Rate of change (ROC) / momentum

Definition

ROC is the percentage change in price over a lookback window — the simplest momentum measure and the one the academic momentum literature actually tests. Where MACD and RSI transform price through smoothing machinery, ROC IS the raw quantity: trailing return. Its plainness is its virtue — it maps one-to-one onto the documented effects.

How it works / structure

• Formula: ROC_t(N) = (P_t / P_{t−N} − 1) × 100; the “momentum” variant is the unscaled difference P_t − P_{t−N}.
• Parameters (engine-executable): window N (the entire content — 21 days probes short reversal territory; 63/126/252 days probe the momentum horizons), skip window (12-1 convention drops the most recent month — strategy-momentum), signal form (sign for time-series use; cross-sectional rank for relative momentum; z-scored ROC for comparability).
• Direct evidence mapping: ROC(252) sign ≈ time-series momentum’s signal (Moskowitz-Ooi-Pedersen); ROC(252 minus 21) rank ≈ the Jegadeesh-Titman sort — the platform prefers ROC in strategy definitions precisely because the citations attach cleanly.

When it applies

Momentum signal construction (both forms), regime description (market trailing returns as state variables), and normalized cross-instrument comparison. When another oscillator’s claim reduces to “trailing return is positive/negative,” the platform restates it in ROC and inherits the real literature.

Risk profile & failure modes

• Horizon inversion: ROC at short windows proxies reversal, at intermediate windows momentum, at multi-year windows long-term reversal — using one window’s lore at another’s horizon inverts the sign of the evidence.
• Two-point fragility: ROC depends only on the endpoints; a single anomalous bar N days ago swings today’s reading (the drop-off artifact in pure form).
• Gap sensitivity: dividend/split adjustments matter — an unadjusted series makes ROC lie (ms-corporate-actions).

Evidence & limits

The momentum citations (Jegadeesh-Titman 1993; Moskowitz-Ooi-Pedersen 2012) ARE ROC evidence — trailing-return sorts and signs, with all their documented caveats (crashes, decay, costs — see strategy-momentum). No indicator in this pillar has a tighter evidence linkage; the caveats transfer at full strength too.

Falsifiable-thesis examples

Illustrations only, not signals:

• “Instruments in universe U with positive 12-month ROC will, as a group, outperform those with negative over the next quarter” — falsified by the two buckets’ returns.
• “X’s ROC(63) turning positive this week precedes a positive next-month return” — falsified at the mark.

Cross-references

• The literature it operationalizes: strategy-momentum, strategy-futures-trend-following
• Transformed cousins: indicator-macd (EMA-differenced), indicator-rsi (gain/loss-balanced)
• Data hygiene: ms-corporate-actions (adjusted series)
• Method: lens-quantitative