Advanced Bull Flag Concepts

2022年12月26日

Have you ever wondered why price action sometimes forms a bull flag pattern?
Have you ever wondered if there is a way to predict whether a bull flag will break out before it actually does so?

In this post, I will try to address these questions by presenting a couple of theories about the nature of bull flags.


Bull Flag Theories

(1) The flag structure of a bull flag tends to form along Fibonacci levels, with the ideal flag proportion being an approximated golden ratio to the flagpole; and

(2) Fibonacci and regression analyses can provide useful insight into whether price will successfully break out of its bull flag pattern, sometimes long before price even attempts to do so.


I will try my best to clearly explain both theories in detail below.

Note: Although this analysis is also generally true for bull pennants, bear flags, and bear pennants, to keep things simple I will focus solely on bull flags. Additionally, this analysis is generally true across timeframes.


Part I - The Basics of a Bull Flag

First, let's begin with the basics. As shown in the image below, bull flags form when an asset is in a strong uptrend. The uptrend forms the flagpole of the bull flag structure.



The flag structure forms when price consolidates, usually in a falling trend. This consolidation phase is often characterized by price oscillators rotating back down while the price retraces only a small part of its prior upward move.

From a market psychology perspective, bull flags often form when most market participants who bought the asset continue to hold it expecting the uptrend to resume, while only a minority of market participants sell (or short the asset) as its price corrects downward. The bull flag pattern is a continuation pattern because it reflects the market's general expectation that price will eventually resume its upward move.

Once the price definitively breaks above the upper channel of the flag (often with strong momentum and high volume), the bull flag pattern is validated. Upon breakout, the expected move up is equal to the vertical height of the flagpole.


Part II - The flag structure of a bull flag tends to form along Fibonacci levels, with the ideal flag proportion being an approximated golden ratio to the flagpole

Here's where things begin to get interesting. Below is the golden ratio.



Two quantities, a and b (where a > b), form the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. (See the equation below)


The equation above shows the Greek letter phi which denotes the golden ratio. Phi is equivalent to a/b when such ratio is also equivalent to (a + b)/a.

Although bull flags can take various forms, it is my hypothesis, based on chart analysis and research, that the most perfectly structured bull flags (ones that also have the highest probability of successful breakouts) occur when the flag forms a golden ratio to the flagpole.

Mathematically, this means that the vertical height of the flagpole is equivalent to (a + b) and the vertical height (i.e. the width) of the flag is equivalent to b. This is also to say that price retraces down to the 0.382 Fibonacci level as measured by applying Fibonacci retracement levels along the flagpole (or to the 0.618 point on the vertical height of the flagpole if one measures from the bottom to top).

I realize that this can be quite confusing, so let’s walk through some visualizations.

Let's first visualize this hypothesis using the golden rectangle. Below is an image of the golden rectangle. A golden rectangle is composed of a square (with sides equal to a) and a smaller golden rectangle (with width equal to b and length equal to a).



Now let's rotate the golden rectangle to better visualize the hypothesized flag pattern.



The bull flag is hypothetically an approximation of the golden rectangle, whereby the width of the flag is in a golden ratio approximation to the length of the flagpole.



In the illustration below, there are multiple bull flags contained within a Fibonacci spiral. The spiral is made up of golden rectangles, with each larger golden rectangle containing a smaller golden rectangle inside it. The smaller golden rectangle is the flag structure, and the length of the larger golden rectangle is the flagpole.

One can think of the Fibonacci spiral and the golden rectangles as a series of bull flags that build on top of each other in a repeating pattern. In this diagram, price is represented by the increasing length of the sides of each golden rectangle. In other words, the price on a chart can be seen as spiraling higher after each bull flag breakout.



Of course, not all bull flags form a structure that approximates the golden ratio, but it is my belief that in forming a bull flag, price action is aspiring to achieve as close of a golden ratio approximation as it can. I believe that the bull flags that best approximate the golden ratio structure also present the highest probability for a successful break out.

To learn more about Fibonacci spirals, including the golden spiral that Fibonacci spirals approximate, you can check out this Wikipedia article: https://en.wikipedia.org/wiki/Golden_spiral


Part III - Fibonacci and regression analyses can provide useful insight into whether price will successfully break out of its bull flag pattern, sometimes long before price even attempts to do so.

To see how Fibonacci levels and regression analysis can give insight into whether a bull flag will break out or break down before it does so, let's consider an example.

Let’s consider the massive bull flag that the iShares Russell 2000 ETF (IWM) formed in 2021.

In 2021, the monthly chart of IWM formed what appeared to be a bull flag, as shown below.



Now let's see why Fibonacci analysis and regression analysis were warning that this bull flag was not likely to break out successfully.

First, IWM's price did not retrace to a Fibonacci level before attempting a breakout (when using the pole as the Fibonacci retracement reference point). In the chart below, we see that price tried to break out, without even so much as retracing down to the highest Fibonacci retracement level: $196.71. By not undergoing Fibonacci retracement, price did not give its oscillators the opportunity to rotate back down fully. Instead, price remained overextended at the time it attempted to break out.



Now let's look at regression analysis. Below is a log-linear regression channel that contains IWM's entire price history. As noted in my prior posts, a regression channel simply indicates how far above or below the mean (or average) price an asset's current price is trading. In the regression channel above, the red line is the mean price, the upper channel line is 2 standard deviations above the mean, and the lower channel line is 2 standard deviations below the mean.



A successful breakout of the bull flag would have taken IWM's price way above its regression channel, to a level that is too many standard deviations above its mean price for us not to question the probability of the breakout’s success. Achieving the full measured move up would have been extremely unlikely, assuming that the regression channel is valid and that price tends to revert back to its mean over time. What was more likely than a breakout was a breakdown, and a reversion back to the mean, which is what ended up happening with IWM.



Another interesting note about IWM’s bull flag is that it presented a false breakout in November 2021. This false breakout was presenting multiple warnings signs including being a UTAD test of a Wyckoff Distribution. As shown below, however, another important clue that the November 2021 breakout would likely fail was that the breakout was not confirmed when comparing IWM to the money supply (M2SL). See the chart below.



One can interpret this chart to mean that in late 2021, IWM’s price was rising because the central bank was increasing the money supply, but not due to improving strength of the underlying companies that comprise the ETF. Using the money supply as a ratio to an asset elucidates the true inherent strength of the asset's value. To understand more about why the money supply can be used in this manner, you can check out my post below.

Part IV - Additional Comments
I have a few additional comments. I usually use Fibonacci levels on a log-scale chart to identify Fibonacci spirals because Fibonacci spirals are logarithmic spirals. However, when using Fibonacci levels based on log scale, the ratios, percentages and numbers, can seem quite confusing because they are logarithmically adjusted. If you choose to replicate my process, please be mindful of this. While using log-scale charts is critical for higher timeframes (e.g. the monthly chart or higher), I have not identified much benefit to using it on shorter timeframes.

In a prior post, I noted that Plug Power (PLUG) is currently forming one of the best-looking log-scale, golden ratio bull flags I have ever seen. If my above hypotheses are true, I would expect to see PLUG move dramatically higher in the years to come. For more information about PLUG, you can read my post linked below. (This is not a solicitation to buy PLUG. Please do your own research and carefully consider all risks.)

At the risk of making this post too long and too dense, I just want to briefly note that it is also my hypothesis, based on observation and research, that the golden ratio is where many S-curve dilemmas are solved. If you don't know what an S-curve dilemma is and you'd like to read about this you can see my post below about Jumping S-Curves.

In short, an S-curve dilemma is another way of conceptualizing the question of whether a bull flag will break out or break down.

I hope that someone finds value in this post. I spent a lot of time studying, researching, analyzing, and cogitating the mathematical nature of price action to reach many of the conclusions here. Thank you for your valuable time in reading my post.

2022年12月27日

ノート

Minor correction: When describing regression channels, I said "the regression channel above" when I meant to say "the regression channel below".

2023年1月10日

ノート

Sharing this log-scale bull flag pattern in the DBC/SPY ratio chart. Fibonacci spirals can even occur in relative price charts!



Question: If this bull flag were to break out, how low do you think the S&P 500 would fall?

Credit to akikostas

2023年4月12日

ノート

Here's another log-scale bull flag.

This one shows the yearly chart of Bitcoin against the M1 money supply.



The golden ratio has been acting as support and as the base of the flag.



What conclusions can you draw from this chart?

In a future post, I'll explain my conclusions and why this chart is showing that Bitcoin is a threat to the fiat system.

2023年10月23日

ノート

It appears that the 9-month chart of the gold has formed a major log-scale golden ratio bull flag. Here are some upside targets that could be reached in the months and years ahead if a breakout occurs.