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Moving Averages by Hand and What They Hide

Five hourly closes on EUR/USD, oldest first: 1.1000, 1.1010, 1.1020, 1.1015, 1.1025. A sixth close arrives at 1.1040.

Compute the five-period simple average of the first five: 1.1000 plus 1.1010 plus 1.1020 plus 1.1015 plus 1.1025 is 5.5070. Divided by five: 1.10140.

Now slide the window. The newest five are 1.1010, 1.1020, 1.1015, 1.1025, 1.1040, summing to 5.5110, so the average is 1.10220.

The close jumped 15 pips from 1.1025 to 1.1040. The average moved only 8 pips, from 1.1014 to 1.1022. The average moved about half as much as price, because it carries four older values along with the new one.

That is lag in numbers. In a longer window, the lag is bigger. A 50-period average would move only a fraction of a pip for the same 15-pip jump.

Now note the distance between price and average: 1.1040 minus 1.1022 is 18 pips. A trader using the average as a pullback target would wait for price to return toward it, but if price moves fast, the average chases and the pullback may never reach it.

This also explains why crossovers arrive late. By the time a short average crosses a long one, price has already moved.

The calculation is trivial and still worth doing by hand once, because it makes lag concrete.

Your turn: calculate a 10-period average of ten closes from your chart and compare it with the last price.

Moving averages are useful as filters but always behind price. On short timeframes, a shorter average or an EMA reduces the lag, but at the cost of more noise.

Working the numbers by hand makes the mechanics clear. The five period average moved from 1.1014 to 1.1022 when the sixth close arrived. Strictly, the change in a simple average equals the new value minus the value that drops out, divided by the period. Here that's 1.1040 minus 1.1000, or 40 pips, divided by five, which is 8 pips. So the average's move depends on what left the window as much as on what arrived. If the dropped value had been 1.1030, the average would have moved only 2 pips. That's one reason simple averages can behave oddly when an old spike drops out of the window.

I ran this on an hourly EUR/USD chart last week. My ten closes, oldest first, were 1.0842, 1.0846, 1.0851, 1.0849, 1.0855, 1.0861, 1.0858, 1.0866, 1.0872 and 1.0880. They add up to 10.8580, so the ten period average is 1.0858, while the last close sat at 1.0880. That is 22 pips between price and the line, even though the move was a smooth grind with no spike in it.

What stood out is that a simple average of n bars lags by roughly (n minus 1) divided by 2 bars. For ten bars that is about four and a half hours, and 1.0858 is almost exactly where price was around the fifth and sixth closes. So the average is not a picture of now, it is a picture of the middle of the window.

Since then I stopped using it as a bounce target in a fast move. I only trust it as a pullback level when the slope is gentle.

The 18 pip gap between price and the average is a useful observation. In a strong trend, price can stay well away from its moving average for long periods, and traders waiting for a pullback to the average may miss the move entirely. In a weaker trend, price returns to the average more often. Measuring the typical distance between price and the average in past trends, perhaps in ATR units, gives a realistic expectation for how deep pullbacks tend to be. That can help set limit orders at levels price is more likely to reach than the average itself.

Exponential moving averages reduce lag by giving more weight to recent prices. A five period exponential average would react more to the 1.1040 close than the simple average does. That makes crossovers arrive earlier, but also produces more false signals, since the average reacts more to noise. There's no free lunch: less lag always comes with more sensitivity to random moves. The choice between simple and exponential averages, and between short and long periods, is a choice about how much lag and how much noise a strategy can tolerate. Testing both on the same data is the only fair way to decide.

Calculating a ten period average by hand once, as the exercise suggests, is a good way to build intuition. After that, the platform does the work, but the understanding of lag remains. Some traders find it helpful to plot two or three averages of different lengths together and watch how they respond to sharp moves. Has anyone here switched from simple to exponential averages, or the other way around? I'd be interested in what made you change, and whether the difference in lag had a noticeable effect on your entries and exits.