How often the stock market goes up, by holding period

A single session has finished positive 52.5% of the time. A calendar year has finished positive 67.3% of the time. Nothing changes between those two rows except how long you leave the money alone: the per-session edge is tiny, it is roughly independent from one session to the next, and the odds of the sum being positive climb with the number of draws. That is the argument for a long horizon stated as arithmetic rather than as advice.

The streaks are the part people misread. There have been 11,863 runs in this history and the longest was 14 sessions, in 26 Mar 1971 to 15 Apr 1971. That sounds remarkable and is roughly what you would expect from 24,781 weighted coin flips. The frequency table shows the shape: each extra day of a run is about half as common as the one before it, which is what independence looks like.

The conditional table asks the question directly — after a run of exactly one, two, three, four or five days in one direction, what did the next session do? The answers sit close to the unconditional rate and they do not line up in a direction. If declines fed on declines you would see the positive share fall as the run lengthens; it does not.

The one genuine asymmetry is the shape of the runs, not their information content. Up runs are longer and their days are smaller; down runs are shorter and their days are larger. The longest losing run in the record, 22 Apr 1966 to 9 May 1966, cost 6.6% across 12 sessions — less than the single worst day in the whole series.