Edition

Thus, testing the system as aThus, whole testing is insufficient the systemtoas derive a whole statements is insufficient for each to derive individual
component. In fact, it is possible to have defect components even though the
statements fo
IFTA JOURNAL 2016 EDITION vidual component. In fact, it is possible to have defect components even
backtest succeeded. A more backtest basic approach succeeded. therefore A morewould basic approach be to empirically thereforetest
would be to emp
each component individually. each However, component thisindividually. approach rarely However, seenthis andapproach fundamental
books within the field oftal technical books within analysis themiss fieldit ofcompletely technical analysis (see Murphy miss it[8]).
completely (see M
is rarely seen and
Instead, statements are commonly Instead, based statements on a few are commonly examples only. basedSuch on aan fewinductive
examples only. Such a
approach, however, cannotapproach, hold whenhowever, considering cannot scientific hold when aspects considering which René would scientific Kempen aspects w
in fact require a deductive in approach. fact require Conclusively, a deductivea approach. concept has Conclusively, to be trader@nepmek.de
systematically
tested considering a variety cally tested of examples considering beforea any variety knowledge of examples canbefore Bücklerstraße deduced any knowledge 13 can
a concept has to be
from the set of results. Indeed, fromthis the set article of results. aims atIndeed, testing this the concept article 52351 aims of Duren, Fibonacci at testing Germanythe concept o
retracements using such a deductive retracements approach. using such a deductive approach.
+49 171 3588941
Fibonaccis Are Human (made)
By René Kempen
Fibonacci ratios
Fibonacci ratios
The Fibonacci numbers 1, 1, The 2, 3, Fibonacci 5, 8, 13, . . . numbers are one of1, the 2, 3, best 5, 8, known 13, . . . are series oneand of the arebest known ser
Abstract
even present in diverse areas nature. even of present nature. The n-th inFibonacci The diverse n-thnumber Fibonacci areas of is built nature. number of the The sum is built n-th of the Fibonacci oftwo
the number is
In this article, a scientific approach to sum retracements of the two is previous numbers, previous
sum of
numbers,
the ortwo in mathematical or
previous
in mathematical
numbers, terms, terms,
orthe in
the n-th mathematical Fibonacci
terms, the n-t
introduced and the myth of Fibonacci retracements number denoted refuted. byThe
f n is defined number
number asdenoted by f by fn is n is defined as
defined as
statistical analysis of the retracement data resulting from the
f
application of the MinMax-process by Maier-Paape to a variety
n = f n−1 + f n−2 for n > 2 f n = f n−1 + f n−2 for n > 2(1)
of stock markets reveals a logarithmic normal with fdistribution of
2 = f 1 = 1. Since the
with
appearance
f 2 = f 1 =
of
1.
the
Since
Elliott-Wave-Theory
the appearance of
(R.N.
the Elliott-Wave-Theory
Elliott,
(R
the retracement values in general. It is deduced 1920, see that [3]), there technical are analysts
1920,
have
see [3]),
been
technical
well acquainted
analysts have
with
been
Fibonacci.
well acquainted
Furthermore,
already levels. While Johannes in a Kepler
with Fibonac
no overall statistically significant retracement more, Since had
already the been appearance Johannes
interested of the Kepler
inElliott-Wave-Theory the
had
ratio
been
of two
interested
consecutive
(R.N. in the ratio of two
local environment the 100% retracement Fibonacci do show significance, numbers f n+1 / f n
Elliott, Fibonacci
. He 1920, numbers
found see that Frost this and f n+1
ratio Prechter, / f n . He
approaches 2005), found technical that this
the value analysts ratio approaches the v
of the
the Fibonacci retracements are not seen empirically.
have been well acquainted with Fibonacci. Furthermore,
already Johannes Kepler had been interested in the ratio of two
Introduction
consecutive Fibonacci numbers fn+1/ fn. He found that this ratio
1
In the field of technical analysis today’s trader can choose
approaches the value 1 of the
between a myriad of different indicators, filters,
golden
and even
ratio
whole
Φ for large
golden
n:
ratio Φ for large n:
trading systems. On the one hand, this shows the creativity of
f
the technical analysis community. On the other hand, however, lim n+1
n→∞ = Φ = 1 + √
golden ratio Φ for large n:
5
golden ratio Φ for large n:
≈ 1.618 . . . .
f n f 2
the variety of tools indicates the complexity of chart analysis.
lim n+1
n→∞ = Φ = 1 + √ 5
f ≈ 1.618 . . . .
The market’s behavior obviously cannot be predicted Generally, by a the set of k-th Fibonacci Generally, ratio lim n+1
the n→∞ F k is given
f
k-th Fibonacci n = Φ by = ratio 1 the + √ 2
5
Flimit k is ≈given 1.618 of the by . . . the .
f n 2
ratio limit of of a Fibonacci
analysis tools.
number with itsGenerally, k-th successor the the ratio k-th of a Fibonacci meaning ratio number theF k following is with givenits byk-th in themathematical successor limit of meaning ratioterms:
of a Fibonacci
Generally, numberthe withk-th its k-th Fibonacci successor ratiomeaning F k is given the following by the limit in of ratio
Consider a specific chart tool—whether it is a simple line, an
(
indicator, or a trading system—that is to be applied to a specific f n f n f
F
market. In this case, the question arises as to whether or k = lim
n+1
... n+k−1
= Φ −k 1 + √ ofterms:
a Fibonacci
number with the following its k-th successor in mathematical meaningterms:
the following in mathematical )
( −k
f
5
n f n f
not n→∞ the f F k = n+k lim f = n+1 flim
n+1
} {{} n+2 f ... f n+k−1
= = Φ −k 1 + √ ) terms: −k
( 5 . n→∞
f n f n+k n→∞
f
f n f =
} {{} n+k
2 . (2)
F k = lim = lim n+1 n+1 f
} {{}
} n+2
{{}
...}
f n+k−1 f
} n+k
{{ } = Φ −k 1 + √ ) −k
2
5
=
. (2)
combination of tool and market works as intended. A certain
n→∞ f n+k n→∞ f n+1 f
→Φ
answer to this question cannot be given, since it would require
−1 →Φ} −1 {{} n+2 f
→Φ −1 } {{} n+k
2
→Φ −1 −1 } →Φ {{ −1 }
→Φ
detailed knowledge of the market’s progression With in the thisfuture.
formula, Withthe thisfirst formula, Fibonacci the first ratios Fibonacci −1 →Φ −1 →Φ
can ratios be can −1 calculated: be calculated:
With this formula, With this the formula, first Fibonacci the
As long as this information is not available, any testing has to be
(
based on historical market data.
1 + √ first ( Fibonacci ratios
) 1 0 + √ ) canratios 0
be calculated: can be calculated:
( 5
F 0 = 5 1 + √ ) 0
F 0 =
= 2
5 = 1
F 0 = 1 = 1
Trading systems are commonly empirically tested by applying
2 ( 2
a backtest. However, trading systems are usually a combination
(
of other tools, such as indicators. Thus, testing the system as a
+ √ ) 1 + √ ) −1
( 5
F 1 = 1 + √ ) −1 −1
5 2
5 ≈ 0.618034 . . .
F
F 1 =
1 =
≈ 0.618034 . . .
( 2 ≈ 0.618034 . . .
whole is insufficient to derive statements for each individual
2 1 + √ ) −2
( 5
component. In fact, it is possible to have defect components even
( F 2
though the backtest succeeded. A more basic approach, therefore,
1 + √ = ) 1 + √ ) −2
−2 2
5 ≈ 0.381966 . . .
F 2 =
≈ 0.381966 . . .
5 2
F 2 =
≈ 0.381966 . . .
would be to empirically test each component individually.
2
However, this approach is rarely seen, and fundamental books Fibonacci retracements
Fibonacci
Fibonacci
retracements
retracements
within the field of technical analysis miss it completely (see The Fibonacci The ratios Fibonacci are applied ratios are in the applied analysis in the ofanalysis trends. While of trends. the basic concept of
Murphy, 2008). Instead, statements are commonly Fibonacci based a The
retracements
a Fibonacci trendWhile has been ratios the fundamental basic are applied concept in inof the a trend field analysis of has technical been of trends. fundamental analysis Whilesince the basic Charles the concept H. Dowof
a trend
few examples only. Such an inductive approach, however, cannot introduced has been it, fundamental the specific characterization in the field of technical of a trendanalysis not unique. since Charles In thisH. article, Dow
field of technical analysis since Charles H. Dow introduced it, the
hold when considering scientific aspects, which The would Fibonacciintroduced in fact ratios the market-technical areit, applied the specific definition the characterization analysis of a trend ofis of trends. used. a While is not unique. the basic In concept this article, of
the
require a deductive approach. Conclusively, a aconcept trendhas hasto been(1) market-technical specific characterization fundamental Definition (market-technical definition of aof in the field of trend) trend a trend is used. is not unique. In this article,
technical analysis since Charles H. Dow
(1)
systematically tested considering a variety of introduced examples before it, the ADefinition the market specific is(market-technical definition
in characterization an up/down-trend trend) of a trend used.
ifof and a trend only if (at is not least) unique. the two last In relevant this article, lows
A market (denotedisby inP1 anand up/down-trend P3) and highs if (denoted and onlyby if P2) (at are least) monotonically the two lastincreasing/de-
creasing.
relevant lows
any knowledge can be deduced from the set of the results. market-technical Indeed, (denoted definition by 1. Definition P1 Otherwise, and P3) ofand (market-technical the
a trend highs (denoted is
is
used.
currently bytrend)
P2) trendless. are monotonically In case of an creasing. (market-technical phase between Otherwise, A a lowthe is and trend) in market an the up/down-trend next is high currently is called if trendless. and the only movement. if In (at case least) Inofthe
ansame up-trend manner, the
up-trend the
this article aims at testing the concept of Fibonacci (1) Definition retracements
using such a deductive approach. A market is in phase the an between phase up/down-trend two between last
a low
relevant
and a high ifthe lows and next
(denoted only the high next if is
by (at low called
P1 least) and is the called P3)
movement. and thehighs two rectracement. In last (denoted
therelevant same In case manner, of lows a
the
(denoted by P1 and down-trend, phase between
P3) and movement a high
highs (denoted and andretracement the next low
by P2) areis are defined called
monotonically the the rectracement. exact opposite In
increasing/decreasing.
Otherwise, In line with market the the market is notation currently isused currently trendless. for defining In trendless. case a trend, of an it uptrend, Inis practical casethe ofto phase anumber up-trend the highs the
way. case of ⋄a
by P2) are monotonically increasing/decreasing. Otherwise, the
down-trend, movement and retracement are defined in the exact opposite way. ⋄
Fibonacci ratios
The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, … phase are one between of the In
a
line and low
with lows between and
the in 1-2-3 the
notation a next manner low and used
high (see the for
is next Voigt defining
called high 2008,[10]). is a
the
trend, called movement. the it ismovement. practical
In the
toIn number the same
the
manner,
highs
and
best known series and are even present in diverse the phase areas of between Now, lows
athe in 1-2-3
high correction manner
and the is the (see
next part Voigt
low where 2008,[10]).
same manner, the phase between is called Fibonacci a high the and ratios the rectracement. next occur. low is particular, In case it ofis
Now, a
common the correction to indicateisthe theamount part where of correction Fibonacci denoted ratiosby occur. the retracement In particular, value it Ris
down-trend, movement common in unities to indicate of
and
the
retracement
preceding the amount movement.
are of correction defined
That is, denoted in
for
the
any
exact
trend by the with
opposite retracement last three
way.
extrema value R⋄
PAGE 4 IFTA.ORG in unities P3
In line with the notation new , P2 of the andpreceding P3 (see figure movement. 1) the retracement That is, for value any Rtrend is given withby
last three extrema
P3 new , P2 andused P3 (see for figure defining 1) the aretracement trend, it is practical to number the highs
and lows in 1-2-3 manner (see Voigt 2008,[10]). R = P2 − P3 value R is given by
new . (3)