Momentum and mean reversion in S&P 500 stocks, 2000–2026

Research note and proof of concept · 8 November 2026 · Price data through 6 November 2026

Start with the overview below (about five minutes). The full report follows it.

Overview: the five-minute version

What we did

The requirements sheet listed four trading ideas. We reviewed all four, then built and ran a full test of the second one, momentum. Its question is simple: if a stock has recently been one of the S&P 500's biggest winners, does it keep beating the market? And do the biggest losers bounce back?

We started there because it can be tested with free data, decades of research exist to check our numbers against, and the same tools will serve the politician-trading idea later.

The short answer is no, not reliably. Between 2000 and 2026, recent winners kept winning in some years and fell behind in others. The effects were small, a few percent over a year, and too weak to tell apart from luck. No version of the strategy beat simply buying and holding SPY over the last ten years.

How the test works

On a typical recent month-end, about 460 index stocks had at least a year of price history. We:

1. measure each stock's return over a recent window (we tried six, from one week to twelve months);
2. sort the stocks and call the top 10%, about 46 of them, the winners, and the bottom 10% the losers;
3. pretend to buy each group at the next day's close (you can't trade at the price you used to decide);
4. follow both groups for a year and, each day, compare their return with the average of all 460 stocks.

We repeat this at every month-end from January 2000 to October 2026, 322 times in all, and average the results to see what typically happens next.

Three details keep the test honest:

• Compare with the average stock, not with zero. In a rising market almost everything goes up; what matters is whether winners went up more.
• Use the index as it was, not as it is. Today's list holds only companies that survived and grew; testing the past with it is like judging a stock picker only by the stocks they still own. We rebuilt the list for every date.
• Practice, then test. Settings were chosen using 2000–2015 only, and 2016–2026 was checked once at the end, like revising with practice papers and then sitting the real exam.

What we found

1. The two periods disagree. Figure B follows the previous 12 months' top 10%. In the practice period they fell steadily behind the average stock, ending the year 4.4% behind; in the test period they ended 2.4% ahead. A pattern worth trading would point the same way in both, and neither result passes a standard significance test.

2. A few extreme years drive the averages. Figure C splits the same measure by the year the winners were picked. Most years land within a few percent of zero, either way. The practice-period loss comes mainly from winners picked in 2000, at the top of the dot-com bubble (42% behind), and in 2008–09, when the previous losers led the rebound (13–16% behind). Without those three years the practice average is +0.4%. Likewise, the test-period gain comes almost entirely from winners picked in 2023 and 2024; without them it is −0.3%.

3. Most winners do not keep winning. Over the six months after being picked, between 47 and 50 out of every 100 winners beat the average stock, about the same as for stocks in general (47 out of 100). Any gain on average comes from a handful that keep rising strongly.

4. Losers bounced back a little. The bottom 10% beat the average stock by up to about 4% over the next year in both periods, which fits the sheet's mean-reversion question. The evidence is weak, though, and the practice figure is flattered by missing data: losers that went bankrupt are not in the free price data.

5. As a strategy, nothing beat SPY. The setting that looked best in the practice period became a portfolio: each month, buy the previous week's top 10% in equal amounts and hold each batch for six months, after trading costs. A second version moved to cash whenever SPY was below its 200-day average. Figure D compares both with SPY and with owning every index stock equally.

In the test period the momentum portfolio returned 13.1% a year against SPY's 14.4%, and its worst fall from a peak was deeper (38% against 34%). The version with the cash rule had a smaller worst fall (31%) but returned only 6.7% a year. It tended to move to cash after the market had already dropped, then miss the quick rebounds (early 2019, 2020, 2025).

6. A good-looking result can still be misleading. In the practice period the momentum portfolio beat SPY by about 6 points a year, which looks like a discovery. But owning every index stock in equal amounts did just as well (Figure D, left). The gain came from equal weighting, which favored smaller index companies in those years, plus some help from the missing bankrupt companies, not from momentum. Checking every result against a benchmark built from the same data is what caught this. (Compared with RSP, a real equal-weight index fund, the missing data added about 1.8 points a year in the practice period and 0.7 in the test period.)

Against the requirements

The sheet asks for a return above buy-and-hold together with a smaller worst loss. In the test period no version met both. The momentum portfolio met neither, and the cash-rule version met only the second.

What this means, and what comes next

With free data, momentum in the 500 largest US stocks has not been strong or consistent enough to trade on its own since 2000. That is still useful: it rules out the simple version before any money goes in, and the tools can be reused. Next steps:

1. Re-run with data that includes delisted companies (Norgate Data, Sharadar or CRSP), which removes the main weakness in the current data.
2. Test a wider set of stocks, such as the Russell 1000 or 3000. Research generally finds momentum stronger among smaller companies.
3. Use the same method on the politician-trading idea, with the date each trade was disclosed as the event, or on company insiders buying their own shares.

The full write-up follows: the review of all four ideas (Section 2), data (3), the model with formulas (4), all results tables (5) and limitations (7).

1. What we set out to do

The requirements sheet (notes/Modeling requirements.csv) lists four ideas:

The work had two parts: a critique of the four ideas (Section 2), and a proof of concept for the one with the best chance of producing a trustworthy answer with free data (Sections 3–5). We chose idea 2. It can be tested with free data, it has decades of academic research to compare against, and the machinery it needs (a historical index membership list, an event study and a backtester) is the same machinery idea 3 needs.

2. Review of the four ideas

2.1 Points that apply to all four

• Requirements should be pass/fail tests fixed in advance. For example: "Over 2016–2026, after 10 basis points of trading cost per trade, the strategy's risk-adjusted return beats SPY's and its worst drawdown is smaller than SPY's." Writing the test down before looking at results stops the goalposts from moving.
• Win rate is a weak target, and 75% is not realistic for daily direction. Published models that predict the next day's market direction usually manage 52–56% accuracy. A backtest showing 75% almost always means the model used information it could not have had at the time of the trade. Win rate also ignores the size of wins and losses: a strategy that wins 40% of the time can beat one that wins 75% of the time. Return per unit of risk (Sharpe ratio) and return per unit of drawdown (Calmar ratio) are better summaries.
• Return above buy-and-hold and drawdown below it is the hardest combination to get. A strategy that sits in cash part of the time usually reduces drawdown and return together.
• Use data as it was known on each date. That means the index members on that date (not today's list), economic figures as first published (not later revisions), a delay between signal and trade, and trading costs.
• Count the variants tested. If you try 24 settings and keep the best one, its backtest will look better than its real prospects. The best setting needs to clear a higher bar, and should be tested once on data that played no part in choosing it.

2.2 Idea by idea

2.3 Other ideas worth testing

• A trend filter on the index, such as holding stocks only while the index is above its 10-month average (Faber 2007). It targets the drawdown requirement directly. We tested a version of it in Section 5.
• Volatility-scaled momentum, which cuts position size when recent volatility is high. Research suggests it handles momentum crashes better than a trend filter (Barroso & Santa-Clara 2015; Daniel & Moskowitz 2016).
• Post-earnings drift: another "how long does a move last" question, with a clean event date.

3. Data

3.1 Which stocks count

A momentum test on "S&P 500 stocks" must use the stocks that were in the index at the time. Today's list contains only the companies that survived and grew, so testing past years with it builds in a large upward bias.

We used the historical membership file from github.com/fja05680/sp500, which records the full list of members on each date the list changed. On each date in our study, a stock is a candidate only if it was a member that day. Across 1999–2026, 1,103 distinct tickers were members at some point.

3.2 Prices

Daily prices adjusted for splits and dividends came from Yahoo Finance. Yahoo has a gap that matters here: it has no data for companies that no longer trade, whether acquired or bankrupt. We found prices for 724 of the 1,103 tickers. Table 3 shows what share of each year's members we could price.

Coverage is good from 2016 on, which is why 2016 onward became the out-of-sample test period. Three problems with tickers needed fixing first:

• Renamed tickers. When a company changes ticker, Yahoo files its whole history under the new one (FB became META; ANTM became ELV; BK became BNY). The membership file uses the old ticker for old dates, so those dates came up empty. We mapped 31 renames to their current tickers, checking each one: the old ticker's membership ends where the new one's begins, and Yahoo's history under the new ticker covers the old period.
• Recycled tickers. Some old tickers now belong to unrelated companies whose Yahoo history overlaps the original company's time in the index. CCU was Clear Channel in the index until 2008; on Yahoo it is a Chilean brewer with data back to 1999. We excluded six such tickers (CCU, CPWR, CSR, EP, PARA, SNT). We also required 12 months of price history before a stock could be ranked, which screens out recycled tickers whose new data starts partway through the old membership.
• Bad prices. We searched for extreme one-day moves among index members. Most were real (financial stocks in 2008–09, for example). Two kinds were not: one-day spikes that reverse the next day, and a mis-adjusted spin-off (Danaher shows a fake +61% day when Fortive was spun off in July 2016). We neutralize these by setting that day's return to zero. Because the cleaning works on daily returns and the price series is rebuilt from them, a bad day no longer leaves a permanent jump in later prices.

3.3 Survivorship bias

Even after these fixes, about half the members in 2000 and a fifth in 2016 are missing, mostly companies that were later acquired or went bankrupt. Two steps limit the damage:

1. Every result is measured relative to the average stock in the same data. If the missing companies would have dragged down everyone's average, the comparison group is lifted by the same amount, and most of the bias cancels.
2. We measure the bias directly. RSP is an ETF that holds every S&P 500 member at equal weight, including the ones that later disappeared. The gap between our equal-weight universe and RSP estimates the bias: about +1.8 percentage points a year in 2003–2015 and +0.7 a year from 2016 (Section 5.6).

Cash returns use the 13-week Treasury bill yield (Yahoo ticker ^IRX). The market benchmark is SPY, with dividends reinvested.

4. The momentum model

4.1 The question in testable form

The sheet asks whether recent top performers keep rising, whether most of them do, for how long, and whether and when they mean revert. In testable form:

At the end of each month, rank every eligible index member by its return over a recent window. Take the top 10% ("winners") and bottom 10% ("losers"). Over the following year, how does each group's return compare with the average eligible stock's, day by day? What share of each group beats the average?

This design is called an event study: the "event" is a stock landing in the top or bottom tenth, and we trace what happens afterwards. Repeating it every month from January 2000 to October 2026 gives 322 events of each kind for each lookback window.

4.2 Notation

• P_i,t: the cleaned, dividend-adjusted price of stock i on trading day t.
• t: a formation date, the last trading day of a month.
• U_t: the eligible universe on t, every stock that is an index member on t, has a price on t, and has a price 252 trading days earlier. Its median size was 311 stocks in 2000–2015 and 464 from 2016.
• L, s: the formation window length and the number of most recent days to skip, both in trading days.
• h: days since the position was opened, from 0 to 252 (about one year).

4.3 Formation: ranking the stocks

Each stock's formation return is its price change over the window:

R_i,t = P_{i, t−s} / P_{i, t−L} − 1

We test six windows:

Stocks in U_t are sorted by R_i,t. The top 10% form the winner group W_t and the bottom 10% the loser group D_t. That is about 31 stocks per group in 2000–2015 and 46 from 2016. Every window uses the same universe, so differences between windows come from the ranking alone.

4.4 Tracking what happens next

Prices at the close on day t are needed to compute the ranking, so nobody could trade at that close. Tracking therefore starts at the next day's close, t+1. Each stock's cumulative return h days later is:

r_i(t, h) = P_{i, t+1+h} / P_{i, t+1} − 1

If a stock's price history ends during the year (for example, it is taken over), its last price is carried forward, as if the position had been turned into cash at that price.

4.5 Measuring relative to the average stock

Each group's return is the simple average of its members' returns, which is what an equal-weighted portfolio bought on day t+1 and held without rebalancing would earn. From it we subtract the same average across the whole universe:

X_W(t, h) = avg_{i ∈ Wt} r_i(t, h) − avg_{j ∈ Ut} r_j(t, h)

The same is done for losers. This excess return answers "did winners do better than the average stock?" rather than "did winners go up?". In a rising market almost everything goes up, so the second question says little about momentum. As explained in Section 3.3, subtracting the average from the same data also cancels most of the survivorship bias.

For the question "do most winners keep winning?", we also record the hit rate: the share of the group whose own return beats the universe average. We compute the same share for the whole universe as a baseline. That baseline sits below 50%, because single-stock returns are skewed: a few very large gains pull the average above what the typical stock earns.

4.6 Averaging over time and testing significance

The curves in Figure 1 are averages of X(t, h) across all formation dates in a period, plotted against h. For the grid in Tables 6–9 we read the average at five holding periods (1 week, 1, 3, 6 and 12 months) and test whether it differs from zero.

The test needs care. Formation dates are a month apart, but a 12-month holding period means consecutive observations share 11 months of returns, so they are far from independent. An ordinary t-statistic would overstate confidence badly. We use the Newey–West (1987) standard error, which allows for this overlap, with the number of lags set to the holding period in months. As a rule of thumb, a t-statistic above 2 in absolute value is evidence of a real effect, and one below 1.5 is consistent with noise.

4.7 Keeping the test honest: the split

The data is split into an in-sample period (formation dates from January 2000 to December 2015), used to explore and choose settings, and an out-of-sample period (January 2016 onward), looked at once with settings already fixed.

A simple date split still leaks. A stock picked in November 2015 and held for 12 months earns most of its return in 2016. We drop any in-sample observation whose holding window ends after 31 December 2015, so in-sample statistics never use 2016 prices. This is why the in-sample count falls from 191 months at a 1-month hold to 179 at a 12-month hold.

4.8 Choosing one setting

To turn the study into a strategy we need one formation window and one holding period. The script picks the pair with the highest in-sample t-statistic for winners from 24 candidates (6 windows × 4 holding periods of 1, 3, 6 or 12 months; the 1-week hold is left out because the portfolio trades monthly). It then applies a gate: if the best t-statistic is below 2, the result does not qualify as a strategy. Picking the best of 24 noisy numbers favors whichever had the luckiest draw, so a modest t-statistic for the winner of that contest means even less than it would for a single pre-chosen setting (see Bailey & López de Prado 2014). The backtest runs either way so the machinery and benchmarks can be checked.

4.9 Turning the signal into a portfolio

The portfolio follows Jegadeesh & Titman (1993). Each month a new cohort of winners is bought at equal weight and held for H months. At any time the portfolio therefore holds the last H cohorts, each with 1/H of the capital. At each monthly rebalance the target weight of stock i is:

w_i = Σ_k=0…H−1 (1/H) · (1/|W_t−k|) · [i ∈ W_t−k]

where the bracket is 1 if the stock was a winner in that month's cohort and 0 otherwise.

Example. With H = 6 and 46 winners per month, each cohort holds 1/6 ≈ 16.7% of capital and each stock in a cohort gets 16.7% / 46 ≈ 0.36%. A stock that was a winner in three of the last six months holds about 1.09%. The portfolio holds up to 276 positions, usually fewer because of repeats.

Between rebalances weights drift with prices. At each rebalance the portfolio is reset to the target weights. Stocks that left the index stay in their cohort until it expires, as they would in a real account.

4.10 Trend filter

A second version applies a simple market filter aimed at the drawdown requirement. At each month-end, if SPY closes below its 200-day moving average, the target is 100% cash for that month. The 200-day setting is the conventional one and was not tuned. The filter was in cash in 30% of in-sample months and 17% of out-of-sample months (22 of 130).

4.11 Costs, cash and execution

• Execution. The signal uses the month-end close; trades fill at the next day's close.
• Costs. 10 basis points (0.10%) of the value traded, charged on both buys and sells. Turnover is the sum of all absolute weight changes at a rebalance. The momentum portfolio turned over about 3.9 times a year, a cost of roughly 0.4% a year. Large S&P 500 stocks usually cost less than 10 basis points to trade at modest size, so this setting is conservative. Run with --cost-bps 25 to stress it.
• Cash. Any uninvested weight earns the daily 13-week T-bill rate.

4.12 Performance measures

5. Results

5.1 Event study

The two periods disagree. In 2000–2015, winners over 6 and 12 months fell behind the average stock steadily for the whole following year. Most of that comes from two episodes. Stocks picked as 12-month winners during 2000, near the top of the dot-com bubble, lagged the average stock by 42% over the following year. Winners picked during 2008 and 2009 lagged by 13–16% as the market rebounded in 2009 and the previous year's biggest losers rallied hardest, a pattern known as a momentum crash (Daniel & Moskowitz 2016). Leaving out formation dates in 2000, 2008 and 2009, the in-sample average for 12-month winners is close to zero (+0.4%). The out-of-sample gain is similarly concentrated: without winners picked in 2023 and 2024 it falls from +2.4% to −0.3%. Figure C in the overview shows the year-by-year results. From 2016, winners on every window pulled ahead slowly, and losers also beat the average slightly.

Where winners did pull ahead, the gain built slowly for most of the year, peaking between trading days 204 and 244 (about 10 to 12 months), and little of it was given back within the year. These are small numbers, however: 2–3% over a year, before asking whether they are distinguishable from noise.

5.2 Formation × holding grid

Each cell is the average excess return over the holding period, with the Newey–West t-statistic in parentheses.

None of the 120 cells has a t-statistic above 2 in absolute value. The largest are −1.8 (12-month winners held 6 months, 2000–2015) and +1.7 (6-month winners held 6 months, 2016–2026). The in-sample sign pattern for winners (mostly negative) does not carry into the out-of-sample period (mostly positive). An effect that real money could rely on would show up in both. Losers beat the average in most cells of both periods, which looks like mean reversion, but the evidence is weak (t-statistics of 1.5 or less), and the in-sample figures are the ones most inflated by survivorship bias: losers that kept falling until they were delisted are missing from the data.

5.3 Do most winners keep winning?

Winners beat the average about as often as any stock does. The modest average gain in Table 8 therefore comes from a minority of winners that keep going up strongly, not from most winners continuing. In 2000–2015 the share was lower still: 41–46% for 12-month holds.

5.4 The chosen setting

The highest in-sample t-statistic among the 24 candidates belonged to 1-week winners held for 6 months: +0.7% excess return, t = 0.9. That is far below the gate of 2, so no setting qualified as a strategy. Out of sample, the same setting returned +0.8% (t = 1.1). Results did not fall apart out of sample; there was simply nothing in-sample to begin with. The backtest below uses this setting to show the machinery and benchmarks at work.

5.5 Backtest

Three things stand out.

The in-sample momentum result is not momentum. In 2000–2015 the momentum portfolio beat SPY by about 6 percentage points a year. Taken alone, that looks like a discovery. But the plain equal-weighted universe did the same (10.8% against momentum's 10.6%). The gap over SPY came from equal weighting, which favored smaller index members after the 2000 technology peak, and from survivorship bias. Without the equal-weight benchmark, this backtest would have been badly misread.

Out of sample, nothing beat SPY. Momentum and equal-weight both trailed SPY by 1–2 points a year, during a decade when the largest companies led the market.

The trend filter's in-sample success did not carry over. In 2000–2015 it cut the worst drawdown from −66% to −21% because it was in cash for much of the 2001–02 and 2008–09 bear markets. From 2016 the market's sharp falls reversed quickly (late 2018, March 2020, April 2025). The filter went to cash after much of the fall had already happened and missed part of each rebound. Its return fell to 6.7% a year, while its worst drawdown (−31.1%) was only slightly smaller than SPY's (−33.7%).

5.6 Survivorship check

RSP's annual fee (about 0.2%) and quarterly rebalancing explain a small part of each gap, so the true bias is somewhat smaller than shown. The bias is real but much smaller than the equal-weight effect. It is also concentrated where we expected: the early years with the worst coverage. Results measured relative to our own universe (Sections 5.1–5.3) are less affected than raw returns.

5.7 Against the requirements

Ideas 1 and 4 in the sheet ask for a return above buy-and-hold and a drawdown below it. Applying the same test to the out-of-sample results:

6. Answers to the questions in the sheet

Does the stock continue to rise? Relative to the average S&P 500 stock, not reliably. From 2000 to 2015, 6- and 12-month winners did worse than average over the next year. From 2016 they did 2–2.5% better over a year. Neither result is statistically reliable.

Do most stocks continue to rise? No. Fewer than half of the winners beat the average stock in any holding period beyond a week, about the same share as for stocks in general.

For how long? When winners did pull ahead (2016–2026), the gain built slowly for about 10–12 months. There was no clean point at which the trend stopped.

Does the stock mean revert? Do most? How long until? Losers beat the average stock by 0.7–4.4% over the following year in both periods, which points toward mean reversion, but none of these results is statistically reliable. Last week's and last month's winners showed at most a weak reversal: in 2000–2015 they lagged the average by 0.3–0.4% over the next one to three months (t-statistics between −1.1 and −1.4), and from 2016 there was none. In older US data, short-term reversal is a well-documented effect.

Buying and then selling after that time. The best in-sample combination was not strong enough to justify trading. Out of sample, the momentum portfolio trailed SPY by 1.3 points a year with a deeper drawdown.

7. Limitations

• Incomplete survivorship correction. Delisted companies are missing (about half of members in 2000). The relative design and the RSP check limit the damage but do not remove it. In-sample results deserve less weight than out-of-sample ones.
• Data vendor quality. Yahoo's adjusted prices sometimes mishandle spin-offs and other corporate actions. We fixed the one clear case we found; others may remain. The membership file and our rename list are maintained by hand.
• Large stocks only. Research generally finds momentum stronger among smaller companies. A null result in the S&P 500 does not rule out momentum in a broader universe.
• One portfolio design. Equal-weighted, long-only, monthly rebalancing, top 10%. Other designs (value weights, long/short, volatility scaling) could behave differently.
• Costs are simplified. A flat 10 basis points per trade, no taxes, no market impact. Reasonable for a small account trading large stocks, but not for a large one.
• Short history for significance. 129 out-of-sample months, heavily overlapping at long holding periods, cannot detect an effect of 2% a year with confidence. The absence of a reliable effect is not proof that there is none.

8. Next steps

1. Survivorship-free data. Re-run with a dataset that includes delisted companies (Norgate Data, Sharadar, or CRSP for academic users). This is the most important step before any result is trusted with money.
2. A broader universe. Extend to the Russell 1000 or 3000, where the academic evidence for momentum is stronger.
3. Volatility-scaled momentum in place of the SPY trend filter.
4. Reuse the event study for idea 3. Replace "month-end" with the disclosure date of each politician's trade, or each corporate insider purchase, and keep the rest of the method unchanged.
5. Record these results in the "Results" column of the requirements sheet, together with the pass/fail tests from Section 2.1.

Appendix A: Reproducing the results

uv sync
uv run python -I scripts/fetch_data.py       # first run ~3 min; cached in data/cache/
uv run python -I scripts/momentum_study.py   # ~30 s; tables to the terminal, charts and CSVs to reports/
uv run python -I scripts/momentum_study.py --cost-bps 25   # stress trading costs

Appendix B: Parameters

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