Forex Trading System- Bull Cycles

OVERVIEW

One of the most fascinating and complex disciplines within the realm of forecasting se-
curity prices is the Elliott wave principle. This is the brainchild of author/analyst Ralph N.
Elliott, who developed his system during the 1930s and 1940s along with an accompany-
ing philosophy about cycles in nature. Elliotticians are quite adamant about Elliott’s sys-
tem even after three-quarters of a century due to its diversity and subjectivity. We
recommend that novice traders visit the following web sites for details: www.elliott
wave.com and www.acrotec.com/ewt.htm.
IDEAL BULL CYCLE

Analysts have identified and cataloged a plethora of unique price patterns like head-and-
shoulders formations, pennants, flags, and wedges. In this current study, we intend to
focus our research and analysis specifically on the ideal bull cycle. (See Figure 28.1.)
This cycle consists of five waves, three upward and two downward. The upward
waves in a bull cycle are called impulse waves and the downward waves are called cor-
rective waves (Elliott’s terms). The ideal bull cycle has the following mathematical con-
straints given that the letters “a” through “f” represent discrete prices (and not wave
lengths).
First, the length of each corrective wave must be less than the length of its preced-
ing impulse wave:
b – c < b – a
d – e < d – c
Second, no valley in a five-wave bull cycle may dip below any preceding peak:
b < e
Elliott’s theory now postulates that a well-behaved five-wave bull cycle will be fol-
lowed by a three-wave bear cycle (See Figure 28.2) with the following price constraints:
i < g < h < f
Note that price “f” is the junction point between the known bull cycle and the esti-
mated bear cycle.
OBJECTIVE

The purpose of this study is to determine the percentage of retracement that the three-
wave bear cycle covers in relation to the height of the preceding five-wave bull cycle. In
the first testing pass to achieve this objective we have selected the streaming tick data
for the EURUSD currency pair over the time period of 1/1/2002 through 12/31/2002. This
amounts to 7,079,300 closing prices.
Dirr ectron
181
FIGURE 28.1Ideal Bull Cycle
FIGURE 28.2Elliott’s Postulation
Tick data was selected in this initial study because this is how session and day
traders view the live streaming data as it is displayed in their forex dealer’s trading plat-
form. Thus, this study focuses on very short-term trading goals.

INITIAL RESULTS

In the current study, we set the box size to one pip (0.0001 USD) and vary the reversalamounts from 2 boxes to 25 boxes. A reversal amount of one box has no filtering potential and is therefore omitted. (See Table 28.1.)

Rev Amt is the reversal amount, the number of boxes required to trigger a reversal
in price direction.
Swings is the number of waves in the swing data or the sum of the peaks and val-
leys less 1. As the reversal amount increases, the number of peaks and valleys de-
creases due to the filtering process.
Matchesdefines the number of occurrences where the test pattern (the ideal bull
cycle) matches a sequence in the swing data.
Ratio is the average ratio between the height of all five waves in the bull cycle di-
vided by the height of the first three waves in the bull cycle:

PRAXIS

Many traders will now ask: How can this information be used as a trading mechanism?
A practical example follows.
Given that the price formation in Figure 28.3 has already occurred with the follow-
ing prices:
a
1.0000
b
1.0010
c
1.0005
d
1.0015
e
1.0012
we can now estimate the market entry point “f” for a short trade to trap the length of the
three-wave bear cycle by first computing the height of the first three waves “a” to “d” in
the bull cycle:
Length = d – a
0.0015 = 1.0015 – 1.000
Next we must project the price of f, the height of the fifth and final wave in the bull cycle:
f = 1.205 (d – a) + a
1.0018 = 0.0018 + 1.0000

To calculate the objective price (the market exit price), we multiply the average
retracement percentage (39.9 percent) times the height of the five waves in the bull
cycle:
Height = f – a
= .0018
Exit Price = f – (Percent Height)
= 1.0018 – (0.399 0.0018)
= 1.0018 – 0.00072
= 1.0011

CAVEAT

As usual, any new trading mechanism has to be thoroughly tested via paper trading be-
fore incorporating it into one’s overall trading system. One drawback in the bull cycle
trading mechanism example is that the standard deviation of the average retracement
percentage is slightly high at 4.9 percent. This means that there is a 68 percent likeli-
hood that the exit price will fall between 35.0 percent and 44.8 percent retracement of
the height of the bull cycle (39.9 – 4.9 and .39.9 + 4.9).
FURTHER STUDIES

In the present cycle study, we have only touched the tip of the iceberg. We intend to delve
much deeper into the predictive value of swing data, varying the dependent variables of
box size, underlying currency pair, raw data intervals, and unique cycle formations.
We were astonished to see how closely the average retracement ratio 39.9 percent
aligned itself with the primary Fibonacci ratio 38.2 percent. This is no coincidence since
many Fibonacci analysts believe that a 38.2 percent retracement indicates that the
three-wave corrective cycle will be followed by a new five-wave impulse cycle in the
same direction of the first impulse cycle.
However, it is these same analysts who believe that if the retracement percentage of
the three-wave corrective cycle reaches 61.8 percent, then a new five-wave impulse cy-
cle is developing in the opposite direction of the original five-wave impulse cycle.
Lastly, we should point out that the ratio of the height of the five waves in the bull
cycle divided by the height of the first three waves in the bull cycle is 1.205. This, too,
is extremely close to the primary Fibonacci number 0.618 multiplied by 2 (that is,
0.618 2 = 1.236).
This initial study is in no way complete, nor is it intended as an affirmation or a refu-
tation of Elliott’s works. Instead it is intended as an unbiased independent analysis
based solely on rigorous statistical methods, although resulting ratios and averages tend
to align with Fibonacci numbers with an accuracy greater than mere coincidence. We
may attribute the slight deviations to simple round-off error. As we increase the size of
the raw quotes in our historical currency database, we will be able to more accurately
determine critical inflection points in the cyclical data.