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Fibonacci (Percentage) Retracements

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The origins of one of the most useful 'retracement' theories for stocks, stock indexes and other markets came from someone who lived in the middle ages. Leonardo Fibonacci was an Italian mathematician who was doing mathematical work in the early 1200's!


Could you discuss what I should make of the market having come back some percentage of the last decline as mentioned in your weekend article? Also what about a trendline breakout you wrote about?


I'll answer the last question first about the possible upside breakout and its potential to suggest (or further 'support') the idea of an upside trend reversal.

In my weekend (5/9) Index Wrap commentary, I featured the S&P 500 (SPX) weekly chart with a highlighted down trendline that had been pierced, although just barely. Had we seen upside follow through this week, it would have suggested a type of upside chart breakout that would have been technically significant.

Since the placement of trendlines can vary a little I often talk about the decisive upside penetration of trendlines as being important. Meaning, instances where there's some distance that gets cleared beyond the trendline. Not that a close above a down trendline is not important; however, as crucial is that there's then upside follow through in the next bar; i.e., the next week in the case of a weekly chart.

If there is NOT this upside follow through above a bearish down trendline, it suggests that the trendline is still acting as an area of resistance. Scant movement above or below a trendline is not significant in terms of a trend reversal unless there is follow through. The weekly SPX chart follows. Note: prices are as of the 5/13 (Wednesday) close.

It looks like LAST week's advance came just up TO the key line of resistance and in the broader scheme of things that is true. If you take a closer up view of the same trendline, the weekly close edged above the trendline as seen in the following chart.

As can be seen in the close up magnified view in my next chart, the recent weekly close did edge above the (downtrend) line as highlighted in the yellow circle below. However, the high of THIS week so far is showing a lower relative high than last week and it looks like SPX is at least temporarily in retreat. The implication is that there is as of yet NO (upside) reversal of the major downtrend since prices just came up to technical resistance and a renewed decline may be underway. Stay tuned on that over the coming weeks!


We owe some debt to Dow for his observations that an intermediate trend often will retrace (give back) anywhere from around 1/3 to 2/3rds of the distance covered by the primary trend, before the major trend resumes. There were further refinements on retracements made by W.D. Gann, a famous stock and commodities speculator of the first half of the 1900's where Gann found it significant to use charts that had retracements noted between a significant low to high or high to low of 1/4, 1/2 and 3/4ths; i.e., 25, 50 and 75 percent.

The origins of one of the most useful 'retracement' theories for stocks, stock indexes and other markets came from someone who lived in the middle ages. Leonardo Fibonacci was an Italian mathematician who was doing mathematical work in the early 1200's!

The number sequence named after Fibonacci is where each successive number is the sum of the two previous numbers; i.e., 1, 2, 3, 5, 8, 13, 21, 34, 55, 144, etc. Any given number is 1.618 times the preceding number (approximately) and .618 times the following number.

There are technical studies or indicators, whose formulas rely on the so-called Fibonacci number sequence, but the main application for most technically oriented traders is to use the 'fibonacci retracements' of .382 or 38%, .50 or 50% and .618 or 62%. The number 5 is in the Fibonacci sequence, and the others are ratios: .618 comes from the percent that each number is OF the next higher number and .382 is the inverse of .618 (100 - 61.8 = 38.2). I'll stick to a common shorthand and round off to 38 and 62%.

I noted in my "Essential Technical Analysis" book, that .38 and .62 were a 'little bit' less and a little bit more than 50%. The little 'bit' being an eighth of a point either way, relative to when stocks traded only in eighths; before stocks traded in 1/100th of a dollar or in decimal points.

What I find most useful in trading is to track what would constitute the 38, 50 and 62% retracement points, after a minor or intermediate price swing. I also sometimes add notation of a line representing a 25% retracement for a shallow correction and 75% for a deep one. Use of these retracements is a very common practice and a quite popular point of reference among profession traders.

There is a simple pragmatic reason for this popularity and that is that buying or selling in these retracement areas often results in coming close to buying at the low and selling at the top. Maybe the saying of buy low, sell high owes something to the common retracements.

You can set most charting applications to calculate retracements ranging from 25% to 38% (.38), 50%, 62 (.62)% and 75% by pointing first at the low, then the high (pullback retracements) or first at the high, then the low (for retracement rallies in a downtrend).

In a countertrend rally within a dominant downtrend - once a minor downside correction begins, check to see if a recent high represented a 38, 50, or 62% retracement relative to the rally starting point OR the last major downswing. If the (up) swing high also failed at or under the key down trendline and was accompanied by an overbought condition, it's a good tip off to short or go into puts.

My initial chart examples relate to my recent discussion of the S&P 500 (SPX) retracement to date of the last major down leg, which involved measuring the upside retracement of the decline from the 8/11 high of last year (2008) at 1313 to the recent SPX low at 667.

To date the SPX retracement amount has been just slightly more than 38% of the last down leg. The 38 percent retracement line is not 'resistance' in the same way a prior high is thought to represent (at least potential) resistance. However the 38% retracement line DOES represent an area where a rally could be expected to run of steam and the area where relative 'weak' rallies will falter. A 'normal' retracement in stocks or indexes is around 50% or half of a prior price swing. Normal here implies a market cycle that is in more normal economic times; e.g., where earnings are not getting so hammered.

A 'normal' trend, one that isn't influenced by extraordinary events and economic conditions, will often see a retracement develop of about half or 50% of the prior move. The most common level to buy or sell is this retracement amount, with an exit if it continues on much beyond 50%; e.g., 5% more.

Within the range of 'normal' is a retracement of 62% or perhaps 2/3rds (66%) and sometimes, not often, 75%, especially in more volatile stocks.

If a retracement exceeds one level, I look for it to go to the next; e.g., if a retracement goes beyond 38%, I anticipate prices heading toward the 50% retracement level. Only if the retracement EXCEEDS 50%, do I look for the next retracement level of 62% as a potential target.

If a retracement exceeds 62%, or a maximum of 66%, then I look for a 'round trip' or a return all the way back to the prior low or high; i.e., suggesting a retest of the low or prior high. The ULTIMATE 'retracement' so to speak is 100 percent of a prior move. This is where double tops or double bottoms form OR there is a new up or down leg.

Going to the leader of the pack in the recent rally, the tech heavy Nasdaq 100 (NDX), the index managed to exceed a 38% retracement of its last big down leg dating from mid-August last year (2008) as highlighted on the NDX daily chart below.

After the advance beyond (above) the 38 Fibonacci retracement level, the NDX rally failed or reversed just about midway TO the line representing a 50% retracement as seen below. The subsequent break below support implied by the 200-day moving average, now suggests keeping track of the percentage retracements of the last advance; i.e., from the 1040 low up to the recent 1436 high.

In keeping with the ideas suggested by retracement theory, a shallow retracement would be 38% and a more normal one that of 50%. Stay tuned on that and track those (38 and 50%) retracement levels. (Not shown here. Take this as trading 'homework').


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