Bollinger Band reversion on the Russell 2000

Micro E-mini Russell 2000 (M2K) · 15-minute bars · 2017 to 2026 · Mean reversion · Bands after John Bollinger

No edge after costs: profit factor 0.84 out of sample.

Profit factor, out of sample: 0.84
Average trade, out of sample: −0.11R
Win rate, out of sample: 33%
Trades, 10 years: 3,079
Max drawdown: $114,172
Pass odds, median plan: 8.1%

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 bollinger Band reversion rules on Micro E-mini Russell 2000 (M2K) 15-minute bars from 2017-07-17 to 2026-10-30: 3,079 trades, with commission and a tick of slippage on every market and stop fill. In sample (to 2024-01-17) it made −0.17R per trade with a profit factor of 0.76; out of sample (from 2024-01-18) −0.11R per trade and 0.84 over 948 trades. 4 of the 16 parameter settings we tried were profitable out of sample. Sized at $250 of risk a trade, simulated 50K evaluations passed 3% to 9% of the time across 36 tracked plans.

1Hypothesis

Fade a 15-minute close outside the 20-bar, 2-standard-deviation Bollinger Bands, targeting the middle band, stop one standard deviation away.

If a close outside the bands is an overreaction, price should return to the 20-bar average more often than it runs another standard deviation.

2Data

Instrument: Micro E-mini Russell 2000 (M2K), traded on the RTY price series (RTY.v.0: the most traded contract, rolled on volume). CME Globex via Databento.
Period: 2017-07-17 to 2026-10-30: 2,396 sessions, 922,339 one-minute bars, built into 61,369 15-minute bars of the regular session (09:30 to 16:00 ET).
Costs: $0.75 commission a contract each way and 1 tick ($0.50) 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: 2024-01-18 on (727 days), after 1,698 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:

Bollinger Bands: the length (20) bar SMA of the 15-minute closes plus and minus k (2) standard deviations, regular-session bars only.
Entry: a bar that closes below the lower band buys at the next bar's open; one that closes above the upper band sells. Signals from 10:00 to 15:00 ET.
Stop: one standard deviation beyond the signal bar's close.
Target: the SMA as it stood at the signal.
Exit: the stop, the target, or flat at 15:55 ET. At most 2 trades a day, one at a time.
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

1"""Bollinger Band mean reversion on Micro E-mini Russell 2000 (M2K) 15-minute bars, regular session.2 3Rules:4  1. Bollinger Bands: the `length` (20) bar SMA of the 15-minute closes plus and minus `k` (2) standard5     deviations, regular-session bars only.6  2. Entry: a bar that closes below the lower band buys at the next bar's open; one that closes above7     the upper band sells. Signals from 10:00 to 15:00 ET.8  3. Stop: one standard deviation beyond the signal bar's close.9  4. Target: the SMA as it stood at the signal.10  5. Exit: the stop, the target, or flat at 15:55 ET. At most 2 trades a day, one at a time.11  6. Size: about `risk_usd` dollars of risk a trade (micro contracts, rounded down, at least 1 and at12     most `max_contracts`).13"""14import qy15 16 17def ready(*values):18    """True when every value is a number (indicators have no value until they have enough data)."""19    return all(v is not None and v == v for v in values)20 21 22class Bot(qy.Strategy):23    """Fade a close outside the Bollinger Bands, target the middle band."""24 25    symbol = "M2K"26    timeframe = "15m"27    session = "rth"28    params = {"length": 20, "k": 2.0, "risk_usd": 250, "max_contracts": 50}29    max_position = 5030    entry_window = ("10:00", "15:00")31    flatten_time = "15:55"32    overnight = False33 34    def setup(self):35        self.mid, self.up, self.lo = self.bbands(self.close, self.p.length, self.p.k)36        self.sd = self.stdev(self.close, self.p.length)37 38    def _size(self, risk_points):39        per_contract = risk_points * self.point_value40        n = int(self.p.risk_usd // per_contract) if per_contract > 0 else 141        return max(1, min(self.p.max_contracts, n))42 43    def on_bar(self, bar):44        mid, up, lo, sd = self.mid[0], self.up[0], self.lo[0], self.sd[0]45        t = bar.dt.hour * 60 + bar.dt.minute + 1546        if not ready(mid, up, lo, sd) or sd <= 0 or not self.position.is_flat or self.orders or self.trades_today >= 2 or not 600 <= t < 900:47            return48        close = bar.close49        f = (up - lo) / close * 10050        if close < lo:51            self.buy(self._size(sd), stop_price=close - sd, target_price=mid, tag=f"BB fade long | f={f:.4f}")52        elif close > up:53            self.sell(self._size(sd), stop_price=close + sd, target_price=mid, tag=f"BB fade short | f={f:.4f}")

4Results

Table 1. In sample (2017-07-17 to 2024-01-17) against out of sample (2024-01-18 to 2026-10-30), after costs.
Statistic	In sample	Out of sample	All
Trades	2,131	948	3,079
Net P&L	−$88,272	−$24,723	−$112,995
Profit factor	0.76	0.84	0.78
Average trade	−0.17R	−0.11R	−0.15R
95% interval of the average	−0.23 to −0.11	−0.20 to −0.02	−0.20 to −0.10
t-statistic of trade R	−5.69	−2.36	−6.03
Win rate	31%	33%	32%
Average win / average loss	1.68	1.72	1.69
Max drawdown	$90,042	$27,226	$114,172
Sharpe ratio (daily, annualized)	−2.37	−1.50	−2.10
Longest losing streak	20	12	20
Long / short profit factor	0.72 / 0.80	0.72 / 0.97	0.72 / 0.85
Average holding time	108 min	107 min	108 min
Commission paid	$36,830	$11,684	$48,513

Cumulative P&LDrawdown from the highOut of sample from 2024-01-18

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, 2017-07-17 to 2026-10-30, at about $250 of risk a trade. The shaded part is out of sample.

In sample (2,131 trades)Out of sample (948)Averages

Averages: −0.17R in sample, −0.11R 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 3,079 points drawn; the fit and the means use all of them. Drag a box to zoom, double-click to reset.

Figure 3. Trade R against the bands' width, log x-axis; the dashed line is the OLS fit (r = 0.08, p < 0.001, n = 3,079; Spearman ρ = 0.46). Out of sample alone: r = 0.10, p = 0.002. 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 4 out of sample.

0.90

0.92

1.01

1.14

0.84

0.79

0.84

1.01

0.88

0.84

0.88

1.08

0.83

0.80

0.91

none

1.5

2.5

Band width (sigma) across, average length (bars) up. Solid outline: the defaults we tested; dashed: the in-sample best.

Hover a cell for both sides of the split.

Band width (sigma) 1.50 to 3.00 across · Average length (bars) 10.0 to 50.0 in depth · Profit factor, out of sample 0.79 to 1.14 as height and shade. Drag or use the arrow keys to turn it.

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

Figure 4. Profit factor across band width (sigma) and average length (bars), 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 clearly helps. Its in-sample best, band width (sigma) 3 and average length (bars) 20, did better out of sample, profit factor 1.08 against 0.84 for the defaults, but over only 171 trades, t = 0.4: too few, or too noisy, to call it a fix.

In-sample yearOut-of-sample year95% interval

Figure 5. Average trade by calendar year with its 95% interval: a year-by-year walk through the history. Lighter bars are in-sample years.

Figure 6. 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 7. 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 8. 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 99.0% [98.4%, 99.3%]; 3% of years ended up; median ending P&L −$12,070, 5th to 95th percentile −$22,247 to −$1,865.

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.

Plan	Pass	Fail	Out of time	Median sessions
AquaFutures Beginner 50K Evaluation	9.0%	87%	5%	26.5
Bulenox 50K Qualification Account (Legacy, Option 2, EOD drawdown)	8.9%	87%	5%	26
FundedNext Futures Flex Challenge 50K	8.6%	91%	0.3%	20
Bulenox 50K Qualification Account (Legacy, Option 1, trailing drawdown)	8.5%	89%	3%	25
Alpha Futures Standard 50K Evaluation	8.2%	90%	1%	25
Alpha Futures Zero 50K Evaluation	8.2%	90%	1%	25
Apex Trader Funding 50K EOD Evaluation	8.2%	90%	1%	25
FTMO Futures Pro 50K Evaluation	8.2%	90%	1%	25
Funded Futures Family 50K Evaluation (standard plan)	8.2%	90%	1%	25
Goat Funded Futures EOD 50K Evaluation	8.2%	90%	1%	25

Scale 0 to 25%.

Figure 9. 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

Regular-session bars only.
One market (M2K).
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 0.84 out of sample. Nothing on the grid clearly helps. Its in-sample best, band width (sigma) 3 and average length (bars) 20, did better out of sample, profit factor 1.08 against 0.84 for the defaults, but over only 171 trades, t = 0.4: too few, or too noisy, to call it a fix. On this reading of the rules, with these costs, the historical record gives no reason to expect a profit.

9References

Bollinger, J. (2001). Bollinger on Bollinger Bands. McGraw-Hill.