Indicators · Trend and moving averages
Kaufman Adaptive Moving Average (KAMA): efficiency ratio explained
How KAMA speeds up in clean trends and slows down in noise using the efficiency ratio, a worked calculation on QQQ, and how Finabase computes and scores it.
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The Kaufman Adaptive Moving Average (KAMA) is a moving average that changes its own speed. When price moves steadily in one direction, KAMA behaves like a fast exponential average and keeps up. When price chops back and forth without getting anywhere, KAMA slows almost to a stop and goes flat. Perry Kaufman described it in his 1995 book Smarter Trading.
The engine behind it is a single, intuitive number, the efficiency ratio: how much of the recent movement actually went somewhere. This guide explains the efficiency ratio, works through the full KAMA update with real Invesco QQQ Trust prices, shows where the adaptation helps and where it does not, and describes how Finabase computes and scores KAMA.
The efficiency ratio
Imagine two stocks that both end ten days $10 higher. The first rose about $1 every day. The second rose $8, fell $6, rose $9, fell $5 and so on, and happened to finish $10 higher too. Both have the same net change. Only the first was trending.
Kaufman's efficiency ratio separates the two:
- Direction = the absolute net change over n bars: |close today − close n bars ago|.
- Volatility = the sum of the absolute changes from each bar to the next over those n bars.
- ER = direction ÷ volatility.
The first stock has ER = 10 ÷ 10 = 1.0. The second has ER = 10 ÷ (8 + 6 + 9 + 5 + …), something like 0.2. ER is always between 0 and 1.
The formula
The scaled constant (SC) slides between the smoothing of a 2-period EMA and a 30-period EMA according to ER, and is then squared. Squaring matters: it makes KAMA much slower when ER is middling. At ER = 0.5 the constant before squaring is 0.365; after squaring it is 0.133, about as fast as a 14-period EMA. At ER = 1 it is 0.6667² = 0.444, about a 3.5-period EMA. At ER = 0 the constant is 0.0645² = 0.0042, roughly a 480-period EMA, close to flat.
A worked example on QQQ, in a trend
On April 24, 2026 QQQ closed at $663.88. Ten sessions earlier it had closed at $611.07.
| Step | Calculation | Result |
|---|---|---|
| Direction | abs(663.88 − 611.07) | 52.81 |
| Volatility (sum of moves) | from Finabase's daily closes | 69.23 |
| Efficiency ratio | 52.81 ÷ 69.23 | 0.763 |
| Scaled constant | (0.763 × (0.6667 − 0.0645) + 0.0645)² | 0.2744 |
| KAMA yesterday | (given) | $648.00 |
| KAMA today | 648.00 + 0.2744 × (663.88 − 648.00) | $652.36 |
With three-quarters of the movement pointing the same way, KAMA closed 27% of the gap to the close in one day, faster than a 10-day EMA (18%).
The same calculation in a choppy patch
On July 22, 2026 QQQ closed at $705.35, only $6.09 below its close ten sessions earlier, but the closes had swung a total of $77.41 along the way.
| Step | Calculation | Result |
|---|---|---|
| Efficiency ratio | 6.09 ÷ 77.41 | 0.079 |
| Scaled constant | (0.079 × 0.6022 + 0.0645)² | 0.0125 |
| KAMA today | 722.53 + 0.0125 × (705.35 − 722.53) | $722.31 |
A $17 gap between price and KAMA moved the line by 21 cents. Both results match Finabase's chart.
KAMA on a real chart
QQQ's year contained both kinds of market. In April it rallied hard off a March 30 low of $555.60; on April 17 the ten-day efficiency ratio reached 1.00, ten straight up closes, and KAMA tracked price closely. From June 22 to July 31 it went nowhere in a wide, jagged range, with closes between $661.73 and $737.95. Over that stretch the SMA (10) swung from $687.74 to $725.40 while KAMA stayed between $694.77 and $729.40, flattening out for days at a time.
Over the full year, QQQ's close crossed its KAMA (10) 35 times and its SMA (10) 43 times. That is a real reduction in whipsaws, 19%, but not a cure. A choppy market that suddenly breaks out still has to wait for ER to rise before KAMA follows, and a trend that reverses sharply has fooled the ER into "trend mode" just before the turn.
How traders use KAMA
As a trend line that goes flat in ranges. The most practical reading is the slope. A flat KAMA says the efficiency ratio is low, so the market is noisy and trend-following signals deserve less trust. A KAMA that starts sloping again says direction has returned.
Price crossing KAMA. Kaufman's own entry idea was to act on KAMA turning, with a filter: require the change in KAMA to exceed a fraction of its recent standard deviation, so that tiny wiggles are ignored.
The efficiency ratio on its own. ER is a useful indicator in its own right. A rising ER says moves are becoming more directional; a falling one says the market is getting choppier. Some traders only take trend trades when ER is above a threshold such as 0.3. Finabase does not plot ER separately, but you can read it from the slope of KAMA.
Pitfalls and limitations
It still lags after a turn. At a sharp reversal the ER over the window is often still high from the prior trend, so KAMA keeps following price, then has to wait for the new direction to become efficient.
Window choice matters. ER over 10 bars is noisy; a stock can show ER 0.8 one week and 0.1 the next. Kaufman's default of 10 suits daily charts; longer windows give steadier but slower adaptation.
The fast and slow constants are fixed in Finabase. TA-Lib's KAMA uses Kaufman's standard fast 2 and slow 30. Platforms that let you change them will produce different values.
Comparison with other adaptive and fixed averages
| Average | What changes its speed | Behaviour in a range | Behaviour in a clean trend |
|---|---|---|---|
| SMA (10) | Nothing | Weaves through price | Lags 4.5 bars |
| EMA (10) | Nothing | Weaves through price | Lags 4.5 bars |
| KAMA (10) | Efficiency ratio | Goes nearly flat | About an EMA(3.5) |
| MAMA | Rate of change of the cycle phase | Steps, then holds | Jumps to catch up |
The MESA Adaptive Moving Average (MAMA and FAMA) explained adapts in a different way, from the speed of the market's dominant cycle. The fixed averages are covered in Exponential moving average (EMA): formula and how to use it and Simple moving average (SMA): formula, crossovers and limits.
How Finabase calculates and scores KAMA
Finabase computes KAMA with TA-Lib's KAMA function on closing prices. The study appears
as "Kaufman Adaptive Moving Average" and defaults to 10 periods (the efficiency-ratio
window). The fast and slow constants are TA-Lib's fixed 2 and 30. It is drawn on the price
chart as an overlay.
In the technical gauge, KAMA (10) is one of the overlay rows: a close at or above KAMA counts as Bullish, below it as Bearish. The Scanner tracks the same KAMA (10) and lists stocks whose close crossed it, with the date. Because KAMA flattens in ranges, a stream of KAMA crossings on one symbol is usually a sign of chop, not of a series of trend changes.
Frequently asked questions
What is a good KAMA setting?
Kaufman's standard is an efficiency-ratio window of 10 with fast and slow constants of 2 and 30, written KAMA(10, 2, 30). Finabase uses exactly that. Longer windows adapt more slowly but more steadily.
What does the efficiency ratio tell you?
The share of recent price movement that was directional. An ER of 1 means every bar moved the same way; an ER of 0 means price ended where it started despite moving around.
Is KAMA better than an EMA?
It whipsaws less in choppy markets and keeps up well in clean trends. On QQQ's 2026 chart it cut crossings by about a fifth compared with a 10-day SMA. It still lags at sharp reversals, and its advantage depends on how much of the time a market spends in chop.
Summary
KAMA measures how efficiently price has been moving and sets its own speed accordingly: as quick as a 3.5-period EMA when ER is 1, nearly frozen when ER is 0. The QQQ examples show both modes, a 27% catch-up on a trending day and a 21-cent move on a choppy one. Its flat stretches are as informative as its crossings. Use it to tell trends from noise, and remember that adaptation still follows, never leads, the market.
Sources and further reading
- Perry J. Kaufman, Smarter Trading (McGraw-Hill, 1995) — the adaptive moving average and efficiency ratio
- Perry J. Kaufman, Trading Systems and Methods, 6th ed. (Wiley, 2019) — adaptive techniques
- TA-Lib — KAMA function reference
- Finabase chart data — QQQ daily bars, 2025-10-30 to 2026-10-29, KAMA and SMA computed by Finabase