Candlesticks, Fibonacci, and Chart Pattern Trading Tools : a synergistic Strategy to Enhance Profits and Reduce Risk

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5
PHI-E
LLIPSES
Because swing formations are easy to identify and integrate into com-
puterized trading environments, traders or managers investing with
smaller accounts often use peak and valley formations. Many profitable
trades are possible as long as there are regular wave patterns and each
impulse wave def ines new highs or new lows by a wide margin. In mul-
tiple corrections with many false breakouts, swing systems are of lit-
tle use since they are based solely on price analysis.
When we add the time element to the market analysis, it f ilters
noise out of the market moves and brings more stability into invest-
ment strategies. This is where PHI-ellipses come in.
Working with PHI-ellipses is not easy. Their basic structure is
simple; but because price patterns may change over time, the f inal
shape of a PHI-ellipse that circumvents a price pattern may also vary.
Initially, the application of PHI-ellipses may seem confusing be-
cause there are different forms and wave structures within a PHI-
ellipse. In addition, PHI-ellipses can sometimes be linked together.
Both skill and imagination are necessary to use PHI-ellipses as in-
vestment tools.
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PHI-ELLIPSES
To deal with this complexity, we f irst describe the basic features
and parameters of PHI-ellipses in detail. We then present examples
that illustrate how to apply PHI-ellipses as Fibonacci devices to real-
time trading.
BASIC FEATURES AND PARAMETERS 
OF PHI-ELLIPSES
The PHI-ellipse is a unique Fibonacci trading tool that can only be
drawn by a computer.
As mentioned in Chapter 3, PHI-ellipses identify underlying
structures of price moves and circumvent price patterns. When a price
pattern changes, the shape of the PHI-ellipse circumventing the re-
spective market price pattern changes, too. Nearly all market price
moves follow the pattern of a PHI-ellipse.
PHI-ellipses are related to the Fibonacci ratio PHI in a similar
way as the Fibonacci summation series, as well as corrections and ex-
tensions (see Chapter 4).
Generally speaking, the ratio of major axis a to minor axis b de-
f ines the shape of an ellipse. Ellipses are turned into PHI-ellipses in
all cases where the ratio of major axis to minor axis e
x
=
(a
÷
b) is a
member number of the PHI series.
To make PHI-ellipses work as tools for chart analysis, we have
applied a (proprietary) transformation to the mathematical formula
that describes the shape of the ellipse. We still consider the ratio of
major axis a to minor axis b of the ellipse, but in a Fischer-transformed
way, in mathematical terms e
x
=
(a
÷
b)*.
We introduce PHI-ellipses as instruments for investments counter-
trending to market action. We observe whether a price move stays
within a PHI-ellipse and invest accordingly if a price move breaks out
of a PHI-ellipse at the very end.
Historical charts show that almost all price moves in commodi-
ties, futures, stock index futures, or stocks can be circumvented with
a PHI-ellipse. However, f inding the correct PHI-ellipse is an art. It
takes skill, experience, patience, and trust in the analysis to effec-
tively use PHI-ellipses as Fibonacci investment tools.
It is impossible to forecast the f inal shape of a PHI-ellipse at the
beginning of a price move. As we later prove on various examples,
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