Fibonacci retracement

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Fibonacci retracement levels shown on the USD/CAD currency pair
Fibonacci retracement levels shown on the USD/CAD currency pair. In this case, price retraced approximately 38.2% of a move down before continuing.

In finance, Fibonacci retracement is a method of technical analysis for determining support and resistance levels.[citation needed] They are named after their use of the Fibonacci sequence.[citation needed] Fibonacci retracement is based on the idea that markets will retrace a predictable portion of a move, after which they will continue to move in the original direction.

The appearance of retracement can be ascribed to ordinary price volatility as described by Burton Malkiel, a Princeton economist in his book A Random Walk Down Wall Street, who found no reliable predictions in technical analysis methods taken as a whole. Malkiel argues that asset prices typically exhibit signs of random walk and that one cannot consistently outperform market averages. Fibonacci retracement is created by taking two extreme points on a chart and dividing the vertical distance by the key Fibonacci ratios. 0.0% is considered to be the start of the retracement, while 100.0% is a complete reversal to the original part of the move. Once these levels are identified, horizontal lines are drawn and used to identify possible support and resistance levels.

Fibonacci ratios[edit]

Fibonacci ratios are mathematical relationships, expressed as ratios, derived from the Fibonacci sequence. The key Fibonacci ratios are 0%, 23.6%, 38.2%, 61.8%, and 100%.

F_{100\%} = \left(\frac{1 + \sqrt{5}}{2}\right)^{0}  = 1 \,

The key Fibonacci ratio of 0.618 is derived by dividing any number in the sequence by the number that immediately follows it. For example: 8/13 is approximately 0.6154, and 55/89 is approximately 0.6180.

F_{61.8\%} = \left({\frac{1 + \sqrt{5}}{2}}\right)^{-1}  \approx 0.618034 \,

The 0.382 ratio is found by dividing any number in the sequence by the number that is found two places to the right. For example: 34/89 is approximately 0.3820.

F_{38.2\%} = \left({\frac{1 + \sqrt{5}}{2}}\right)^{-2}  \approx 0.381966 \,

The 0.236 ratio is found by dividing any number in the sequence by the number that is three places to the right. For example: 55/233 is approximately 0.2361.

F_{23.6\%} = \left({\frac{1 + \sqrt{5}}{2}}\right)^{-3}  \approx 0.236068 \,

The 0 ratio is :

F_{0\%} = \left({\frac{1 + \sqrt{5}}{2}}\right)^{-\infty}  = 0 \,

Other ratios[edit]

The 0.764 ratio is the result of subtracting 0.236 from the number 1.

F_{76.4\%} = 1- \left({\frac{1 + \sqrt{5}}{2}}\right)^{-3}  \approx 0.763932 \,

The 0.786 ratio is :

F_{78.6\%} = \left({\frac{1 + \sqrt{5}}{2}}\right)^{-\frac{1}{2}}  \approx 0.786151 \,

The 0.500 ratio is derived from dividing the number 1 (second number in the sequence) by the number 2 (third number in the sequence).

F_{50\%} = \frac{1}{2}  = 0.500000 \,

Academic studies[edit]

Bhattacharya, Sukanto and Kumar, Kuldeep (2006) A computational exploration of the efficacy of Fibonacci sequences in technical analysis and trading. Annals of Economics and Finance, Volume 7, Issue 1, May 2006, pp. 219-230.

Chatterjee, Amitava, O. Felix Ayadi, and Balasundram Maniam. "The Applications Of The Fibonacci Sequence And Elliott Wave Theory In Predicting The Security Price Movements: A Survey." Journal of Commercial Banking and Finance 1 (2002): 65-76.

Tai-Liang Chena, Ching-Hsue Chenga, Hia Jong Teoha. Fuzzy time-series based on Fibonacci sequence for stock price forecasting. Physica A: Statistical Mechanics and its Applications, Volume 380, 1 July 2007, Pages 377–390.


  • Stevens, Leigh (2002). Essential technical analysis: tools and techniques to spot market trends. New York: Wiley. ISBN 0-471-15279-X. OCLC 48532501. 
  • Brown, Constance M. (2008). Fibonacci analysis. New York: Bloomberg Press. ISBN 1-57660-261-3. 
  • Posamentier, Alfred S.; Lehmann, Ingmar (2007). The fabulous Fibonacci numbers. Amherst, NY: Prometheus Books. ISBN 1-59102-475-7. 
  • Malkiel, Burton (2011). A random walk down Wall Street: the time-tested strategy for successful investing. OCLC 50919959. 
  • MFTA Pershikov, Viktor (2014). The Complete Guide To Comprehensive Fibonacci Analysis on FOREX. ISBN 978-1607967606. 

External links[edit]