the blue dots gives a sense of the variability that can be expected around this most probable scenario. The real S&P 500 price trajectory is shown as the red wiggly line.