🧭 Momentum indicators: RSI, MACD, stochastic and divergences

🎯 In 30 seconds: Momentum indicators measure how fast and how consistently price is moving. RSI compares average gains with average losses on a 0 to 100 scale. MACD is the gap between a 12-day and a 26-day exponential moving average, with a 9-day signal line. The stochastic shows where the close sits within the recent high-low range. All three are calculated from price, so they add no new information; they repackage it. They are most useful for spotting a trend slowing down (divergence) and for timing entries in the direction of the trend. "Overbought" in a strong uptrend often just means the trend is strong.

What momentum means

In physics, momentum is mass times speed. On a chart, momentum means how fast price is moving and how one-sided the recent moves have been. A stock that rose on 12 of the last 14 days has strong upward momentum, even if the total move is modest.

Momentum indicators are also called oscillators because they swing back and forth, either within a fixed range (RSI and stochastic, 0 to 100) or around a zero line (MACD).

One idea to hold onto through this whole chapter: every indicator here is a formula applied to past prices. It cannot know anything the price chart does not already show. Its value is that it makes certain features (speed, slowing, stretched moves) easier to see and to test.

RSI: the Relative Strength Index

RSI was introduced by J. Welles Wilder in his 1978 book New Concepts in Technical Trading Systems. The standard setting uses 14 periods.

Step by step (Wilder's method):

1. For each day, compute the change from the prior close. A rise is a gain; a fall is a loss, recorded as a positive number. A day that rises has a loss of 0, and vice versa.
2. First average gain = sum of gains over the first 14 days / 14. First average loss = sum of losses over the first 14 days / 14.
3. After that, smooth each day: Average gain = (prior average gain x 13 + today's gain) / 14, and the same for losses.
4. RS = average gain / average loss
5. RSI = 100 minus 100 / (1 + RS)

If the average loss is zero, RSI is 100. If the average gain is zero, RSI is 0. Because of the smoothing in step 3, RSI values depend slightly on how much history the software starts from, so two platforms can show a point or two of difference.

Worked example: RSI by hand

Hypothetical daily price changes over 14 days: +0.50, minus 0.20, +0.30, +0.40, minus 0.60, +0.20, +0.10, minus 0.30, +0.70, +0.20, minus 0.10, +0.40, minus 0.20, +0.30.

On day 15 the stock falls $0.50. Gain = 0, loss = 0.50.

One down day of $0.50 dropped RSI by more than 7 points. That shows how RSI works: it measures the balance of recent ups and downs, not the price level.

Reading RSI

• Above 70 is traditionally called overbought; below 30 oversold. These words only mean the recent moves were very one-sided. They do not mean price must reverse.
• The 50 line splits up-momentum from down-momentum. In many uptrends, RSI pullbacks stop around 40 to 50 and rallies push it to 70 or higher. In downtrends the pattern flips: rallies stall around 50 to 60.
• In ranges, the 70 and 30 levels work better, because price itself keeps reversing.

MACD: Moving Average Convergence Divergence

MACD was developed by Gerald Appel in the late 1970s. It has three parts:

• MACD line = 12-day EMA of closes minus 26-day EMA of closes.
• Signal line = 9-day EMA of the MACD line.
• Histogram = MACD line minus signal line, drawn as bars.

If you have read Moving averages, MACD is just the distance between a fast and a slow EMA. When the fast one pulls away above the slow one, MACD rises; when they converge, MACD falls toward zero.

Example with hypothetical numbers: the 12-day EMA is $52.40 and the 26-day EMA is $51.10. MACD = $52.40 minus $51.10 = 1.30. If the signal line is 1.05, the histogram is 1.30 minus 1.05 = 0.25. Positive and rising histogram bars mean the fast EMA is pulling away faster than recently. Shrinking bars mean momentum is fading even if price is still rising.

Common readings:

• Zero line: MACD above zero means the 12-day EMA is above the 26-day EMA, a short-term uptrend.
• Signal crossovers: MACD crossing above its signal line is read as bullish, below as bearish. These come often and many fail in choppy markets.
• Histogram turning: the earliest of the three, and also the noisiest.

MACD is measured in dollars, not a fixed 0 to 100 scale. A MACD of 1.30 on a $50 stock is large; on a $500 stock it is tiny. Do not compare MACD values across stocks.

The stochastic oscillator

The stochastic, developed by George Lane in the late 1950s, asks: where did today's close land within the range of the last 14 days?

%K = (Close minus lowest low of 14 days) / (highest high of 14 days minus lowest low of 14 days) x 100

%D = 3-day simple average of %K

Example: over 14 days the high was $48 and the low $40. Today's close is $46. %K = ($46 minus $40) / ($48 minus $40) x 100 = 6 / 8 x 100 = 75. The close is three-quarters of the way up the range.

The raw version above is the "fast" stochastic. The more common "slow" stochastic smooths %K with a 3-day average first, then takes %D as a 3-day average of that. Readings above 80 are called overbought and below 20 oversold, with the same caution as RSI.

Divergences

A divergence is when price and the indicator disagree:

• Bearish divergence: price makes a higher high, but the indicator makes a lower high. The second push up had less force behind it.
• Bullish divergence: price makes a lower low, but the indicator makes a higher low. Selling pressure is fading.

Divergences are a warning that a trend is slowing. They are not a timing signal. In a strong trend, momentum can diverge several times in a row while price keeps going. A sensible rule is to treat a divergence as a reason to tighten your stop or take partial profits, and to wait for the price structure itself (a break of the last higher low, see Trends) before acting on it.

Why three indicators is not three opinions

RSI, MACD and the stochastic all come from the same closing prices over similar windows. When all three say "overbought", that is one fact counted three times. Adding indicators makes a chart feel more certain without adding evidence.

A better approach: pick one momentum tool, learn exactly how it behaves, and pair it with something different, such as trend structure, a support or resistance level, or volume.

What the evidence says

A large survey of research on technical trading rules counted 95 modern studies: 56 found positive results, 20 negative and 19 mixed. The same survey warned that most studies had problems such as data snooping (trying many rules and reporting the best one), choosing rules after the fact, and difficulty measuring risk and trading costs.

So the fair position is: momentum tools can help you organize what you see and time entries, but no oscillator setting has a proven, reliable edge on its own after costs. Treat any rule you build with them as a hypothesis to test. Does technical analysis work? shows how. Note too that "momentum" in academic research usually means something different: ranking stocks by their past 3 to 12 month returns. That is covered in Momentum trading.

Try it

1. In a spreadsheet, enter 30 days of closing prices for any stock or index and compute RSI with Wilder's steps. Compare your last value with a charting site. A small difference is normal; a big one means a step is wrong.
2. In the strategy backtester, test two versions of an RSI rule on the same stock: (a) buy when RSI falls below 30, sell above 70; (b) buy when RSI dips below 40 while price is above its 200-day average, sell when price closes below the 50-day. Compare trades, win rate, average loss and drawdown.
3. On five charts, find one bearish divergence each. Write down what happened over the next 20 days. Count how many led to a real trend change and how many did not.

Sources

• StockCharts ChartSchool: Relative Strength Index (RSI)
• StockCharts ChartSchool: MACD (Moving Average Convergence/Divergence Oscillator)
• StockCharts ChartSchool: Stochastic Oscillator (Fast, Slow and Full)
• RePEc: Park and Irwin, What Do We Know About the Profitability of Technical Analysis? (Journal of Economic Surveys, 2007)