Free lesson · Technical analysis

Renko: price-driven bricks and the missing time axis

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Start with the idea

Renko emits a brick after a sufficient price move rather than at a fixed time. A brick chart changes the sampling clock.

Symbols, units & horizon

P_brick: last synthetic brick close in price units
B: positive fixed brick size
d: existing direction, +1 up or −1 down
P_next: continuation threshold
P_reverse: reversal threshold in the stated two-brick convention

When and why to use this

Use price-event sampling or brick states as research features. Compare methods at matched observation frequency and retain a calendar-time execution ledger.

Choose brick size, anchor, source observations and reversal convention. Fixed-size, ATR-based and high/low methods produce different charts.
This lesson uses close-only observations, a fixed size and a two-brick reversal convention. It does not infer the intrabar path.
A continuation needs one brick of movement beyond the last brick close. A reversal needs two sizes in the opposite direction; the first reverse brick skips one size in its opening coordinate.
A large source-price jump may create several bricks at one timestamp. Those are not separate opportunities to transact at every synthetic boundary.
Retain the source timestamp and actual observed price for every emitted brick. A brick-count holding period is not a fixed-duration holding period.
Changing an ATR-based size retrospectively can repaint historical bricks. Freeze calibration rules and update them causally.

P_{n e x t} = P_{b r i c k} + d B, P_{r e v e r s e} = P_{b r i c k} - 2 d B

Specified chart rule · derivation and arithmetic

Renko: price-driven bricks and the missing time axis

Suppose the latest up brick closes at 106 and B=2. The next up threshold is 108.
The reversal threshold is 106−2×2=102. A close at 103 is insufficient.
At source close 101, create the down brick from 104 to 102. It is timestamped at that source observation, not at an imagined trade through 102.

Work it by hand

After that reversal, the next continuation threshold is 100. A source close of 101 produces no second down brick.

Use the rule

Fix the definition, units and information timestamp.
Compute the example and inspect the graph.
Compare with a simple baseline on untouched periods after costs.

Before moving on

Write the exact rule, its availability time, an invalidation condition and a fair out-of-sample test.

Research checkpoint · reviewed 12 September 2026

Status: 2026 arXiv preprint. Data, construction and evaluation sections reviewed; no independent replication performed.
Sample: Binance BTCUSDT USDT-margined perpetual futures, January 2020–December 2025; aggregated trades versus one-minute OHLCV. Six constructions include Renko, range, volume and dollar bars.
Connection: control data resolution and observation frequency when comparing bar types. The study uses adaptive calibration; this lesson uses fixed, close-only bricks and is not a replication.
Limits: one instrument/venue, construction-specific assumptions and statistical quality criteria. A more regular bar series does not establish executable net profits.

Fayyaz et al. · tick versus minute information bars (2026 preprint) ↗

Python implementation

Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.

def renko_thresholds(last_close,size,direction):
    if size<=0 or direction not in (-1,1): raise ValueError("Positive size and direction +/-1 required")
    return last_close+direction*size,last_close-2*direction*size

print(renko_thresholds(106,2,1))

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