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Golden Ratio and Financial Trading
20 Feb 2018
Written By Young Ho Seo
Finance Engineer and Quantitative Trader
Introduction to Golden Ratio 0.618 for financial trading
When I look back, even during my math class in the university, the golden ratio or Fibonacci number was not so popular topics. However, I still remember that a particular technique called a “Golden Section Search” was taught along with Newton’s method. Well, just like many of the students, I forgot about this technique after passing the exam. Many years later, the term “Golden ratio” keep coming back more and more during my research with financial market data (If you are not sure what the Golden ratio is, please check the appendix at the end of this article.) I realized that the importance of Golden ratio might be far more significant than what the financial trader think. Firstly, many geometry or shape found in nature including trees, leaves, flowers, etc, are often built upon the golden ratio and the derived ratios (i.e. Fibonacci ratios). Even there were some interesting research showing the relationship between the golden ratio and beauty. Now you can tell that the frequent occurrence of the Golden ratio is natural phenomenon. What do you think about the financial market? As you know, financial market is made by man. Would the Golden ratio play an important role in the financial market? If so, it would be quite surprising. The truth is yes. The Golden ratio 0.618 and other derived ratios (i.e. Fibonacci ratios) like 0.382 and 0.500 are considered as important. In fact, the belief about the Golden ratio was there for more than 85 years. I am referring to the work by Ralph Nelson Elliott in 1938. The use of Golden ratio for the financial market can go back even more. Whether you are user of the Golden ratio and the Fibonacci ratio for your financial trading (see appendix), you will be kept surprising reading this article until the end. We have built a scientific tool to reveal the precise structure of the financial market. The scientific tool can not only extract the useful information for your financial trading but also it can be used to make some interesting inference about the financial market. Now to start with, let us understand how to use the golden ratio and Fibonacci ratio for the financial trading first.
How to use the Golden Ratio and Fibonacci Ratio for financial trading
The most common way to apply the golden ratio and Fibonacci ratio is to use two price swing points in your chart. To identify the two swing points, you can simply use the peak trough analysis provided on our website. It is free of charge for use and for sharing (http://algotrading-investment.com). You can have a multiple options to identify the swing point in your chart. However, there are automated tools (the peak trough analysis) for the task, we will not discuss too much on how to detect the swings points manually.
Figure 1: Basics of Fibonacci ratio measurement (or Shape ratio measurement).
Figure 2: Basics of Fibonacci ratio measurement (or Shape ratio measurement).
Anyway, after you have identified the swing points, you can measure the ratio of two price swing points as shown in Figure 1 and 2. The ratio of price height of two swing points often expected to be close to the golden ratio or the Fibonacci ratio. We use this knowledge for our trading as shown in Figure 3 and Figure 4. In Figure 3 and Figure 4, we expect that the price will reverse at 38.2% (0.382) Fibonacci ratio. This analysis is called Fibonacci retracement analysis. This analysis is useful to check the corrective phase of the market. In the chart, we can easily spot where it reverse. Based on this idea, we can make our trading plan. This is the typical strategy used by millions of forex and stock market traders.
Figure 3: Fibonacci Retracement drawn over daily EURUSD candlestick chart for bearish setup.
Figure 4: Fibonacci Retracement drawn over daily EURUSD candlestick chart for bullish setup.
Trading with Fibonacci retracement and expansion is relatively simple. Now there are advanced trading strategies using the Golden ratio and Fibonacci ratio too. We can introduce the two trading strategies in brief. One of them are Harmonic pattern trading. The other one is Elliott wave trading. In harmonic Pattern trading, we identify three or four successive swing points to identify the reversal trading opportunities. Just like Fibonacci retracement and expansion, the ratios measured between three or four successive swing points are expected to be the Golden ratio or Fibonacci ratio. In Elliott wave trading, we use around three to five swing points to identify the trading opportunities. The ratios of these swing points are the Golden ratio and Fibonacci ratios. In Elliott wave trading, the Golden ratio 0.618 and 1.618 are highly emphasized whereas in harmonic pattern trading, the other Fibonacci ratios are equally used to construct the harmonic patterns.
Figure 5: Butterfly pattern formed in EURUSD H4 timeframe.
Figure 6: Impulse Wave 12345 pattern formed in EURUSD D1 timeframe.
Figure 7: Corrective Wave ABC pattern formed in EURUSD D1 timeframe.
Revealing the Financial Market Structure using Equilibrium Fractal Wave Index
So far, we have introduced three trading strategies based on the Golden ratio and the Fibonacci ratios. These trading strategies are based on the assumption that there will be the frequent occurrence of the Golden ratio and Fibonacci ratios in the financial market. However, not necessarily we have much scientific evidence to support this assumption. I think these trading strategies can become more popular if there is more scientific evidence to support the trading logic and rational behind the Golden ratio and the Fibonacci ratios. To reveal the financial market structure precisely, we have made a scientific framework called Equilibrium fractal wave. To reveal the market structure, we need to understand what ratios the market is made up including both Fibonacci ratios and non-Fibonacci ratio. Using the framework of the Fibonacci ratio analysis can limit our understanding since we can only study Fibonacci ratios. Therefore, we use the generic term called “Equilibrium Fractal Wave” to describe the price geometry made up from the two price swing points (or three points) in your chart as shown in Figure 1 and Figure 2.
By definition, an equilibrium fractal wave is a simple triangle made up from two price swing points. It is precisely identical to the triangle introduced in Figure 1 and Figure 2. We refer to the ratio (Y2/Y1) as the shape ratio in equilibrium fractal wave. The shape ratio represents the shape of each equilibrium fractal wave and it is an identifier used to reveal the market structure. The shape ratio can include any ratios including Fibonacci ratios and non-Fibonacci ratios in our study.
Figure 8: One unit (or one cycle) of equilibrium fractal wave.
To reveal the market structure, we use the quantity called Equilibrium fractal wave (EFW) index. The equation of the EFW index is shown below:
Equilibrium Fractal Wave (EFW) Index = number of the particular shape of equilibrium fractal wave (the shape ratio = Y2/Y1) / number of peaks and troughs in the price series.
The equation is straightforward to calculate in any charting package. The EFW index is a quantity describing how frequently we can detect the particular shape ratio (Y2/Y1) in the financial market. For example, if the Golden ratio 0.618 is really dominating in the financial market, we should have a highest EFW index among all ratios. Otherwise, our belief on the Golden ratio can be wrong or less optimal. It is the same for other Fibonacci ratios. If you were using the Fibonacci ratios 0.382 (38.2%), you should expect the EFW index of 0.382 to be higher. Otherwise, you were trading less optimal strategy for your investment. To reveal the market structure, we can create a distribution of EFW index from the ratio 0.1 to the ratio 3.0. We list the distribution of EFW index for EURUSD, GBPUSD and USDJPY in Figure 9, 10 and 11.
Figure 9: EFW Index Distribution for EURUSD Daily Timeframe from 2009 09 02 to 2018 02 20 (Label inside callout box, left: Ratio, right: EFW Index, vertical axis: EFW index, horizontal axis: ratio from 0.1 to 3.0).
Figure 10: EFW Index Distribution for GBPUSD Daily Timeframe from 2009 09 02 to 2018 02 20 (Label inside callout box, left: Ratio, right: EFW Index, vertical axis: EFW index, horizontal axis: ratio from 0.1 to 3.0).
Figure 11: EFW Index Distribution for USDJPY Daily Timeframe from 2010 05 30 to 2018 02 20 (Label inside callout box, left: Ratio, right: EFW Index, vertical axis: EFW index, horizontal axis: ratio from 0.1 to 3.0).
You can immediately recognize several important factors in this analysis. Firstly, each financial market has the different footprint of the EFW index distribution. This justifies their own unique behaviour of each financial instrument. Secondly, our belief on the Golden ratio and the Fibonacci ratios are less optimal rather than wrong. We can tell that the Golden ratio and the Fibonacci ratios stay in the top of the league table for three currency pairs. However, still some other ratios are ranked highest in the table. For example, the ratio 0.66, 0.50 and 0.75 stayed in the top of the table. It should be noted that for each financial instrument, there is a preferred ratio for your trading. If you were trading using the ratio 0.618 for GBPUSD, then it was far less optimal. You should have used the ratio 0.500 instead. In Figure 12, we have calculated the EFW index over the rolling window for GBPUSD daily timeframe. The rank of each ratio does not change often. We can tell that the market structure is stable over the time. Therefore, the revealed market structure in Figure 9, 10 and 11 might be at least semi-permanent characteristics of each financial instrument.
Figure 12: EFW index for GBPUSD D1 timeframe from 2007 01 04 to 2018 01 20.
What is your belief now and how you are going to trade?
This article revealed some important information for your trading, that no one have revealed before. We were trying to answer the question on the Golden ratio and the Fibonacci ratio, which were not answered last 100 years. In our analysis, we have revealed the market structure of the financial market using the scientific tool called the EFW index. If you were trading using the Golden ratio and the Fibonacci ratio, you might be shocked a bit. Now you know what to do to improve your trading. It is only the scientific analysis can help you to win in the financial market. Many traders including myself might be curious why the Golden ratio is less optimal or not optimal for some financial instruments. Well, honestly I do not have the right answer for it. I think that no one has the right answer but we can only guess. In nature, the golden ratio or other Fibonacci ratios are repeating in much higher precision than the financial market. The less precise nature in the financial market might be due to the higher noise in the financial market because of too many diverse players. Another possible explanation might be that the profitability of the Golden ratio and some Fibonacci ratios might be exhausted because too many of us were using them every day. Therefore, the EFW index distribution in Figure 9, 10 and 11 might be showing the distorted image of the financial market. Please feel free to write me on FinancialEngineerPro21@gmail.com if you have a better explanation about why the Golden ratio is less or not optimal for the financial market.
Appendix (Golden ratios and Fibonacci ratios)
The Fibonacci Ratio is used by millions of forex and stock market traders every day. It is a mega popular tool in the trading world. If you do not know what the Fibonacci ratio is, here is the simple explanation. Fibonacci ratio is the ratio between two adjacent Fibonacci numbers. To have a feel about the Fibonacci ratios, here is the 21 Fibonacci numbers derived from the relationship: Fn = Fn-1 + Fn-2.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, …………………
Once the Fibonacci numbers are reasonably large, you can just pick up any two adjacent Fibonacci numbers above to derive the ratio. For example, we will find that 4181/6765 = 0.618 and 1597/2584 = 0.618. Here 0.618 is called as the golden ratio. The golden ratio is one of the most important Fibonacci ratios. The rest of Fibonacci ratios are derived by using simple mathematical relationship like inverse or square root or etc. Table below shows the list of Fibonacci ratios you can derive from the Golden ratio 0.618.
Type Ratio Calculation
Primary 0.618 Fn-1/Fn of Fibonacci numbers
Primary 1.618 Fn/Fn-1 of Fibonacci numbers
Secondary 0.382 0.382=0.618*0.618
Secondary 2.618 2.618=1.618*1.618
Secondary 4.236 4.236=1.618*1.618*1.618
Secondary 6.854 6.854=1.618*1.618*1.618*1.618
Secondary 11.089 11.089=1.618*1.618*1.618*1.618*1.618
Secondary 0.500 0.500=1.000/2.000
Secondary 1.000 Unity
Secondary 2.000 Fibonacci Prime Number
Secondary 3.000 Fibonacci Prime Number
Secondary 5.000 Fibonacci Prime Number
Secondary 13.000 Fibonacci Prime Number
Secondary 3.142 3.142 = Pi = circumference /diameter of the circle
Table 1: Fibonacci ratios and corresponding calculations to derive each ratio.
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Simple Explanation on Repainting, Recalculating, and Static Algorithm in Technical Analysis for the Financial Trading
3 Feb 2018
Written By Young Ho Seo
Finance Engineer and Quantitative Trader
The technical analysis is a key to successful trading. Even if you are a fundamental trader, you will need to use technical analysis for the precise control of your entry and exit in your trading. If we count the usage of every technical analysis on the earth, nearly at least a half billion of traders will use technical analysis. The problem is that not everyone is using the technical analysis in the right manner. The purpose of this article is to clear the overly spread misunderstanding about what people called “Repainting technical indicators” in the community. At the beginning, I thought that it would be only matter for starters. Later, I met many forex traders claiming 3 to 5 years of trading experience. However, most of these traders still do not have much clue what is really the repainting indicator except small portion of traders among them. Search on google was disappointing too. Some articles poorly explained on the topic of the repainting. Some articles were almost uninformative to continue to read. Some articles were almost devastated many of excellent technical analysis by some language of witch-hunting. Especially the affected technical analysis on those witch-hunting include:
• Market Profile (invented by J. Peter Stdidlmayer)
• Fractal indicator (invented by Bill Williams)
• Fourier transform and many other signal processing algorithm (invented by Joseph Fourier and many others)
• ZigZag indicator
• Fast moving average including many zero-lag or non-lag moving average family
• Harmonic Pattern (invented by H.M. Gartley, any many others later on)
• Other technical analysis algorithm
The above technical analysis and their algorithm are used by several millions of traders and scientists every day. If you are doubt, just google to look for the internet community using those technical analysis. If those technical analysis and their algorithms are repainting and bad, then why so many people are using them? Well, I think that this will remain as a myth to you until you can clear the misunderstanding about the repainting indicator.
What is really a repainting indicator?
Firstly, what does the repainting means? In the Cambridge dictionary, “repaint” is a verb with a meaning “to paint something again”. In Collins dictionary, “repaint” have a meaning “to apply a new or fresh coat of paint”. The meaning of repainting is almost identical in both dictionary. The example provided by the Cambridge dictionary is:
“The white walls were repainted in pastel shades.”
Two examples provided by the Collins dictionary are:
“Now they kill the crew, repaint and rename the ship, change the flag and papers and steal the cargo, and any other cargo they can find.” (Robert Wilson, INSTRUMENTS OF DARKNESS, 2002)
“But before that – in just an hour or two – a squad of men from the RASC were going to arrive to repaint the interior of the hospital.” (Aldiss Brian, SOMEWHERE EAST OF LIFE, 2002)
You can tell that the term “repainting” is often used to remove or to hide old colours or patterns on the surface by applying new fresh coat of paint. Based on this, in the repainting indicator, the indicator lines or values are repainted every time so that old indicator lines or values can not be found any longer. Is this the case for the above technical analysis algorithm?
Simple answer is no. The above algorithms have nothing to do with repainting. Above technical analysis algorithms keep the old indicator lines or values as they are. Just the latest values can change. For example, in the case of the daily market profile, except today’s market profile, all the past market profile will remain the same. It does not matter how many days you go back to the past, all the past market profile will remain the same. Then why the latest value or indicator line can change? It is because the algorithm is doing recalculation while the latest price is updating in the last candle bar.
The repainting indicator will not keep any old indicator lines or old values since repainting will override all the past values to something new. Literally, the repainting indicator is the random indicator due to some serious bugs or internal logic problem inside the indicator. When the repainting happens, 9 out of 10, it is due to some irritating bugs inside the algorithm.
However, there is also human problem too about the repainting indicator. It is because people use the term “repainting” and “recalculating” interchangeably on the net. This is incorrect and false information. It might start with one or few trader who do not have much experience in trading at the beginning. However, I can tell that this misunderstanding was growing and spreading fast like virus on the net last few years.
Now, if you can tell the difference between repainting and recalculating, then it is good. If not, still do not worry. We will tell you how to differentiate the repainting and recalculating indicators. The best way to differentiate between repainting and recalculating indicator is by asking this question “Does technical analysis algorithm keeps the old values (or old indicator lines) unchanged except the latest value?” Now consider the simple moving average with the period of 10 as shown in Figure 1. The latest moving average value can change as the new price arrives. The rest of moving average value will stay the same. Likewise, in Figure 2, the latest fractal value can change as the new price arrives. However, except the first fractal, rest of fractals will not change. Likewise, in Figure 3, the first zigzag value can change as the new price arrives. However, except the first zigzag value, rest of zigzag will not change. The same goes for the market profile and other technical analysis algorithm.
Figure 1: Simple Moving average with the period 10 in EURUSD.
Figure 2: Fractal indicator in EURUSD.
Figure 3: Zigzag indicator in EURUSD.
Figure 4: Market profile indicator on EURUSD.
Why not avoiding recalculating?
Now one might ask. Can we avoid recalculating? Well, yes you can avoid the recalculating simply by not calculating your algorithm over the last candle bar or by not generating the last value of the indicator. This is called a static algorithm because they are not responsive to the latest price value. For example, simply imagine that if the indicator calculates your moving average values except the first candle bar, then you will get the static moving average indicator. Such a moving average indicator will not have any responsiveness to the new price arrivals. It is static. You can achieve the same by just using open price of the candle bar. Likewise, if you calculate the fractals from the second candle bar, then you will get the static fractal indicator too. For the fractal indicator, you cannot use open price because you need either high or low price of the candle bar. For some technical analysis algorithm, just ignoring the latest candle bar is not sufficient to turn the indicator to static. Some indicators like zig zag or market profile requires certain length of data to calculate one indicator value. In that case, you can simply skip to generate latest value and generate from the second values. For example, if you skip today’s market profile and generate the market profile from yesterday, then you will have the static market profile too. Likewise, you can generate your zigzag from second value too skipping to generate the first zigzag value. If your indicator or pattern detection scanner is using the zigzag indicator, you can also turn them into static one by using the zigzag values from second one (i.e. using the static zig zag).
With the static algorithm or static indicator, you can avoid recalculating. Well sounds easy and wonderful. However, you will experience a serious problem soon. The problem is that you are the only one looking at the lagging information whereas all the other traders are working with the decent latest information for more profits. For example, if you are looking at yesterday’s market profile alone, then you will not able to find what is happening today. All disciplined trader will work with yesterday’s market profile as well as today’s market profile. Likewise, if you detect harmonic patterns with the statics zigzag indicator, then you can only detect the patterns after many candle bars. In Figure 5, you can tell that you do not have any advantage of using the static zigzag indicator to detect harmonic patterns. Especially using the static zigzag indicator, your Reward/Risk ratio will be very poor. You can only detect the harmonic pattern after the price has moved too much in the direction using the static zigzag indicator. Recalculating zigzag indicator will report the appearance of harmonic pattern way faster than the static zigzag indicator. With recalculating zigzag indicator, you have a much better opportunity to enter the market while the sufficient profit is left for you. So do you still prefer the static indicator? Well the choice is entirely up to you.
Figure 5: Harmonic Pattern Detection timing using recalculating zigzag indicator and static zigzag indicator.
How Harmonic Pattern Plus and Price Breakout Pattern Scanner help you to achieve the best performance for your trading?
Our Harmonic Pattern Plus (and Harmonic Pattern Scenario Planner) and Price Breakout Pattern Scanner uses the recalculating algorithm to find the latest pattern faster. When the pattern is detected, you will still have an opportunity to enter for the sufficiently good reward/risk ratio for your trading. Yes, they can change if new high or new low price arrive to the market. However, we provide the locking feature to help your trading. This means that you can pin down the pattern in your chart. Once you pin down the pattern in your chart, you do not have to worry about to lose the pattern in your chart because they will stay in your chart forever. To do so, simply click on the “Lock” button in your chart.
Figure 6: Harmonic Pattern Plus (Harmonic Pattern Scenario Planner) locking feature.
Figure 7: Price Breakout Pattern Scanner locking feature.
Link to Harmonic Pattern Plus (Harmonic Pattern Scenario Planner) and Price Breakout Pattern Scanners.