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

PHI-Ellipses on Constant Scales in the S&P 500 Index
If we can demonstrate that PHI-ellipses work with many products over
a longer period, we can be conf ident in our investments. It is only on
constant scales that we see the similarities of different PHI-ellipses.
Each PHI-ellipse varies in shape, length, or width, but the underlying
principles based on the Fibonacci summation series and the ratios
from the PHI series never change.
There is no standard PHI-ellipse that is the average f it for 
every price move. However, the magic of PHI-ellipses lies in their
ability to dynamically adjust to ever-changing price patterns in the
markets.
We have analyzed more than two years of S&P 500 Index daily
bar data from December 1998 to December 2000, and have backtested
the PHI-ellipses.
The total stream of data over the 25 months is separated into
three charts, as shown in Figure 5.36. By choosing a set of appropri-
ate PHI-ellipses and waiting for market pricing to move out of the
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PHI-ellipses at their f inal points, our sample investments follow
the price pattern in the S&P 500 Index with few exceptions.
Taking into account the 15 attached and overlapping PHI-
ellipses analyzed in the previous section on daily bar data in the S&P
500 Index and the total 23 PHI-ellipses shown in Figure 5.36, the dy-
namic nature of PHI-ellipses becomes evident.
Figure 5.36
S&P 500 chart from 12–98 to 12–00. Attached and overlapping
PHI-ellipses on a constant scale.
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