Trend lines and channels

What the drawing actually is 

A rising trend line is drawn underneath price, through swing lows. A falling trend line is drawn above price, through swing highs. Two points fix it, because two points fix any straight line, and it is then extended to the right across bars that had not printed when it was drawn. Nothing else is involved in the construction, and no property of the market enters it. The inputs are swing points, which the previous lesson established are themselves a product of a confirmation setting and a timeframe, so every ambiguity in those inputs is already inside the line before a ruler touches the screen.

The line's content is arithmetic and only arithmetic. Two points give a slope and a starting value, and every value the line takes from there is that arithmetic continued. Where the line runs past the last bar, it is not measuring anything, because there is nothing yet to measure. It reports what a straight line fitted to two past points would read at a future position, which is a statement about the line rather than about the instrument.

The slope is a rate, not an angle 

Slope is rise divided by run: the price distance between the two anchor points divided by the number of bars between them. Its units are price per bar, which makes it specific to the timeframe it was drawn on, since a bar on an hourly chart and a bar on a daily chart are different amounts of time. The same two turning points measured on two timeframes give two different numbers for the same underlying movement, and neither number is the correct one.

The angle a line makes on a screen is a separate thing from its slope, and the two are routinely confused. Screen angle depends on how many bars are visible, how tall the price pane is and how far the axis is zoomed, so the same line at the same rate can look shallow on one monitor and steep on another. Commentary describing a trend line as unsustainably steep is describing a rendering at least as much as a rate, which is why the observation rarely survives being moved to a different chart window.

Which points get touched changes the line 

A chart in an established move offers more than two swing lows, and any pair of them defines a line. The pairs are not equivalent. Two lows close together fix a slope from a short run, so a small difference in either price swings the extended line a long way; two lows far apart fix a slope that ignores everything between them. Both lines are drawn correctly. They simply are not the same line, and they do not say the same thing about the bars they pass through.

The two lines end two units apart twenty bars after the last anchor, which is the smaller half of the finding. The larger half is that they disagree about the history already printed. On one drawing the line was traded through in the middle of the sequence; on the other it was not, and a description built on the first line contains an event that the description built on the second line does not contain at all. The chart did not change. The choice of anchors changed.

Extremes or closes, and the shape of the axis 

Two further choices are made before a line exists, and both are conventions with active adherents. The first is which price the line touches. One tradition anchors on the extremes actually reached, the low of the bar for a rising line and the high for a falling one, on the reasoning that those prices traded. Another anchors on closing prices only, on the reasoning that a single extreme can be one transaction that nothing confirmed while a close is where a period came to rest. A line drawn on closes generally sits inside a line drawn on extremes, so price can be beneath one and above the other simultaneously.

The second is the price axis itself. On an arithmetic axis equal price distances occupy equal vertical space; on a logarithmic axis equal percentage changes do. A straight line on one of those axes is a curve on the other, so an instrument whose price has doubled over the span being drawn will carry a visibly different trend line under each setting. The difference is negligible over short spans and large over long ones, and it is a setting in the charting software rather than a property of the market, which means two chartists can produce incompatible drawings without either of them touching the anchors.

A channel is a copy of the line 

A channel adds one line to the drawing and no new information. The trend line is copied, the copy is moved to the opposite side of price without changing its slope, and it is positioned so that it reaches the most extreme point on that side over the same span. Because the copy is parallel by construction, the vertical distance between the two lines is identical at every bar, and that distance is the channel width. The width is a consequence of where the single extreme point happened to sit, not a measurement repeated across the data.

The two edges of a channel therefore have unequal standing, and drawings rarely make that visible. The trend line rests on at least two points and can be examined against a third. The parallel rests on one, and a single unusually long bar anywhere in the span sets it for the whole drawing. Some traditions re-anchor the parallel each time a further extreme prints, which keeps it current at the cost of a channel whose width changes; others fix it once and let price run outside it, which keeps the width stable at the cost of a boundary the data has already passed.

What a broken line describes 

A break is price printing on the far side of a line. Since the line is a construction rather than a feature of the instrument, a break is an event in the drawing: it records that the market went somewhere a person's extension of two earlier points did not cover. The previous section is the proof of that, because the same three lows produced one line that price traded through and one line that price did not, over identical bars.

Practitioners apply filters to decide when a crossing counts, and the filters exist because unfiltered crossings are common and are frequently followed by a return to the original side. The usual ones are a close beyond the line rather than an intrabar touch, a stated percentage or a stated multiple of recent range beyond it, and two consecutive closes beyond it. Each filter reports fewer crossings than the one before it and reports them later, and the two properties are the same property: any test that discards brief excursions can only do so by waiting to see whether the excursion was brief.

Where practitioners disagree 

The oldest argument is about whether the drawing should be done by hand at all. The hand drawn tradition treats anchor selection as a skill and accepts that two chartists will produce different lines. A quantitative tradition replies that the freedom is the flaw, and fits a line by regression across every bar in a window or builds the boundaries from a volatility measure, so the same window always returns the same line. The hand drawn side answers that a regression line is anchored on nothing in particular and passes through the middle of price rather than touching the turning points the technique was named for. Neither position has displaced the other, and charting software ships both.

The second argument concerns why anyone expects a line to matter. One account says widely watched lines matter because they are widely watched, so orders cluster near them. The obvious objection is the subject of this lesson: if the anchors, the price used, the axis and the break filter are all choices, then no two chart readers are watching the same line, and a level that everybody draws differently is not a level everybody sees. A narrower version of the account survives, that round numbers and prior swing levels attract attention on their own, but that is a statement about levels, which the previous lesson covered, rather than a statement about the diagonal drawn between them.

What is left when both arguments are set down is narrow and worth stating plainly. A trend line is a description of a handful of past swing points, chosen by a person, rendered on a scale they selected, and continued past the data by arithmetic. Several such lines can be drawn on one chart, all of them constructed correctly, disagreeing with one another about what has already happened.