Trading More Than One

The standard advice is to read three charts and act only when they agree. On the sixty bars of the last six lessons, three widths of the same tape agree on nine bars in forty, and all three call a trend on seven — which is what a filter that hard does to your trade count. Whether that exchange is worth making is arithmetic, and it has two break-even points rather than one: a filter raises your expectancy per trade the moment it removes any higher share of losers than winners, and raises your money only once that share exceeds your profit factor. Almost everything sold as a filter lives in the gap between those two.

Prerequisites: Lesson 38, which established that a wider chart is the same tape regrouped rather than a second source, and lesson 19, whose worked system and sample arithmetic the second half of this lesson runs on.

How often three charts agree

The measurement is straightforward on a series we already have. Take the sixty bars of lessons 32 through 38 and build three charts from them: every bar, every second bar, every fourth bar. On each chart compute lesson 36’s ratio over its own last five closes and call the tape trending when the reading is above 0.4 — the same quantity, the same threshold, on each of the three. Then carry each chart’s answer down to the base bars it covers, which is what a trader does when the daily label governs every fifteen-minute bar inside that day. Forty base bars have all three answers available.

The three charts do not call the tape trending at the same rate. The narrow one says trending on 18 of the 40, the middle on 28 and the wide on 28. That difference alone is worth sitting with: the wide chart, which is supposed to supply the sober background, is the one calling a trend most often, because averaging over four bars removes the reversals that were making the narrow reading small. Nothing about the wide chart is more conservative. It is smoother, which is a different property.

Below, how often each pair of charts gives the same answer, against how often they would give the same answer if the two readings were unrelated coins with those same rates.

Charts compared	Bars they agree on, of 40	Share	Share if the readings were unrelated
every bar and every second bar	22	55%	48%
every bar and every fourth bar	16	40%	48%
every second bar and every fourth	20	50%	58%
all three at once	9	23%	27%

Read the last column first. Two of the three pairs agree less often than unrelated readings would, and so does the three-way agreement. On this stretch the confirmation is not there. Three views of one tape, computed with one formula at one threshold, land on the same answer about as often as three coins with the same bias would, and the pair furthest apart in width lands together less often than that.

That is one series of forty bars and it cannot establish a general fact, and consecutive bars are not forty separate observations. What it can do is retire the assumption. Nobody who recommends three-chart agreement has told you the agreement rate on your instrument, and until you have measured it you do not know whether your third chart is a second witness or an echo.

What requiring agreement costs

Now the count. Of the forty bars, all three charts call the tape trending on seven. Two charts call it on twenty-two, one on nine, and none on two. So a rule that goes long only when all three agree acts on 7 of the 40 bars. Put beside the narrow chart on its own, which called a trend on 18 of them, the rule has deleted 11 of 18 candidate longs — sixty-one per cent of them — and 7 of 18 is the number to hold on to, because every arithmetic that follows is about what happens to a strategy whose trade count has been cut like that.

Worse, the seven is the friendly answer. Run the same measurement with a ten-close window on each chart instead of five and the widest chart never calls the tape trending at all across the twenty bars where all three can be read, so the three-chart rule produces no trades whatever. With an eight-close window the widest chart does call a trend, on 8 of its 28 readable bars, and the three-chart rule still produces nothing at all: not once do all three agree that the tape is trending. The setting that made the framework look workable was the one chosen for it, which is lesson 38’s point arriving on schedule.

What a filter has to do to be worth having

A filter is any rule that deletes some of the trades you would otherwise have taken, and every filter deletes two kinds. Call the share of your losers it removes its accuracy and the share of your winners it removes its damage. No filter has damage of zero; the ones that claim to are being described by somebody who did not log the trades they skipped.

There are two questions you can ask of it and they have different answers. The first is whether your expectancy per trade goes up. Work it through and the condition falls out with everything cancelling: expectancy improves whenever the accuracy exceeds the damage by any margin at all. Remove 41 per cent of your losers and 40 per cent of your winners and your average trade gets better. That is a very low bar and it is the bar almost every filter is sold against.

The second question is whether you end up with more money, and that condition is different. The money you save is the deleted losers; the money you forgo is the deleted winners. The filter comes out ahead only when the accuracy exceeds the damage by more than the ratio of your gross winnings to your gross losses — your profit factor. And notice which way that cuts: the better your strategy already is, the more accurate a filter has to be to add anything to it. A profit factor of two demands a filter that removes losers at more than twice the rate it removes winners. A strategy that is losing money can be improved by a filter that is barely better than a coin.

Lesson 19’s worked system makes it concrete. It wins 45 per cent of the time at two to one, so a hundred trades produce 45 winners worth 90R and 55 losers worth 55R: a profit factor of 1.64, an expectancy of 0.35R and 35R of profit. Below, what various filters do to it, with the last column in lesson 19’s own units — the trades needed to establish that the edge exists at all, converted to weeks at four candidate trades a week before filtering.

Filter removes	Trades kept per 100	Expectancy per trade	Total profit	Weeks to establish the edge
nothing	100.0	0.35R	35.0R	36
half the losers, no winners	72.5	0.86R	62.5R	8
30% of losers, 10% of winners	79.0	0.54R	42.5R	19
half the losers, 40% of winners	54.5	0.49R	26.5R	34
half the losers, half the winners	50.0	0.35R	17.5R	71
80% of losers, 40% of winners	38.0	1.13R	43.0R	7

The fourth row is the one to memorise. That filter raises the expectancy from 0.35R to 0.49R, a gain of nearly forty per cent, and it takes the profit from 35R down to 26.5R. Both are true at once and neither is a mistake. It is a good filter by the measure everybody quotes and a bad one by the measure everybody trades for, and the reason is that its accuracy of one half beats its damage of two fifths but does not beat the profit factor of 1.64.

The last row makes the same point from the other side. Removing four fifths of the losers costs two fifths of the winners and is still worth having, because four fifths against two fifths is a ratio of two, and two is above 1.64. A filter can be brutal and still pay, or gentle and still cost. The ratio is what decides it, and the ratio has to be measured.

The third cost, which nobody prices

The fifth row is the one that should be uncomfortable, because it is what an uninformative filter does. Removing half the losers and half the winners is what a rule that knows nothing does: it deletes a random half of everything in front of it. The expectancy is unchanged at 0.35R, exactly as the condition predicts. The profit halves. And the last column doubles: 71 weeks instead of 36 to establish that the edge exists at all, because lesson 19’s sample requirement is unchanged while the trade rate has halved.

That column is the cost the three-chart rule imposes whether or not it works. Read it across the table and it does not move the way the other columns do. The trap row, which loses you money, takes 34 weeks against 36 — essentially unchanged, because the filter raised the expectancy enough to shrink the sample needed by almost exactly as much as it shrank the trade rate. A filter that genuinely works buys the time back: half the losers and no winners takes 8 weeks instead of 36, because the edge got large enough to see quickly. A filter that does nothing spends it.

So the three columns can move independently, and a filter can be sold on any one of them. Requiring three charts to agree cut this series from forty bars to seven. Before you accept that, you are entitled to know which of the three columns it moved and in which direction, and none of the three is knowable from the framework. All three come out of a record that includes the setups you skipped.

Problems

1. Measure the agreement rate on your own instrument before you require it. Pick your three widths and one rule that gives each a yes or no — a moving-average side, a structure direction, whatever you actually use. Score forty bars on all three. Count how often each pair agrees, then work out how often they would agree if the two were unrelated: multiply the two yes rates together, add the product of the two no rates. If your observed agreement is not comfortably above that number, your third chart is not a second witness and you should stop treating its confirmation as evidence.
2. Get the two rates your filter actually has. This one needs the record of setups you did not take, which is the whole reason to log them. Over your last hundred candidate setups, count four numbers: the losers your filter removed, the losers it let through, the winners it removed, the winners it let through. The first pair gives you its accuracy, the second its damage. Almost nobody has these numbers, and almost everybody has an opinion about the filter.
3. Compute the ratio your filter has to beat. Add up every winning trade in your record and every losing trade separately; divide the first by the second. That is the number your accuracy has to exceed your damage by. Then check it against what you measured in the second exercise. If the ratio comes out below one, your strategy is losing money and almost any filter helps, which is worth knowing for a different reason. How to Collect a Base Rate is how the count is kept honest.

Sources. David M. Green and John A. Swets, “Signal Detection Theory and Psychophysics” (Wiley, 1966), for the framework the two rates come from — every decision rule is described by the pair, not by either alone, and moving one always moves the other. J. M. Bates and C. W. J. Granger, “The Combination of Forecasts” (Operational Research Quarterly, 1969), for the founding result on combining predictions, whose central term is the correlation between them: two forecasts that agree by construction add almost nothing to each other. Robert T. Clemen, “Combining Forecasts: A Review and Annotated Bibliography” (International Journal of Forecasting, 1989), for twenty years of the same finding restated across fields — the gain from a second opinion is governed by how much it disagrees with the first.

Every width discussed so far has been shorter than a day, and the widest chart in the table was fifteen bars of a sixty-bar series. Widen it once more and something new appears that is not a longer version of the same thing: the market stops and starts. Prices gap between one session and the next, the level that was live at four o’clock may be nowhere near the price at nine-thirty, and the swing rule of lesson 32 has to be told what to do about a stretch of price that never traded. Lesson 40 is about structure that spans more than one day: what carries over, what is created by the gap itself, and which of yesterday’s levels are still worth marking this morning.

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