How
Does a Study of Rabbits Lead
to a Strategy for Trading Futures? ...
By: Catherine
Davey
Client Adviser
Tricom Futures Services
Although his
name is as famous in trading circles as Ralph Elliot and W.D.Gann,
Leonardo Fibonacci was the forefather of both these market gurus
but never traded a single equity or futures contract. Fibonacci
is not famous for picking the crash of 1929, or the explosive gold
rally of the late 70's. His biggest contribution to the world of
technical trading was the result of a study on the breeding logistics
of rabbits.
Origins
The Fibonacci
number sequence was discovered by this Italian mathematician in
the late 1100's, and was the result of trying to solve the following
problem:-
Suppose a pair
of rabbits upon reaching sexual maturity at age one month gives
birth each month to a new pair of rabbits - one of each sex. All
the descendents do the same and no rabbits die or run away. How
many rabbits will there be in n months?
The solution is represented thus:-
Fn
= Fn-1 + Fn-2
(n > 3)
The recurrent relationship generates a sequence of integers known
as the Fibonacci sequence.
The Sequence
The Fibonacci sequence is expressed thus:-
1 1 2 3 5 8 13 21 34 55 . . . infinity
The sum of any two adjacent numbers creates the next higher number
in sequence.
For Example:
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
5 + 3 = 8
Nature
The number sequence
is more than just a mathematical quirk. The logarithmic spiral
which is constructed with the golden ratio, describes a growth
pattern seen throughout the universe. For example the number of
branches on a tree increases each year in the ratio of successive
Fibonacci numbers. A study on the navel height of 65 women found
that it averaged 0.618 of their total height. The pattern is evidenced
in everything from shells and flowers to galaxies.
Human Behaviour
The golden ratio
was known to the ancient Greek and Egyptian mathematicians. It
was used in the construction of the Parthenon and the Great Pyramid
of Gizah. The numbers are now recognised as a form of natural
harmony that are manifest in everything from art and architecture
to music. Therefore it is not surprising that the Fibonacci growth
spiral should be applied to the financial markets since they represent
one of the purest forms of mass human behaviour.
Special Qualities
In trading terms,
the most important quality is the Golden Mean. The ratios of the
consecutive Fibonacci numbers approach 1.618 (after the first
4 numbers in sequence) The inverse of this is 0.618. The higher
the numbers, the closer the ratio will approach the golden mean.
Other interrelated properties include:-
- Between alternate
numbers the ratio is 2.618 or the inverse 0.382
- 1.618 squared
equals 2.618
- 1.618 plus
1 equals 2.618
- 0.618 squared
equals 0.382
- 1 minus 0.618
equals 0.382
- 1.618 multiplied
by 0.618 equals 1
Application
The Golden Mean
together with the numbers that result from the special properties,
provide a powerful tool to analyse the markets. Both ratios and
the individual numbers are used to to determine time and price
levels, draw arcs, fan lines, time cycles and construct oscillator
indicators.
To demonstrate
the mechanics of a Fibonacci retracement, suppose a new high in
the SPI occurs at 2850 after rallying from 2750, and begins to
retrace. The total move up is 100 points. To find possible support
levels where the downtrend will cease and the uptrend resume,
the Fibonacci retracement levels are calculated:-
Low 2750
High 2850
Total Move 100 points
Possible Retracements:-
|
61.8% |
100
x 0.618 = 62 |
2850
- 62 = 2788 |
| 50% |
100 x 0.50 = 50 |
2850
- 50 = 2800 |
| 38.2% |
100
x 0.382 = 38 |
2850
- 38 = 2812 |
* 50% is commonly used and can also be derived from the Fibonacci
numbers by dividing the second and third numbers in the sequence.
The use of Fibonacci to draw retracement levels is be far the
most common, and in my opinion, most reliable application.
Simple Uses
Applying this
knowledge to a systematic trading strategy is a matter for another
discussion. However, as a secondary analysis tool, a quick calculation
of possible Fibonacci retracement levels can serve a dual purpose.
Firstly, when already in a trade, as the trend suffers the inevitable
pull-back, the trader can take heart that the pause in trend may
halt at the Fibonacci retracement level.
The strength
of the underlying trend will be reflected in the size of the Fibonacci
retracement. Thus, the Fibonacci retracment levels can be considered
when placing a stop-loss order. Knowing that a retracement of
more then 38% will indicate a reasonable pull-back in the trend,
a stop-loss can be placed just outside this level. This is especially
useful when working a trailing stop on a trade that is already
profitable.
Secondly, when
entering a market on a pull-back, the 62% retracement can be a
safe and relatively inexpensive entry level. Combining this with
an 85% level as the stop-loss, can minimise risk and exit you
from a pull-back that may in fact be a reversal in trend.
All Ordinaries Index
From the study
of the last bull run in the All Ordinaries Index, it is obvious
that Fibonacci's contribution to the study of price action is
relevant today. The uptrend since the large corrective move in
October 1997, provides more then coincidental evidence of the
All Ordinaries observance of Fibonacci retracement levels. A quick
comparison of the Fibonacci levels against the actual retracements
reveals a startling regularity. Nearly every retracement trough
on the chart is either a 38% or 62% level to within a few ticks.
Conclusion
Although there
are more complex trading systems using Fibonacci based analysis,
the use of simple retracement levels is one of the best technical
analysis apparatus. The use of Fibonacci price retracements is
a standard tool of most professional technical analysts, and for
this reason alone, should not be ignored by the private trader
when studying price action.
I am happy to
discuss Fibonacci trading strategies, and give Fibaoncci based
recommendations. Tricom are holding a free seminar "Trading with
Fibonacci" on Monday 11th of May. If you would like a copy of
the chart of the All Ordinaries Index with details of the Fibonacci
levels discussed above, or wish to reserve a seat on the upcoming
seminar please call Catherine at Tricom on 1800 810-488.
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