Divergence

A divergence is price disagreeing with a number computed from price. Two settings decide whether one exists at all: a swing rule and an oscillator period. On the sixty closes below, ordinary values of those two give three divergences, or two, or one, or none — and before any of that, the swing rule alone decides whether there are thirty-three places to look or five.

Prerequisites: Lesson 32, whose swing rule this lesson borrows and whose closes it continues, and lesson 8, because the one kind of divergence that compares price against something other than price is the one measured against executed volume.

Sixty closes, six settings

Here are sixty closes. The first twenty are the closes from lesson 33, so the series starts from one you have already checked. They are 100.7, 101.5, 100.4, 102.8, 101.5, 104.1, 102.6, 102.1, 105.3, 103.7, 106.7, 104.6, 103.0, 105.7, 102.2, 104.9, 100.8, 103.2, 99.4 and 101.6; then 100.5, 100.0, 99.1, 98.2, 99.1, 99.5, 98.8, 99.2, 99.6, 100.0, 99.5, 99.9, 100.3, 101.5, 102.1, 103.0, 103.4, 103.1, 102.4 and 101.3; then 101.7, 102.1, 103.1, 104.4, 104.8, 105.6, 106.6, 106.1, 106.7, 105.9, 106.7, 105.9, 106.9, 106.6, 105.8, 107.1, 106.8, 106.0, 107.0 and 106.5. The lowest close is 98.2, at bar 24. The highest is 107.1, at bar 56.

Mark the swing highs and lows on the closes — on the closes, not on the bar highs and lows, because the oscillator is computed from closes and comparing it against a different series would quietly add a fifth choice. Then read RSI at each swing and count regular divergences: consecutive swing highs where price rose and the oscillator fell, consecutive swing lows where price fell and the oscillator rose.

Swing rule	Pairs available to compare	Divergences at RSI 7	Divergences at RSI 14
1 close either side	33	3	3
2 closes either side	15	2	1
3 closes either side	5	1	0

Read the second column before the others. It is not a count of divergences; it is a count of the places where one could be found at all. Sixty closes offer thirty-three comparable pairs of consecutive swings under the loosest rule and five under the tightest, and no divergence can exist outside them. Before an oscillator has even been chosen, the swing rule has already ruled out six sevenths of the possible signals.

Then the counts. Three at one setting and none at another, and in between a row where the two oscillator periods disagree with each other: at two closes either side, a seven-period RSI finds two divergences and a fourteen-period RSI finds one. Same closes, same swings, same definition of a divergence. The difference is a number in a settings box, and it is the difference between a signal existing and not existing.

Where the signal actually fired

Every divergence on this series is bearish, and all of them sit between bars 47 and 56, across four marginal higher closes: 106.6, then 106.7, then 106.9, then 107.1. The entire run of new highs is half a point wide on a series whose range is nearly nine points. That is what the loose setting detected — not a rally running out of buyers, but a flat top being crossed off four times, a tenth or two of a point at a time.

The two-close rule with a fourteen-period RSI keeps exactly one of those four: bars 53 to 56, price from 106.9 to 107.1 while the oscillator falls from 63.6 to 62.3. The same swing rule with a seven-period RSI keeps that one and adds another, spanning bars 37 to 53 — a comparison reaching sixteen bars back rather than three, and therefore a different claim about a different move. At three closes either side the fourteen-period RSI reports nothing at all, because by then only five comparable pairs remain and none of them qualifies.

Why a second push reads lower

There is a reason divergences cluster where these did, and it has nothing to do with buyers. RSI is a ratio of averaged up moves to averaged down moves over a fixed window. Take two fourteen-bar windows in which every up bar is exactly 1.0 and every down bar is exactly 0.4. The only difference between them is how many there are of each.

Window	Up bars	Down bars	Average gain	Average loss	RSI 14
First	10	4	0.714	0.114	86.2
Second	7	7	0.500	0.200	71.4

Every up bar in the second window is the same size as every up bar in the first, and every down bar matches too. Nobody bought less on any bar. The reading fell by nearly fifteen points because the advance occupied seven of the fourteen slots instead of ten, which halves the net move across the window from 8.4 points to 4.2. If that second window began from a higher base — which it would, the first window having lifted price there — it ends at a higher price with a lower oscillator, and that is a textbook bearish divergence with nothing behind it but pace.

Notice also what the reading cannot see. Double every move in the second window and both averages double, the ratio between them does not move, and the number is 71.4 again. A window with twice the size of move behind it reads identically. Whatever a divergence on an oscillator measures, it is not how much was bought.

The kind that really is two witnesses

One family escapes all of this: price against executed volume. Delta is not computed from the closes. It is a count of what actually traded and on which side, and lesson 8 is where it comes from. When price makes a higher high on less aggressive buying, two different measurements disagree, and that is the shape the picture was promising all along.

It has a defect of its own, and it is a close relative of the one above. A second push almost always carries less delta than the first, because the traders willing to pay up went in on the first one; that is close to what makes it a second push. So a reduction is the ordinary case rather than a warning, and a figure like sixty-six per cent means nothing until you know what an ordinary second push does on your instrument. That is a distribution to go and collect, not a threshold to be handed. How to Collect a Base Rate is where the collecting is set out, and the third problem below is the version of it that applies here.

Problems

1. Count the places before you count the signals. Take sixty consecutive closes from your own instrument. Mark the swing highs and lows on the closes at one either side, then again at three either side, and for each count the pairs of consecutive same-type swings — not the divergences, just the pairs. That is the number of opportunities each setting grants itself before it has looked at an indicator. Most people have never seen the ratio between their two numbers.
2. Change one number and recount. On the same sixty closes at your usual swing rule, mark every regular divergence using a seven-period RSI, then again using a fourteen-period one. Write down how many each finds and, more usefully, how many are found by both. The ones that survive both settings are the only ones that were not a property of the setting.
3. Calibrate the second push before you treat a reduction as a warning. Take twenty two-push moves on your instrument, winners and losers alike, with no trades required. For each, compute the delta on the first push and on the second, and record the fraction of the first that is missing from the second. Sort the twenty. Your threshold is not a number from a lesson; it is somewhere near the top of that distribution, and a reduction sitting at its median is what a second push does on an ordinary day. How to Collect a Base Rate is how the count is kept honest.

Sources. J. Welles Wilder Jr., New Concepts in Technical Trading Systems (Trend Research, 1978), for the original definition of the relative strength index, including the smoothing that carries his name and that the simple-average version quietly replaces. Rama Cont, Arseniy Kukanov and Sasha Stoikov, “The Price Impact of Order Book Events” (Journal of Financial Econometrics, 2014), for the finding this lesson leans on when it separates the two families: price changes track the imbalance between buy and sell order flow, which makes executed flow a measurement of something rather than a restatement of the price it moved. William Brock, Josef Lakonishok and Blake LeBaron, “Simple Technical Trading Rules and the Stochastic Properties of Stock Returns” (Journal of Finance, 1992), for the discipline this lesson’s table borrows: when a rule has parameters, every parameter setting is reported, not the one that came out best.

The next lesson closes the module by going back to a promise it made in lesson 27. A sweep is price reaching past a level to trigger the orders resting there and then coming back, and the module has referred to sweeps repeatedly without ever defining one. Lesson 35 defines it, says when a reclaim is evidence and when it is noise, and then asks the question the title is about: what a second sweep of the same level means, given that the first one was supposed to have cleared it.

Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.