# fibonacci for the faithful ... repeat

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Hmmm.. repeat of original post for those interested in advanced technical trading...

Technical tool insight: Fibonacci ratios

Fibonacci ratios are percentage price targets based on the Fibonacci series, a number sequence named after the 13th century Italian mathematician Leonardo da Pisa Fibonacci. Fibonacci actually derived the number series from the Hindu-Arabic numerics and mathematics he studied and was instrumental in popularizing in the Western world.

Traders use Fibonacci ratios to estimate the size of a future price move, either one in the opposite direction of the most recent trend move, or the next leg of an existing trend.

Calculation: The Fibonacci series

The Fibonacci series is a number progression in which each successive number is the sum of the two immediately preceding it. The series begins with 1 and continues as follows: 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on.

Application: Fibonacci ratios and price targets

As the series progresses, the ratio of a number in the series divided by the immediately preceding number approaches 1.618, the golden ratio found in architecture (e.g., the dimensions of the Parthenon) and many natural phenomena (shell spirals, plant growth). The inverse, .618 (.62), has a similar significance. (Fibonacci originally used the series to mathematically answer the question of how many offspring a pair of rabbits would produce given certain conditions.)

Some traders believe Fibonacci ratios manifest themselves in the markets in the way price moves relate to each other in size (and duration, a subject that will not be covered here). Traders use different variations of Fibonacci numbers and their ratios to generate price forecasts.

For example, say a market rallied from 40 to 60 and then pulled back to 50. A common method for finding a possible price target for the next anticipated up move is to multiply the rally (20 points) by the Fibonacci ratio 1.618 (or .618) and add the result (20*1.618 = 32.36) to the pullback low (50 + 32.36 = 82.36). This type of price estimation plays a large role in the Elliott Wave Principle, an analytical approach that categorizes price moves as ãwavesä of different magnitudes. Figure 1 (above) shows a long-term uptrend in the S&P 500 index (SPX). The first leg began in late 1994 and topped out in mid-1996. The length of this move was 238.22 points from low to high and 231.53 points from the respective closes of the low and high bars. Table 1 (below) shows price targets based on multiplying the two measurements of the first leg of the trend by the Fibonacci ratio of 1.618. The results were added to the low and the close of the July 1996 low bar to project possible price targets for the next leg of the uptrend. As Figure 1 shows, the price target estimated from the lows and highs was fairly close to the high of the trading range that began in 1997 and lasted into early 1998. The target calculated from the closes was a little higher.

This example highlights one of the nuances of using this kind of analysis: Do you measure price moves and targets from low to high or close to close? Others include: Should you project the next price move from the retracement low (as was done in Figure 1) or from the high of the price move? Which Fibonacci ratio should you use? Traders often use complex extrapolations of Fibonacci numbers in their trading, which is one reason some traders avoid this type of analysis. At some point, it becomes possible to create a Fibonacci ãratioä that will fit almost any chart.

A more popular use of Fibonacci ratios is to calculate likely retracement levels. (A retracement, or pullback, is a countertrend move that occurs after a price trend.) The most popular ratios (rounded off) are .38, .50 and .62 , which all result from dividing one number from the Fibonacci series by another number later in the series (e.g., 3 divided by 8, 1 divided by 2, 8 divided by 13).

For example, if a stock broke out of a trading range and rallied from 25 to 55, potential retracement levels could be calculated by multiplying the distance of the move (30 points) by the .38, .50 and .62 Fibonacci ratios and then subtracting these results from the high of the price move. In this case, retracement levels of 43.6 [55 ö (30*.38)], 40 [55 ö (30*.50)] and 36.4 [55 ö (30*.62)] would result.

Figure 2 (below) shows 38-, 50- and 62-percent retracement levels based on the retracement of a down move on a 10-minute chart of the Nasdaq 100 tracking stock (QQQ). Price rallied to the 38-percent retracement level, pulled back and rallied to this level a second time. In addition, the dashed line the QQQ pulled back to (and consolidated around before first reaching the 38-percent line) is a less-commonly referenced Fibonacci ratio, 23.6 (13 divided by 55), often rounded to 24. These levels can be used either to enter new trades in anticipation of reversals, or take profits on existing positions. In the earlier hypothetical example, a trader who shorted when the stock reversed after hitting 55 might take profits (either total or partial) as the market approached a Fibonacci retracement level. A trader looking to go long might buy when the stock reached one of the retracement levels and turned back to the upside.

Key points

Traders sometimes point to price moves that fall in the general vicinity of a Fibonacci level as evidence of the validity of the approach. However, when it comes to getting in and out of trades, general vicinity is usually not good enough ÷ especially for short-term traders.

As the chart examples illustrate, forecasting price targets with Fibonacci ratios is not a precise science. As with any other trading tool, it is advisable to consult other inputs or approaches before making a trade decision. Fibonacci-ratio retracements or projections can be used as confirming or secondary tools that may indicate a price reversal or pause in a general price range, not a specific price level. Independent, specific signals can be used to generate trade signals. For example, the Fibonacci retracement levels calculated off the uptrend in the S&P 500 index (see Figure 3, above) provided few, if any usable reference points for trading. The index did briefly bounce after first touching the 38-percent level, but the subsequent downthrusts essentially ignored the other levels. However, the SPX made an almost perfect retracement to the 38-percent level of the 2000-2001 decline after establishing the September 2001 low (see Figure 4, below).

Perhaps the most pragmatic way to use Fibonacci ratio retracements and projections is to be aware of these levels, and if the market you are trading begins to stall out or show signs of reversing when it reaches one, factor this information into how or if you implement a trade.

Bottom line

Unlike other technical tools that essentially trigger trades in reaction to price or indicator patterns, Fibonacci ratios are typically used to forecast price action. Because of the uncertainty of this kind of analysis, it is always wise to use Fibonacci-based signals as a supplement to a larger trading plan or system, not as the foundation upon which to build one.

References

Fibonacci analysis is popular in a variety of disciplines outside trading, and there is no shortage of Fibonacci resources on the Internet. Here are a few to get you started:

ð Fibonacci Numbers and the Golden Section: www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/

ð The Fib-Phi link page: http://pw2.netcom.com/~merrills/fibphi.html

ð Fibonacci biography and number series background:
www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html

Technical Tool Insight is not intended to recommend (or disavow) any indicator, trading tool, methodology or school of thought. The goal is simply to explain the background and mechanics of well-known trading concepts and their most common uses, and to give the reader the basis for further research, through which he or she should determine the value of the concept."
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