The Candle Is a Summary

A candle keeps five numbers and throws away everything else that happened in its interval. Knowing exactly which five, and what the discarded part would have told you, is what decides which questions a chart can answer and which it cannot. Below are two five-minute intervals that produce the same five numbers, pixel for pixel, and the same bracket makes 0.35 in one of them and loses 0.15 in the other.

Prerequisites: Lesson 2, for where a price comes from, and lesson 3, for the transaction a candle is made of.

What that costs, in money

The abstraction becomes a number as soon as you put a bracket around it. Say you are long from the open at 100.20, with a stop at 100.05 and a target at 100.55 — 0.15 of risk against 0.35 of reward.

In interval A the third print is 100.60, which is through your target, and the low at 100.00 comes after. You made 0.35. In interval B the second print is 100.00, which is through your stop, and the high comes after. You lost 0.15. Same open, same high, same low, same close, same volume: one bar, two outcomes half a point apart, which is three and a third times what you were risking.

This is not a curiosity. Any test you run on candle data hits it whenever a bar contains both your stop and your target, and the software has to assume an order for them. Some assume the stop, some walk the bar open–high–low–close, and the assumption is a free parameter that nobody writes in the results. Lesson 63 is where that gets priced properly; the point here is that the ambiguity is in the data format, not in the software.

When the summary is enough

Which gives a rule you can apply to any question before you ask a chart to answer it.

The candle answers it	What kind of question
Exactly	Did price reach 100.55? How far did it travel? What was the net change? How much traded?
Ambiguously	Would this bracket have been filled — but only when one of the two levels lies inside the bar’s range. When both do, the bar cannot say.
Not at all	In what order did it happen? Who was crossing the spread? Where in the range did the volume sit?

Read the top row again, because it is the part people skip when they hear that candles discard information. Every question about level and distance is answered exactly and there is nothing better to consult. It is the questions about sequence and about who that fall off the end, and those are the questions the rest of this module is for.

What this does not settle

That the discarded information is available to you. It is, mostly, and the next two lessons are how: lesson 7 is the record itself, one transaction at a time, and lesson 8 is the aggressor side the candle dropped. Where in the bar the volume sat is lesson 29.

Nor does it say which interval to use. Shorter bars discard less of the order, because there is less order inside them to discard, and there is no interval at which nothing is lost except the transaction record itself — which is not a chart. The efficiency figures above come with their own condition: both estimators assume price is observed continuously and drifts nowhere, so the real gain on a market that gaps and opens is smaller than the theoretical one.

And it does not make patterns worthless. A pattern is a claim about four prices, and the candle records those four prices exactly. What a pattern cannot support is a claim about who was buying, because that field was never in the file.

The five numbers are also five numbers according to somebody. Feeds disagree about whether the open is the first print or the previous close, about which off-exchange prints belong in the volume, and about how a halt is stitched back in afterwards. Two providers can hand you the same bar with different figures in it, so the exactness this lesson keeps claiming is exactness relative to one file.

And A and B were built to collide. Nothing above measures how often two materially different paths really do produce the same five numbers on a live instrument, and the honest answer is that this page does not know. That is what the first problem is asking, and it is a better question than it looks: a collision that happens twice a year is a curiosity, and one that happens twice a session is a reason to distrust every pattern you have ever traded.

A candle is an honest summary of four prices and a total. Almost every argument about what one means is an argument about the part it did not keep.

Problems

1. Build the twin. Write a third six-print interval with the same open, high, low, close and total volume as A and B, in which nearly all of the 10,000 shares trade at the low rather than spread across the range. Say which of the five numbers your version changes, and what the difference would have told you if you could see it.
2. Count the compression. On your own instrument, open the time and sales window and count the prints inside one five-minute bar. Multiply by four, for the four fields each print carries, and compare that with five. Then say which of the four fields you would most want back, and what you would do with it.
3. Find an ambiguous bar. Take your last twenty trades, or twenty you planned. Find one whose entry bar, or the bar after it, contains both your stop and your target. Work out the result under each assumption about which came first, and state the difference in currency and as a multiple of what you were risking.

Sources. Michael Parkinson, “The Extreme Value Method for Estimating the Variance of the Rate of Return” (Journal of Business 53, 1980), for the high-low estimator and its efficiency. Mark Garman and Michael Klass, “On the Estimation of Security Price Volatilities from Historical Data” (Journal of Business 53, 1980), for the same question asked with all four prices. Larry Harris, Trading and Exchanges (Oxford, 2003), chapter 3, on what a transaction record contains and what a summary of it can be asked to support.

You now know what a chart is made of, and what was thrown away to make it. The next lesson goes back for the record it was made from, and finds that one of the four columns on it was never reported by anybody. It is worked out on your behalf, and it is right about four times in five.

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