The Maths Every Day Trader Should Know
Does the same price distance mean the same thing all day?
Explore why a daily volatility measure can describe the next few hours differently across sessions, holding periods, and recent market activity.
By ContextChart Research · 4 min
Published
Give the ruler a clock
Try it yourself
Activity across the selected hours
7.20
Relative to an entry at 02:00 UTC
4.50×
- Illustrative hourly activity
- 02:00 comparison
- Selected hours
Read the plotted values
| UTC hour | Illustrative hourly activity |
|---|---|
| 0 | 0.45 |
| 1 | 0.4 |
| 2 | 0.35 |
| 3 | 0.35 |
| 4 | 0.4 |
| 5 | 0.5 |
| 6 | 0.7 |
| 7 | 1 |
| 8 | 1.3 |
| 9 | 1.2 |
| 10 | 1.1 |
| 11 | 1.15 |
| 12 | 1.5 |
| 13 | 1.8 |
| 14 | 2 |
| 15 | 1.9 |
| 16 | 1.6 |
| 17 | 1.25 |
| 18 | 1 |
| 19 | 0.8 |
| 20 | 0.65 |
| 21 | 0.6 |
| 22 | 0.55 |
| 23 | 0.5 |
02:00 comparison window
1.60 units
Whole-day activity · unchanged
23.05 units
The selected window begins at 12:00 UTC and ends at 16:00 UTC. The shaded bands mark the two holding windows; crossing midnight wraps to the left edge. The daily total has stayed unchanged while the clock changes the hours you will encounter.
A constructed activity profile in arbitrary units, not measured or current instrument data. Adding hourly activity illustrates the clock effect; it is not an estimator of a holding period’s high–low range.
The idea
An instrument can have one daily ATR value while its next few hours behave very differently at different times of day.
That is easy to see in many markets. A busy overlap of trading sessions and a quiet late-session period share the same daily ruler. They do not necessarily share the same expected near-term movement.
Your intended hold matters too. A distance that is substantial over an hour may be ordinary over several hours. A daily measurement supplies useful background, but the question at entry is more specific: how much movement would be usual from this hour over this holding period?
A better-matched ruler does not remove uncertainty. It improves the comparison. A distance, cost, or excursion expressed in that unit has a more consistent meaning across the conditions being measured.
The amount of movement a distance represents depends on when you enter and how long you intend to hold.
How this experiment works
Compare the illustrative session profiles while changing the entry hour and holding period. Watch the reference movement change even when the broad daily level stays the same.
The demonstration explains the clock effect. The linked research supplies the separate historical measurement. An illustrative activity curve is not a current forecast for an instrument.
How we use this
Our ATR-as-a-unit study tested daily measures, chart-timeframe measures, an hour-of-entry profile, and recent activity across 35 instruments.
In that sample, adding the clock and recent activity made the unit steadier across the tested hours and holding periods. The improvement appeared in both halves of the study. This gave our range work a more relevant question than simply choosing a different ATR lookback.
The research also exposed what the estimate missed. Scheduled US releases and shock periods still produced more movement than the unit anticipated. We keep those limitations alongside the result. A more consistent estimate of size is not a demonstrated improvement in trade win rate.
From our research · Observed prices
Same daily reference. Different four hours.
These two EURUSD windows come from the original study, rather than the constructed activity profile above. The daily ATR reference was unchanged between these entries. The next four-hour high-low ranges were different. Both charts use the same scale.
Show hourly prices
| UTC | Open | High | Low | Close |
|---|---|---|---|---|
| 12:00 | 1.16131 | 1.16199 | 1.16104 | 1.16199 |
| 13:00 | 1.16200 | 1.16274 | 1.16187 | 1.16218 |
| 14:00 | 1.16217 | 1.16310 | 1.16187 | 1.16307 |
| 15:00 | 1.16308 | 1.16338 | 1.16261 | 1.16261 |
Show hourly prices
| UTC | Open | High | Low | Close |
|---|---|---|---|---|
| 19:00 | 1.16287 | 1.16300 | 1.16223 | 1.16231 |
| 20:00 | 1.16231 | 1.16251 | 1.16216 | 1.16230 |
| 21:00 | 1.16229 | 1.16259 | 1.16213 | 1.16259 |
| 22:00 | 1.16264 | 1.16271 | 1.16241 | 1.16258 |
Was it only this example?
Across 35 of 35 instruments, the time-aware unit had a lower four-hour measurement-dispersion score than daily ATR in this sample. Lower means the future range was steadier relative to its entry-time unit. It does not mean more profitable trades.
Inspect an instrument and the method
| Daily ATR | 0.719 |
|---|---|
| ATR + hour | 0.573 |
| ATR + hour + recent activity | 0.521 |
Scored 1 February 2025–2 October 2026 on hourly bars across FX, metals, oil, equity indices and BTCUSD. The score is the interquartile range of log(next four-hour high-low range ÷ unit known at entry). A constant multiplier cannot improve this score. Hour profiles use past observations; the original study checks earlier estimates against changes to future bars.
These historical windows were selected to explain the mechanism. The aggregate covers the study universe, not just those windows. Prices do not establish intrabar trade ordering or executable fills. Release windows and shock days still exceeded the unit’s ordinary estimates. This study did not demonstrate a profit or win-rate improvement.
Read the study scope, findings and limits ↗Source: ContextChart Research, “ATR as a unit”, 22 October 2026. Snapshot extracted from the original report; prices are historical, not a live feed.
Show the maths
A schematic version of the idea is:
Expected-range unit = recent activity level × usual profile for this hour and hold × recent activity adjustment
Each component must use information available at entry. A completed day's high and low cannot be used to size a forecast made earlier that same day.
The study assessed the spread of log(actual forward range ÷ unit known at entry) for each instrument. A narrower spread meant the ruler gave more consistent scale. Multiplying every unit by a constant would not improve that score.
What this does not establish
The expected range is an estimate, not a boundary price must respect. The range of a future window also differs from the adverse excursion a particular trade experiences. This lesson supplies a better comparison question, not an entry hour or stop recommendation. Compare this with what price does along the way.