Wonder if anyone has looked into this: The number of times the S&P closes near (within 0.1%) of it's HOD or LOD has gone through some interesting changes. If you assume randomness and independance, then the closing minute should be no more special than any other minute, therefore the probability that the close approaches HOD or LOD should be infintesimal. From 1960 to 1981, this held true, the number of times the S&P closed near HOD or LOD was few and far in between. From 1982 on however, the number jumps to 87 trading days - which is 34.5% of the time! The introduction of the S&P futures and thus of index arb is cited as the reason for this. It stays high and goes higher (consistent with the growth of index arb) until 1997, when it falls back to 82 trading days. Now in 1997, the eminis and decimalization was introduced. Since 1997, it has been falling slightly. There are several interesting conclusions that can be drawn from this, I think, and I share this in the hope that someone might provide some insight. peace

I'm satisfied that randomness and independence in S&P trading are figments of Paul Samuelsohn's learned imagination. Clearly the price action of the S&P 500 is chaotic (in the complex Markov-chain sense) and the serial dependency of prices can be not just observed but quantified. However I do see a possible connection with the Market Logic idea of "trend days." I'm no ML savant, so I can only relate in a very general way how ML describes the markets. The Market Profile is a frequency distribution of Time-Price Opportunities (TPOs). Forgive me if you already know all about this. Days when prices break out or break down from an initial "balance area" and move to new levels are called "trend days" and their TPO distributions have sizeable tails. On such days the close is predominantly near the HOD or LOD. Consequently the growing frequency from 1982 to 1997 of days with closes near the extremes must closely parallel the prevalence of what ML calls trend days. The beginning of the period does coincide with the advent of index arbitrage but what process began in 1997 that would cause a gradual decline of the frequency of trend days? Has there been a decline in index arb? Certainly there was an end to the long uptrend but that came later. Could the declining trend days have been an early warning of the coming turn? An interesting thing to study.