Fibonacci Price Retracements

What is it?

Fibonacci price retracements is a support and resistance indicator that is used to determine possible support and resistance levels. Like Fibonacci fans, Fibonacci Retracements levels based on the mathematical relationships, expressed as ratios, between the numbers in the Fibonacci summation series.

The Fibonacci summation series of numbers is simply the sum of the two preceding numbers starting with 0 and 1, and continues on to infinitely. The first few numbers in the sequence are as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. Fibonacci retracements is based on the common mathematical relationships or ratios between these numbers.

How is it calculated?

The key Fibonacci retracement levels are found by performing various mathematical operations on the numbers in the Fibonacci summation series, and on the results of those operations.

  • The first ratio of 61.8%, which is the inverse of "golden ratio" or the "golden mean" (i.e., the inverse of 1.61%), is found by dividing a number in the sequence by the number that follows it. For example: 8 ÷ 13 = 0.6153, 34 ÷ 55 = 0.6182 and 55 ÷ 89 = 0.6179.
  • The 38.2% ratio is found by dividing a number in the sequence by the number that appears two places to the right of it. For example: 8 ÷ 21 = 0.3809, 21 ÷ 55 = 0.3818 and 55 ÷ 144 = 0.3819. It is also found by subtracting 0.618 from 1 (1 – 0.618 = 0.328) and by finding the square of 0.618 (0.618 x 0.618 = 0.382).
  • The 23.6% ratio is found by dividing a number in the sequence by the number that appears three places to the right of it. For example: 8 ÷ 34 = 0.2352, 21 ÷ 89 = 0.2359 and 34 ÷ 144 = 0.2361. It is also found by subtracting 0.382 from 0.618 (0.618 – 0.382 = 0.236) and by multiplying ratio 0.382 by 0.618 (0.382 x 0.618 = 0.236).
  • The ratio of 78.6% is found by finding the square root of 61.8%. Some traders prefer to use the ratio of 76.4% which is found by subtracting 0.236 from 1.00 (1.00 – 0.236 = 0.764).
  • In addition to these four ratios, the 0% and 100% retracement levels are also use to mark the start of the retracement and a full retracement of the previous move, and the 50% retracement level is used to mark the mid-point between the swing high and the swing low of the wave. The 50.0% level is not a Fibonacci ratio, per se, but is a point of interest on the charts that the retracement adheres to from time to time.

How is it used?

Fibonacci retracement is based on the idea that markets will retrace a predictable portion of the previous movement before price action resumes in the direction of the larger trend. This is based on the fact that the financial markets do not trend in a straight line. Instead the trend is interrupted by retracements that tend not to exceed the previous wave.

When using Fibonacci retracements, a technical analyst waits for the market to turn and then divides the previous trend movement, or wave, by the Fibonacci retracement ratios, starting from the previous high to the low in an uptrend and in the opposite direction in a down trend. Horizontal lines are then drawn at these levels and are used a possible support levels if the larger trend is an uptrend, or as possible resistance levels if the larger trend is a down trend. These thus become places at which the trader could buy in a larger uptrend or sell in a larger down trend. The most significant levels are usually the 61.8% level and the 38.2% level. The 23.6% level and the 78.6% (or 76.4%) levels are not as significant.

Multiple Fibonacci retracement studies can also be drawn starting from different peaks in a down trend or different lows in an uptrend. The end points for the different retracements are the same most recent turning point. This creates multiple levels with areas were two or more retracement levels are in close proximity being more significant. It is important that the end point for multiple retracements studies have the same, most recent swing high or swing low as their end points.

Unlike support and resistance lines, old Fibonacci retracement levels do not retain significance once broken. They do not change from support levels to resistance levels once the previous high or low has been broken. When the previous high or low has been broke, new Fibonacci retracements should be drawn once the next swing high or swing low has been formed.

Chart Example

The following is a 4-hour chart of the Euro/USD with Fibonacci Retracements drawn from significant high and lows made on May 14, 2013 and May 15, 2013 respectively. Notice how the subsequent reaction rally met resistance at the 38.2% retracement level before moving lower.


Euro/USD chart with Fibonacci Retracements
Fibonacci Retracements on a 4 Hour Euro/USD chart


Wealth Warning

Trading equities, options, derivatives, currencies, commodities or any other financial security can offer significant returns BUT can also result in significant losses if the market moves against your position. It requires a strong commitment to skill development, knowledge acquisition, and emotional control. It should be treated as a business with a clear business plan, a risk analysis, and set of attainable goals. The risk associated with trading the vagaries of the stock markets is probably the most important consideration as it has a profound effect on emotional control. You should not trade the stock markets with money you cannot afford to lose as there is considerable exposure to risk in any stock market transaction.

Furthermore, the past success of any trading method, strategy, or system is only indicative of future success. Under no circumstances should past success be construed as a guarantee of future success!


How do you know if you've drawn the Fibonacci lines from the right levels?

When drawing Fibonacci retracement lines, there are usually a number of swing highs and lows you could use for your retracement study. Choosing which levels to use can be a challenge at first but here are a few simple guidelines that will eliminate most of the uncertainty.

In a retracement study you would want to locate support or resistance levels in a countertrend price swing. The previous swing would be viewed as the dominant trend and you would be looking for a resumption of that trend. The important thing here is that you're looking for the current price swing to turn back in the direction of the dominant trend. Different swings can be used for this study but your retracement study should have the swing low in an uptrend or the swing high in a down trend as the zero point as you want to find a level where this last swing might end and where the dominant trend might resume.

Another useful trick is to check if the market respected those levels in earlier price movements, particularly the 32.8% and 61.8% levels. If the levels were respected previously, they would probably hold some significance going forward.


Related Indicators:

Support and Resistance Indicators

Support and Resistance
Support and Resistance

Support and Resistance indicators are usually drawing tools such as Andrews' Pitchfork, Gann Lines and Fibonacci Retracements that are drawn directly on the price chart. These indicators are usually a set of lines that attempt to forecast areas of support and resistance in an existing trend. They indicate where the trend could meet support or resistance. Most of these indicators also indicate the possible end of the existing trend. This occurs when the support or resistance line is broken.

When the support or resistance ...


Fibonacci Extensions

Fibonacci Extensions
Fibonacci Extensions

Fibonacci price extensions is a support and resistance indicator that is similar to Fibonacci retracements in that applies Fibonacci ratios to the recent swing high and swing low to determine possible support and resistance levels. However, extensions studies make use of ratios that exceed the 100% ratio.

The key Fibonacci ratios for extension studies are the ratio of 127.2%, 161.8%, 261.8%, and 423.6%. Of these, the 161.8% and 261.8% ratios are the most significant levels. These levels are drawn when the market has ...


Fibonacci Fans

Fibonacci Fans
Fibonacci Fans

Fibonacci fans are similar to Gann lines and Speed Resistance Lines (SRL). As with other Fibonacci studies, Fibonacci fans are based on the ratios between the numbers in the Fibonacci sequence with the ratios being used to subdivide the price wave and plot trendlines originating from the same point across the chart, resulting in a fan.

The popular Fibonacci ratios used for the fan lines are the 61.8%, 50.0% and 38.2% ratios but the 23.6% and 78.6% ratios can also be used to plot the trend lines. When using Fibonacci fans, you subdivide the swing ...


Further Reading: