By Cornelius Luca

Monitoring the health of the prevailing trend is a fundamental responsibility for any trader. And while at times you will benefit from such moves as the downtrend that occurred in the dollar/Norwegian krone (USD/NOK) in the fourth quarter of 2004 (see Figure 1), such relentless trends are the exception rather than the rule.

Even the strongest trends are typically subject to several pullbacks or retracements (shorter-term countertrend moves). Many traders rely on Fibonacci numbers to determine likely retracement price points. The most popular of these so-called Fibonacci levels are the ratios .382, .50 and .618, or 38.2 percent, 50 percent, and 61.8 percent. (Actually, 50 percent is not even a Fibonacci retracement level, but it is bundled with this group because of its high technical significance.) The basic application of these percentages is that a market will often pause or correct when it retraces 38.2 percent, 50 percent, and 61.8 percent of the most recent price trend.

In addition to these ubiqui tous horizontal Fibonacci lines, there are two other ways to apply the Fibonacci ratios for retracement analysis: fan lines and arcs. We will focus on fan lines and compare them to the standard horizontal Fibonacci retracement lines.

Fibonacci review

The Fibonacci ratios are named after

Leonardo of Pisa, an Italian mathematician who introduced the Hindu-Arabic number series that would eventually bear his name to Western Europe in his work titled Liber Abaci (Book of Calculations) approximately eight centuries ago.

The Fibonacci sequence is a number series for which every new number is the sum of the previous two numbers:


Although currencies have a reputation for strong trends, the down move in the U.S. dollar/Norwegian krone in late 2004 is relatively rare; price trends are more typically interrupted by periodic retracements, or corrections.

U.S. dollar/Norwegian krone (USD/NOK), daily


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