Quote from MAESTRO:
Argument #4
Letâs construct a simple one dimensional discrete random walk using the following rules. We would flip an unbiased coin and every time it lands on âheadsâ we would draw a step (size 1) up and every time it lands on âtailsâ we would draw a step down. It is well known that on average this random walk would deviate from itâs initial starting point by sqrt ( 2 * N / pi) where N is the number of flips (mean deviation of the walk). This walk will have standard deviation equal to sqrt (N).
The chart below is a weekly chart for SPX. The lines above and below present one standard and one mean deviation of 100 point steps (steps are plotted on the chart in green). It is self evident that this particular chart is extremely close to a pure random walk outcome. It could be shown that if we used not a constant step but a percentage based step the similarity would be even closer. Also, if we take under consideration the reduction of the US dollar buying power over this period of time we would have an exact match between SPX weekly chart and pure random walk. These observations were confirmed by us without a hint of a doubt on hundreds different securities and on thousands different time frames.