The oscillator that every other oscillator descends from
Rate of Change and its cousin Momentum are the simplest oscillators that exist — literally "where is price now vs N bars ago, expressed as a number." Every other oscillator in this course (RSI, Stochastic, MACD, CCI, Williams %R) is either a smoothed version of this, a normalized version, or a ratio-of-two-things version.
Murphy's framing is unambiguous:
The concept of momentum is the most basic application of oscillator analysis. — John Murphy
And Kaufman's:
The most basic of all trend indicators is momentum (M), the change of price over some period of time. — Perry Kaufman
So this is where momentum analysis starts. Everything downstream is sophistication added to this core idea.
Two formulas, same idea
Momentum (absolute difference)
Today's close minus the close from N bars ago. In price units (dollars, yen, whatever). Murphy and Kaufman agree this is the base definition.
Rate of Change (percent)
Same thing, expressed as a percentage. Unit-less, comparable across instruments.
Murphy also uses a ratio form:
Where V is today's close and V_x is the close x days ago. This puts the midpoint at 100 instead of 0 (100 = unchanged). Mathematically equivalent to the standard percent form up to a shift.
Kaufman's pedantic note worth noting:
Rate of change used by financial analysts is not the same as it is defined in physics. Momentum is called speed in physics, and the rate at which momentum changes is the rate of change.
In physics, velocity ≠ acceleration. In TA, the terms are used loosely — "Momentum" and "ROC" refer to the same concept, differing only by whether you express it as points or percent.
Default period
Murphy repeatedly defaults to N = 10:
The popularity of the 10 day momentum [is] based largely on the 28 day trading cycle.
N = 12 is also common in practice (and aligns with MACD's fast EMA). Longer periods (25, 50, 100) exist for multi-day swing and macro analysis.
The zero-line crossover
The primary signal. Murphy:
A crossing above the zero line would be a buy signal, and a crossing below the zero line, a sell signal.
When M or ROC crosses zero, it means price has reversed direction vs the N-bar reference point.
- ROC > 0 → price higher than N bars ago → momentum bullish
- ROC < 0 → price lower than N bars ago → momentum bearish
- ROC = 0 → price exactly equal to N bars ago
Play with it
Watch the zero line. In strong uptrends ROC stays decidedly above zero; in downtrends decidedly below. In sideways markets ROC oscillates tight around zero, generating false signals every few bars.
This is why you never trade raw ROC alone. It's too noisy. Almost every "real" oscillator in the toolkit is raw momentum with a smoothing or normalization layered on:
| Indicator | What it adds to raw momentum |
|---|---|
| RSI | Separates gains from losses, smoothes with Wilder α, bounds to 0–100 |
| Stochastic | Normalizes close against N-bar range, bounds to 0–100 |
| MACD | Two EMAs → their difference is the "momentum" |
| CCI | Deviation from SMA, scaled by mean deviation |
| Williams %R | Mirror of Stochastic — range-position |
Every one of these is momentum with a coat.
The leading property
One detail Murphy emphasizes:
Because of the way it is constructed, the momentum line is always a step ahead of the price movement. It leads the advance or decline in prices.
How? Because ROC at bar t depends on bar t − N. When price rallies strongly from t − N forward, ROC captures that change immediately at bar t — before a smoothed indicator (like a moving average) can catch up. ROC is literally the first derivative of price over N bars; smoothers add lag on top.
This is why momentum-based divergence is such a popular concept: momentum peaks before price peaks, because the rate of change slows even while price still ticks higher.
The lack-of-bound problem
Murphy identifies the main weakness of raw momentum directly:
One problem with the momentum line … is the absence of a fixed upper and lower boundary.
Without bounds, "overbought" and "oversold" are context-dependent — a momentum reading of 10 means something different on a $50 stock than on a $500 stock. Even ROC's percentage normalization doesn't help comparably across regimes: a 5% 10-day ROC is extreme in low-vol periods, routine in high-vol.
Murphy notes this is precisely why Wilder built RSI: "The RSI formula not only provides the necessary smoothing, but also solves the latter problem by creating a constant vertical range of 0 to 100." Every bounded oscillator in the curriculum is a solution to this problem.
Statistical testing — a rare concrete one
Kaufman reports one ROC-based backtest worth citing. Woodshedder's system uses 5-day ROC crossovers against 252-day ROC on S&P futures, 1998–2017:
52 trades, 53% of them profitable for 20 years from 1998. — Kaufman, citing Woodshedder
53% win rate over 20 years on ~52 trades is modest but real. One of the few hard-statistic results on a pure-momentum system in the classical-TA literature.
Hidden traps
- Treating raw ROC as a trade signal. Noisy. Needs smoothing or a trend filter.
- Confusing Momentum and ROC. Same concept, different units. Don't mix in one system.
- Using absolute Momentum to compare across instruments. 10-point momentum on oil and 10-point momentum on gold are not comparable readings. Use ROC (percent) for cross-asset work.
- Ignoring that ROC depends entirely on bar t − N. If the reference bar was a freak spike, today's ROC is distorted. Kaufman calls this the "end-point problem" of any window-based indicator.
- Expecting leading behavior to be reliable. ROC leads in character (divergence, slope) but doesn't predict specific reversal timing.
- Picking very short N. ROC(3) is just noise; ROC(100) is just trend direction in slow motion. Match N to the holding horizon you care about.
Quick check
ROC crosses from −2 to +1. What's the plain-English meaning?
What you now know
- Momentum (points) and ROC (percent) are the same concept — today's close vs close N bars ago — on different scales.
- Default N = 10 (Murphy), though 12 and longer are common.
- Zero-line cross is the primary signal: flip in direction vs the N-bar reference.
- ROC leads price — by construction, since it's a first-derivative calculation — which is why momentum divergence precedes price reversal.
- Unbounded — cross-instrument or cross-regime comparison requires the percent form, not raw momentum.
- This is the primitive. RSI / Stochastic / MACD / CCI / Williams %R all sit on top of this core idea. Understanding ROC is understanding the foundation.
- Kaufman's one backtest: Woodshedder's 5/252 ROC crossovers on S&P futures, 52 trades 1998–2017, 53% profitable. Modest but real.
More Indicators unit complete. You've now covered every major indicator in the classical-TA canon — MAs, RSI, MACD, Stochastic, Bollinger, ATR, ADX, Parabolic SAR, Keltner/Donchian, Ichimoku, Williams %R, CCI, and the momentum primitive that underlies them all.
Next up: the Strategies & Systems unit — applying everything you've learned into concrete rule-based trading systems. Opening Range Breakout, the Turtle rules, mean reversion, backtesting pitfalls, Pine Script.