Stats › Intraday and market microstructure › High and low timing
When the day's high and low happen
Ask a room of day traders when the high and low of the session get set and most will say the morning. They're right, and the reason they're right is only partly about the market. A large chunk of it is arithmetic that would hold for a coin flip.
That's the thing this page is built around. Under a pure random walk the time at which a series hits its maximum follows the arcsine law, which is U shaped: extremes pile up at the beginning and the end of any window for no reason at all. So before you can say the open is special, you need to know what the null says. For the first hour of a 6.5 hour session, the null says 25.7%.
Then you compare. US stocks in one study come in at 49% for the high. E-mini S&P 500 futures come in at 33.0%. Both beat the null, one comfortably and one narrowly, and the honest answer to which is right is that they measure different instruments over different decades using different sessions. Two of the three sources here are private studies rather than exchange or journal publications, and I've labelled them at every point.
In a study of 55 US stocks over 60,300 daily samples from 2003 to 2009, the day's high fell in the first hour on 49% of days and the day's low on 46%, against a random walk baseline of 25.7%. In E-mini S&P 500 futures over 2,686 days from 2015 to 2025 the same figures are 33.0% and 40.4%. On SPY over 3,774 days, one extreme or the other was in place by 10:30 on roughly 75% of days. The surprise is the other end: in the stock sample only 19% of highs and 20% of lows landed in the final hour, which is *below* the 25.7% you'd get from a random walk. And the one peer reviewed test I found, on S&P 500 index futures, could not reject the random walk at all.
Members only
The rest of this page is for members
Below this point there are 8 sections, 1 chart, 1 table and 5 named sources, roughly 1850 words of it. Every figure carries the source it came from and the date the data is from.
You can keep browsing every statistic in the library for free. The intro and the summary are always open.