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Reliable Signals Based on Fisher Transform for Algorithmic Trading

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  • Algorithm Invest

Abstract and Figures

Trading and investment on financial markets are common activities today. A very high number of investors, companies, public or private funds are buying and selling every day with a single purpose: the profit. The common questions for any market participant are: when to buy, when to sell and when is better to stay away from the market risk. In order to answer all these questions, many trading strategies are used to establish the best moments to entry or to exit the trades. Due to the large price volatility, a significant part of the trades is set up automatically today by computers using algorithmic trading procedures. For this particular field, special aspects must be met in order to automate the trading process. This paper presents one of these mathematical models used in automated trading systems, a method based on the Fisher transform. A general form of this method will be presented, the functional parameters and the way to optimize them in order to reduce the risk. It will be also suggested a method to build reliable trading signals with the Fisher function in order to be automated. Three different trading signal types will be explained together with the significance of the functional parameters in the price field. A code sample will be included in this paper to prove the simplicity of this method. Real results obtained with the Fisher trading signals will be also presented, compared and analyzed in order to show how this method can be implemented in algorithmic trading.
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Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | Volu m e 11 | Is s ue 1 | Pag es: 8 7 -102
RELIABLE SIGNALS BASED ON FISHER TRANSFORM
FOR ALGORITHMIC TRADING
Cristian PĂUNA1
DOI: 10.2478/tjeb-2018-0006
Trading and investment on financial markets are common
activities today. A very high number of investors,
companies, public or private funds are buying and selling
every day with a single purpose: the profit. The common
questions for any market participant are: when to buy,
when to sell and when is better to stay away from the
market risk. In order to answer all these questions, many
trading strategies are used to establish the best moments
to entry or to exit the trades. Due to the large price
volatility, a significant part of the trades is set up
automatically today by computers using algorithmic
trading procedures. For this particular field, special
aspects must be met in order to automate the trading
process. This paper presents one of these mathematical
models used in automated trading systems, a method
based on the Fisher transform. A general form of this
method will be presented, the functional parameters and
the way to optimize them in order to reduce the risk. It will
be also suggested a method to build reliable trading
signals with the Fisher function in order to be automated.
Three different trading signal types will be explained
together with the significance of the functional parameters
in the price field. A code sample will be included in this
paper to prove the simplicity of this method. Real results
obtained with the Fisher trading signals will be also
presented, compared and analyzed in order to show how
this method can be implemented in algorithmic trading.
Keywords:
Financial markets, Fisher transform, Algorithmic trading,
High frequency trading, Automated trading systems
JEL Classification:
M15, O16, G23, M21
1 PhD Student, Economic Informatics Doctoral School, Academy of Economic Studies, Romania.
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
88
1. Introduction
To be involved in the financial market is on trend today. Millions of private traders or investors
are buying and selling every day different kind of equities, stocks, indices, commodities or
currencies. The reason is only one: the profit, as difference b etween the buy and the sell
price. Each participant tries to buy cheap and to sell more expensive after a time period. The
idea is simple but many times the market price is turning against the trade. A common
scenario is after a period when the price increased and a buy trade is set up, the price starts
to decrease continuously. Sometimes the opening price cannot be retrieved and the trade
turns into a loss. These cases can be avoided or managed using a good trading strategy.
The main questions of each trader or investor participating in the financial markets are: when
to buy, when to sell and when it would be better not to trade. The perfect trading strategy
does not exist. To answer the common questions regarding the trading decisions, many
trading strategies were developed. As a result of the widespread development of the
electronic trading, under the conditions of the high price volatility on the financial markets
today, an important part of the trades is set up automatically.
“In electronic financial markets, algorithmic trading refers to the use of computer programs
to automate one or more stages of the trading process” (Nuti, Mirghaemi, Treleaven &
Yingsaeree, 2011, p.22). Algorithmic trading seems to be the future of this field, as long as
“large general financial volatility may increase uncertainty about the economic environment,
with long-lasting effects as investors demand a higher risk” (Funke & Goldstein, 1996, p.215).
Today the trading decisions are built almost instantly by computers using algor ithmic
procedures. This paper will present one of these computational models.
The method presented is based on fisher transform applied to the time price series. A first
version of this method was presented by Ehlers (2002). The methodology to apply Fisher
transform in algorithmic trading is a subject less developed in the literature. A generalized
form of the Fisher transform for algorithmic trading will be presented in this paper together
with the parameters that can be optimized in order to reduce the risk. It will be presented a
practical method to use the Fisher function in order to generate automated trading signals
for financial markets. To answer the questions regarding the buy and sell moments, and to
build a possibility to automate these decisions, a practical method to compute trading signals
based on the Fisher function will be included in this article. Three different trading signal
types will be explained together with the significance of their functional parameters. A code
sample for the Fisher indicator will be inserted in this paper in order to show the simplicity of
this method. To prove the method, some real trading results obtained with the Fisher trading
signals will be presented, compared and analyzed in order to qualify the method.
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
89
Figure 1: Similarity between the time price evolution and the square wave probability function.
In any financial market, due to the economic news releases and as result of the changes in
time of the investors' risk appetite, the price makes local maximum and minimum points on
a time interval. Based on this conjecture the price evolution between two maximum points
can be considered similar with the so called wire distribution, the square wave probability
function which registers maximum values at the ends of the interval and makes a minimum
point on the middle. Building a mathematical transformation of the price function to a
particular known function limited into [-1; 1] interval, can give us the possibility to predict the
maximum and the minimum points of the price just analyzing the transformation function.
This idea is usually applied in engineering but, as we will see the method gives us very good
results for the financial markets. Finding the minimum point of the transformation function
will indicate when the price series will turn in order to increase again to the new values of the
next maximum local price. This will give us a method in order to build a trading signal to
automate the decision about when to buy and when to sell depending on the values and due
to the variation of the Fisher function.
2. Fisher Function
The method suggested is based on the assumption that the price makes local maximum
points time to time. Between two maximum points a local minimum price always exists.
Usually this is a common behavior of the price in financial markets even the number of the
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
90
time intervals between two maximum points varies. Starting from this idea we will use a
transformation function between the price function and a known function that will describe
the square wave probability function presented in Figure 1. This transformation is just a
similarity between the two, when the price reaches a maximum value the price transformed
function makes a maximum. When the price reaches a minimum value, the model function
will have a minimum point. The model function is known and described by the conditions
imposed for its first derivate, as we will see below.
There are several functions used in practice to make this price transformation. The common
parts of all these functions is that they are described on [ -1; 1] interval and they have the
same behavior of the first derivate: a root of the first derivate in the middle of the interval
(corresponding with the minimum price value), high values of the first derivate on the ends of
that interval (corresponding with the maximum points of the price at the end of the time
interval considered), negative first derivate on [ -1; 0] (as price descending from the local
maximum point to the minimum) and positive first derivate on [0; 1] interval (as the price
increases again after the minimum local point to the next maximum local point). In this paper
we aim to present the usage of the Fisher transform function in order to describe the first
derivate of the price transformation. The Fisher function is:
x
x
xf 1
1
ln
2
1
)('
(1)
where ln is the natural logarithm.
Figure. 2. Fisher transform function
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
91
2.1. Fisher transformation
As can be seen in figure 2, the Fisher function respect all conditions imposed for the first
derivate of the wire function assimilated with the price behavior on a time interval . The
derivate has a root in that interval and it takes negative and respectively positive value s
before and after the root. The variable x is defined in the [-1; 1] interval. The price function
defined on the time interval is transformed into a function into a new space defined in the
interval [-1; 1]. The transformation conditions are defined using only the first derivate of the
transform function. Working only with the first derivate, the analytical form of the
transformation function is not important because the model will continue to use only the first
derivate of that function. To find the function anyone can integrate the formula (1).
“Based on the assumption that the price cycle will continue into the future” (Ehlers, 2002, p.
40), analyzing the Fisher function will determine when a local minimum point was passed in
order to predict the next ascending period of the price values to the next local maximum
value. This will be assimilated with a buy trading signal. When the first derivate of the
transformation function will pass through zero, the minimum point for the price is nearby. We
use the “nearby” term because the price in financial market is not a continuous function. The
price is given as a discontinued value in time. The values in a time interval can be defined as
a global polynomial interpolation function. To simplify the model, the price function can be
assimilated with a Spline function (Berbente, Mitran & Zancu, 1997, p. 9), as a straight line
between two consecutive time points.
Having the transform function defined by the formula (1) we can make a real time analysis if
we link the price values with the x value of that function. Because the x is defined on [-1; 1]
interval we have to reduce the price interval. For than we will consider formula (2). For a time
series where the price value for the (i) interval is noted with (pi), we can consider the
transformation:
minmax
min
pp pp
pi
i
(2)
In the formula (2), the terms (pmin) and (pm ax) are the minimal and respectively the maximal
values of the price in the considered time interval. Due to the fact that the price in financial
markets historical data is given by a particular data structure which define High, Low, Open
and Close values on each time unit, the price Fisher Indicator will use an average price value
for each time unit given by:
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
92
(3)
and the general form of the price transformation for a time price series is given by the formula:
1
minmax
min
i
i
ip
pp pp
p
(4)
where α, β and δ are optimization coefficients in order to improve the method. Ehlers (2004)
propose the coefficients: α=0.66, β=0.5 and δ=0.67. We found that optimization of these
parameters can gives different optimal values for each financial market, for a specified
number of time units (n). These parameters are very important to be optimized depending on
the market and on the timeframe used for model application, especially when it is about the
Fisher trading signals included in the third chapter of this paper.
The optimization method for the functional parameters of the Fisher transform is to consider
different values for each parameter and to compute the trading results for a longer period of
time, based on the historical price series. For each set of functional parameters the gradient
of the Fisher transform function will be different and as consequence the trading results will
be different because of some delays of the trading signals.
2.2. Fisher indicator
The Fisher transform of the price for Frankfurt Stock Exchange Deutsche Aktienindex DAX30
(Börse, 2018) for a 65 days interval is presented in figure 3. The current Fisher transform
values for the current interval are represented together with the values for the last time
interval, in order to reveal more accurate the turning points of the Fisher transform function.
As can be seen in figure 3, when the Fisher function turns, the price follows the same direction
even sometimes there is a small delay between the two functions. This is the behavior
assured by the formula (4) transformation. The Pearson’s correlation indicator between the
price evolution and the Fisher transform function, calculated for a period of ten years, with a
time interval variable between 20 and 100 time units, for DAX30 index, with different
timeframes, has values between the minimum 0.62315 and the maximum 0.99983. The
correlation indicator was calculated considering the price transformation presented, with
variation of 1 value for the ascending price intervals and 0 values for descending price
intervals. The values obtained indicate a very good and positive correlation between the
increasing or decreasing of the price and the evolution of the fisher function. The high values
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
93
of the correlation indicator makes this method reliable, fact confirmed by the results
presented later.
Analyzing the Fisher indicator, a good prediction can be made at least in order to decide the
direction of the price for the next period. It is assumed that the method presented here does
not intend to predict the price value for the next time interval. The method intends to estab lish
when the price passed the minimum point and is ready to entry in the next increasing period.
The method presented here can gives us an indication for entry and exit signals based only
on the Fisher values not on the price values. As can be seen in Figure 3, after the Fisher
function passed through zero value, the price starts to increase to a local maxim um point.
This can be assimilated with a prediction in order to establish the direction of the price not
the next value of the price. When the price sl ows down from the ascending movements, we
can see the Fisher indicator turning into a descending interval. A complete trading signal can
be built between B and C points in Figure 3, at B a buy signal can be generated by the Fisher
function and at C point an exit trade signal can be delivered by the same transform function.
As can be seen, the decisions in this model are based only on the transform function not on
price values. In the next chapter we will see how automated trading signals can be built in
order to trade the Fisher function . Some real trading results will be presented in chapter 4.
Figure 3. Price Fisher transform indicator for daily price of DAX30.
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
94
Figure 4. Price Fisher transform indicator code in Multi Query Language
A sample code for the price Fisher transform indicator in multi query language (MQL) is
presented in figure 4. As can be seen, the implementation in algorithmic trading of this
method is a simple one. This is the most important advantage of this method . The good results
obtained and the simplicity of the method make this model to be a very attractive one.
3. Trading signals
The intended purpose of the method presented is to automate the trade. To include the Fisher
function in an algorithmic trading program means to bui ld some logical trading conditions.
We will call these conditions as trading signals. These will be Boolean variable with an explicit
meaning: when a buy signal is “true”, the software will send an automated buy order; when a
sell signal is “true”, the program will send a sell order. It is assumed that if in a moment of
time a buy signal is “true”, the model must assure that the sell signal is set as “false”. While
the trading signals are depending on the monotony of the Fisher function, this last
assumption is by default respected as we will see.
To build trading signals using the Fisher transform of the price means to analyze the turning
points of the Fisher function. Based on the hypothesis that the price evolution is similar with
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
95
the wire distribution function (Figure 1), near a minimum point of the Fisher function the price
reaches also a minimum point and the future values of the price will increase in order to
register a new maximum point. This can be a buy signal.
After the maximum point of the Fisher function, when the Fisher values starts to decrease,
based on the same assumption, the price will turn down to decreasing values. This means
the buy signal is no longer available; a sell decision must be in place. Usual the buy decision
is not taken immediately after the turning point; another one or two time units are expected
to generate a good signal confirmation. The buy signal can be built as:
 
211 iiiii FFFFBuySignal
(5)
where (Fi) is the time value of the Fish er function, (ʌ) is the logical and operator and ξ is the
minimal gradient parameter in order to filter the trades. When the distance between (F i) and
(Fi-1) is very small, the price movement is not yet a significant one and the trade can fail. For
this reason, using a higher ξ value will generate better trades. This functional parameter is a
subject of the optimization process for each market. Analyzing the Fisher graph we can see
that the condition (5) is also available in some points nearby the local max imum values of the
Fisher function. This means some buy trades accomplished with (5) can be opened near the
turning points of the price, which definitely is not a good idea. In order to avoid this, the buy
signal is changed with two additional conditions as:
     
iiiiiii FFFFFFBuySignal 211
(6)
where ρ is a distance from the 0 value of the Fisher function where the buy signal is not any
more considered. In practice also too early signals do not give very good results and to avoid
these cases the signal is not considered when the (Fi) value is outside the interval [-ρ; ρ]. The
ρ parameter is also an optimization process and it is established statistically by repetitive
optimizations using a large interval of the price series. As we can see, the buy signal defined
by (6) uses only the price Fisher transform function values. The price values are not there and
the model do not try to predict the price values. We will call this signal the Fisher signal. In
the same manner the sell signal can be built for markets where short positions can be
considered with the formula:
     
iiiiiii FFFFFFSellSignal 211
(7)
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
96
A particular point of the Fisher function is the zero point (A point in Figure 3.). This is the point
where the minimal value of the price is present. After this point the price values start to
increase. For very volatile markets where the price does not have large increase periods or to
trade with shorter timeframe, as all cases in high frequency trading, the point A is considered
the only one available Fisher signal using the relations
     
     
iiiii
iiiii FFFFSellSignal
FFFFBuySignal
00
00
1
1
(8)
Once the Fisher function has gone through zero ascending, a buy signal is considered. When
the Fisher function has gone through zero descending, a sell signal is considered. We have
to mention that the Fisher trading signals are only entry points in the market. The exit points
are treated separately and they are not the subject of this paper. The trading signals given by
(6) and (7) are usually very accurate for higher values of ξ. When the gradient of the Fisher
function has small values, meaning the ξ parameter is smaller, a lot of trades can be
generated by the Fisher signal but some of them are false signals because the changes of
the price are not important ones. For these cases additional conditions can be applied in
order to build reliable trading signals. A good filter for the Fisher transform function is the
price cyclicality function (Păuna & Lungu, 2018). Noted with (PCYi), the price cyclicality
function will complete the Fisher trading signals:
     
     
iiiiii
iiiiiii PCYPCYPCYPCYPCYPCY
FFFFFFBuySignal
211
211
(9)
where φ define the trust interval for the PCY function. The usage of (PCYi) in relation (9) makes
a significant filtration for the Fisher signals in order to consider only that trades with an
ascending cyclicality function and exclude all the cases when the price is oversold or
overbought by limiting the values of the PCY in the [-φ; φ] interval. We will call this signal the
Fisher cyclicality trading signal. As will be seen in the next chapter, the signals given by (9)
formula will generate a higher number of trades than the simple Fisher signal accomplished
with (6).
A good particularity of the Fisher transform function is that the methodology can be applied
not only to the price values. A particular indicator can be obtained applying the Fisher
transform to the moving average of the price. Starting from the s ame assumption that the
moving average will take a minimal local value between two maximal local values, applying
the Fisher transform to the moving average of the price w ill give us the possibility to predict
higher values of the moving average after a minimum point of the Fisher function.
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
97
Figure 5. Fisher transform of the moving average of the price
The Fisher transform applied to the 10 period exponential moving averages for a daily price
time series of DAX30 Index is presented in figure 5. As we can see, after the D point a
significant increase in values of the moving average occurs, meaning that a significant
upward movement of the price can be expected until the E. Trading signals with the Fisher
transform of moving average of the price can be built similarly with (6), (7), (8) and (9)
formulas.
4. Trading results
It this chapter we present the trading results obtained with the Fisher trading signals
indicated above. The results were obtained using TheDaxTrader (Păuna, 2010), an automated
trading system that uses Fisher signals in order to generate buy trades for DAX30 index. The
results presented in table 1. were obtained in the period 01.06.2015 31.05.2018 using a
fixed target of 10 points for each trade. This consideration takes place instead of an
additional exit signal conditions that are not subject for this paper.
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
98
The DAX30 index was traded as contract for differences (CFD) with a spread of 1 point. The
exposed capital involved and the risk management were accomplished using the “Global Stop
Loss Method” (Păuna 2018). The price Fisher transform and the cyclicality function were
computed for H4 timeframe interval. An additional condition was imposed regarding the hourly
intervals of the executed trades between 8:00 and 16:00 coordinated universal time (UTC). In
table 1. are presented the trading results for:
Fisher trading signals given by (6) with ξ=0.45 and ρ=0.50;
Fisher trading signals given by (8) with ρ=0.50;
Fisher cyclicality trading signals given by (9) with ξ=0.10, ρ=0.50 and φ=5 and
all the above signals assembled together. The capital evolution for these last results is
presented in Figure 6.
Table 1. Trading results obtained with the long Fisher signals
Total trades
Losing
trades
Profit
Drawdown
RRR
Absolute
drawdown
Absolute
RRR
(6)
ξ=0.45 ρ=0.50
10
0
2578
3744
1:0.69
2729
1:0.94
(8)
ρ=0.50
138
0
36802
7690
1:4.79
6320
1:5.82
(9)
ξ=0.10 ρ=0.50 φ=5
40
0
10323
8896
1:1.16
6323
1:1.63
(6), (8) and (9)
assembled together
159
0
42370
9079
1:4.67
6321
1:6.70
Figure 6. Capital evolution as a result of all Fisher trading signal types assembled together
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
99
As we can see, the number of trades made by the signal with (6) formula for a high value of ξ
is reduced. A significant number of trades can be generated for lower values of the ξ
parameter but the drawdown of the results is higher, a part of these involving a higher risk.
For the trading results presented, all functional parameters were optimized in order to obtain
no losing trade and to reduce the risk involved.
As we can see in the figure 6, the presented trading model permits this objective to be
realized. No losing trade was registered in a 35-month interval. This fact allows us to say that
the trading signals obtained with Fisher method are reliable trading signals.
A significant large number of trades were made by the trading signal (8). A very good risk to
reward ratio (RRR) was obtained for this type of signal. As we can see in the table 1, for each
1 dollar risked the 4.79 dollars were obtained as profit. The drawdown ref lects the exposure
capital; it is the risk recorded during the trades. The absolute drawdown represents the
drawdown from the initial capital. As we can see both values are in the normal interval, much
lower valued than the profit obtained.
The signals made by (9) are also significant when it is about the number of trade executed
and the profit level obtained. All three signal types assembled together gives us a very good
return. With only 159 trades during a period of 35 months, the Fisher trading signals
produced 42,370 dollars profit with a maximum risk of 9,079 and an absolute drawdown
1:6.70 trading DAX30 Frankfurt Stock Exchange Index.
Based on the fact that the trading methodology presented in this paper makes a significant
number of profitable trades with a very low number of losing trades (even with no losing trades
for the proper optimization parameters set as it was seen above), the Fisher trading
methodology deserve a special attention. In addition, the simplicity of this model makes it
attractive for algorithmic trading.
In order to reveal the advantages of the fisher methodology we have made a comparison with
other known trading methods. The results presented in Table 2. were obtained using
algorithmic trading in the same period of time (01.06.2015 31.05.2018), on the same
financial market (DAX30) with the same ten points target.
The known trading methods used were the “Moving averages perfect order methodology”
(Lien, 2009), “Parabolic stop and reverse methodology” (Wilder, 1978) and “Relative strength
index methodology” (Connors & Alvarez, 2009). Each method was optimized to obtain the
best efficiency for the traded financial markets. In Table 2 it can be seen that Fisher
methodology makes a significant larger number of trades with the higher risk and reward ratio
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
100
(RRR). These results are an additional confirmation that Fisher transform gives us a reliable
trading methodology for algorithmic trading.
Table 2. Comparison between Fisher trading signals and other known trading methodologies
Total
trades
Losing
trades
Profit
Drawdown
RRR
Absolute
drawdown
Absolute
RRR
Fisher signals
(6), (8) and (9)
159
0
42370
9079
1:4.67
6321
1:6.70
Moving averages
perfect order signals
96
28
18045
8712
1:2.07
5871
1:3.07
Parabolic stop and
reverse signals
102
31
18816
6011
1:3.13
5418
1:3.47
Relative Strength
Index signals
68
6
16372
5901
1:2.77
5272
1:3.10
The author uses the Fisher trading signals presented in this paper since 2010 year. This
methodology was included in TheDaxTrader automated software from the beginning. The
results obtained with this methodology were always the same. With a proper optimization
parameters set, the Fisher signals generate only profitable trades in the stock markets. This
methodology was tested, implemented and used with the same good results for a
representative number of financial markets: Deutscher Aktienindex (DAX30), Dow Jones
Industrial Average (DJIA30), Financial Times London Stock Exchange (FTSE100), Cotation
Assistée en Continue Paris (CAC40), Swiss Stock Exchange Market Index (SMI20), Australian
Securities Exchange Sydney Index (ASX200), Tokyo stock Exchange Nikkei Index (Nikkei225),
NASDAQ100 Index, Standard & Poor’s Index (S&P500) and Small Capitalization US Index
(Russell2000). Also with good and stable results the Fischer methodology presented in this
paper were applied for Gold and Bent Crude Oil financial markets starting with 2012 year.
5. Conclusions
Fisher price transformation can predict the turning points of the price. Buy and sell trading
signals can be built based on the Fisher function’s values. The prediction for a future price
value is not an objective of this method. The only one minimal point of the Fisher function on
the considered interval permits to determine when the price start to increase to a new local
maximum value. This point is the base for a buy signal. The sell signals are met in the same
way working with the descending intervals of the Fisher function.
Being exclusively a mathematical model, the Fisher signals can be automated for algorithmic
trading. The functional parameters of the Fisher methodology presented must be optimized
DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Ye a r 2018 | V olum e 11 | Iss u e 1 | P a ges: 87102
101
for each traded market. There is no general parameter set. Each market has its own behavior;
the optimal trading results are met when the functional parameters of the Fisher method are
optimized especially for that market.
Good trading results are obtained combining the Fisher trading signals with other indicators,
especially to avoid the cases when the price is overbought or ov ersold. These two concepts
are not included in the Fisher model; additional functions can be added in order to filter the
extreme price intervals. The Fisher method can be also applied to predict the evolution of any
other indicator such as moving average. In this way a considerable number of combined
trading signals can be built.
With the right parameters set, the Fisher trading signals can generate trading results with a
good risk to reward ratio. Even “loses are a part of trading” (Ward, 2010, p.137) and must to
be accepted from time to time, the right parameters set can gives us a long line of winning
trades with no losing trade as we saw. With these results it can be said that Fisher signals
are reliable trading signals for financial markets and a very good solution for algorithmic
trading.
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Connors, L., & Alvarez, C. (2009). Short Term Trading Strategies That Work. A Quantified Guide
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Ehlers, J.F. (2002). Using the Fisher Transform. Stocks & Commodities, V(20:11), 40-42.
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DOI: 10.2478/tjeb-2018-0006
PĂUNA, C. (2018).
Reliable signals based on Fisher transform for algorithmic trading
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... For the currency and commodities markets, reliable models and trading strategies can be found in [8]- [10]. Original investment strategies optimized for automated capital investment software can be found in [11]- [15]. ...
... The strange evolution is due significant volatility on the currency market following the Brexit news [24]. To avoid cases like the one presented above, a limit condition imposed for the distance of the price from the PPL are used: (11) and for high-frequency trading: ...
... More limit conditions can be described with additional algorithms based on the direct of inverse Fished transform of the price, presented in [11] and [12]. In these cases also the limits are too restrictive for long trends because they are imposed only in the asymptotic stage of those indicators. ...
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In electronic financial markets, algorithmic trading refers to the use of computer programs to automate one or more stages of the trading process: pretrade analysis (data analysis), trading signal generation (buy and sell recommendations), and trade execution. Trade execution is further divided into agency/broker execution (when a system optimizes the execution of a trade on behalf of a client) and principal/proprietary trading (where an institution trades on its own account). Each stage of this trading process can be conducted by humans, by humans and algorithms, or fully by algorithms.
Frankfurt Stock Exchange Deutsche Aktienindex DAX30 Components
Börse. (2018). Frankfurt Stock Exchange Deutsche Aktienindex DAX30 Components. Retrieved from http://www.boerse-frankfurt.de/index/dax
Short Term Trading Strategies That Work. A Quantified Guide to Trading Stocks and ETFs
  • L Connors
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Connors, L., & Alvarez, C. (2009). Short Term Trading Strategies That Work. A Quantified Guide to Trading Stocks and ETFs. New Jersey, US: TradingMarkets Publishing Group.
Using the Fisher Transform
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Ehlers, J.F. (2002). Using the Fisher Transform. Stocks & Commodities, V(20:11), 40-42.
Day Trading Swing Trading the Currency Market Technical and Fundamental strategies to Profit from Market Moves US
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Lien, K. (2009). Day Trading & Swing Trading the Currency Market. Technical and Fundamental strategies to Profit from Market Moves, US: John Wiley & Sons.