Last half hour’s share of the day: no change detected

The short answer

No, not that we could detect. SPY’s last half hour (15:30 to 15:59 Eastern) carried 10.26% of the day’s price movement in 2018 to 2019 and 9.83% in 2023 to 2024, and QQQ’s carried 7.62% and 7.01% (movement means each minute’s price change squared and added up, so big moves count most).

The test could only have seen a change of about a fifth of the share or more, so a smaller change could be there unseen.

The price source may differ between the two periods (see Limits), so a change between them, had we found one, could not be called market behaviour.

What to do with this

• Before you accept a claim that late-day moves are getting bigger, ask for the share by year and the smallest change its test could see. Here the last half hour’s yearly share ran from 8.67% to 13.80% in SPY (QQQ 6.44% to 10.78%); neighbouring years typically differed by 2.20 percentage points in SPY (1.03 in QQQ) and by as much as 3.15 (2019 to 2020) and 3.07 (2020 to 2021), against 0.43 and 0.61 between the two periods.
• Judge a move on your chart by the half hour it came in: the same move says less in a half hour where moves are typically bigger. In 2023 to 2024 SPY’s typical move was 1.34 times an average half hour’s in the first half hour, 1.13 in the last and 0.81 at 13:30, its quietest (each is the square root of the half hour’s share over an even 7.69%). QQQ’s last half hour is below an even spread (7.01%, 0.95 times).
• Use the spreadsheet below to see where your own stock’s day moves, or to check your typing against the 30-minute figures for SPY and QQQ from this page’s study. It cannot test whether late-day moves are getting bigger: a log of 20 to 100 sessions can only show a gap from the study’s average of 7.0 points or more in SPY (4.6 in QQQ), against the study’s own 2.11 (1.51).

How we tested

We used recorded one-minute prices for SPY and QQQ, regular hours only (09:30 to 15:59 Eastern, 390 bars a day), from May 2018 to December 2024. The two periods are the earliest part of that data and its latest two years; 2020 to 2022 are in no test and shown year by year. Early closes, days with missing minutes and 24 January 2023 (dropped by a rule set before any price was opened) were left out, leaving 1,656 SPY and 1,659 QQQ sessions, 414 and 495 of SPY’s in the two periods.

For each session we took each window’s share of the day’s movement and compared its average in the two periods, SPY and QQQ separately. To see how far chance alone could move the gap, we redrew whole calendar months at random 100,000 times, and shuffled which months belong to which period 100,000 times as a second check. “Detected” needs an adjusted p under 0.05 across six tests (SPY and QQQ, each in the first half hour, the last half hour and the last ten minutes). The windows, periods and tests were written down before the results were opened, though the periods were chosen after earlier tests.

Check it yourself

You can measure the 30-minute version in a spreadsheet, from a 30-minute chart with regular hours only. One sheet, row 1 for headings, thirteen data rows for each session:

The steps

Worked lines use SPY on 2 January 2024, a recorded session, with its prices to the cent.

• 1. Open a 30-minute chart of one symbol, regular hours only, and for each of a session’s 13 bars write the date in A and the bar’s start in B. Worked: 2 January 2024, bars from 09:30 to 15:30.
• 2. In C write each bar’s close; in D type the session’s 09:30 open on its first row, then =C2, =C3 and so on down. Worked: the first row has D 472.16 and C 472.27; the 15:30 bar has D 470.91 and C 472.60.
• 3. In E write =LN(C2/D2)*100 and in F write =E2^2, copied down. Worked, 15:30 bar: LN(472.60/470.91)*100 is +0.3582, squared 0.1283.
• 4. In G write =F2/SUMIFS(F:F,A:A,A2), the bar’s share of that day’s movement. Worked: the day’s F adds up to 0.2551, so the 15:30 bar’s share is 0.1283 ÷ 0.2551, 50.30% from the unrounded values.
• 5. Log more sessions the same way (SPY or QQQ from 2023 or 2024 if you want to check against the study), then read =AVERAGEIFS(G:G,B:B,"15:30") for the last half hour. Worked: the study’s 30-minute version gives SPY 10.81% in 2018 to 2019 and 10.53% in 2023 to 2024, QQQ 7.94% and 7.59%, which run 0.32 to 0.70 percentage points above the study’s one-minute figures for the same periods.

The worked session

What a small log can say

A log fills slowly: each session is thirteen prices, and the last half hour’s share swings a lot from session to session (its typical distance from the average across SPY sessions in 2023 to 2024 is about 15 points), so a short log’s average is mostly noise.

Averages of every run of 20, 50 and 100 consecutive 2023 to 2024 sessions wander by about 3.8, 3.0 and 2.5 points in SPY. A gap of 2.8 times that wander is the smallest an ordinary one-test check catches four times in five, and the table gives it. Your gap is your average minus the study’s 30-minute figure; a smaller gap than the table shows is “cannot tell”.

The table is for SPY and QQQ: for another stock, dividing its session spread by the square root of the sessions gives too small a gap (SPY at 100 sessions: 4.3 points against 7.0), because neighbouring sessions resemble each other.

Limits

No change detected is not “no change”. At the six-test bar the test could only have seen about 2.11 points in SPY’s last half hour and 1.51 in QQQ’s (21% and 20% of the 2018 to 2019 share), and at the ordinary one-test bar 1.64 and 1.17; a smaller change could be there unseen. The last half hour also missed the ordinary bar (raw p 0.43 in SPY, 0.12 in QQQ).

• Prices: the files do not say where they come from, so a change of source between the periods cannot be ruled out. It would touch the change we measured, and we cannot say which way it would push the share. Two warning signs: a check of trading volume flagged a jump in early 2020, which a re-check ties to the March 2020 volume surge and reads as probably not a new source, though the flag was not cleared; and the share of minutes in which the price did not change at all fell by more than half between the periods (SPY’s last half hour 3.50% to 1.65%, QQQ’s 4.44% to 1.61%), which is unexplained. Until it is explained, an era difference cannot be called market behaviour.
• Earlier tests: this is one of at least 40 tests run on these SPY and QQQ prices, this study’s six included, with no allowance across them, and the periods were chosen after the earlier ones, so an occasional lucky detection is expected. The first half hour’s raw p-values (0.02 for SPY and 0.04 for QQQ) become 0.12 once the six tests are allowed for, so that change is not confirmed.
• Coverage: two large ETFs that move closely together, so their agreement is not two independent confirmations, and two periods: 2023 (8.67%) and 2024 (10.97%) straddle the 2018 to 2019 average, so pooling hides a jump. The last half hour ends at 15:59, so the closing auction is not measured. Nothing after 2024 was read, and no cause, direction or level was studied.
• Share, not size: a share that holds could sit on a bigger or smaller day, and because the parts add to 100%, a fall in the first half hour’s share goes with a rise elsewhere.
• Noise: one-minute moves include the bid-ask bounce (prices hopping between the buying and selling quote) and price rounding. SPY’s price rose, so one cent fell from 0.0035% to 0.0021% of its price and rounding weighs less. Five-minute returns mute both and give −0.17 for SPY and −0.58 for QQQ.
• Other views (five-minute returns, absolute moves, no event days such as third Fridays, Fed days, Russell index rebalance days and month-ends, and May to December alone) each give a slightly smaller share later, by under a point. Comparing 2023 to 2024 with 2018 to 2019, every estimate of the change leans slightly down, never up (−0.17 to −0.80 percentage points), but a fall that small is within what luck can produce. Seven of those eight ranges include zero; the exception is QQQ without event days (−0.80, range −1.55 to −0.02), which carries no allowance for the tests run together.