# Momentum and Rate of Change (ROC)

Momentum and rate of change (ROC) are simple technical analysis indicators showing the difference between today’s closing price and the close N days ago. Momentum is simply the difference,

Momentum = Close(today) – Close(N days ago)

Rate of change scales by the old close, so as to represent the increase as a fraction,

Rate of change = (Close(today) – Close(N days ago)) / Close(N days ago)

“Momentum” in general refers to prices continuing to trend. The momentum and ROC indicators show that by remaining positive while an uptrend is sustained, or negative while a downtrend is sustained.

How To Use

A crossing up through zero may be used as a signal to buy, or a crossing down through zero as a signal to sell. How high (or how low when negative) the indicators get shows how strong the trend is.

The way momentum shows an absolute change means it shows for instance a \$3 rise over 20 days, whereas ROC might show that as 0.25 for a 25% rise over the same period. One can choose between looking at a move in dollar terms or proportional terms. The zero crossings are the same in each, of course, but the highs or lows showing strength are on the respective different bases.

SMA (simple moving average)

Momentum is the change in an N-day simple moving average (SMA) between yesterday and today, with a scale factor N, ie.

Momentum/N = SMA(today) – SMA(yesterday)

This is the slope or steepness of the SMA line, like a derivative. This relationship is not much discussed generally, but it’s of interest in understanding the signals from the indicator.

When momentum crosses up through zero it corresponds to a trough in the SMA, and when it crosses down through zero it’s a peak. How high (or low) momentum gets represents how steeply the SMA is rising (or falling).

The TRIX indicator is similarly based on changes in a moving average (a triple exponential in that case).

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