Month-end’s last 15 minutes: bigger, direction unclear

The short answer

The last quarter hour of a month-end session moved farther than usual, and this study could not tell which way. Before the closing cross (the auction that sets the official close), SPY’s middle month-end window moved 0.18% of its price against 0.12% on ordinary days of the same month, about 1.5 times as far. QQQ agrees.

Up and down came out even, 39 months each. The test could only have seen a lean about as large as the average window move, so “not detected” does not mean “no lean”.

Part of the size gap comes from Fridays and a few other special days. With those set aside the gap is about half, and too few months remain to tell it from zero.

What to do with this:

• The typical month-end window travels farther, but the gap is small in dollars. SPY’s middle (median) window was 18 basis points (bp, hundredths of a percent) against 12 bp on ordinary days, a gap of about 6.5 bp, or $0.38 at the recorded 15:45 price on 31 December 2024 ($586.27). The plain average is 27 bp against 15, pulled up by one day, 28 February 2020 (280 bp).
• These are net changes from 15:45 to 16:00. The swing inside the window was larger, and this page gives no number for it. The study also did not look at whether a level holds, so it says nothing about what price did at a Prism wall, flip or expected-move edge.
• Treat direction as unknown: the study could not have seen a lean below 24 to 27 bp (allowing for its 8 tests), so “not detected” is not “no lean”.
• In a back-test, report month-end sessions apart from ordinary days: Fridays and a few special days (listed under Limits) carry part of the gap.

How we tested

The events are the last regular session of each month, May 2018 to December 2024: 80 months, less 29 November 2019 and 29 November 2024, which closed at 13:00 and have no full last 15 minutes, leaves 78 for each of SPY and QQQ. Prices are recorded one-minute bars.

Each month-end is compared with the average of its ordinary days, one to three a month, and separately with the session before and after it. Within each month we shuffled which day counts as the month-end 100,000 times to see how often chance alone matches the real gap, and allowed for the 8 tests run together (two ETFs, size and direction, two comparisons).

Check it yourself

A log of your own cannot confirm this study for years (see the table under What a small log can say), so treat the study as your reference. Steps 1 to 4 give one month-end’s window size in bp, to set beside the 18 and 12 above; do them that evening, while the month’s earlier weeks are still on your chart. Steps 5 and 6 keep a log.

One sheet, one row per session, a month-end row first and then its ordinary days:

The steps

Worked lines use SPY in 2024-12, a recorded month-end, with its recorded bar closes to the cent.

• 1. Pick the last regular session of a month, not a 13:00 half day. Type its date in A, ME in B and, in C, =TEXT(A2,"yyyy-mm"). Worked: 31 December 2024, a Tuesday, so C is 2024-12.
• 2. Add its ordinary days below it, ORD in B: the same weekday in the other weeks of that month, skipping the first three sessions, the third Friday (monthly options expiry) and any 13:00 half day. Use the ones still on your chart, at least one. Worked: that month’s Tuesdays were the 3rd (in the first three sessions, skipped), the 10th (used), the 17th (used), the 24th (a 13:00 half day, skipped) and the 31st (the month-end itself).
• 3. Read D and E in Eastern time. D is the close of the bar ending 15:45 (some platforms stamp it 15:44) and E the close of the last regular bar (stamped 15:59). Worked: row 2 is 31 December 2024 (ME): D 586.27, E 586.01; row 3 is 10 December 2024 (ORD): D 602.70, E 602.87; row 4 is 17 December 2024 (ORD): D 604.03, E 604.24.
• 4. Fill F with =ABS(E2-D2)/D2*10000 and G with =(E2-D2)/D2*10000, copied down. Worked: row 2 F 4.43, G −4.43; row 3 F 2.82, G +2.82; row 4 F 3.48, G +3.48.
• 5. On the month-end row only, H is =F2-AVERAGEIFS(F:F,C:C,C2,B:B,"ORD") and I is =G2-AVERAGEIFS(G:G,C:C,C2,B:B,"ORD"). Worked: H is 4.43 minus the average of 2.82 and 3.48, +1.28 bp; I is −4.43 minus the average of +2.82 and +3.48, −7.58 bp. The figure’s month view uses ATR, where this month-end was not the bigger one (recorded ATR $7.59 against $4.12 and $3.46), so bp and ATR can disagree on one month.
• 6. After each month-end read =AVERAGE(H:H), your size gap, and =3.8*STDEV(H:H)/SQRT(COUNT(H:H)), the smallest size gap your log could see four times in five (STDEV is the spread of the gaps; 3.8 is the study’s multiple for one test, 4.8 for its 8 tests). The same two formulas on I do it for direction. Worked with the study’s 78 SPY month-ends: STDEV of H was 37.0 bp, so 3.8 × 37.0 ÷ √78 = 15.9 bp; for I, 45.0 bp gives 19.4 bp.

What a small log can say

A log fills slowly: one month-end is one event, and SPY, QQQ and every stock on the same day are one event, not many. The table gives the smallest gap a log of each length could see four times in five, scaled from the spread of the study’s SPY gaps (yours will differ; step 6 recomputes it). One very large day, 28 February 2020, widens that spread (22.7 bp without it against 37.0), so the size bars are cautious. The lean column allows for one test only; the study’s bar, with 8, was 24 to 27 bp.

Limits

No difference detected in the 15 minutes before the closing cross is not “no difference”. The direction tests could only have seen a lean of about 24 to 27 bp, larger than the whole size gap, so a smaller lean could be there unseen. The counterweight: all four direction 95% ranges sit between −0.081 and +0.056 ATR, so a lean as large as SPY’s size gap (+0.097 ATR) is outside every one. The 95% ranges describe these months, not later ones.

• Coverage: the window stops before the closing cross, so the study cannot say what the auction itself did. It covers two large ETFs and 78 month-ends; no trade, cost, wall or flip is involved. The four size tests are one finding measured four ways. On the two left-out 13:00 month-ends SPY’s last 15 minutes moved +0.011 ATR on 29 November 2019 and −0.138 ATR on 29 November 2024. In 3 of the 78 months only one ordinary day was available to compare with.
• Calendar: the size gap is not shown to come from the date. A Friday month-end can carry extras the match does not remove, such as option expiries and index reviews, and this study did not measure which. 32 of the 78 month-ends are Fridays, 12 fall in May or November (the MSCI index review months: the month, not the day of the change), 3 were Fed decision days (31 July 2019, 31 January 2024 and 31 July 2024) and 2 were Russell reconstitution days, the yearly rebalance of the Russell indexes (28 June 2019 and 28 June 2024). Fridays are not the whole story: other weekdays still show a positive gap. With all of those set aside 36 month-ends remain and the gap is about half, with a range that reaches zero: on that few months the study cannot tell the calendar from luck. Quarter-end months carry the smaller gap, but the ranges overlap, so the data neither supports nor rules out quarter-end rebalancing.
• Method: the bars for a smaller log assume monthly gaps roughly bell-shaped, and one very large day widens their spread. The “smallest lean caught 4 times in 5” bars come from a simulation read from the study, not re-run here. Reading your own log after every month-end and stopping when a gap looks large finds luck; read it at the sizes in the table.
• Timing: the study’s plan was set before its results were opened, but the only record of that order is the study’s own log, not the shared record of all our studies.