# 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.

## 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%.

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

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

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).

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