🎚️ Momentum oscillators: RSI, stochastic and rate of change

🎯 In 30 seconds: RSI weighs recent up moves against down moves. The stochastic asks where the close sits inside the recent high to low range. Rate of change compares today’s price with one from a fixed number of bars ago. All three are rearrangements of past prices, so they are best used to describe how a move is behaving, not to predict a turn. Their readings mean different things in a trend and in a range, and each has a quirk in its math that can fool you.

Why oscillators exist

A price chart shows direction well but makes speed hard to judge. An oscillator turns speed into a line that swings within a band, so you can compare this week’s push with last month’s at a glance.

The chapter on momentum indicators walks through a full 14-day RSI calculation. This chapter covers what that math implies, the settings people change, and two oscillators it did not cover in depth.

RSI: what the smoothing does

J. Welles Wilder Jr. published the Relative Strength Index in 1978. It averages gains and losses separately, divides one by the other, and squeezes the result onto a 0 to 100 scale. The default look-back is 14 bars.

Wilder’s averaging keeps 13/14 of yesterday’s value and adds 1/14 of today’s. That behaves like an exponential average of about 27 bars. Two things follow:

• Old moves fade slowly. A big drop three weeks ago still pulls RSI down a little today.
• One large bar moves it a lot. A single day equal to several normal days can swing RSI by 10 points or more.

A quick check on the scale: if average gains are three times average losses, RS is 3 and RSI = 100 minus 100 / 4 = 75. If gains and losses are equal, RS is 1 and RSI is 50. To reach 90, gains must average nine times losses. That is why readings above 85 are rare on daily charts.

Reading RSI in context

• Shifting ranges. In a healthy uptrend, RSI often swings between roughly 40 and 80, and dips toward 40 are where pullbacks tend to end. In a downtrend the band slides to about 20 to 60. When RSI stops reaching its usual highs, the trend may be tiring.
• Failure swings. Wilder described a pattern that uses RSI alone: RSI tops above 70, drops, rallies to a lower peak, then falls below its prior dip. The mirror version works at the bottom. It is a way of saying momentum broke its own structure.
• Shorter settings. A 2 to 5 bar RSI hits extremes almost every week. Some short-term traders use it to find stretched pullbacks inside a longer trend. A 20 to 25 bar RSI barely leaves the 40 to 60 band.

The stochastic: location inside the range

The stochastic oscillator compares the close with the highest high and lowest low of the last 14 bars. %K = (close minus lowest low) / (highest high minus lowest low) × 100. The idea behind it: in a rising market, closes tend to land near the top of the recent range.

Worked example with a hypothetical stock, QOLV. Over 14 days its highest high is $25 and its lowest low is $20, so the range is $5. Three closes in a row:

%D, the signal line, is the 3-bar average of %K: (90 + 80 + 60) / 3 = 76.7. %K has dropped below %D, which readers call a bearish cross. Notice that QOLV only slipped $1.50, yet the oscillator fell 30 points. A narrow range makes the stochastic jumpy.

There are three versions. The fast stochastic plots raw %K. The slow stochastic smooths %K over 3 bars first, which is the most common default (14, 3, 3). The full stochastic lets you set both smoothing lengths.

Williams %R is the same idea measured from the top: it reads 0 when the close equals the high of the range and minus 100 when it equals the low. On QOLV day 1 it would read minus 10. Stochastic RSI applies the stochastic formula to RSI values instead of price, which makes it move even faster and spend much of its time pinned at 0 or 100.

Rate of change and the drop-off effect

Rate of change (ROC) is the simplest of the three. ROC = (today’s close minus the close n bars ago) / the close n bars ago × 100. The plain momentum indicator is the same difference in dollars without the division. Common settings are 10, 12 or 20 bars on daily charts.

Example: a hypothetical stock closes at $55 today and closed at $50 ten days ago. ROC(10) = 5 / 50 × 100 = 10%.

ROC has no upper or lower limit, so there is no fixed overbought line. Readers compare it with the stock’s own history instead, or watch it cross zero.

Its quirk is that the old price matters as much as today’s. When a low price from ten days ago leaves the window, ROC changes even if today’s price does not. That is the drop-off effect.

Where they mislead

• Oversold in a downtrend. A falling stock can sit below 30 on RSI or 20 on the stochastic for weeks. Each “oversold” buy in that stretch loses.
• Settings change the story. The same chart can look stretched on a 7 bar RSI and calm on a 21 bar one. If you try many settings and keep the one that fit the past best, you have fitted noise.
• Three oscillators, one input. RSI, the stochastic and ROC all come from the same closes. When they agree, you have one observation, not three.
• Gaps and thin ranges. A stock that gaps on news jumps straight to an extreme reading. A stock in a tight range makes the stochastic flip from top to bottom on small moves.

On evidence: Park and Irwin’s 2007 survey found that many studies reported profits from technical rules but that many also had weaknesses such as data snooping and missing costs. No oscillator threshold has shown a dependable edge on its own. Treat any oscillator rule as an idea to test with honest testing.

Sources

• J. Welles Wilder Jr., New Concepts in Technical Trading Systems (1978), RSI and failure swings
• John J. Murphy, Technical Analysis of the Financial Markets (1999), oscillators and rate of change
• Perry J. Kaufman, Trading Systems and Methods, momentum and oscillator calculations
• Park and Irwin (2007), “What Do We Know About the Profitability of Technical Analysis?” Journal of Economic Surveys
• Moneydesks Technical Analysis tool: Indicator guide entries for RSI, stochastic, Williams %R, Stochastic RSI and ROC