The pattern seems to re-peat on one stock chart afteranother: An equity reachesan all-time-high price beforebeginning to plunge. Then, almostprecisely when it has fallen by a spe-cific percentage38.2 or 68.1 per-centit hits its floor and begins tobounce back up.

Whats happening? Technical ana-lysts say an explanation can be foundin Fibonacci numbers, a near mysti-cal sequence of numbers that oftenseems to describe the behavior oflarge systems, including financialmarkets.

I wanted to follow up from an arti-cle I wrote early last year about usingFibonacci retracements to help timecertain market turning points (Fi-bonacci Numbers Work in MysteriousWays, BLOOMBERG, February 1998).Although much of that article wasdedicated to describing the Fibo-nacci sequence and the mathematics

behind it, the more useful part, as faras a trader or salesperson is con-cerned, lay in how to apply Fibonaccinumbers to a chart. In this follow-up article, I review several examplesof a specific technique I introducedbriefly in that previous article. TD Absolute Retracement, a retracementmeasuring technique discovered bywell-known trading system and modeldesigner Tom DeMark, is usefulwhen charting a security thats tradingat an all-time high or a multiyear low.

First, some quick background on the strange world of Fibonaccinumbers may be useful. Leonardo Fibonacci was a 13th-century mathe-matician who brought to promi-nence the numerical sequence thatbegins 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,89 and that goes on infinitely. Thepattern is: the sum of any two con-secutive numbers equals the nextnumber in the sequence. Fibonaccinumbers frequently appear in na-ture: A daisy has 21 clockwise and 34counterclockwise florets in the mid-dle of the flower. A sunflower has 55 clockwise and 89 counterclockwiseflorets. The ratios between Fibonaccidigits are significant as well. The re-lationship of any number in the se-quence to the next highest numberapproaches 0.618 after the first fournumbers; the relationship of alter-nate numbers approaches 0.382.Those two decimals, which of courseadd up to the number one, appearfrequently as ratios in market move-ments. Combined with other tools,they can be clues that assist in find-ing the most profitable times to buyand sell.

One obstacle to applying Fibonaccinumbers to stock charts has been theproblem of deciding which marketturning points to use as referencepoints. Traditionally, recent top andbottom prices for a stock are used as

Absolut(e) RetracementsFor technical analysts

who want to predictmarket turns by using

Fibonacci numbers,heres a technique

that minimizes the guesswork

By Rick Bensignor

FIGURE 1. Type DELL GPO , tab down, adjust the RANGE field as shown,and press . To draw absolute retracement lines, mouse-click on the Fibonacci keyon the Bar Chart screen. Click on the September 29, 1998, high and then on the dottedline corresponding to a stock price of zero. To see the zero-price line, change the y-axisscale by holding down the mouse button and dragging down prices on the right

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points between which to measurepercentage retracements. But youshouldnt choose a retracementpoint from a subjective viewing of a chart; the points you pick to deter-mine your retracements should bemade on some type of methodicaland consistent basis. If, for example,a stock recently traded at its all-timehigh and then began to sell off, how would you choose which low to compare that recent high with in order to draw your Fibonacci retracements? Type MRK GPO D to see a one-year barchart of Merck & Co. that illustratesthis point.

Merck stock reached its all-time-high price of 87.375 on March 19,1999. Which low would you compare

that high with in order tomake your Fibonacci re-tracements: the most recentlow in January 1999? thedouble-bottom low of earlyOctober 98, when moststocks tanked? the low ofSeptember 1? June 4? April

27? You could pick whichever lowyou felt like, calculate your retrace-ments, and then hope that if the mar-ket sells off enough, it would hit oneof your retracement levels at the sametime some other technical buy signalscame in, so you could have more con-fidence in purchasing the security.

But that scenarios far too subjec-tive. A more objective way to select retracement points comes from ab-solute retracementsthe Fibonacciretracement methodology created byDeMark specifically for when securi-ties are trading at all-time highs orlows. Heres DeMarks technique,which mechanizes the approach and

eliminates the guessinggame: when a stock, com-modity, or currency is atits all-time high, take raw

percentage figures of the actual highprice and calculate down. For an example, figure 1 is a one-year chart

of Dell Computer Corp. Lets lookback to the fall of 1998, when Dell wasclimbing steadily in what was then a succession of all-time highs. Comethe end of September, the stockpeaked just shy of 35 and then itplummeted with the whole marketinto the first week of October.

As the market sold off from its late-September highs, from which lowwould you have constructed your Fi-bonacci retracement: the September1 low, the June 1 low, or the mid-March low? The answer is, none ofthem. Because Dell had been at anall-time high, you wouldnt measurefrom some prior low, yet you woulduse the popular Fibonacci numbersof 38.2 percent and 61.8 percent.How? By calculating those percent-age levels against the high price itself.For instance, the late-Septemberhigh was 34.625. Because that was anall-time high, measure 0.618 and0.382 of that high price. The result-ing prices are 21.40 and 13.23. OnOctober 8, even though it closed at24.22, Dell stock hit a low of 20.375,just below a 38.2 percent sell-off. The Fibonacci retracement held themarket and pointed to a major buyopportunity.

Coincidence? Nonsense? Voodoo?Look at the following additional examples, and note, too, that theyrenot obscure, no-liquidity issues.

Figure 2 displays a one-year chartof Morgan Stanley Dean Witter & Co.At that time, the mid-July 1998 highof 97.50 was the all-time high. Asshown in the previous example,when a stocks at an all-time high youshould take 61.8 percent and 38.2percent of that high price to calcu-late two retracement levels. Youdcome up with 60.26 and 37.25. Well,the market stormed through the first Fibonacci retracement level60.26but stopped exactly at 38.2percent of its all-time high.

Look at another brokerage stockthat had its problems in 1998: MerrillLynch. In figure 3, note the all-timehigh in July 1998, at 109.125. Take38.2 percent of that price, and you

FIGURE 2. Type MWD GPO D . Draw absolute retracement lines by using the high price on July 21, 1998. After changing the price range and drawing the Fibonacci lines, you can double-mouse-click anywhere in the price graph to return the graph to its original scale

92 June 1999 Bloomberg

Absolute retracements arent a trading system but a useful tool

For an overview of the Fibonacci technical analysis package available on the Bloomberg service, type IDOC FIBONACCI 1 .

Type IDOC for more information on the function

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get 41.69. The stock closed slightlylower than that figure in early Octo-ber 1998 and then doubled in the ensuing six weeks.

Publishing company Ziff-Davis isanother example. Just one day aftermaking its all-time high in December1998, at 23.938, it sold off to 15within one quarter point of a 38.2percent retracement (0.618 X 23.938 =14.79) and then instantly ralliedabout 33 percent.

So does this method forspotting market turningpoints always work? No, noform of analysis works everytime. Fibonacci retracements arent a trading system, but when combinedwith other indicators and ideas, theycan add to your arsenal.

One last thought: if this conceptworks for measuring from all-timehighs, does it work from all-timelows? It does, with slightly differentcalculations. When a market hasbeen trashed and sells off to all-timeor multiyear lowsthe determina-tion becomes slightly subjective onyour partfind the lowest low andmeasure 138.2 percent and 161.8percent of that low price. Those lev-els often act as ceilings for reboundsoff the all-time lows.

For example, look at the weeklychart of First Israel Fund, a closed-end equity fund investing primarilyin Israeli securities. The fund was es-tablished in late 1992, it peaked inearly 1994, and it then sold offstrongly into early 1995 at $9 ashare, its all-time-low price. Multiplythe low price times 1.382, and youget 12.438. Note how many timeslater in 199512.438 held on aweekly closing basis. In fact, thehighest subsequent close for all of1995 was 12.625a mere 0.187point more than the 138.2 percentretracement level. Furthermore,161.8 percent of 9 equals 14.562,which, if you were to look into 1997,was slightly less than half a pointfrom the first quarters high of 15(figure 4).

Maybe youre a believer in measure-ment of market movement; maybeyoure not. But regardless of whichway you lean, you should have littledoubt that, in fact, Fibonacci num-bers work in mysterious ways.

Any comments? Type MAGAZINE. For printouts, typeMAGZ .

Rick Bensignor is an applications specialist for Bloomberg in New York

FIGURE 3. Type MER GPO D . Use the high price from July 13, 1998, for your absolute retracement reference point

FIGURE 4. Type ISL GPO W . Notice how the price of the First Israel Fundstalled at retracement levels of 12.438 in mid-1995 and 14.562 in 1997

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