Is price drawn to its moving average?

01Question

"Price always comes back to the moving average." It is one of the first things traders learn to see on a chart, and it is usually said as if the average pulls price toward it, like a magnet or a rubber band. But a moving average is made from price. Every new bar moves it toward the latest price, so if anything is being drawn, it is the average.

Both can be measured. Each time price stretches away from its average and the two meet again, the gap that closed was closed partly by price moving and partly by the average moving. We ask how that split falls, and then the question that decides whether any of it means something: does a market with no memory at all behave any differently?

02Splitting a return in two

An excursion is the stretch between two bars whose range touches the average. If the close got at least one ATR from the average somewhere in it, we call its end a return, and we start the clock at the furthest close. From there to the touch, price travelled some distance toward the level where they met, and the average travelled the rest. The two parts add up to the gap exactly.

Figure 1 shows one return of each kind. On the left, price fell back to a slowly rising average. On the right, price went sideways and drifted slightly further away, and the average came all the way to it. On a chart both look like "price came back to the average".

03Who did the travelling

Across 135,996 hourly returns to EMA(20), price did most of the travelling in 81%. The average did most in 15%, and in another 3.7% price was moving away when the average caught up with it. Figure 2 lays out a hundred of them, beside the same count for shuffled markets.

A shuffled market is built from the real one: each bar's open, high, low and close, taken relative to the previous close, put back in random order. It keeps the market's volatility and the shape of its bars and loses all memory, so no level can attract it. If price were drawn to its average, the real grid would show more blue than the shuffled one. It shows 81% against 81%.

Figure 3 places every return by its two parts. The cloud is the same shape in both panels. Price does most of the work because price is more volatile than an average of itself: EMA(20) moves about a tenth of the way toward price each bar, and price moves a full bar's range.

04The anatomy of a return

Figure 4 follows the median return from the furthest point to the touch, with time stretched so every return runs from 0 to 1. Price comes down most of the way; the average rises to meet it for the last part. The dashed lines are the shuffled markets, almost on top of the real ones.

05Across timeframes and averages

The pattern holds on 4-hour and daily bars and for a slower average. With SMA(50) the average did most of the travelling less often, 12% of hourly returns, because a 50-bar simple average moves less per bar than a 20-bar exponential one. In every row of Figure 5 the real and shuffled bars are close to the same length.

The real markets had slightly fewer returns than their shuffled copies on every row. Fewer touches means longer excursions: real markets trend a little more than shuffled ones, so they stay away from their average a little longer before coming back.

06Market by market

Pooling can hide markets that behave differently. Figure 6 shows each market's share of returns where the average did most of the travelling, real against shuffled.

The differences are small and mostly one-sided in forex: real pairs had the average doing most of the work +1.4 pts more often than their shuffled copies (90% interval +0.8 to +2.0). That fits pairs that drift sideways while their average catches up, a mild form of the "average drawn to price" idea. In crypto the difference is nil.

07Does the average hold?

The other half of the folklore is that a moving average acts as support or resistance: price touches it and turns back. After each touch we watched which came first, a move one ATR back out on the side price came from, or one ATR through to the other side.

Real touches held 53.1% of the time and shuffled ones 53.2%. The fast average "holds" slightly more often than not, but it does so in a market with no memory as well, because the average lags: at the touch it is still pointing the way price came from. The slower SMA(50) held slightly less often than not, 48.4% real and 48.1% shuffled; neither number is about the market. Crypto held a little less often than its shuffled copies (−0.8 pts, −1.2 to −0.4), consistent with trends that carried through the average.

08What this means for a rule

None of this says a moving average is useless. It says that two of the things traders read into one, that price will come back to it and that it will hold, happen just as often in random data. A rule built on "price returns to the average" will find that it does, and so will the same rule on a coin toss. The test that matters is whether what you do at the average beats the same action at a random time, which is the comparison Paper No. 2 makes for crossovers.

• Expect a return to the average; it is close to certain and carries no information on its own.
• Price usually does most of the travelling, because it is more volatile than its own average.
• A touch that "holds" slightly more often than not is the average's lag, not support.
• Judge a rule against a baseline, such as random entries or a shuffled market, not against zero.

09Methodology

Every figure in this paper comes from the definitions below.

Data

1-hour candles built from 1-minute Twelve Data candles stored by SixOne8, 6 October 2022 to 30 September 2026, folded to 4-hour and daily bars on the app's own grid. The first 300 bars of each series warm the averages and the ATR up.

Universe

All 81 forex, metals and crypto markets in the SixOne8 catalogue with history from October 2022: 37 currency pairs, 4 metals and 40 crypto markets.

Averages

EMA(20), SMA-seeded as the app computes it, and SMA(50). ATR(14), Wilder's smoothing.

Touch

A bar whose low is at or below the average and whose high is at or above it.

Return

An excursion between two touches in which a close got at least one ATR from the average. Measured from the furthest close; the last close still one ATR away is a second starting point, reported in the data file and leading to the same conclusions.

Split

Price's part: how far the close at the start was from the average's value at the touch. The average's part: how far the average moved from the start to the touch. Both toward each other, in ATRs at the start.

Held

After a touch, whether a close one ATR back out on the original side came before a close one ATR through on the other, within 120 bars.

Shuffled

Each market's bars as ratios to the previous close, permuted at random and rebuilt from the first close; three shuffles per market and timeframe, pooled.

Statistics

Per-market differences, then a bootstrap over markets (2,000 resamples) for 90% intervals.

10Limitations

Shuffling bars removes memory but also removes the daily rhythm of volatility, and the weekend gaps in forex and metals land at random times. A different definition of a touch (a close beyond the average rather than a range through it) or a larger distance than one ATR would change the counts, though not the comparison with shuffled markets, which uses the same definitions. Four years is one sample of market conditions.

11Test it yourself