Momentum Indicators: ROC, RSI and MACD

Momentum describes the pace and direction of price change over a specified interval. Indicators transform historical prices into reference measures. They can describe strengthening or fading movement, but do not determine what the next return will be.

Use the same chart interval when comparing indicators. “14 periods” means 14 daily intervals on a daily chart and 14 weekly intervals on a weekly chart.

The calculations use the 60 hypothetical ABC Ltd closing prices from the Session 9 RSI teaching workbook. ROC, RSI and MACD below share that same input, so their differences come from their formulas. The charts are teaching examples, not current prices or recommendations.

An n-period ROC needs n + 1 closes. A 10-period ROC compares the current close with the close ten intervals earlier, not the earliest of ten listed observations. A zero denominator is invalid.

Price can remain above its n-period-ago value while that percentage advantage narrows. ROC may fall because the current price changes, because the comparison price moves forward, or both. A falling ROC does not necessarily mean today’s close fell.

No universal thresholds apply across instruments and intervals. Unlike RSI, ROC is not bounded above by 100. With positive prices its lower limit is −100%. Any extreme-value rule should specify the instrument, lookback and historical method used to set it.

RSI compares smoothed positive and negative price changes over a lookback. The “relative strength” in its name compares gains with losses within one price series; it is not a direct comparison with another stock or an index.

Include zero gains on down days and zero losses on up days. Divide by n, rather than by the number of winning or losing sessions. A 14-period initial RSI requires 15 closes.

These inputs and the result were checked against the workbook’s “3. RSI Calculation” sheet.

Wilder’s update uses α = 1/n, unlike the common EMA coefficient 2/(n + 1). Replacing it with a fresh rolling average or a standard EMA changes the indicator.

RSI above 70 is conventionally described as overbought and below 30 as oversold. These labels summarise recent imbalance, not inevitable reversal. RSI can remain extreme during a strong trend. At 50, smoothed gains and losses are equal under the stated formula.

If average loss is zero and average gain is positive, RSI is 100. If average gain is zero and average loss is positive, RSI is 0. If both are zero, the ratio is indeterminate; this calculator explicitly reports 50 as a neutral convention. Platforms may handle the all-flat case differently.

The conventional daily settings are 12, 26 and 9, but they must be stated. MACD is expressed in price units rather than percentages and has no fixed 0–100 scale. Its numerical magnitude is not directly comparable across differently priced securities.

This lesson seeds each price EMA from the first full-window SMA. With 12/26 settings, the first MACD appears at observation 26. A signal seeded from the first nine available MACD values appears at observation 34, together with the first histogram. Platforms using other seeds or more prior history can show different initial values.

The supplied slides rounded the third signal to 6.0 and histogram to 1.0. The table above retains precision through the recurrence, then rounds for display. The first signal is a supplied starting value, not a nine-observation seed calculated from this four-row excerpt.

MACD moving from at/below its signal to above it is a bullish momentum crossover; the reverse is bearish. The histogram changes sign with the same relation. A positive histogram describes MACD above the signal, not necessarily MACD above zero.

MACD above zero means the fast price EMA exceeds the slow price EMA. MACD below zero means the fast EMA is lower. A signal-line crossing compares MACD with its own smoothing line. It can happen while both remain negative or both remain positive.

No. A positive histogram shrinking toward zero means MACD’s advantage over its signal is narrowing. Price could still rise. A negative histogram moving toward zero likewise describes a narrowing negative gap, not proof of a bullish trend reversal.

Match swings from the same timeframe and use only information available then. A swing identified using later observations cannot be used as a real-time signal on the earlier date. Divergence can persist through further price movement and may never produce the anticipated reversal.

ROC compares two endpoint prices, RSI summarises smoothed gains and losses, and MACD compares recursively smoothed price levels. They use different memory and scaling. For example, a bullish MACD signal-line crossing can occur while ROC remains negative because the longer comparison period is still down. Agreement is not three independent votes: all three transform the same prices.

First state the trend and previously marked price zones. Then use a selected indicator for a precise question, such as whether recent losses are dominating or whether an EMA gap is changing. Define confirmation, invalidation and execution rules separately. More indicators do not automatically improve a method.

Use matching prices, ordering, timeframe, parameters, corporate-action treatment and warm-up history. For RSI check Wilder smoothing and all-flat handling. For MACD check both price-EMA seeds and the signal seed. A discrepancy can be methodological rather than an arithmetic error.

• Using 14 prices rather than 14 price changes for the first RSI.
• Averaging only winning days when calculating average gain.
• Treating overbought as an automatic sell or oversold as an automatic buy.
• Confusing histogram zero with MACD zero.
• Rounding intermediate values or counting a continuing state as a fresh crossover.
• Evaluating a strategy without costs, executable timing or out-of-sample data.