MEAN REVERTING DYNAMICS It can be shown that the number of expected equity value "high and low" transitions scales with the square root of time, meaning that the cumulative distribution of the probability of an equity's "high or low" exceeding a given time interval is proportional to the reciprocal of the square root of the time interval, (or, conversely, that the probability of an equity's "high or low" exceeding a given time interval is proportional to the reciprocal of the time interval raised to the power 3/2 [Sch91, pp. 153]. What this means is that a histogram of the "zero free" run-lengths of an equity's price would have a 1 / (l^3/2) characteristic, where l is the length of time an equity's price was above or below "average.") This can be exploited for a short term trading strategy, which is also called "noise trading." The rationale proceeds as follows. Let l be the run length, (ie., the number of time intervals,) that an equity's value has been above or below average, then the probability that it will continue to do so in the next time interval will be: Pt = erf (1 / sqrt (l + 1))...................(1.128) where Pt is the "transient" probability. Naturally, it would be desirable to buy low and sell high. So, if an equity's price is below average, then the probability of an upward movement is given by Equation (1.128). If an equity's price is above average, then, then the probability that it will continue the trend is: Pt = 1 - erf (1 / sqrt (l + 1)) ..............(1.129) Equations (1.128) and (1.129) can be used to find the optimal time to trade one equity for another.