技术指标：RSI、MACD 与布林带的怀疑论指南

The most-searched question about technical indicators is some version of “which ones are best”. This sheet answers a different question first: what is an indicator, mathematically? Once you can see what RSI, MACD, and Bollinger Bands actually compute, the “best indicator” question mostly dissolves — and what replaces it is a smaller, more defensible toolkit. Possibly an empty one. That would be a respectable outcome too.

The uncomfortable starting point: every indicator is price, transformed

Open any charting platform and you can choose from hundreds of indicators. Every one of them is built the same way: take the recent open, high, low, and close values, apply a formula, draw the result. Nothing else goes in. There is no extra feed of information — no order-flow data, no economic insight, no knowledge of what other traders are planning. An indicator is the chart you are already looking at, run through a calculation.

That does not make indicators useless. A transformation can make a real property of price easier to see — how fast it has been moving, how widely it has been swinging. A thermometer does not create the temperature, and an indicator does not create the momentum it displays. The trouble starts when the display is mistaken for a forecast. Every formula on this sheet summarises the past; none of them contains the future, and the marketing that surrounds them routinely suggests otherwise.

It helps to remember where these tools come from. Most of the classic indicators were designed in the 1970s, before charting software, as compressions a trader could update by hand with a pencil and a column of closing prices. The formulas were kept simple on purpose. The computers arrived, the constraint disappeared — but the formulas stayed, and a layer of mystique grew over arithmetic that was always meant to be done at a kitchen table.

So this sheet works through the three most-used indicators with the formulas open. The goal is not to make you adopt them. It is to make sure that if you do, you know exactly what the line on your screen is saying — and what it is not saying.

RSI: what “overbought” actually measures

The Relative Strength Index compares how much price gained on its up periods with how much it lost on its down periods, across a window of usually 14 periods. The result is squeezed onto a scale from 0 to 100, with 70 conventionally labelled “overbought” and 30 “oversold”.

Read the formula slowly and the mystique drains out. RSI above 70 means one thing: recent up-moves were much larger than recent down-moves. It is a precise statement about the last 14 periods. It says nothing about period 15.

The famous failure follows directly from that. In a strong uptrend, up-moves outweighing down-moves is the definition of the situation — so RSI climbs above 70 and stays there, sometimes for weeks, while price keeps rising. Selling because the market is “overbought” is, in that situation, selling because the market is going up.

Put numbers on it. EUR/USD is trending upward and the daily RSI reads 75. A trader sells one standard lot at 1.0850, reasoning that overbought means a reversal is due. The trend continues 60 pips higher — at $10 per pip, the position is $600 down. Had the reversal arrived instead, the same 60 pips would have earned the same $600. The arithmetic is perfectly symmetrical, and RSI did not tilt it. The indicator reported, correctly, that the recent past was strongly bullish — and the trader read that as a prediction that it would stop.

The popular refinement, divergence — price makes a new high while RSI makes a lower high — is weaker evidence than its reputation suggests. It records that the latest push was less one-sided than the previous one, which is sometimes how trends end and often how they pause. Treated as an observation to weigh, it is harmless; treated as a standalone trigger, it routinely fires for weeks while the trend continues.

Where RSI is defensible: in a sideways range, an extreme reading is one piece of evidence that the latest push is stretched relative to that range's recent history — evidence to be weighed alongside the levels themselves. As a trigger on its own, the trend case above is waiting for you.

MACD: momentum borrowed from moving averages

MACD — moving average convergence divergence — sounds like a different species, but its parts are familiar. Take a fast exponential moving average and a slow one. The MACD line is the distance between them. Smooth that line with a third moving average, called the signal line, and the classic instruction is to act when the two cross.

Everything the moving-averages sheet says about lag applies here twice over. A moving average is a delayed summary of price; MACD is the gap between two of them, smoothed by a third. When the MACD line crosses its signal line, the shift in momentum it announces has already happened — the cross is the paperwork arriving after the event.

In a market that trends for weeks, that lag costs little: you enter late, but there is plenty of move left. In a sideways market it is expensive. Price turns every few days, each turn is announced late, and a trader following the crosses ends up selling near each low and buying near each high — the whipsaw pattern that every crossover method shares, because they share the same ingredient.

Again, numbers. A choppy fortnight on EUR/USD produces three MACD signal crossings. Each is entered with one standard lot and abandoned 25 pips later when the move fails to follow through: three losses of $250, $750 in total. The same 25 pips in the trader's favour would have paid $250 each time — the mechanics are symmetric, and in a whipsaw the late entries simply land on the wrong side more often than not. Nothing malfunctioned. The formula did exactly what it does: it reported turns, at a delay.

The less-quoted parts of MACD are the more honest ones. The histogram shows whether the gap between the averages is widening or narrowing — a readable description of momentum building or fading. And the zero line marks where the fast average sits relative to the slow one, which is a serviceable trend filter. Used that way — as a slow, smoothed answer to “is the pressure building or fading?” on a higher timeframe — MACD describes. Used as an entry trigger, it inherits every weakness of the averages it is made from.

Bollinger Bands: volatility envelopes, not buy and sell lines

Bollinger Bands draw a 20-period simple moving average, then two bands above and below it, each two standard deviations away. Standard deviation is a measure of ▲volatility — how widely recent prices are scattered around their own average. Quiet markets pull the bands tight; turbulent ones push them apart.

If price changes followed the tidy bell curve that the formula borrows from statistics, about 95% of closes would fall inside the bands. Real price changes are not that tidy — large moves occur far more often than the bell curve predicts — so band touches are routine events, not rare extremes.

That single fact dismantles the most common use. “Price touched the upper band, so sell” assumes the touch is exceptional. It is not — and in a trend it is the opposite of a sell case: price can walk along the upper band for days, touching it again and again while climbing, exactly the way it parks RSI above 70. A trader who sells one standard lot into a 120-pip band-walk is $1,200 down by the end of it; the same 120 pips of genuine reversal would have earned $1,200. The touch never changed those odds. It described the volatility, nothing more.

What the bands genuinely describe is regime. A “squeeze” — bands at their tightest in months — records that volatility is unusually low, and unusually quiet periods do tend to be followed by expansions. But the bands say nothing about the direction of the expansion. A squeeze on EUR/USD that resolves with a 50-pip breakout pays $500 to one side and charges $500 to the other, and the formula is indifferent about which side you were on.

Where they are defensible: as a running record of volatility — context for stop distances, position sizes, and what “a big move” currently means on this pair. As buy and sell lines, they were never designed for it, a point their inventor has spent decades repeating to little effect.

Redundancy: why five indicators often equal one, five times

Here is the experiment that quietly ends most indicator collections. Put RSI, stochastic, MACD, momentum, and rate-of-change under one chart and watch them for a week. They rise together, fall together, and reach their extremes together — because all five are transformations of the same input: recent closing prices. They are five rephrasings of one sentence.

Sorted this way, a menu of hundreds collapses to roughly two families that matter in spot FX: how fast price has been moving (momentum) and how widely it has been swinging (volatility). The third family on stock charts, volume, barely applies here — spot forex has no central exchange, so a platform's “volume” is a count of price updates at one broker, not the market's traded amount.

The same redundancy hides inside a single indicator at multiple settings. RSI at 7, 14, and 21 periods is not three opinions; it is one calculation at three smoothing levels. And tuning those settings until the indicator fits the recent past has a name — curve-fitting — and a reliable outcome: the settings that won the past rarely win the future, because what they learned was the noise.

The cost of ignoring all this is not just clutter. Five agreeing indicators feel like five independent confirmations, and that feeling changes behaviour: more conviction, larger sizes, more trades taken. Since the five agree because they share an input, the extra conviction is unearned. A dashboard of restatements is one of the quieter engines of ▲overtrading — every wiggle in price arrives five times, each arrival dressed as new evidence.

A defensible setup: at most two, fully understood — or zero

If, knowing all of the above, you still want indicators on your chart, the defensible version is small and deliberate. At most two, drawn from different families — one momentum, one volatility — so that the second one adds a dimension instead of an echo. And each must pass a three-part understanding test:

• You can compute it by hand from a column of closes — at least once, slowly.
• You can state in one sentence what it measures, without using the words “buy” or “sell”.
• You can name the market condition in which it reliably misleads, because every indicator has one.

Zero is also defensible. Price, levels, and structure — the raw chart that every indicator is computed from — contain everything the indicators contain, at full resolution. Plenty of competent traders work from bare charts, not as a purity exercise but because the original carries more detail than any summary of it.

What is not defensible is the search this sheet began with: the hunt for the best indicator, the magic setting, the combination that finally works. Any rule built on an indicator — any rule at all — earns trust exactly one way: written down, tested across enough trades for luck to cancel out, and measured. That arithmetic has its own sheet, on expectancy and edge, and it is where this road honestly leads.