Do any of these samples of sage advice sound familiar?

“Don’t buy it here, but wait for a pullback.I

would wait and sell on a bounce. What does this

really mean? Where and when do you act? Here’s

one technique for calculating retracement levels

using that tried-and-true favorite, Fibonacci ratios,

as well as using momentum to define the trend.

Markets trend in a zigzag manner: rallying, leveling off, and surging again, only to be hit by a wave of profit-taking before settling into a trading range, awaitingthe next reason to advance or retreat.

This activity carries on in the general direction of the trend, easily seen on a price chart. Technically, the trend should beconsidered up as long as the market unfolds with a series of higher lows and higher highs. Similarly, the trend is considered down if the price action is a series of lower lows, with lower highs before each new low.A market is considered not to be in a trend if the price movement manifests itself in a series of fits and starts or if it fails to sustain levels beyond the previous extreme points, often reversing and forming the range. During an uptrend, good traders will buy the pullbacks,positioning themselves with the trend, taking advantage of the market’s tendency to ebb and flow.

When the market is in a downtrend, however, the strategy is to sell rallies, awaiting for the downtrend to resume.

So what is the appropriate strategy to calculate price levels for buying pullbacks or selling rallies? One popular technique is to calculate and project a

percentage retracement of the prior swing and use that as an entry level. But what percentage retracement is suitable? One popular set of retracement levels is

based on a mathematical series discovered by an Italian mathematician more than 700 years ago.

**SON OF BONACCI**

Fibonacci ratios, which are used by traders, is based on the work of the 13th-century Italian mathematician Leonardo of Pisa, better known by his nickname,

Fibonacci (an abbreviation of filius Bonacci; filius is Latin for “son of”). Fibonacci, through the process of solving a mathematical riddle, discovered a unique

mathematical sequence or series wherein the ratio of any two consecutive numbers approximates 1.618 or its inverse, 0.618. The Fibonacci sequence is the sum

of any two adjacent numbers that forms the next number in the series. The first 14 terms in the sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,

377. The ratios of each two consecutive numbers from the series are 1, 0.50, 0.666, 0.60, 0.625, 0.615,0.619, 0.618, 0.618..., and between alternate numbers,

the ratio is 2.618 and its inverse, 0.382.

The Fibonacci ratio is also referred to as the Golden Ratio or the Golden Mean. These ratios or proportions are often noted to be the mathematical basis for various aspects of nature,music and art. Recently, in a television interview, a

reconstructive plastic surgeon detailed how he set out to understand what the attributes of the facial features of physically attractive people were. He studied different cultures to see if he could find any consistencies of those attributes among them. Eventually, his research led him to using Fibonacci ratios for proportioning facial features. He even designed a computer template using Fibonacci ratios as an aid during reconstructive surgery.

Technicians use the Fibonacci ratios for percentage retracement measurements for establishing positions and Fibonacci-based multiples of trends to set profit objectives. Is this paradigm for modeling nature and art appropriate for trading the markets? Perhaps. If you look on a chart, markets do appear to resemble the path of a river, meandering from periods of stillness and apparent apathy to swiftly moving ahead, only to suddenly reverse, leaving investors with the sense that their favorite stock has just gone over a waterfall. Whether or not you accept the premise, using Fibonacci ratios can provide you with price levels to trade off of, as well as profit objectives.

**TREND AND COUNTERTREND**

An advancing market will often run a quick series of daily bars, three or four days in a row, with the high of each day exceeding the previous day’s high and the low of each day holding above the previous day’s low. Then the market will spend a few days in congestion,perhaps retracing the previous advance,then again trending upward. Ideally, you should see this retracement as an opportunity to place a position in the direction of the trend, trading like the pros buying a pullback, not chasing the market.But first: To calculate a retracement, you have to identify the beginning and ending points of the trend to be retraced. One technique for labeling these points is known as an isolated high or low, which I first read about in Charles Drummond’s How to Make Money in the Futures Markets. Drummond defines an isolated high as a day with a lower high one bar before and after; an isolated low is a day with a higher low one bar prior and one bar following.

These patterns,which make up three bars, represent a support area for the isolated low and a resistance levelfor the isolated high (Figure 2). The isolated low for an uptrend would be the beginning point of a short-term uptrend or the market only entering a simple sideways trading range before a downtrend continued. Because the market has held support for up to three days, price action indicates that demand was strong enough or the abatement of selling stopped the decline, which could in turn lead to higher prices. Likewise, an isolated high would be the end point of the short-term uptrend, leading to a possible reversal or atrading range.