Fig. 4 extends figures 1 and 2 by performing a sensitivity analysis on the simple log-periodic formula (continuous lines in figures 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 figure 2, we have generated 10 realizations of an artificial S&P500 by adding white noise to the black solid line. The white noise (shown as the blue dots) is drawn from a student distribution with 3 degrees of freedom and with a variance equal to that of the residuals of the fit of the real data by the black continuous curve. We have then fitted each of these 10 synthetic noisy clones of the S&P500 by our log-periodic formula. This yields the bundle of 10 curves shown here 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.