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Does the first half hour predict the last? Intraday momentum in S&P 500 futures

Micro E-mini S&P 500 (MES) · 5-minute bars · 2016 to 2026 · Momentum · The rule of Gao, Han, Li and Zhou (2018)

No edge after costs: profit factor 0.85 out of sample.

Profit factor, out of sample
0.85
Average trade, out of sample
−0.04R
Win rate, out of sample
48%
Trades, 10 years
2,626
Max drawdown
$60,449
Pass odds, median plan
0.1%

Hypothetical results. These results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under- or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.

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Abstract

We backtested the first-half-hour intraday momentum rules on Micro E-mini S&P 500 (MES) 5-minute bars from 2016-01-11 to 2026-10-30: 2,626 trades, with commission and a tick of slippage on every market and stop fill. In sample (to 2023-08-03) it made −0.12R per trade with a profit factor of 0.61; out of sample (from 2023-08-04) −0.04R per trade and 0.85 over 788 trades. 0 of the 16 parameter settings we tried were profitable out of sample. Sized at $250 of risk a trade, simulated 50K evaluations passed 0% to 0% of the time across 36 tracked plans.

1Hypothesis

The return from yesterday's close to 10:00 ET has been found to predict the return of the last half hour. Trade the last half hour in its direction.

If the first half hour's move carries information that is traded late in the day, the last half hour should move in the same direction more often than not.

2Data

Instrument
Micro E-mini S&P 500 (MES), traded on the ES price series (ES.c.0: front month, rolled on the calendar). CME Globex via Databento.
Period
2016-01-11 to 2026-10-30: 2,746 sessions, 1,056,820 one-minute bars, built into 210,816 5-minute bars of the regular session (09:30 to 16:00 ET).
Costs
$0.75 commission a contract each way and 1 tick ($1.25) of slippage on every market and stop fill. Limit orders fill when price touches them; market orders fill at the next bar's open and stops at their price, each with one tick of slippage; when a bar touches both the stop and the target, the stop counts.
Position size
About $250 of risk a trade: micro contracts, rounded down, at least one. R is a trade's net P&L divided by its risk at entry.
Out of sample
The last 30% of weekdays: 2023-08-04 on (846 days), after 1,974 in-sample days. The rules were fixed before either side was run.

3Method

Our reading of the publicly described rules; the creator may trade it differently. The rules, exactly as the code runs them:

  1. The first half hour's return runs from the previous session's 16:00 ET close to 10:00 ET.
  2. Entry: at entry_min (15:30 ET, as minutes after midnight: 930), buy if that return was positive and sell if it was negative, when its size is at least min_r1_pct (0%).
  3. Exit: flat at 15:59 ET, the end of the last half hour.
  4. Stop: 3 times ATR(14) of the 5-minute bars, wide enough to leave the half hour alone; it gives each trade a defined risk for sizing and for R.
  5. Size: about risk_usd dollars of risk a trade (micro contracts, rounded down, at least 1 and at most max_contracts).
bot.py, the file the engine ran
"""Intraday momentum: the first half hour's return predicts the last half hour's, on Micro E-mini S&P 500 (MES). The trading rule of Gao, Han, Li and Zhou (2018), run on 5-minute regular-session bars. Rules:  1. The first half hour's return runs from the previous session's 16:00 ET close to 10:00 ET.  2. Entry: at `entry_min` (15:30 ET, as minutes after midnight: 930), buy if that return was positive     and sell if it was negative, when its size is at least `min_r1_pct` (0%).  3. Exit: flat at 15:59 ET, the end of the last half hour.  4. Stop: 3 times ATR(14) of the 5-minute bars, wide enough to leave the half hour alone; it gives     each trade a defined risk for sizing and for R.  5. Size: about `risk_usd` dollars of risk a trade (micro contracts, rounded down, at least 1 and at     most `max_contracts`)."""import qy  def ready(*values):    """True when every value is a number (indicators have no value until they have enough data)."""    return all(v is not None and v == v for v in values)  class Bot(qy.Strategy):    """Trade the last half hour in the direction of the first."""     symbol = "MES"    timeframe = "5m"    session = "rth"    params = {"entry_min": 930, "min_r1_pct": 0.0, "risk_usd": 250, "max_contracts": 50}    max_position = 50    entry_window = ("15:00", "15:55")    flatten_time = "15:59"    overnight = False     def setup(self):        self.atr_line = self.atr(14)        self.day = None        self.prev_close = self.last_close = None        self.r1 = None     def _size(self, risk_points):        per_contract = risk_points * self.point_value        n = int(self.p.risk_usd // per_contract) if per_contract > 0 else 1        return max(1, min(self.p.max_contracts, n))     def on_bar(self, bar):        if bar.date != self.day:            self.day = bar.date            self.prev_close = self.last_close            self.r1 = None        self.last_close = bar.close        t = bar.dt.hour * 60 + bar.dt.minute + 5        if t == 600 and self.prev_close:            self.r1 = (bar.close / self.prev_close - 1) * 100        if t != self.p.entry_min or self.r1 is None or abs(self.r1) < self.p.min_r1_pct or self.r1 == 0:            return        atr = self.atr_line[0]        if not ready(atr) or not self.position.is_flat:            return        qty = self._size(3 * atr)        if self.r1 > 0:            self.buy(qty, stop_atr=3, tag=f"Momentum long | f={self.r1:.4f}")        else:            self.sell(qty, stop_atr=3, tag=f"Momentum short | f={self.r1:.4f}")

4Results

Table 1. In sample (2016-01-11 to 2023-08-03) against out of sample (2023-08-04 to 2026-10-30), after costs.
StatisticIn sampleOut of sampleAll
Trades1,8387882,626
Net P&L−$52,938−$6,769−$59,707
Profit factor0.610.850.67
Average trade−0.12R−0.04R−0.10R
95% interval of the average−0.15 to −0.09−0.09 to 0.00−0.12 to −0.07
t-statistic of trade R−8.16−1.82−7.83
Win rate41%48%43%
Average win / average loss0.890.940.90
Max drawdown$54,381$7,543$60,449
Sharpe ratio (daily, annualized)−3.11−1.00−2.50
Longest losing streak131013
Long / short profit factor0.56 / 0.670.85 / 0.850.64 / 0.72
Average holding time27 min28 min28 min
Commission paid$18,906$3,864$22,770
Cumulative P&LDrawdown from the highOut of sample from 2023-08-04

Drag across the chart to zoom into a period, double-click to reset.

Figure 1. Cumulative P&L after costs and its drawdown from the running high, 2016-01-11 to 2026-10-30, at about $250 of risk a trade. The shaded part is out of sample.
In sample (1,838 trades)Out of sample (788)Averages

Averages: −0.12R in sample, −0.04R out of sample.

Figure 2. The distribution of trade results in R, as a share of each side's trades. Bars are in sample; the line is out of sample.
In sampleOut of sampleQuintile mean, 95% intervalOLS fitDensity contours

1,600 of 2,657 points drawn; the fit and the means use all of them. Drag a box to zoom, double-click to reset.

Figure 3. The last half hour's return against the first half hour's, every day of the sample, linear axes; the dashed line is the OLS fit (r = 0.01, p = 0.71, n = 2,657; Spearman ρ = −0.04). Out of sample alone: r = −0.05, p = 0.18. Squares are the means of five equal-count bins, with 95% intervals.
In sampleOut of sampleQuintile mean, 95% intervalOLS fitDensity contours

1,600 of 2,626 points drawn; the fit and the means use all of them. Drag a box to zoom, double-click to reset.

Figure 4. Trade R against the first half hour's return; the dashed line is the OLS fit (r = −0.02, p = 0.22, n = 2,626; Spearman ρ = −0.04). Out of sample alone: r = −0.02, p = 0.64. Squares are the means of five equal-count bins, with 95% intervals.

5Robustness

We reran the strategy on a grid of 16 settings of its two main parameters, each on the full history with the same split. 0 were profitable in sample and 0 out of sample.

0.50
0.78
0.68
0.64
0.55
0.25
0.76
0.71
0.69
0.58
0.10
0.89
0.79
0.81
0.72
0
0.92
0.85
0.85
0.76
900
915
930
945

Entry (minutes after midnight ET) across, smallest first-half-hour move (%) up. Solid outline: the defaults we tested; dashed: the in-sample best.

Hover a cell for both sides of the split.

Entry (minutes after midnight ET) 900.0 to 945.0 across · Smallest first-half-hour move (%) 0.00 to 0.50 in depth · Profit factor, out of sample 0.55 to 0.92 as height and shade. Drag or use the arrow keys to turn it.

Drag to rotate; ctrl or ⌘ and scroll to zoom.

Figure 5. Profit factor across entry (minutes after midnight ET) and smallest first-half-hour move (%), as a map and as a surface of the same grid. Values above 4 are drawn at 4.

What would change it

Nothing on the grid helps. Its in-sample best, entry (minutes after midnight ET) 900 and smallest first-half-hour move (%) 0.5, had profit factor 0.74 in sample but 0.78 out of sample, against 0.85 for the defaults.

In-sample yearOut-of-sample year95% interval
Figure 6. Average trade by calendar year with its 95% interval: a year-by-year walk through the history. Lighter bars are in-sample years.
Figure 7. Average trade in three volatility regimes: terciles of the 20-session average of the daily range (% of the open), up to the day before the trade (regular session). The cut-offs use the whole period, so this describes, it doesn't forecast.
Figure 8. Average trade by weekday and by the hour of entry (New York time), with 95% intervals.
Median25th to 75th percentile5th and 95thRuin: down $2,000
Figure 9. 2,000 simulated years of 252 sessions, drawn session by session from the whole backtest (days without trades included), with 48 paths drawn; red paths lost $2,000 at some point. Risk of ruin 96.8% [95.9%, 97.5%]; 0.7% of years ended up; median ending P&L −$5,527, 5th to 95th percentile −$9,049 to −$1,730.

6Prop-firm implications

The backtest's sessions run through the rules of 36 tracked 50K evaluations: 2,000 runs of up to 60 sessions each, with the drawdown and daily limits checked against each trade's intraday low. Intervals are Wilson 95% intervals of the simulation. A simulation of the past, not the chance that anyone passes.

PlanPass odds, 95% intervalPassFailOut of timeMedian sessions
Alpha Futures Standard 50K Evaluation0.1%46%54%53
Alpha Futures Zero 50K Evaluation0.1%46%54%53
Apex Trader Funding 50K EOD Evaluation0.1%46%54%53
Apex Trader Funding 50K Intraday Trailing Drawdown Evaluation0.1%49%51%53
AquaFutures Beginner 50K Evaluation0.1%24%76%53
Bulenox 50K Qualification Account (Legacy, Option 1, trailing drawdown)0.1%27%73%53
Bulenox 50K Qualification Account (Legacy, Option 2, EOD drawdown)0.1%24%76%53
Earn2Trade Gauntlet Mini $50K0.1%46%54%53
Earn2Trade Trader Career Path TCP500.1%46%54%53
Elite Trader Funding 50K 1-Step Evaluation0.1%49%51%53
Scale 0 to 10%.
Figure 10. Simulated pass odds by plan, best first, with each plan's fail and out-of-time shares and the median sessions to a pass.

7Limitations

  • Gao et al. studied the SPY ETF; this tests the S&P 500 micro future, with futures costs.
  • The added wide stop rarely matters in half an hour, but it exists.
  • A backtest on the past, with fills simulated from one-minute bars; live fills, queues and outages differ.

8Conclusion

No edge after costs: profit factor 0.85 out of sample. Nothing on the grid helps. Its in-sample best, entry (minutes after midnight ET) 900 and smallest first-half-hour move (%) 0.5, had profit factor 0.74 in sample but 0.78 out of sample, against 0.85 for the defaults. On this reading of the rules, with these costs, the historical record gives no reason to expect a profit.

9References

  1. Gao, L., Han, Y., Li, S. Z., and Zhou, G. (2018). Market Intraday Momentum. Journal of Financial Economics, 129(2), 394-414.

Every number on this page comes from the MES bot above, run by our backtest engine on our own data. We publish what doesn't work as well as what does, and we don't tune rules to look good.

Hypothetical results. These results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under- or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.