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Tested patterns · re-tested each quarter

What the market data shows: tested patterns in US stocks.

Tested as of

Beliefs about stock prices are often repeated and rarely checked: that a stock which jumped keeps rising, that the most-traded stocks beat the market, that cash is safer when the market is below its trend. Each is tested here on the daily prices of every US stock since 2017, period by period, and tested again every quarter. A pattern counts only when it holds in both of the two most recent periods.

Prices through · 48 tests

3 patterns hold in the recent data.

Of the other 45 tests, 24 show no measurable effect and 21 are unstable. Every test is listed below by subject.

What each result means.

Holds 3
The effect has the same direction in both recent periods and is clearly larger than chance in each (t of at least 2), and the three checks agree.
No measurable effect 24
In both recent periods the effect is within what chance alone produces (t under 2).
Unstable 21
Anything else: the direction changed, only one period shows an effect, or a period had too few cases to measure.

t is the average divided by its standard error: at 2 or more, an effect that size is unlikely to be chance.

How every test is run
  • A finding counts only if it holds in recent data: 2017 onward by period, the last two periods deciding.
  • One event per stock per 63 sessions; events averaged by calendar month; months weighted equally; Newey-West t over months.
  • Every situation is defined on information from before the event, and the sign must survive entry at the next close, a same-tier benchmark, and removing names that stopped trading or traded flat.
  • A line holds when its last two periods have the same sign with |t| at least 2 and the checks agree; no measurable effect when |t| is under 2 in both; unstable otherwise. Only a line that holds governs.

The average stock against the S&P 500

Average liquid stock against the S&P 500

Unstable · 2021-23: −8.4 points a year (t −3.1) · 2024-26: −3.7 points a year (t −1.4)

What was tested, every period and the method

How the average liquid stock (equal weight, median dollar volume of the prior 63 sessions) did against the S&P 500.

Average liquid stock against the S&P 500: result by period
Period Average, points a year t Median Cases Stocks, % a yearS&P 500, % a year
2017-20 +0.4 0.1 −2.5 1,007 14.714.3
2021-23 · decides −8.4 −3.1 −5.9 753 1.610.1
2024-26 · decides −3.7 −1.4 −3.1 633 14.117.8
2017-26 (all) −3.5 −1.4 −3.5 2,393 10.513.9

Measured against: S&P 500.

Every session from 2017, the equal-weight return over the next 63 sessions (log growth) minus the S&P 500's, times four for a year; sessions averaged within the calendar month; Newey-West t over months, lag 3. Liquid as for the event tests; a stopped stock keeps its last close.

Average $5-20M stock against the S&P 500

Unstable · 2021-23: −11.3 points a year (t −3.2) · 2024-26: −3.2 points a year (t −0.8)

What was tested, every period and the method

How the average liquid stock of the $5-20M tier (equal weight, median dollar volume of the prior 63 sessions in $5-20M a day) did against the S&P 500.

Average $5-20M stock against the S&P 500: result by period
Period Average, points a year t Median Cases Stocks, % a yearS&P 500, % a year
2017-20 +1.2 0.2 −2.7 1,007 15.514.3
2021-23 · decides −11.3 −3.2 −7.0 753 −1.310.1
2024-26 · decides −3.2 −0.8 −1.3 633 14.617.8
2017-26 (all) −3.9 −1.2 −3.9 2,393 10.013.9

Measured against: S&P 500.

Every session from 2017, the equal-weight return over the next 63 sessions (log growth) minus the S&P 500's, times four for a year; sessions averaged within the calendar month; Newey-West t over months, lag 3. Liquid as for the event tests; a stopped stock keeps its last close.

Average $20-100M stock against the S&P 500

Unstable · 2021-23: −8.3 points a year (t −3.1) · 2024-26: −5.2 points a year (t −2.0)

What was tested, every period and the method

How the average liquid stock of the $20-100M tier (equal weight, median dollar volume of the prior 63 sessions in $20-100M a day) did against the S&P 500.

Average $20-100M stock against the S&P 500: result by period
Period Average, points a year t Median Cases Stocks, % a yearS&P 500, % a year
2017-20 −0.6 −0.1 −2.8 1,007 13.714.3
2021-23 · decides −8.3 −3.1 −5.6 753 1.810.1
2024-26 · decides −5.2 −2.0 −4.3 633 12.717.8
2017-26 (all) −4.2 −1.7 −3.9 2,393 9.713.9

Measured against: S&P 500.

Every session from 2017, the equal-weight return over the next 63 sessions (log growth) minus the S&P 500's, times four for a year; sessions averaged within the calendar month; Newey-West t over months, lag 3. Liquid as for the event tests; a stopped stock keeps its last close.

Average $100M-1B stock against the S&P 500

Unstable · 2021-23: −5.0 points a year (t −2.4) · 2024-26: −3.2 points a year (t −1.4)

What was tested, every period and the method

How the average liquid stock of the $100M-1B tier (equal weight, median dollar volume of the prior 63 sessions in $100M-1B a day) did against the S&P 500.

Average $100M-1B stock against the S&P 500: result by period
Period Average, points a year t Median Cases Stocks, % a yearS&P 500, % a year
2017-20 +0.6 0.3 −1.6 1,007 14.914.3
2021-23 · decides −5.0 −2.4 −4.1 753 5.010.1
2024-26 · decides −3.2 −1.4 −3.0 633 14.717.8
2017-26 (all) −2.2 −1.6 −2.4 2,393 11.713.9

Measured against: S&P 500.

Every session from 2017, the equal-weight return over the next 63 sessions (log growth) minus the S&P 500's, times four for a year; sessions averaged within the calendar month; Newey-West t over months, lag 3. Liquid as for the event tests; a stopped stock keeps its last close.

Average over $1B stock against the S&P 500

No measurable effect · 2021-23: −2.8 points a year (t −0.4) · 2024-26: +7.4 points a year (t 1.8)

What was tested, every period and the method

How the average liquid stock of the over $1B tier (equal weight, median dollar volume of the prior 63 sessions in over $1B a day) did against the S&P 500.

Average over $1B stock against the S&P 500: result by period
Period Average, points a year t Median Cases Stocks, % a yearS&P 500, % a year
2017-20 +19.1 8.7 +19.1 250 61.042.0
2021-23 · decides −2.8 −0.4 −1.4 753 7.310.1
2024-26 · decides +7.4 1.8 +5.6 633 25.217.8
2017-26 (all) +4.7 1.3 +6.3 1,636 22.918.3

Measured against: S&P 500.

Every session from 2017, the equal-weight return over the next 63 sessions (log growth) minus the S&P 500's, times four for a year; sessions averaged within the calendar month; Newey-West t over months, lag 3. Liquid as for the event tests; a stopped stock keeps its last close.

How far apart stocks end up

Spread of 63-session returns across liquid stocks

Holds · 2025: 25.9% (t 18.6) · 2026: 27.4% (t 15.9)

What was tested, every period and the method

The standard deviation of 63-session returns across all liquid stocks, by year: how far apart the best and worst stocks end up, and so how much picking the right ones can be worth.

Spread of 63-session returns across liquid stocks: result by period
Period Average, % (standard deviation) t Median Cases
2017 15.3 46.8 15.0 251
2018 17.4 39.5 17.1 251
2019 17.7 30.7 17.4 252
2020 32.3 10.1 29.8 253
2021 20.5 24.8 19.7 252
2022 19.9 69.3 19.6 251
2023 20.0 25.0 19.1 250
2024 21.9 19.5 20.8 252
2025 · decides 25.9 18.6 26.8 250
2026 · decides 27.4 15.9 27.2 131
2017-26 (all) 21.6 21.6 19.7 2,393

Every session, the cross-sectional standard deviation of the next 63 sessions' returns (capped at +1000%, stopped stocks at their last close); sessions averaged by calendar month; Newey-West t, lag 3.

After a one-day jump

After a one-day jump, next 21 sessions

No measurable effect · 2022-23: +0.4% (t 1.2) · 2024-26: −0.3% (t −0.9)

What was tested, every period and the method

Stocks liquid the day before (any tier) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (up): their return over the next 21 sessions against the average liquid stock.

After a one-day jump, next 21 sessions: result by period
Period Average, % over 21 sessions t Median Cases
2017-19 −0.1 −0.4 0.0 6,216
2020-21 −0.4 −0.9 −1.2 5,505
2022-23 · decides +0.4 1.2 +0.5 5,132
2024-26 · decides −0.3 −0.9 −1.0 8,691
2017-26 (all) −0.1 −0.7 −0.5 25,544

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day jump, next 21 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 −0.1 0.00.0−0.1
2020-21 −0.4 −0.3−0.4−0.4
2022-23 +0.4 +0.2+0.4+0.4
2024-26 −0.3 −0.1−0.3−0.3

After a one-day jump, next 63 sessions

No measurable effect · 2022-23: −0.2% (t −0.5) · 2024-26: −0.8% (t −1.5)

What was tested, every period and the method

Stocks liquid the day before (any tier) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (up): their return over the next 63 sessions against the average liquid stock.

After a one-day jump, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 −0.3 −1.0 −0.4 6,216
2020-21 −0.9 −0.9 −4.7 5,505
2022-23 · decides −0.2 −0.5 −0.2 5,132
2024-26 · decides −0.8 −1.5 −2.9 8,253
2017-26 (all) −0.6 −1.9 −1.8 25,106

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day jump, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 −0.3 −0.2−0.3−0.3
2020-21 −0.9 −1.0−0.9−0.9
2022-23 −0.2 −0.3−0.2−0.2
2024-26 −0.8 −0.6−0.8−0.8

After a one-day jump, $5-20M a day, next 21 sessions

No measurable effect · 2022-23: +0.1% (t 0.3) · 2024-26: −0.7% (t −0.9)

What was tested, every period and the method

Stocks liquid the day before ($5-20M a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (up): their return over the next 21 sessions against the average liquid stock.

After a one-day jump, $5-20M a day, next 21 sessions: result by period
Period Average, % over 21 sessions t Median Cases
2017-19 −0.2 −0.7 −0.6 2,532
2020-21 −0.3 −0.5 −1.6 2,063
2022-23 · decides +0.1 0.3 +0.3 1,973
2024-26 · decides −0.7 −0.9 −1.5 2,894
2017-26 (all) −0.3 −1.1 −0.8 9,462

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods at least one check does not keep the direction of the main result.

After a one-day jump, $5-20M a day, next 21 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 −0.2 −0.2−0.1−0.2
2020-21 −0.3 −0.3−0.3−0.1
2022-23 +0.1 −0.2+0.3+0.1
2024-26 −0.7 −0.4−0.7−0.7

After a one-day jump, $5-20M a day, next 63 sessions

No measurable effect · 2022-23: −0.5% (t −0.5) · 2024-26: −0.8% (t −0.6)

What was tested, every period and the method

Stocks liquid the day before ($5-20M a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (up): their return over the next 63 sessions against the average liquid stock.

After a one-day jump, $5-20M a day, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 +0.1 0.2 −0.9 2,532
2020-21 +0.1 0.1 −4.7 2,063
2022-23 · decides −0.5 −0.5 −0.9 1,973
2024-26 · decides −0.8 −0.6 −3.7 2,769
2017-26 (all) −0.3 −0.4 −2.4 9,337

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods at least one check does not keep the direction of the main result.

After a one-day jump, $5-20M a day, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +0.1 +0.3+0.20.0
2020-21 +0.1 +0.2−0.1+0.3
2022-23 −0.5 −0.7+0.1−0.5
2024-26 −0.8 −0.5−1.0−0.8

After a one-day jump, $20-100M a day, next 21 sessions

No measurable effect · 2022-23: +0.5% (t 0.9) · 2024-26: −0.2% (t −0.9)

What was tested, every period and the method

Stocks liquid the day before ($20-100M a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (up): their return over the next 21 sessions against the average liquid stock.

After a one-day jump, $20-100M a day, next 21 sessions: result by period
Period Average, % over 21 sessions t Median Cases
2017-19 −0.1 −0.6 +0.2 2,534
2020-21 −0.7 −1.4 −1.3 2,197
2022-23 · decides +0.5 0.9 +0.7 1,966
2024-26 · decides −0.2 −0.9 −0.7 3,337
2017-26 (all) −0.1 −0.8 −0.3 10,034

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods at least one check does not keep the direction of the main result.

After a one-day jump, $20-100M a day, next 21 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 −0.1 0.0−0.1−0.1
2020-21 −0.7 −0.8−0.6−0.6
2022-23 +0.5 +0.4+0.4+0.5
2024-26 −0.2 +0.1−0.1−0.2

After a one-day jump, $20-100M a day, next 63 sessions

Unstable · 2022-23: −0.1% (t −0.3) · 2024-26: −0.8% (t −2.1)

What was tested, every period and the method

Stocks liquid the day before ($20-100M a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (up): their return over the next 63 sessions against the average liquid stock.

After a one-day jump, $20-100M a day, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 −0.9 −1.7 −0.2 2,534
2020-21 −1.1 −0.8 −4.4 2,197
2022-23 · decides −0.1 −0.3 −0.6 1,966
2024-26 · decides −0.8 −2.1 −2.7 3,146
2017-26 (all) −0.8 −2.0 −1.7 9,843

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day jump, $20-100M a day, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 −0.9 −0.7−0.7−0.9
2020-21 −1.1 −1.4−1.1−1.0
2022-23 −0.1 −0.4−0.1−0.1
2024-26 −0.8 −0.7−0.5−0.8

After a one-day jump, $100M-1B a day, next 21 sessions

Unstable · 2022-23: +1.0% (t 2.7) · 2024-26: −0.6% (t −1.4)

What was tested, every period and the method

Stocks liquid the day before ($100M-1B a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (up): their return over the next 21 sessions against the average liquid stock.

After a one-day jump, $100M-1B a day, next 21 sessions: result by period
Period Average, % over 21 sessions t Median Cases
2017-19 +0.4 1.4 +0.2 1,207
2020-21 +0.3 0.3 −1.0 1,306
2022-23 · decides +1.0 2.7 +0.7 1,196
2024-26 · decides −0.6 −1.4 −1.1 2,420
2017-26 (all) +0.3 0.9 −0.3 6,129

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day jump, $100M-1B a day, next 21 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +0.4 +0.3+0.3+0.4
2020-21 +0.3 +1.0+0.4+0.3
2022-23 +1.0 +1.0+0.8+1.1
2024-26 −0.6 −0.5−0.7−0.6

After a one-day jump, $100M-1B a day, next 63 sessions

Unstable · 2022-23: +1.3% (t 2.4) · 2024-26: −0.6% (t −0.9)

What was tested, every period and the method

Stocks liquid the day before ($100M-1B a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (up): their return over the next 63 sessions against the average liquid stock.

After a one-day jump, $100M-1B a day, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 −0.1 −0.1 +0.3 1,207
2020-21 −1.9 −1.3 −5.5 1,306
2022-23 · decides +1.3 2.4 +1.0 1,196
2024-26 · decides −0.6 −0.9 −2.2 2,292
2017-26 (all) −0.3 −0.7 −1.3 6,001

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day jump, $100M-1B a day, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 −0.1 −0.1−0.6−0.1
2020-21 −1.9 −1.9−1.2−1.9
2022-23 +1.3 +1.3+0.7+1.6
2024-26 −0.6 −0.4−0.8−0.6

After a one-day jump, over $1B a day, next 21 sessions

Unstable · 2022-23: +1.2% (t 1.1) · 2024-26: +2.5% (t 2.2)

What was tested, every period and the method

Stocks liquid the day before (over $1B a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (up): their return over the next 21 sessions against the average liquid stock.

After a one-day jump, over $1B a day, next 21 sessions: result by period
Period Average, % over 21 sessions t Median Cases
2017-19 +2.2 2.0 +2.6 43
2020-21 −1.9 −1.1 −1.4 95
2022-23 · decides +1.2 1.1 −0.2 80
2024-26 · decides +2.5 2.2 +1.9 221
2017-26 (all) +1.2 1.7 +0.7 439

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day jump, over $1B a day, next 21 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +2.2 +2.1+1.2+2.2
2020-21 −1.9 −0.8−2.0−1.9
2022-23 +1.2 +0.7+1.1+1.2
2024-26 +2.5 +2.1+1.3+2.5

After a one-day jump, over $1B a day, next 63 sessions

Unstable · 2022-23: +2.5% (t 0.8) · 2024-26: +6.1% (t 3.2)

What was tested, every period and the method

Stocks liquid the day before (over $1B a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (up): their return over the next 63 sessions against the average liquid stock.

After a one-day jump, over $1B a day, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 +5.6 1.4 +3.0 43
2020-21 −1.0 −0.3 −6.3 95
2022-23 · decides +2.5 0.8 +0.8 80
2024-26 · decides +6.1 3.2 +0.2 203
2017-26 (all) +3.6 2.1 +0.4 421

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day jump, over $1B a day, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +5.6 +5.2+2.4+5.6
2020-21 −1.0 −1.0−0.9−1.0
2022-23 +2.5 +2.8+0.1+2.5
2024-26 +6.1 +6.0+3.2+6.1

After a one-day drop

After a one-day drop, next 21 sessions

Unstable · 2022-23: +0.3% (t 1.0) · 2024-26: +0.6% (t 3.2)

What was tested, every period and the method

Stocks liquid the day before (any tier) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (down): their return over the next 21 sessions against the average liquid stock.

After a one-day drop, next 21 sessions: result by period
Period Average, % over 21 sessions t Median Cases
2017-19 +0.1 0.5 −0.3 6,203
2020-21 0.0 −0.0 −0.8 4,675
2022-23 · decides +0.3 1.0 −0.1 4,988
2024-26 · decides +0.6 3.2 −0.3 7,829
2017-26 (all) +0.3 1.9 −0.3 23,695

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day drop, next 21 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +0.1 +0.3+0.1+0.2
2020-21 0.0 −0.10.00.0
2022-23 +0.3 +0.2+0.3+0.3
2024-26 +0.6 +0.4+0.6+0.6

After a one-day drop, next 63 sessions

No measurable effect · 2022-23: +0.3% (t 0.5) · 2024-26: +0.5% (t 1.0)

What was tested, every period and the method

Stocks liquid the day before (any tier) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (down): their return over the next 63 sessions against the average liquid stock.

After a one-day drop, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 +0.2 0.6 −0.5 6,203
2020-21 −1.2 −1.4 −3.2 4,675
2022-23 · decides +0.3 0.5 −0.3 4,988
2024-26 · decides +0.5 1.0 −1.7 7,431
2017-26 (all) 0.0 0.0 −1.2 23,297

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day drop, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +0.2 +0.3+0.3+0.2
2020-21 −1.2 −1.2−1.2−1.3
2022-23 +0.3 +0.2+0.3+0.3
2024-26 +0.5 +0.4+0.4+0.5

After a one-day drop, $5-20M a day, next 21 sessions

No measurable effect · 2022-23: −0.1% (t −0.1) · 2024-26: +1.1% (t 1.9)

What was tested, every period and the method

Stocks liquid the day before ($5-20M a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (down): their return over the next 21 sessions against the average liquid stock.

After a one-day drop, $5-20M a day, next 21 sessions: result by period
Period Average, % over 21 sessions t Median Cases
2017-19 −0.4 −1.1 −0.4 2,364
2020-21 −0.1 −0.2 −0.4 1,588
2022-23 · decides −0.1 −0.1 −0.4 1,780
2024-26 · decides +1.1 1.9 −0.1 2,359
2017-26 (all) +0.2 0.6 −0.4 8,091

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods at least one check does not keep the direction of the main result.

After a one-day drop, $5-20M a day, next 21 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 −0.4 −0.1−0.3−0.3
2020-21 −0.1 −0.6−0.2−0.1
2022-23 −0.1 −0.1+0.2−0.1
2024-26 +1.1 +1.1+1.1+1.1

After a one-day drop, $5-20M a day, next 63 sessions

No measurable effect · 2022-23: −0.3% (t −0.3) · 2024-26: +2.1% (t 1.4)

What was tested, every period and the method

Stocks liquid the day before ($5-20M a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (down): their return over the next 63 sessions against the average liquid stock.

After a one-day drop, $5-20M a day, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 +0.2 0.3 −0.9 2,364
2020-21 −2.8 −1.7 −2.9 1,588
2022-23 · decides −0.3 −0.3 −0.8 1,780
2024-26 · decides +2.1 1.4 −0.5 2,252
2017-26 (all) 0.0 −0.0 −1.1 7,984

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods at least one check does not keep the direction of the main result.

After a one-day drop, $5-20M a day, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +0.2 +0.4+0.3+0.2
2020-21 −2.8 −2.6−3.3−2.8
2022-23 −0.3 −0.3+0.2−0.3
2024-26 +2.1 +2.4+1.9+2.1

After a one-day drop, $20-100M a day, next 21 sessions

No measurable effect · 2022-23: +0.2% (t 0.5) · 2024-26: +0.2% (t 0.8)

What was tested, every period and the method

Stocks liquid the day before ($20-100M a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (down): their return over the next 21 sessions against the average liquid stock.

After a one-day drop, $20-100M a day, next 21 sessions: result by period
Period Average, % over 21 sessions t Median Cases
2017-19 +0.6 0.9 −0.3 2,590
2020-21 −0.2 −0.6 −1.4 1,932
2022-23 · decides +0.2 0.5 −0.2 1,905
2024-26 · decides +0.2 0.8 −0.3 3,053
2017-26 (all) +0.2 0.9 −0.4 9,480

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods at least one check does not keep the direction of the main result.

After a one-day drop, $20-100M a day, next 21 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +0.6 +0.6+0.6+0.6
2020-21 −0.2 0.0−0.1−0.2
2022-23 +0.2 +0.1+0.1+0.2
2024-26 +0.2 −0.3+0.3+0.2

After a one-day drop, $20-100M a day, next 63 sessions

No measurable effect · 2022-23: +0.6% (t 0.8) · 2024-26: −0.9% (t −1.8)

What was tested, every period and the method

Stocks liquid the day before ($20-100M a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (down): their return over the next 63 sessions against the average liquid stock.

After a one-day drop, $20-100M a day, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 +0.3 0.4 −0.3 2,590
2020-21 −0.3 −0.4 −4.1 1,932
2022-23 · decides +0.6 0.8 −0.7 1,905
2024-26 · decides −0.9 −1.8 −2.5 2,897
2017-26 (all) −0.1 −0.3 −1.6 9,324

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day drop, $20-100M a day, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +0.3 +0.2+0.5+0.2
2020-21 −0.3 −0.5−0.3−0.4
2022-23 +0.6 +0.4+0.6+0.5
2024-26 −0.9 −1.3−0.5−0.9

After a one-day drop, $100M-1B a day, next 21 sessions

Unstable · 2022-23: +1.2% (t 2.5) · 2024-26: +0.4% (t 1.2)

What was tested, every period and the method

Stocks liquid the day before ($100M-1B a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (down): their return over the next 21 sessions against the average liquid stock.

After a one-day drop, $100M-1B a day, next 21 sessions: result by period
Period Average, % over 21 sessions t Median Cases
2017-19 +0.2 0.9 −0.1 1,293
2020-21 +0.1 0.1 −0.9 1,201
2022-23 · decides +1.2 2.5 +0.8 1,304
2024-26 · decides +0.4 1.2 −0.4 2,316
2017-26 (all) +0.4 2.0 −0.2 6,114

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day drop, $100M-1B a day, next 21 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +0.2 +0.3+0.1+0.3
2020-21 +0.1 +0.3+0.1+0.1
2022-23 +1.2 +1.0+0.9+1.2
2024-26 +0.4 +0.2+0.3+0.4

After a one-day drop, $100M-1B a day, next 63 sessions

Unstable · 2022-23: +1.1% (t 2.4) · 2024-26: +0.3% (t 0.5)

What was tested, every period and the method

Stocks liquid the day before ($100M-1B a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (down): their return over the next 63 sessions against the average liquid stock.

After a one-day drop, $100M-1B a day, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 +0.2 0.4 0.0 1,293
2020-21 +0.5 0.2 −3.0 1,201
2022-23 · decides +1.1 2.4 +0.6 1,304
2024-26 · decides +0.3 0.5 −1.6 2,187
2017-26 (all) +0.5 0.8 −0.8 5,985

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day drop, $100M-1B a day, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +0.2 +0.3−0.3+0.3
2020-21 +0.5 +0.3+1.2+0.5
2022-23 +1.1 +1.0+0.5+1.2
2024-26 +0.3 +0.3+0.2+0.3

After a one-day drop, over $1B a day, next 21 sessions

No measurable effect · 2022-23: +1.8% (t 1.1) · 2024-26: +1.7% (t 1.0)

What was tested, every period and the method

Stocks liquid the day before (over $1B a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (down): their return over the next 21 sessions against the average liquid stock.

After a one-day drop, over $1B a day, next 21 sessions: result by period
Period Average, % over 21 sessions t Median Cases
2017-19 +2.6 1.9 +1.3 40
2020-21 −1.9 −1.2 −0.3 76
2022-23 · decides +1.8 1.1 +0.6 73
2024-26 · decides +1.7 1.0 +1.1 216
2017-26 (all) +1.2 1.4 +0.5 405

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods every check keeps the direction of the main result.

After a one-day drop, over $1B a day, next 21 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +2.6 +3.1+0.7+2.6
2020-21 −1.9 −1.6−2.5−1.9
2022-23 +1.8 +2.1+1.2+1.8
2024-26 +1.7 +1.4+0.5+1.7

After a one-day drop, over $1B a day, next 63 sessions

No measurable effect · 2022-23: +1.9% (t 0.9) · 2024-26: +1.5% (t 0.6)

What was tested, every period and the method

Stocks liquid the day before (over $1B a day) with a one-day move of at least 3 standard deviations of its prior 63 sessions and at least 4% against the S&P 500 (down): their return over the next 63 sessions against the average liquid stock.

After a one-day drop, over $1B a day, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 +2.4 1.4 +2.0 40
2020-21 −1.7 −0.4 −0.3 76
2022-23 · decides +1.9 0.9 +0.7 73
2024-26 · decides +1.5 0.6 +0.3 204
2017-26 (all) +1.1 0.8 +0.7 393

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price).

In the deciding periods at least one check does not keep the direction of the main result.

After a one-day drop, over $1B a day, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +2.4 +2.6−2.5+2.4
2020-21 −1.7 −2.0−2.9−1.7
2022-23 +1.9 +1.9−1.3+1.9
2024-26 +1.5 +1.5−1.6+1.5

After a rise, a fall or a pullback

After a rise of 50% from entry, next 63 sessions

No measurable effect · 2022-23: −0.5% (t −0.2) · 2024-26: +1.1% (t 0.6)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock rose 50% from the entry close: its return over the next 63 sessions against the average liquid stock.

After a rise of 50% from entry, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 −0.3 −0.2 −0.6 783
2020-21 +1.7 0.9 −3.3 1,167
2022-23 · decides −0.5 −0.2 +0.4 435
2024-26 · decides +1.1 0.6 −0.9 1,662
2017-26 (all) +0.4 0.5 −1.3 4,046

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods every check keeps the direction of the main result.

After a rise of 50% from entry, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 −0.3 −0.2−0.2−0.5
2020-21 +1.7 +1.5+2.0+1.6
2022-23 −0.5 −0.5−0.5−0.5
2024-26 +1.1 +1.4+1.1+1.1

After a rise of 50% from entry, next 126 sessions

Unstable · 2022-23: +1.2% (t 0.5) · 2024-26: +4.2% (t 2.7)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock rose 50% from the entry close: its return over the next 126 sessions against the average liquid stock.

After a rise of 50% from entry, next 126 sessions: result by period
Period Average, % over 126 sessions t Median Cases
2017-19 +1.3 0.8 −0.7 783
2020-21 −1.1 −0.4 −7.3 1,167
2022-23 · decides +1.2 0.5 +2.1 435
2024-26 · decides +4.2 2.7 −0.7 1,403
2017-26 (all) +1.5 1.3 −2.1 3,788

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods every check keeps the direction of the main result.

After a rise of 50% from entry, next 126 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +1.3 +1.5+1.4+1.0
2020-21 −1.1 −1.4−0.5−1.5
2022-23 +1.2 +1.4+1.1+1.3
2024-26 +4.2 +4.5+4.2+4.2

After a rise of 100% from entry, next 63 sessions

No measurable effect · 2022-23: +4.4% (t 1.1) · 2024-26: +1.1% (t 0.4)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock rose 100% from the entry close: its return over the next 63 sessions against the average liquid stock.

After a rise of 100% from entry, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 +2.1 0.7 −1.6 185
2020-21 +3.1 0.9 −5.9 456
2022-23 · decides +4.4 1.1 +1.9 107
2024-26 · decides +1.1 0.4 −2.3 626
2017-26 (all) +2.5 1.6 −3.3 1,375

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods every check keeps the direction of the main result.

After a rise of 100% from entry, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +2.1 +3.6+2.2+2.9
2020-21 +3.1 +2.9+3.4+2.7
2022-23 +4.4 +4.3+4.5+4.5
2024-26 +1.1 +0.9+1.2+1.1

After a rise of 100% from entry, next 126 sessions

Holds · 2022-23: +8.6% (t 2.1) · 2024-26: +4.9% (t 2.1)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock rose 100% from the entry close: its return over the next 126 sessions against the average liquid stock.

After a rise of 100% from entry, next 126 sessions: result by period
Period Average, % over 126 sessions t Median Cases
2017-19 +0.6 0.1 −2.6 185
2020-21 +1.2 0.2 −11.4 456
2022-23 · decides +8.6 2.1 +5.3 107
2024-26 · decides +4.9 2.1 −3.9 495
2017-26 (all) +3.5 1.5 −5.5 1,243

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods every check keeps the direction of the main result.

After a rise of 100% from entry, next 126 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +0.6 +0.9+0.6+0.7
2020-21 +1.2 +1.0+1.8+0.9
2022-23 +8.6 +8.5+8.9+8.7
2024-26 +4.9 +4.8+4.8+4.9

After a fall of 30% from entry, next 63 sessions

No measurable effect · 2022-23: −0.5% (t −0.4) · 2024-26: +0.6% (t 0.5)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock fell 30% from the entry close: its return over the next 63 sessions against the average liquid stock.

After a fall of 30% from entry, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 +1.0 0.7 −0.8 1,006
2020-21 −0.3 −0.1 −3.1 1,368
2022-23 · decides −0.5 −0.4 +0.4 1,262
2024-26 · decides +0.6 0.5 −2.4 1,486
2017-26 (all) +0.3 0.4 −1.2 5,122

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods every check keeps the direction of the main result.

After a fall of 30% from entry, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +1.0 +1.2+1.0+1.0
2020-21 −0.3 −0.9−0.3−0.4
2022-23 −0.5 −0.7−0.4−0.5
2024-26 +0.6 +0.3+0.5+0.7

After a fall of 30% from entry, next 126 sessions

No measurable effect · 2022-23: −0.1% (t −0.1) · 2024-26: +1.4% (t 0.6)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock fell 30% from the entry close: its return over the next 126 sessions against the average liquid stock.

After a fall of 30% from entry, next 126 sessions: result by period
Period Average, % over 126 sessions t Median Cases
2017-19 −0.2 −0.1 −2.2 1,006
2020-21 +0.1 0.0 −7.8 1,368
2022-23 · decides −0.1 −0.1 −0.8 1,262
2024-26 · decides +1.4 0.6 −5.7 1,330
2017-26 (all) +0.3 0.2 −3.7 4,966

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods at least one check does not keep the direction of the main result.

After a fall of 30% from entry, next 126 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 −0.2 +0.10.0−0.6
2020-21 +0.1 −0.8−0.3−0.3
2022-23 −0.1 −0.4+0.1−0.1
2024-26 +1.4 +0.7+1.3+1.6

After a fall of 50% from entry, next 63 sessions

No measurable effect · 2022-23: −1.5% (t −0.8) · 2024-26: +3.7% (t 1.3)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock fell 50% from the entry close: its return over the next 63 sessions against the average liquid stock.

After a fall of 50% from entry, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 −0.8 −0.3 +2.3 307
2020-21 −0.6 −0.1 +5.0 598
2022-23 · decides −1.5 −0.8 −0.1 446
2024-26 · decides +3.7 1.3 −0.3 543
2017-26 (all) +0.3 0.2 +1.6 1,894

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods every check keeps the direction of the main result.

After a fall of 50% from entry, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 −0.8 −1.1−0.8−0.9
2020-21 −0.6 −1.9−1.3−0.6
2022-23 −1.5 −1.5−1.2−1.4
2024-26 +3.7 +2.5+3.6+3.8

After a fall of 50% from entry, next 126 sessions

No measurable effect · 2022-23: −0.8% (t −0.3) · 2024-26: +7.4% (t 1.9)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock fell 50% from the entry close: its return over the next 126 sessions against the average liquid stock.

After a fall of 50% from entry, next 126 sessions: result by period
Period Average, % over 126 sessions t Median Cases
2017-19 −0.2 −0.1 −2.9 307
2020-21 −1.6 −0.1 +0.2 598
2022-23 · decides −0.8 −0.3 −3.5 446
2024-26 · decides +7.4 1.9 −5.5 498
2017-26 (all) +1.3 0.4 −2.9 1,849

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods every check keeps the direction of the main result.

After a fall of 50% from entry, next 126 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 −0.2 +0.1+0.1−0.4
2020-21 −1.6 −2.4−3.0−1.1
2022-23 −0.8 −1.4−0.5−0.6
2024-26 +7.4 +5.9+7.2+7.6

After doubling, then 25% below the peak, next 63 sessions

No measurable effect · 2022-23: −2.3% (t −0.5) · 2024-26: +5.8% (t 1.5)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock doubled from the entry close and then closed 25% below its highest close since entry: its return over the next 63 sessions against the average liquid stock.

After doubling, then 25% below the peak, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 +3.3 1.0 +1.1 80
2020-21 +2.9 0.9 −8.1 244
2022-23 · decides −2.3 −0.5 −0.9 60
2024-26 · decides +5.8 1.5 −2.7 336
2017-26 (all) +2.8 1.3 −3.5 720

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods every check keeps the direction of the main result.

After doubling, then 25% below the peak, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +3.3 +2.0+3.4+3.1
2020-21 +2.9 +2.3+3.3+2.8
2022-23 −2.3 −3.6−2.2−2.3
2024-26 +5.8 +5.5+5.7+5.8

After doubling, then 25% below the peak, next 126 sessions

Unstable · 2022-23: −2.6% (t −0.5) · 2024-26: +10.6% (t 2.4)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock doubled from the entry close and then closed 25% below its highest close since entry: its return over the next 126 sessions against the average liquid stock.

After doubling, then 25% below the peak, next 126 sessions: result by period
Period Average, % over 126 sessions t Median Cases
2017-19 +4.8 0.8 +5.4 80
2020-21 +8.5 1.0 −7.3 244
2022-23 · decides −2.6 −0.5 −3.1 60
2024-26 · decides +10.6 2.4 −2.5 246
2017-26 (all) +5.7 1.6 −3.9 630

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods every check keeps the direction of the main result.

After doubling, then 25% below the peak, next 126 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +4.8 +3.8+4.6+3.4
2020-21 +8.5 +8.1+8.8+7.9
2022-23 −2.6 −3.7−2.3−2.6
2024-26 +10.6 +10.6+10.4+10.5

After doubling, then 35% below the peak, next 63 sessions

Unstable · 2022-23: too few cases · 2024-26: +10.8% (t 1.5)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock doubled from the entry close and then closed 35% below its highest close since entry: its return over the next 63 sessions against the average liquid stock.

After doubling, then 35% below the peak, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 +25.2 1.1 −0.8 45
2020-21 +6.1 1.4 −9.0 157
2022-23 · decides too few cases 38
2024-26 · decides +10.8 1.5 −3.0 208
2017-26 (all) +9.7 1.7 −5.3 449

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods at least one check does not keep the direction of the main result.

After doubling, then 35% below the peak, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +25.2 +20.4+25.2+25.2
2020-21 +6.1 +2.3+6.3+6.3
2022-23 too few cases too few casestoo few casestoo few cases
2024-26 +10.8 +12.4+10.6+10.8

After doubling, then 35% below the peak, next 126 sessions

Unstable · 2022-23: too few cases · 2024-26: +20.3% (t 2.8)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock doubled from the entry close and then closed 35% below its highest close since entry: its return over the next 126 sessions against the average liquid stock.

After doubling, then 35% below the peak, next 126 sessions: result by period
Period Average, % over 126 sessions t Median Cases
2017-19 +18.5 1.3 −3.5 45
2020-21 +13.5 1.1 −14.5 157
2022-23 · decides too few cases 38
2024-26 · decides +20.3 2.8 −3.3 163
2017-26 (all) +14.2 2.3 −7.8 404

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods at least one check does not keep the direction of the main result.

After doubling, then 35% below the peak, next 126 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 +18.5 +15.0+18.1+18.5
2020-21 +13.5 +9.8+14.8+13.6
2022-23 too few cases too few casestoo few casestoo few cases
2024-26 +20.3 +20.6+20.0+20.3

After doubling, then 50% below the peak, next 63 sessions

Unstable · 2022-23: too few cases · 2024-26: +7.7% (t 1.8)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock doubled from the entry close and then closed 50% below its highest close since entry: its return over the next 63 sessions against the average liquid stock.

After doubling, then 50% below the peak, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 too few cases 18
2020-21 −2.3 −0.7 −2.7 77
2022-23 · decides too few cases 20
2024-26 · decides +7.7 1.8 +3.7 97
2017-26 (all) +2.2 0.7 +0.4 212

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods at least one check does not keep the direction of the main result.

After doubling, then 50% below the peak, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 too few cases too few casestoo few casestoo few cases
2020-21 −2.3 −2.6−1.4−2.7
2022-23 too few cases too few casestoo few casestoo few cases
2024-26 +7.7 +7.7+7.3+7.7

After doubling, then 50% below the peak, next 126 sessions

Unstable · 2022-23: too few cases · 2024-26: +8.2% (t 0.9)

What was tested, every period and the method

Strong stocks (within 15% of their 252-session high and in the top fifth by 126-session return) bought every 21 sessions; the first session within a year that the stock doubled from the entry close and then closed 50% below its highest close since entry: its return over the next 126 sessions against the average liquid stock.

After doubling, then 50% below the peak, next 126 sessions: result by period
Period Average, % over 126 sessions t Median Cases
2017-19 too few cases 18
2020-21 −1.9 −0.2 −16.7 77
2022-23 · decides too few cases 20
2024-26 · decides +8.2 0.9 +7.6 76
2017-26 (all) +3.7 0.6 −6.7 191

Measured against: average liquid stock.

One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months (lag 1, 3 or 6 for 21, 63 or 126 sessions). Liquid: median dollar volume over the prior 63 sessions at least $5M, close at least $3 a share and 252 sessions of history, all at the close before the entry. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average stock of the same liquidity tier, and without names that stopped trading or traded flat (daily moves under 0.5%, as when pinned to a deal price). Strong stocks are bought on each of 21 staggered monthly calendars; each calendar's events are deduplicated on their own, its monthly means are taken, and the calendars are averaged month by month (n is per calendar), so no single buying day decides the result.

In the deciding periods at least one check does not keep the direction of the main result.

After doubling, then 50% below the peak, next 126 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 too few cases too few casestoo few casestoo few cases
2020-21 −1.9 −2.6+0.4−2.6
2022-23 too few cases too few casestoo few casestoo few cases
2024-26 +8.2 +11.5+6.8+8.2

Stocks that trade heavily on a few days only

Liquid on the mean but not the median, next 63 sessions

Holds · 2022-23: −7.1% (t −3.9) · 2024-26: −13.1% (t −9.0)

What was tested, every period and the method

Stocks whose dollar volume over the prior 63 sessions averages at least $5M a day while its median is below $5M (a few heavy days carry them over the floor): their return over the next 63 sessions against the S&P 500.

Liquid on the mean but not the median, next 63 sessions: result by period
Period Average, % over 63 sessions t Median Cases
2017-19 −1.8 −1.8 −3.3 2,336
2020-21 −0.2 −0.0 −7.7 2,209
2022-23 · decides −7.1 −3.9 −6.8 1,692
2024-26 · decides −13.1 −9.0 −12.1 3,026
2017-26 (all) −5.6 −3.6 −7.1 9,263

Measured against: S&P 500.

The stocks in that state at the close before the entry (close at least $3 a share, 252 sessions of history). One event per stock per 63 sessions; events averaged within the calendar month, months weighted equally; Newey-West t over months, lag 3. A stock that stops trading keeps its last close; returns capped at +1000%. Checked with entry at the next close, against the average $5-20M stock, and without names that stopped trading or traded flat.

In the deciding periods every check keeps the direction of the main result.

Liquid on the mean but not the median, next 63 sessions: the average under each check
Period Main result Bought at the next closeAgainst stocks of the same liquidityWithout stocks that stopped trading or traded flat
2017-19 −1.8 −1.9−0.7−1.8
2020-21 −0.2 +0.3−1.5−0.4
2022-23 −7.1 −6.6−5.2−7.2
2024-26 −13.1 −12.8−12.4−13.1

The most-traded stocks

The 30 most-traded stocks against the S&P 500

No measurable effect · 2021-23: −4.0 points a year (t −0.6) · 2024-26: +10.2 points a year (t 1.7)

What was tested, every period and the method

The 30 liquid stocks with the highest median dollar volume over the prior 63 sessions, equal weight, held 63 sessions, against the S&P 500.

The 30 most-traded stocks against the S&P 500: result by period
Period Average, points a year t Median Cases Stocks, % a yearS&P 500, % a year
2017-20 +9.7 3.0 +8.0 1,007 24.014.3
2021-23 · decides −4.0 −0.6 +1.2 753 6.110.1
2024-26 · decides +10.2 1.7 +7.7 633 28.017.8
2017-26 (all) +5.5 1.7 +6.3 2,393 19.513.9

Measured against: S&P 500.

Every session from 2017, the equal-weight return over the next 63 sessions (log growth) minus the S&P 500's, times four for a year; sessions averaged within the calendar month; Newey-West t over months, lag 3. Liquid as for the event tests; a stopped stock keeps its last close.

The 50 most-traded stocks against the S&P 500

No measurable effect · 2021-23: −4.5 points a year (t −0.8) · 2024-26: +7.3 points a year (t 1.7)

What was tested, every period and the method

The 50 liquid stocks with the highest median dollar volume over the prior 63 sessions, equal weight, held 63 sessions, against the S&P 500.

The 50 most-traded stocks against the S&P 500: result by period
Period Average, points a year t Median Cases Stocks, % a yearS&P 500, % a year
2017-20 +7.2 3.3 +5.4 1,007 21.514.3
2021-23 · decides −4.5 −0.8 −0.9 753 5.510.1
2024-26 · decides +7.3 1.7 +5.8 633 25.117.8
2017-26 (all) +3.5 1.4 +3.7 2,393 17.513.9

Measured against: S&P 500.

Every session from 2017, the equal-weight return over the next 63 sessions (log growth) minus the S&P 500's, times four for a year; sessions averaged within the calendar month; Newey-West t over months, lag 3. Liquid as for the event tests; a stopped stock keeps its last close.

The 100 most-traded stocks against the S&P 500

No measurable effect · 2021-23: −5.7 points a year (t −1.4) · 2024-26: +4.1 points a year (t 1.2)

What was tested, every period and the method

The 100 liquid stocks with the highest median dollar volume over the prior 63 sessions, equal weight, held 63 sessions, against the S&P 500.

The 100 most-traded stocks against the S&P 500: result by period
Period Average, points a year t Median Cases Stocks, % a yearS&P 500, % a year
2017-20 +4.4 2.4 +2.6 1,007 18.714.3
2021-23 · decides −5.7 −1.4 −3.2 753 4.410.1
2024-26 · decides +4.1 1.2 +3.9 633 21.917.8
2017-26 (all) +1.2 0.6 +1.9 2,393 15.113.9

Measured against: S&P 500.

Every session from 2017, the equal-weight return over the next 63 sessions (log growth) minus the S&P 500's, times four for a year; sessions averaged within the calendar month; Newey-West t over months, lag 3. Liquid as for the event tests; a stopped stock keeps its last close.

How a portfolio's stocks are weighted

Sizing by inverse volatility against equal weight

Unstable · 2021-23: +1.4 points a year (t 2.1) · 2024-26: −0.8 points a year (t −0.6)

What was tested, every period and the method

Random 15-name books of strong stocks held 63 sessions: weighting by inverse volatility of the prior 63 sessions' daily returns (at most 25% a name) against equal weight, in growth a year.

Sizing by inverse volatility against equal weight: result by period
Period Average, points a year t Median Cases Equal weight, % a yearInverse volatility, % a yearInverse variance, % a year
2017-20 −1.8 −1.8 −1.4 1,007 16.414.613.3
2021-23 · decides +1.4 2.1 +0.5 753 0.82.22.9
2024-26 · decides −0.8 −0.6 −0.7 633 16.415.614.6
2017-26 (all) −0.5 −0.8 −0.5 2,393 11.511.010.4

Measured against: equal weight.

Every session, 10 random books from the strong stocks (seed 11); the difference in mean log growth over 63 sessions, times four; sessions averaged by calendar month; Newey-West t, lag 3. A stopped stock keeps its last close.

Sizing by inverse variance against equal weight

Unstable · 2021-23: +2.1 points a year (t 2.0) · 2024-26: −1.8 points a year (t −0.7)

What was tested, every period and the method

Random 15-name books of strong stocks held 63 sessions: weighting by inverse variance of the prior 63 sessions' daily returns (at most 25% a name) against equal weight, in growth a year.

Sizing by inverse variance against equal weight: result by period
Period Average, points a year t Median Cases Equal weight, % a yearInverse volatility, % a yearInverse variance, % a year
2017-20 −3.1 −1.8 −2.4 1,007 16.414.613.3
2021-23 · decides +2.1 2.0 +1.1 753 0.82.22.9
2024-26 · decides −1.8 −0.7 −1.4 633 16.415.614.6
2017-26 (all) −1.1 −1.0 −1.1 2,393 11.511.010.4

Measured against: equal weight.

Every session, 10 random books from the strong stocks (seed 11); the difference in mean log growth over 63 sessions, times four; sessions averaged by calendar month; Newey-West t, lag 3. A stopped stock keeps its last close.

Holding cash when the market is below its trend

Cash while the S&P 500 is below its 200-day average

No measurable effect · 2022-23: +0.4 points a year (t 0.1) · 2024-26: −4.2 points a year (t −1.6)

What was tested, every period and the method

A book of strong stocks re-formed every 21 sessions, held in cash on each session after the S&P 500 closed below its 200-day average, against the same book always invested.

Cash while the S&P 500 is below its 200-day average: result by period
Period Average, points a year t Median Cases With the cash rule, % a yearAlways invested, % a yearS&P 500, % a yearInvested, % of sessionsSwitches, count
2017-19 −2.2 −0.8 0.0 36 9.712.214.791.014
2020-21 +2.1 0.2 0.0 24 26.123.523.488.06
2022-23 · decides +0.4 0.1 0.0 24 −4.4−4.71.656.024
2024-26 · decides −4.2 −1.6 0.0 34 13.218.221.092.06
2017-26 (all) −1.4 −0.5 0.0 118 10.812.315.384.050

Measured against: always invested.

The book is 21 staggered tranches, each re-formed every 21 sessions on its own day, so no single re-formation day decides the result. Daily returns, equal weight (a stopped stock at its last close), cash earns nothing; the difference in log growth by calendar month, times twelve for a year; Newey-West t over months, lag 1. Growth a year of each, the S&P 500's, the share of sessions invested and the number of switches by period.

What skill in ranking stocks is worth

Ranking skill and breadth for a 20-name book

Unstable · 2021-23: −8.7 points a year (t −3.0) · 2024-26: −4.7 points a year (t −1.9)

What was tested, every period and the method

A 20-name book picked by a signal with a given rank correlation (skill) to the next 63 sessions' returns, choosing among 40, 400 or all liquid stocks, in growth a year. The measured line is the no-skill book (all ranked) against the S&P 500; the table shows what each level of skill adds.

Ranking skill and breadth for a 20-name book: result by period
Period Average, points a year t Median Cases 20-name book, % a yearS&P 500, % a year
2017-20 −0.1 −0.0 −2.8 1,007 14.214.3
2021-23 · decides −8.7 −3.0 −6.4 753 1.410.1
2024-26 · decides −4.7 −1.9 −4.2 633 13.217.8
2017-26 (all) −4.0 −1.7 −4.0 2,393 9.913.9

Measured against: S&P 500.

Growth a year by skill, 2017-26; the S&P 500: 13.9% a year
Skill 20 names from 40, % a year20 names from 400, % a year20 names from all stocks, % a year10 names from 40, % a year10 names from 400, % a year10 names from all stocks, % a year30 names from 40, % a year30 names from 400, % a year30 names from all stocks, % a year
Skill 0.00 10.29.89.99.99.59.410.310.110.0
Skill 0.02 11.513.114.011.913.013.710.913.013.9
Skill 0.03 12.114.716.112.814.715.911.314.515.9
Skill 0.04 12.716.218.113.816.518.111.615.917.8
Skill 0.05 13.317.720.114.718.320.311.917.419.8
Growth a year by skill, 2021-26; the S&P 500: 13.7% a year
Skill 20 names from 40, % a year20 names from 400, % a year20 names from all stocks, % a year10 names from 40, % a year10 names from 400, % a year10 names from all stocks, % a year30 names from 40, % a year30 names from 400, % a year30 names from all stocks, % a year
Skill 0.00 7.06.66.86.56.36.17.16.87.0
Skill 0.02 8.310.011.38.79.910.77.89.811.2
Skill 0.03 9.011.613.59.611.813.08.211.413.2
Skill 0.04 9.613.315.610.613.715.48.512.915.3
Skill 0.05 10.214.917.711.615.617.88.914.417.4

Every session, 8 paired draws (seed 21): one noise vector and one draw of names serve every skill and breadth. Signal = skill × normal score of the realised rank + noise. Mean log growth times four. The book is re-selected every 63 sessions, so the table is an upper bound.

What an average stock did next, by situation

Stocks grouped by how much they trade (the median dollar value a day over the last 63 sessions) and whether they had a one-day jump or drop in the last five sessions: their average return over the next 21 and 63 sessions against the average liquid stock, in the most recent period, with the result's state.

Base rates by trading volume and recent move
Trades a day, and recent move Next 21 sessions, %Next 63 sessions, %
$5-20Ma one-day jump in the last five sessions −0.7 2024-26 · no measurable effect −0.9 2024-26 · no measurable effect
$5-20Ma one-day drop in the last five sessions +1.3 2024-26 · unstable +2.3 2024-26 · no measurable effect
$5-20Mno one-day jump or drop in the last five sessions −0.2 2024-26 · unstable +0.2 2024-26 · unstable
$20-100Ma one-day jump in the last five sessions 0.0 2024-26 · no measurable effect −1.1 2024-26 · unstable
$20-100Ma one-day drop in the last five sessions −0.3 2024-26 · no measurable effect −0.9 2024-26 · no measurable effect
$20-100Mno one-day jump or drop in the last five sessions −0.1 2024-26 · no measurable effect −0.5 2024-26 · unstable
$100M-1Ba one-day jump in the last five sessions −0.4 2024-26 · unstable −0.5 2024-26 · unstable
$100M-1Ba one-day drop in the last five sessions +0.1 2024-26 · unstable +0.5 2024-26 · no measurable effect
$100M-1Bno one-day jump or drop in the last five sessions 0.0 2024-26 · no measurable effect 0.0 2024-26 · no measurable effect
over $1Ba one-day jump in the last five sessions +2.0 2024-26 · no measurable effect +5.6 2024-26 · unstable
over $1Ba one-day drop in the last five sessions +1.5 2024-26 · no measurable effect +3.3 2024-26 · no measurable effect
over $1Bno one-day jump or drop in the last five sessions +0.9 2024-26 · no measurable effect +2.9 2024-26 · unstable