Fibonacci Numbers and Stock Retracements

By Dr. Winton Felt

In any trend there are moves and counter moves.  In an up-trend, the up thrusts will be larger than the counter thrusts.  The reverse is true in a downtrend.  The countertrend moves are often about 50% of the move in the prevailing trend.  This 50% counter move is more of a tendency than a rule.  For example, the counter move may be any amount, but there is a tendency for countertrend moves to take a stock to certain high-probability levels before resuming  the primary trend.  These high-probability levels generally fall within a range of as little as 23% or as much as 66%.  A stock that pulls back more than 66% should be avoided.  It is signaling a possible reversal in trend.  The trend is certainly not very strong at that point.  The odds are high that the stock will retrace 100% of its previous move.  In a very strong trend, the stock will often undergo counter moves on the order of 33%, and sometimes less.  We could consider approximately 50% to be typical..

Constructing Fibonacci arcs is a very popular method of estimating the probable extent of a price retracement.  Before we describe the arcs, a little information about the basis of those arcs might be helpful.  The Fibonacci sequence is 1,1,2,3,5,8,13,21,34, and so on, where the sum of any two consecutive numbers equals the next higher number in the sequence.  Also, after the first four numbers, the ratio of any number in the sequence approaches .618 of the next higher number.  That is, the ninth number in the sequence divided by the tenth number is approximately .618 and the result gets closer to .618 the further out in the sequence you go to compute the ratio.  The ratio of any number to the next lower number in the sequence is approximately 1.618.  This is the inverse of .618.  Finally, the ratios of alternate numbers in the sequence approach 2.618 and its inverse approaches .382.  For example, 144/55 = 2.6181818, and 55/144 = .3819444.

Fibonacci ratios appear throughout nature.  They also appear in market behavior patterns. For example, when a stock makes a significant upward move there is usually a subsequent minor decline as traders take their profits.  Market observers have discovered that the relationship between the stock’s rise and the downturn that follows is frequently a Fibonacci relationship.  It is not necessary to know how Fibonacci numbers are defined or the mathematical relationship between two Fibonacci numbers in a sequence.  It is sufficient to know that the most significant Fibonacci retracements (expressed as percentages) are 23.6%, 38.2%, 50%, and 61.8%.  A 23.6% “retracement” is not a 23.6% drop in the price of a stock.  It is a giving up of 23.6% of the gain achieved by the last profitable move of the stock. 

For example, if the stock moved from $40 to $50 the percentage retracements used would then represent retracements of $2.36, $3.82, $5.00, and $6.18, respectively.  These amounts would be subtracted from the recent high.  The expected support levels in a decline from the $50 high would therefore be at $47.64 for the 23.6% retracement, $46.18 for the 38.2% retracement, $45 for the 50% retracement, and $43.82 for the 61.8% retracement.  Our stockdisciplines.com traders might place their stop losses just below one of these retracement levels.  Thus, the stop losses will be triggered only if the expected support at these levels does not materialize.  Our traders may also review Fibonacci retracement levels in formulating a buy strategy.  For example, when a stock begins to rebound from a Fibonacci retracement level, that "bounce" is evidence of support, and it may also be considered to be a "trigger event" or buy signal.  In a trend retracement, the most important areas of support or resistance are at 38.2% and 50%.  The 23.6% level also offers support for stocks in a very strong trend.