OVERVIEW
Many trading systems are based on special numbers, like certain integers, Fibonacci
numbers, prime numbers, trigonometric relationships, and the like. It comes as no
surprise that a 50 percent retracement holds a tantalizing fascination with many
traders.
This special case is called the 50 percent retracement principle and implies but
does not adamantly state that when the second wave retraces the first wave by ex-
actly 50 percent, then the height of the third wave will approximate the height of the
first wave.
The ideal 50 percent retracement is depicted in Figure 24.1.
However the 50 percent principle is not a proven theory, merely a principle. If
the 50 percent principle could be trusted with a very high degree of certainty, the
impact on the currency markets (all markets, for that matter) would of course be
cataclysmic.
TESTING APPROACH
We are interested in knowing just how much faith traders can put into the 50 percent
principle and if it should be incorporated as an integral part of any profitable tradingsystem. This study is a continuation of the analysis performed in the previous chapteron measured moves but focuses solely on the specialized case of 50 percent retrace-ment. Our approach is again statistical in nature and will involve the 7,000,000+ EURUSD
currency pair database. In the reversal algorithm, we maintain the box size as constant
(1 pip = 0.0001 USD).
INITIAL RESULTS
Our initial computer run generated the table in Table 24.1. The column headers are de-
fined as:
Rev Amtis the reversal amount for the swing algorithm.
Y-Valueis 100 wave 3/wave 1.
Std Devis the standard deviation of the dependent variables (y-values).
Swingsis the number of peaks and valleys in the swing data created by the reversal
algorithm.
Matchesdefines the number of 50 percent retracements that occurred in that set of
swing data.
The bottom-line statistics for the 50 percent principle using the current database are:
Average Retracement of Third Wave = 74.83%
Average Standard Deviation for Third Wave = 30.15%
Given a bull wave of 20 pips followed by a bear wave of 10 pips, this information can be
represented graphically as shown in Figure 24.2.
Thus, there is a 68 percent likelihood the peak of wave 3 will fall between 18.94 pips
and 31.00 pips. In this particular case (20-pip bull wave and 10-pip bear wave), the 50
percent retracement principle implies that the peak (or valley) of the third wave may
reach 30 pips (20 – 10 + 20 = 30).
Given that we allow the 50 percent principle to include the range of one standard
deviation on either side of the forecast value (24.97 pips), then the principle holds true.
However, if we enforce a strict single-point discrete forecast, then the retracement of
the third wave is only 74.83 percent of the first wave and the principle falls short of its
expectation.
Also interesting to note in Figure 24.2 is that the highest percentage of retracement,
78.39 percent, occurred when the reversal amount was set to 21 boxes. This may be a
unique property of the EURUSD pair during the 2002 calendar year, though.
INCREASING TOLERANCE
The study required that the retracement percent be a perfect 50 percent. Since technical
analysis is not an exact science, we feel that an exact 50 percent retracement constraint
is too mathematically rigorous, particularly as the reversal amount in the swing algo-
rithm increases. Therefore, some tolerance should be permitted. We will increase our
zone of acceptable candidates to encompass the range 47.5% <= retracement percent-
age <= 52.5% instead of a strict 50 percent. The additional 5 percent leeway increases
the number of matches, which may help stabilize the percentages and standard devia-
tions. (See Table 24.2.)
Average Retracement of Third Wave = 67.35%
Average Standard Deviation for Third Wave = 28.61%
We need only to add these two numbers together to determine if the height of the third
wave will equal the height of the first wave:
67.35% + 28.61% = 95.96%
The result of adding a ±2.5 percent tolerance range did not improve the case for the
50 percent retracement principle.
We increased the tolerance percentage one final time to 45% <= retracement per-
cent <= 55% and produced the following averages:
Average Retracement of Third Wave = 66.63%
Average Standard Deviation for Third Wave = 28.24%
A ±5% tolerance range produces the following maximum retracement sum:
66.63% + 28.24% = 94.87%
Again the result falls short of the basic premise of the 50 percent principle. In de-
fense of the 50 percent principle, though, we admit that it was originally applied to stockprices nearly a century ago and we are applying it to one specific currency pair for onespecific time frame (1/1/2002 to 12/31/2002). Future studies in the 50 percent principle will involve different time frames in the EURUSD pair and even different currency pairs.
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