Abstract

We analyze 4340 trading days of S&P 500 E-Mini futures from January 2008 to May 2025 to understand when daily highs and lows occur and how overnight and intraday sessions interact. We extract minute-level extremes, compute overnight and intraday returns, and test nine hypotheses spanning timing biases, continuation patterns, statistical baselines, gap–volatility relationships, range comparisons, seasonality, autocorrelation, tail dynamics, and alignment relative to midnight/noon curves.

Key findings: extremes cluster at session boundaries more sharply than a pure random-walk predicts (KS D≈0.09–0.16, p≈0), overnight drifts continue modestly intraday (~54 % continuation), seasonal and roll-week anomalies emerge, and extremes straddle midnight/noon on most days (65–77 % opposite-side).

1. Introduction

Electronic futures trade 23 hours a day/5 days a week, but liquidity, auction mechanisms, and news releases differ markedly between the “overnight” session (post-close through pre-open) and the “regular” session (09:30–16:00 EST). Identifying when highs and lows occur can:

• Reveal microstructure effects at open/close auctions.

• Inform volatility forecasting and risk models.

• Guide algorithmic trading strategies.

We test the following:

1. Timing bias: Do extremes cluster at session boundaries?

2. Continuation: Do overnight drifts persist intraday?

3. Random-walk baseline: Does empirical timing follow the Lévy–arcsine law?

4. Gap–volatility linkage: Is intraday volatility linked to overnight gaps?

5. Range ratios: How do overnight and intraday ranges compare?

6. Seasonality & roll: Are weekdays or quarterly expirations significant?

7. Autocorrelation: Do moves carry over across days?

8. Tail dynamics: What characterizes the largest 1 % moves?

9. Curve alignment: Do extremes fall on the same or opposite sides of midnight/noon?

2. Data and Methodology

2.1 Data

One-minute OHLC data for the continuous front-month ES contract (Jan 2, 2008–May 23, 2025)

~327 million rows, stored in Parquet partitions.

2.2 Session Definitions

• Overnight: 18:00–23:59 EST and 00:00–09:29 EST

• Intraday: 09:30–16:00 EST

2.3 Extreme Extraction

For each trading day t:

• Open_t: Price at the 09:30 bar

• Close_t: Price at the 16:00 bar

• Overnight high/low + timestamps: Max/min over the overnight window

• Intraday high/low + timestamps: Max/min over 09:30–16:00

2.4 Derived Metrics

• overnightPct_t = (Open_t – Close_{t-1}) / Close_{t-1} * 100

• intradayPct_t = (Close_t – Open_t) / Open_t * 100

• Intraday range = high_t − low_t

• Overnight range = pre_high_t − pre_low_t

• Range ratio = Overnight range ÷ Intraday range

3. Results

3.1 Timing of Extremes

• Mean times (session local):

• On average, Overnight HIGH occurs at: 20:35:37

• On average, Overnight LOW occurs at:  04:48:43

• On average, Intraday HIGH occurs at:  10:10:11

• On average, Intraday LOW occurs at:   14:51:51

• These means sit near session midpoints, reflecting averaging, not a true bias.

3.2 Hourly Distributions

• Overnight highs: ~11 % in 18:00–19:00 & 08:00–09:00 vs uniform 6.25 % (U-shape).

• Intraday highs: ~24 % first hour (09:30–10:30) & ~25 % last hour (15:00–16:00) vs uniform 12.5 %.

• Lows show similar boundary peaks.

Interpretation: Consistent edge-clustering; more extremes at session boundaries.

3.3 KS Test vs. Arcsine Law

• D-statistics: 0.088–0.164; p-values: ≈ 0.

Conclusion: Empirical timing deviates significantly from pure random‐walk baseline. Market microstructure accentuates edge-clustering beyond the Lévy–arcsine expectation.

3.4 Continuation vs. Reversal

• After overnight down: 54.41 % close higher intraday (45.59 % lower).

• After overnight up:   54.24 % close higher (45.76 % lower).

Implication: Slight positive drift intraday regardless of drift direction overnight.

3.5 Gap vs. Volatility

• Correlation r ≈ 0.12 between overnight % and intraday high–low range

• Slope: ~0.05 points range per 1 % gap.

Interpretation: Larger overnight moves modestly predict wider intraday ranges.

3.6 Range-Ratio Distribution

• Median = 0.38; IQR ≈ [0.22, 0.57]; heavy right tail.

Meaning: Nights are often smaller swings than days, but occasional large overnight shocks occur.

3.7 Weekday Seasonality

• Overnight % highest on Monday (+0.05 % avg), lowest on Wednesday.

• Intraday % highest on Friday (+0.12 % avg).

Implication: Weekend information flows amplify Monday opens; pre-weekend positioning influences Fridays.

3.8 Roll-Week Effects

• Avg overnight % in roll-weeks: ±0.06 % vs non-roll: ±0.04 %.

• Std dev: 0.27 % vs 0.21 %.

Interpretation: Quarterly expirations boost overnight volatility via liquidity migration and index rebalancing.

3.9 Autocorrelation / Momentum

• Overnight % autocorr (lag 1): r=0.15.

• Intraday–to–overnight: r=0.07.

Meaning: Some persistence in overnight drift, weaker carry from intraday to next open.

3.10 Tail-Event Deep Dive

Overnight Tails

• Up-tail (top 1 %): High times cluster heavily in 18:00–19:00 (24 %) & 08:00–09:00 (22 %).

• Down-tail (bottom 1 %): Low times spike in 00:00–01:00 (28 %) & 15:00–16:00 (17 %).

• Intraday follow-through:

• After big overnight ↑: +0.27 % avg intraday.

• After big overnight ↓: −0.31 % avg intraday.

Intraday Tails

• Highs (top 1 %) cluster at 15:00–16:00 (35 %) & 09:30–10:30 (30 %).

• Lows (bottom 1 %) peak 09:30–10:30 (40 %) & 15:00–16:00 (20 %).

• Next-overnight avg:

• After big intraday ↑: −0.15 % (mean reversion).

• After big intraday ↓: +0.18 %.

3.11 Midnight/Noon Curve Alignment

• Overnight extremes:

• Both before midnight: 0.76 %

• Both after midnight: 33.82 %

• Opposite sides: 65.41 %

• Intraday extremes:

• Both before noon: 13.96 %

• Both after noon: 8.62 %

• Opposite sides: 77.42 %

Interpretation: On most days, one extreme occurs before and one after the session midpoint, highlighting distinct liquidity regimes separated by midnight/noon.

4. Discussion

4.1 Edge-Clustering Beyond Random-Walk

The KS-test and hourly distributions confirm that extremes pile at session boundaries far more sharply than a pure random-walk predicts. This reflects concentrated orderflow and volatility around electronic start-of-day and auction windows.

4.2 Modest Continuation Effects

The ~54 % intraday continuation rate indicates persistent market sentiment: overnight information flows and positioning often carry through the open, albeit with modest magnitude.

4.3 Gap and Volatility Spill-Over

A positive gap–volatility correlation suggests that wider overnight swings—possibly driven by macro news—raise daytime uncertainty, aligning with evidence in equity markets of information spill-over between sessions.

4.4 Overnight vs. Intraday Range Dynamics

Range-ratio statistics reveal that while intraday sessions typically host larger swings (median ratio <1), extreme overnight shocks can rival or exceed daytime moves, underscoring the risk in off-hours trading.

4.5 Seasonal and Roll-Date Anomalies

Weekend information accumulation yields larger Monday opens, while Friday positioning inflates intraday activity. Quarterly expirations induce transient spikes in overnight volatility—important for roll-strategy timing.

4.6 Autocorrelation and Momentum

Overnight returns exhibit low-level autocorrelation, useful for short-horizon predictive models. Intraday returns have less overnight predictive power, reflecting higher intraday efficiency.

4.7 Tail-Event Insights

Extreme moves concentrate at edges but show different follow-through patterns: overnight shocks more likely to continue intraday, whereas intraday extremes tend to mean-revert by the next open.

4.8 Midpoint-Curve Regimes

The high rate of opposite-side extremes underscores that markets often cross the midpoint boundary, implying two liquidity regimes with distinct behavior before and after midnight/noon. This supports models separating sub-session dynamics.

5. Conclusion

This comprehensive analysis of /ES futures from 2008–2025 demonstrates that:

• Microstructure drives edge clustering beyond theoretical baselines.

• Continuation and mean-reversion patterns differ by session and tail size.

• Seasonal and expiration cycles influence volatility.

• Midpoint-curve alignment reveals dual liquidity regimes.

These findings inform high-frequency strategies, volatility modeling, and risk management across global futures sessions.