移动平均线：它抹平了什么，又隐藏了什么

A moving average is the most popular line ever drawn on a price chart, and it is nothing more than arithmetic: take the last N closes, average them, repeat at every new candle. That modesty is worth holding onto, because moving averages have accumulated a reputation their arithmetic cannot support — dynamic support, golden crosses, lines the market supposedly respects. This sheet computes one by hand, explains the two main variants and the conventional settings, and then tests the famous crossover against a worked example. The conclusion is not that moving averages are useless. It is that they are a summary of the past — genuinely useful for context, structurally late at every turn, and never an oracle.

The arithmetic: one average, computed by hand

Do this once with real numbers and the indicator loses its aura. Take twenty EUR/USD daily closes — illustrative figures, as everywhere in this survey. Add them up; divide by twenty. That is the whole indicator:

Tomorrow, the newest close joins the sum, the oldest one drops out, and the result shifts slightly — that is all the "movement" in a moving average. Plotted at every candle, these averages join into the smooth line on your chart. The smoothing is real: day-to-day noise mostly cancels out, and what survives is the neighbourhood price has been living in for the last twenty periods.

The lag is just as real, and it is structural, not a flaw to be tuned away. Suppose the market turns hard: after that calm stretch averaging 1.0862, price drops 60 pips in a day to 1.0802. The new close is only one of twenty inputs, so the average moves roughly a twentieth of the distance — about 3 pips — while price moved 60. The line will keep pointing up for days after the turn. Whatever a moving average tells you, it tells you late; that is the price of the smoothing, paid at exactly the moments traders most want speed.

The EMA: tighter to price, and what that costs

The exponential moving average attacks the lag by weighting recent closes more heavily — each new close gets a fixed share of the result, and every older close fades geometrically toward zero. The weighting itself is one line of arithmetic:

The effect on the chart: the EMA hugs price more closely and turns earlier at genuine reversals. The cost is exact and unavoidable: by trusting the newest closes more, the EMA also trusts noise more. Every meaningless two-day wobble pulls it around in miniature, producing more changes of slope — and, if you act on slope, more false starts. SMA versus EMA is not a contest with a winner; it is one trade-off, smoothness against responsiveness, and you choose where on it to stand.

20, 50, 200: conventions, not constants

Charting platforms ship with the same default lengths, and entire commentary industries are built on them. It is worth being clear about what these numbers are: roughly a month, a quarter, and a year of daily candles, rounded to memorable figures decades ago. They persist because everyone watches them — which gives them a mild self-fulfilling quality worth knowing about, and no physical authority whatsoever.

Use them as shared vocabulary, not physics. "Price found support at the 50-day" is a sentence about a coincidence that sometimes repeats because many people watch the same line — it is not a property of the number 50. If you ever feel the urge to optimise — to search for the setting that would have worked best last year — notice that this is curve-fitting the past, and the past has already been traded.

Crossovers: the appeal, the lag, and a worked whipsaw

Cross two averages — say a 20 over a 50 — and you get the most famous mechanical rule in retail trading: fast line above slow means up, fast below slow means down, and the crossing moment is the event. (On daily charts, the 50/200 version is dignified with names: golden cross and death cross.) The appeal is genuine — the rule is objective, always on, and removes every decision. The cost arrives in two instalments. First, lag squared: each average already trails price, and the crossing of two trailing lines happens later still — deep into the move it announces.

Second, the whipsaw, and this deserves real numbers. In a trending stretch the rule earns its reputation: the 20 crosses above the 50 at 1.0850 — forty pips after the actual low, because lag — and the trend carries on to 1.0910, where the reverse cross takes you out. Sixty pips, about $600 on one standard lot at $10 per pip. Now run the identical rule in a sideways month: cross up at 1.0850, the "trend" stalls immediately, and the reverse cross arrives at 1.0820. Minus 30 pips — $300 gone — and ranging markets routinely print two or three of these in a row before any trend appears. Same rule, same arithmetic, symmetrical money: the mechanism that paid $600 in the trend charges $300 per false start in the range, and nothing inside the indicator tells you which market you are standing in.

The dignified names deserve one extra sentence of honesty. A golden cross on the daily chart — the 50 crossing above the 200 — sounds like an event, and financial media report it as one. Arithmetically it is the news that the average of the last quarter has overtaken the average of the last year: a confirmation that a major uptrend has been in progress for months, arriving months into it. Studies of golden-cross returns disagree with each other depending on market and era — which is itself the finding. A signal whose edge depends on which decade you test it in is not a law; it is a description of trends that already happened, wearing a name.

Honest uses: context, not commands

What survives all this is still worth having. A moving average is an honest one-glance summary of where price has recently been, and that supports two sober uses. As a trend filter: "is price above or below its 200-day?" is a crude, robust way to sort markets into healthier and weaker halves before applying any other judgement. And as context: the distance between price and its average is a rough gauge of how stretched the recent move is, readable in pips without ceremony. In quiet conditions the line behaves; when ▲volatility spikes, price detaches from any average for days — expect the summary to fail precisely when the market is most interesting.

What the arithmetic cannot support is the oracle role: entries taken because price "bounced off" a line, exits taken because a lagging summary finally noticed a turn that happened last week. A moving average states where the market has been. You already knew the market would not tell you where it is going; do not let a smoothed version of the past pretend otherwise. The next sheet on this route — a skeptic's guide to RSI, MACD, and Bollinger Bands — applies the same test to the rest of the indicator menu, with the same standard: understand what the arithmetic measures, or leave it off the chart.