# Fibonacci retracement

(Redirected from Fibonacci ratio)
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. See Trend Lines. The significance of such levels, however, could not have been statistically confirmed.[1] Arthur Merrill, CMT determined there is no reliable standard retracement; not 50%, 33%, 38.2,61.8%,or any other. See his book "Filtered Waves."

## Fibonacci ratios

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%.

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

The key Fibonacci ratio of 0.618 is derived by dividing two consecutive numbers ${\displaystyle n}$ and ${\displaystyle n+1}$ in the Fibonacci sequence, as ${\displaystyle n}$ approaches infinity. For example: 8/13 is approximately 0.6154, and 55/89 is approximately 0.6180.

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

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.

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

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.

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

The 0 ratio is :

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

### Other ratios

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

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

The 0.786 ratio is :

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

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).

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

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. http://epublications.bond.edu.au/business_pubs/32/

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.

## References

1. ^ Kempen, René (2016). "Fibonaccis are human (made)" (PDF). IFTA Journal.
• 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.