Fibonacci Number and Ratio Analysis
Price action therefore, for the most part, is a consequence of expectation. Hence, it is
not so much about whether an indicator actually works, but rather it is more about
the expectation that the market participants have about an indicator that really
matters. Traders and analysts observe price reacting very frequently with uncanny
accuracy at various significant Fibonacci levels every day in the markets. Fibonacci
levels may or may not have any real significance with respect to the underlying
structure of the markets, but if there are enough market participants willing to risk
capital based on a popular indicator reading, this will impact the performance of
that indicator. As more traders rely and act on the signals from a certain indicator,
the greater will be the potential for a larger reaction in price when those signals ap-
pear. This in turn will attract even more traders. This positive feedback cycle is an
example and natural consequence of the self‐fulfilling prophecy in action. And as
with any positive feedback loop, it is essentially an unstable system, especially when
there is an increasing number of traders who start to take preemptive action in the
markets, eroding the reliability of the signals. This may help explain why indicators
slip in and out of popularity, and on a larger scale, why markets rise and fall.
In short, price action is essentially behaviorally driven, mainly by expectation
and investor bias. Future price action is the result of market participants acting on
what they believe to be a true reflection of what is and may be transpiring in the
markets. It is their collective perception that matters, be it accurate or misguided.10.9 Geometrically versus Numerically Based Fibonacci Operations
We must be circumspect when applying Fibonacci ratios to charts. Basically, there
are two ways to apply Fibonacci operations like retracements, extensions, expan-
sions, and projections.10.9.1 the Numerically based approach to Fibonacci
Operations
The first is to assign a numerical value, that is, price, to various peaks and troughs
used to perform these Fibonacci operations. Hence, the observed range that will be
employed to calculate these Fibonacci operations is just the difference in price be-
tween, for example, a significant peak at point A and a significant trough at point
B, that is, (A – B). As we have seen earlier, the observed price range (A – B) form
the basis for all Fibonacci operations, be it to pinpoint retracement, extension,
expansion, or projection price targets.
If we perform Fibonacci operations by calculating the levels using assigned
numerical values, then it makes no difference whether ratio (logarithmic) or linear
(arithmetic) scaling is used on the chart. There will be no discrepancy in the calcu-
lated or projected Fibonacci‐based price targets. Compare the three retracement
levels in Figure 10.34 to those in Figure 10.35. They give the same price levels for
the retracement percentages within the observed price range.
In Figure 10.34, we see that the Fibonacci retracement price levels represent the
38.2 percent, 50.0 percent, and 61.8 percent values as calculated from the peak, within