Lesson 5: Fibonacci Retracements

# Fibonacci Sequence

• The Fibonacci Sequence is a series of numbers that seem to consistently occur in nature. The discovery of this phenomenon is credited to the 13th century mathematician, Leonardo Fibonacci.
• The method to calculate the sequence is to add any Fibonacci number together with the number that immediately precedes it in the sequence.
• Using this formula, and assuming the first two numbers are zero and one, you can calculate the first ten numbers in the Fibonacci Sequence as follows:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 2
2 + 1 = 3
3 + 2 = 5
5 + 3 = 8
8 + 5 = 13
13 + 8 = 21
21 + 13 = 34

Therefore, the first ten numbers in the Fibonacci Sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.

The number of petals on flowers are often aligned with Fibonacci numbers; especially 3, 5 and 8. Black-Eyed Susans and some Daisies have 13 and 21 petals.

## Fibonacci Ratios

• From the Fibonacci Sequence comes a series of ratios, and it is these ratios that are of special significance to traders.
• The most important Fibonacci ratio is 61.8% - it is sometimes referred to as the "golden ratio" or "golden mean" and is accepted as the most "reliable" retracement ratio.
• The Golden Ratio is arrived at by dividing any number in the sequence by the number that immediately follows it. No matter which number you choose, the answer will always be very close to the mean average of 0.618, or 61.8%. For example:

• 8 divided by 13 = 0.615 = 61.5%
• 13 divided by 21 = 0.619 = 61.9%
• 21 divided by 34 = 0.617 = 61.7%
• The other two Fibonacci Ratios that forex traders use are 38.2% and 23.6%. These two ratios seem to have a lower level of success, but are still included for analysis purposes.
• The 38.2% ratio is derived by dividing any number in the sequence by the number found two places to the right. For example:

• 8 divided by 21 = 0.380 = 38.0%
• 144 divided by 377 = 0.381 = 38.1%
• 6765 divided by 17,716 = 0.381 = 38.1%
• In a similar fashion, the 23.6% ratio consists of any number in the sequence divided by the number that is three places to the right:

• 5 divided by 21 = 0.238 = 23.8%
• 34 divided by 144 = 0.236 = 23.6%
• 6765 divided by 28,667 = 0.235 = 23.5%
• In addition to these three ratios, most trading systems also show retracement levels at 50% and 100%. It is this series of ratios that are superimposed over a price chart in the form of Fibonacci Retracement Lines as indicated in the following price chart example:

Price Chart with Fibonacci Retracement Lines Placed Over a Closing Price Chart
Lesson 5 Topics

1. Introduction

2. The Fibonacci Sequence

This is for general information purposes only - Examples shown are for illustrative purposes and may not reflect current prices from OANDA. It is not investment advice or an inducement to trade. Past history is not an indication of future performance.

Trading FX and/or CFDs on margin is high risk and not suitable for everyone. Losses can exceed investment.