Fig. 4 extends Figs. 1 and 2 by performing a sensitivity analysis on the simple log-periodic formula (continuous lines in Figs. 1 and 2), in order to assess the reliability and range of uncertainty of the prediction. Using the fit shown in black solid lines in Fig. 2, we have generated 10 realizations of an artificial S&P500 by adding GARCH noise to the black solid line. GARCH means "generalized auto-regressive conditional heteroskedasticity". It is a process often taken as a benchmark in the financial industry and describes the fact that volatility is persistent. 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 to ensure the agreement between the statistical properties of these synthetic time series and the known properties of the empirical distribution of returns. The fits are shown as the bundle of 10 curves in magenta. This bundle of predictions is coherent and suggests a good robustness of the prediction. The typical width of the blue dots give a sense of the variability that can be expected around this most probable scenario. The real S&P500 price trajectory is shown as the red wiggly line.