Fibonacci In Theory:
What is the Fibonacci Sequence?
An Italian mathematician called Leonardo Pisano (Fibonacci) revealed the Fibonacci sequence to the Western world in 1202, in a book called Liber Abaci. It was the first known European book based on Arabian and Indian mathematics, and the sequence was used to solve a maths problem involving the birth rate of a pair of rabbits in isolation.
Starting with the numbers ‘0’ and ‘1’, the two numbers are added together to provide the next number in the sequence. Or to put it another way, the current number in the sequence is the sum of the two previous numbers. The pattern is then repeated indefinitely.
0 + 1 = 1
1 + 1 = 2
2 + 1 = 3
The number rises exponentially and quite rapidly so, as the 30th number in the sequence is 121,393. Here are the first 15 numbers in the sequence and a graphical representation of how it rises exponentially.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377
The Golden Ratio
The intriguing thing about this sequence is that each number rises by a ratio of approximately 1.68 (or 168%, or Phi – 1.61803). This is known as the ‘golden ratio’ and frequently crops up in nature.
For example, spiral galaxies and the relative length of body parts follow the golden ratio, and the number of petals on a flower usually sits somewhere along the Fibonacci sequence; a daisy has 34 petals, a lily has 3, a chicory has 21. And as the golden ratio has been known for centuries, it was only a matter of time before it was to be utilised on trading floors.
By dividing numbers along the sequence by a fixed amount (eg. every 2, 3 or 4 numbers), ratio’s consistently present themselves with an astonishing degree of accuracy. And it is these ratio’s which traders are fixated upon.
- Current number / next number = 0.6182
- Current number / two numbers ahead = 0.382
- Current number / 3 numbers ahead = 0.236
Converted to a percentage, you will now see popular Fibonacci ratios which are commonly used in retracement and projection tools.
Popular ratios for traders to use include
- 50% *
* Whilst 50% is not an actual Fibonacci ratio, you will regularly find it on the default setting of a trading platform because some markets can show a strong tendency to react around that level.
Fibonacci Ratios in Finance
Fibonacci Retracements and Expansions
The two popular tools for traders are the Fibonacci retracement and Fibonacci expansion. Derived from the ratios mentioned above, they are generally used to perform these common functions:
- Fibonacci Retracement: As the name implies, the Fibonacci retracement tool can be used to measure the depth of a correction. The trader would measure the distance between a trough and a peak in an uptrend, to project potential support levels beneath the latest peak. In a downtrend, a retracement is measured from the peak to trough to provide potential resistance levels above the most recent trough. By default, you will typically find the ratio’s 38.2%, 50% and 61.8% are present on a retracement tool, although others can be added.
- Fibonacci Expansion: Also referred to as a Fibonacci extension or projection, it tool can be used to forecast future prices or profit objectives. Popular expansion ratios include 61.8%, 100% and 161.8% (the golden ratio). However, three points must be connected to measure and project the expansion ratios. The projection begins from the 3rd point, and it projects a ratio of the distance between points 1 and 2.
Fibonacci Rations in Practice
The Fibonacci retracement and expansion tools are readily available within the MT4 platform. There are also other Fibonacci tools available such as the fan, arc and channel which implement a timing element to the equation. But for today we’ll focus on the retracement and expansion tools as they focus purely on price element and more widely used among the trading community.
Typical uses of Fibonacci retracement and expansion include:
- Finding support and resistance levels
- Define profit objectives
- Aid with stop loss placement
- Fine tuning entry levels
Find Support or Resistance Levels with Fibonacci Ratios
In the example below, we can see how a retracement on GBP/CHF stopped almost perfectly at the 38.2% Fibonacci retracement level. As a correction against a bearish move is being measured, the retracement tool is looking for potential resistance levels to mark the end of the correction.
In practice, a trader would have noted that there was a strong move lower from the 1.2220 high which stalled at 1.1580. When prices started to turn higher, they would not have yet known whether the trend would continue lower or reverse even higher. But they could have measured the decline (from A to B) to anticipate a potential level of resistance (C) at the 38.2% retracement level.
If prices retrace and respect the 38.2% like seen above, a trader could wait for bearish momentum to return before assuming a swing high has formed. A more aggressive trader may use the level to fade into (sell short) around the Fibonacci level and assume the level will hold.
To show how this can look ahead of a move we can use analysis of the Nasdaq 100 we originally released on the 3rd September 2020. At the time we could see it had been trading in strong uptrend but, after suffering its worst session in 6-months, we knew it had either began a correction or a trend reversal.
After measuring the bullish move from the March low to September high, we noted the 23.6% Fibonacci retracement level coincided with the 50-day eMA. This could serve as a target for bears, or a potential opportunity for bears to enter if it holds as support.
The following day, support was found just above the 23.6% Fibonacci level and formed a bullish hammer. This may have enticed some bulls to enter if price action broke above the daily bullish hammer, although the volatility of the candle may be too high. Regardless, subsequent price action was very choppy, and prices cut through the 23.6% Fibonacci level which rendered it unreliable as a level of support. But the fact that prices did initially stall at that level suggests it was valid, even if only for a short while.
The Fibonacci expansion tool can also be used to find support or resistance. In this example, USD/CHF had been trading within in a bearish trend but prices had begun to retrace higher. To help identify the end of a correction and highlight a potential resistance level, points A to B are measured and then projected form point C.
Note that price action initially stalled at the 61.8% level. Although as it then pushed higher, the 100% and 161.8% levels are now in focus for potential resistance levels.
Taking this a step further, both projections and retracement ratios can be combined to highlight zone of potential support and resistance. Using USD/CHF again, notice how the initial rally from the lows stalled just around the 38.2% retracement ratio. As prices are now trading at new cycle highs, the next potential level of resistance (or bullish target) is around the Fibonacci resistance zone between the 100% projection and 61.8% retracement levels.
Project Profit Objectives with Fibonacci Ratios:
Targets can also be projected with the Fibonacci expansion tool. Of course, there is no guarantee prices will always reach these targets, but the trader must utilise them and manage their risk just as with any other form of analysis for those unsuccessful trades.
In this recent example of DJIA (US30), the leg higher between 27,458.22 and 28,528.90 projected a 61.8% and 100% expansion level from the 28,092.90 low around the next two swing highs.
And the leg lower between 28,383.20 to 27,558.94 projected the end of the next trough to be around the 161.8% expansion. Interestingly we also saw prices react around the 61.8% expansion before accelerating lower and finally stalling around the 161.8% projection.
Fine Tune Entry Levels:
Fibonacci ratios don’t have to be restricted to swing highs or lows and can also be used to measure individual candles. In this example we show how it can be used to place a sell-limit order within the range of a large candle.
The DAX 30 (DE30) had sold off sharply overnight which caught the interest of an EOD trader (end of day) for a potential short position. Yet as price action is holding above the bearish candle’s low, they suspect prices may try to retrace before breaking to new lows.
As there are no obvious technical levels to play around on the daily chart, they decide to use a Fibonacci retracement tool to set an entry and an exit order, by measuring the large bearish candle.
In this example a short-limit order was set just below the 38.2% level with a stop just above the 61.8% level. So, if prices retrace towards 38.2% or 50% without testing the 61.8% level, the EOD trader has entered a swing trade short. Of course, there is a risk that prices may move lower without triggering the trade (a missed opportunity), or simply accelerating higher and stopping the trader out.
How to apply Fibonacci in MT4
By default, only the retracement tool is visible on the MT4 toolbar.
To include the expansion tool:
Right mouse click over the toolbar > select ‘customize’ > search for ‘Fibonacci Expansion’ within the ‘Available:’ menu > select insert > close