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Additional Limit Conditions for Breakout Trading Strategies

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Abstract and Figures

One of the most popular trading methods used in financial markets is the Turtle strategy. Long-time passed since the middle of 1983 when Richard Dennis and Bill Eckhardt disputed about whether great traders were born or made. To decide the matter, they recruited and trained some traders (the Turtles) and give them real accounts and a complete trading strategy to see which idea is right. That was a breakout trading strategy, meaning they bought when the price exceeded the maximum 20 or 50 days value and sold when the price fell below the minimum of the same interval. Since then many changes have occurred in financial markets. Electronic trading was widespread released and financial trading has become accessible to everyone. Algorithmic trading became the significant part of the trading decision systems and high-frequency trading pushed the volatility of the financial markets to new and incredible limits nowadays. The orders are built and sent almost instantly by smart computers using advanced mathematical algorithms. With all these changes there are many questions today regarding the breakouts strategies. Are the Turtle rules still functional? How can the Turtle strategy be automated for algorithmic trading? Are the results comparable with other modern trading strategies? After a short display of the history and the system's rules, this paper will find some answers to all these questions. We will reveal a method to automate a breakout strategy. More different trading strategies originating from the Turtle rules will be presented. A mathematical model to build the trading signals will be described in order to automate the trading process. It was found that all of these rules have a positive expectancy when they are combined with modern limit conditions. The paper will also include trading results obtained with the methods presented in order to compare and to analyze this capital investment methodology adapted especially for algorithmic trading.
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Informatica Economică vol. 23, no. 2/2019 25
DOI: 10.12948/issn14531305/23.2.2019.03
Additional Limit Conditions for Breakout Trading Strategies
Cristian PĂUNA
Economic Informatics Doctoral School
Bucharest Academy of Economic Studies
cristian.pauna@ie.ase.ro
One of the most popular trading methods used in financial markets is the Turtle strategy. Long
time passed since the middle of 1983 when Richard Dennis and Bill Eckhardt disputed about
whether great traders were born or made. To decide the matter, they recruited and trained
some traders (the Turtles) and give them real accounts and a complete trading strategy to see
which idea is right. That was a breakout trading strategy, meaning they bought when the price
exceeded the maximum 20 or 50 days value, and sold when the price fell below the minimum of
the same interval. Since then many changes have occurred in financial markets. Electronic
trading was widespread released and financial trading has become accessible to everyone.
Algorithmic trading became the significant part of the trading decision systems and high-
frequency trading pushed the volatility of the financial markets to new and incredible limits
nowadays. The orders are built and sent almost instantly by smart computers using advanced
mathematical algorithms. With all these changes there are many questions today regarding the
breakouts strategies. Are the Turtle rules still functional? How can the Turtle strategy be
automated for algorithmic trading? Are the results comparable with other modern trading
strategies? After a short display of the history and the system’s rules, this paper will find some
answers to all these questions. We will reveal a method to automate a breakout strategy. More
different trading strategies originating from the Turtle rules will be presented. A mathematical
model to build the trading signals will be described in order to automate the trading process.
It was found that all of these rules have a positive expectancy when they are combined with
modern limit conditions. The paper will also include trading results obtained with the methods
presented in order to compare and to analyze this capital investment methodology adapted
especially for algorithmic trading.
Keywords: Financial markets, Breakout strategy, Turtle strategy, trading signals, algorithmic
trading, high-frequency trading, automated trading systems.
Introduction
In the middle of 1983, the most famous
commodities trader at that time, Richard
Dennis was disputing an interesting idea with
his partner and friend Bill Eckhardt. The
subject was about whether a good trader is
born or made by education and training. The
issue is still interesting today, even the answer
was given a long time ago. “Richard believed
that he could teach people to become great
traders. Bill thought that genetics and aptitude
were the determining factors” [1].
To decide the matter, they took large
advertising announcements in Barron’s, Wall
Street Journal and New York Times. “Over
1,000 people had applied and only 40
applicants had been granted for an audience
with Denis. Only 13 ultimately were chosen,
with another 10 selected for a follow-on
program the next year” [2]. The first group of
traders was trained for two weeks at the end of
December 1983. After the training, they
received real money accounts funded with
capital between 500,000$ and 2,000,000$
somewhere in February 1984 in order to apply
the trading strategy for which they were
trained. The students were called “the
Turtles”: “we are going to grow traders just
like they grow turtles in Singapore” [3] said
Richard Dennis to someone after he just
returned from Asia.
The Turtle experiment remains maybe the
most famous experiment in financial trading
history until now. It was proved that trading
abilities can be learned. Richard Dennis
proved that with a complete trading system,
1
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defined by a simple set of rules, “people with
little or no trading experience” [1] can become
excellent traders. Due to the facts, the Turtle
experiment is important also because he
revealed and proved that the Turtle strategy
used in trading is consistent and a reliable one.
Many changes have occurred in financial trad-
ing in the last decades. Electronic trading was
widespread released. “Electronic trading (ET)
is the method that use information technology
to bring together buyers and sellers in a virtual
market place using an electronic trading plat-
form and a network that links all participants”
[4]. Using ET, financial trading has become
accessible to everyone. An impressive number
of private or institutional investors or trades is
participating in markets every day with a sin-
gle purpose: the profit. In the trading decisions
process, algorithmic trading became a signifi-
cant part of any informational system.
Today, the orders are built and sent almost in-
stantly by smart computers using advanced
mathematical algorithms. The high-frequency
trading pushed the volatility of the financial
markets to new and incredible limits nowa-
days on markets where ”there is an exponen-
tial over-reaction to an action” [5]. With all
these changes there are many questions re-
garding the Turtle strategy today. First of all,
we are asking if the Turtle rules still functional
in the new market conditions. It was found
that there are several trading strategies deriv-
ing from the original Turtle system with posi-
tive profit expectancy that can be used with
good returns in algorithmic trading (AT). In
this paper, it will be presented a way to auto-
mate these models for automated trading sys-
tems (ATS).
A mathematical model to build the trading
signals will be described in order to automate
the trading process based on the presented
strategies. It was found that all of these trading
strategies have positive profit expectancy. The
paper will also include trading results ob-
tained with the methods presented in order to
compare and to analyze this trading method-
ology adapted especially for algorithmic trad-
ing.
2 The Turtle Strategy
Starting from the Curtis Faith disclosures, an
original Turtle member that decide to make
public the Turtle trading system rules in order
to stop the scams and commercial activities
with this kind of information, the original
Turtle strategy rules are about to describe all
aspects regarding the markets traded, the
position sizing, the entry rules, the stop loss
conditions, the exits and the tactics when it is
about large liquidity. All these rules can be
found widely on [1]. In this section, we will
present them on short, as based for the trading
strategies that will be presented in the next
chapter.
Regarding the market traded, the original
turtle system was trading futures contracts of
the most liquid US markets: 30 Years US
Treasury Bonds, 10 Years US Treasury Note,
Coffee, Cocoa, Sugar and Cotton
commodities on New York Exchange, gold,
Silver and Copper in Comex, Crude and
Heating Oil and Unleaded Gas on New York
Mercantile Exchange and Swiss Franc,
Deutschmark, British Pound, French Franc,
Japanese Yen, Canadian Dollar, S&P 500
Stock Index, Eurodollar and 90 Day US
Treasury Bill on Chicago Mercantile
Exchange.
Regarding the position sizing, the turtle
system uses a sizing algorithm depending on
the US dollar volatility on the market. The
concept is known today as “Market true
Range” and it was at that time a very advanced
methodology to establish the traded volume,
especially to the fact that the electronic
trading was not yet invented. The size was
established as 1% of the trading capital
divided by the market dollar volatility
received as input data depending on the
historical price movements form the last days.
The method can be used even today in order
to set the trading volume depending on the
price volatility.
Regarding the entry rules, the turtle system
has two strategies. Both were breakouts
strategies, one on shorter-term based on a 20-
days breakout, the other for longer-term,
based on a 50-day breakout. “A breakout is
defined as the price exceeding the high or low
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of a particular number of days” [1]. For the
shorter-term system, when the price exceeds
the 20-days high, a buy order was initiated. If
the price follows under the last 20 days
minimum value, a short order is executed. For
the longer-term entries, the 50 days minimum
or maximum point was the decisive factor.
The entry made by the above conditions
regarding the 20 days extreme points it was
ignored if the last breakout trade had resulted
as a winning trade. He signals related with the
50 days maximum and minimum points were
traded whether the previous breakout had
been a winner or a losing trade.
The Turtle trading system has an adding
position option. The initial entry is made on
one unit according to the position size
methodology. At half of the average range in
price movement, the turtle system adds a
position of one unit too. If the market
continues to grow, after another half of the
normalized average range another unit will be
added, until the maximum four units accepted.
The entries were initiated consistently, and
this gave a positive expectancy just “because
most of the profits in a given year might come
from only two or three large winning trades”
[1].
The stop-loss strategy involved by the Turtles
was set up an automated stop at 2% of the
account. In order to keep the total position risk
at a minimum, if additional units were added,
the stop for the earlier units was raised with
0.5% at the last entry point. All the opened
positions have the same stop-loss defined by
the last entry trade. An alternative stop loss
strategy made with 0.5% risk was tested by
Turtles system on different markets.
Regarding the exits, the Turtle system is a
breakout system. It is known that most
breakouts do not result in trends. Even so,
closing the winning positions too early can cut
significantly the profit expectation. The
entries for the 20 days extreme points were
closed when 10 days low or high occurs. The
long positions were closed at the 10 days low
price level; the sell positions were closed at
the 10 days high price level. For the trades
opened for longer periods, considering the 50
days breakout, the exits were made following
the 20 days low and high. From the practice,
these kinds of exits can erase the profit for a
significant part of the trades and this is the
main reason for the low expectancy of the
Turtle system today. Another exit strategy
must be found in order to improve the system
in the new electronic trading environment and
the new volatility conditions in today’s
markets.
The last element of the turtle system is
regarding the tactics related to the market
orders. The turtles usual placed limit orders
instead of market orders because the limit
orders offer a chance for better fills in
nonelectronic market execution and less
slippage than did the market orders. Today
these can be made equally even it is about
large volume traded. For the periods when the
market runs fast with thousands of dollars per
contract in minutes, the Turtles waited for a
more stable market before to place their
orders. Today the volatility is much higher
than the 1984 year this specificity must be also
improved in the trading system in order to
have enough trades to count the profit at the
end of a period.
As a conclusion the turtle strategy is a
breakout trading system with a volume de-
pending on the price volatility and exits de-
pending on the price action. The system tries
to catch longer trades using exits depending
on the minimum price level for a period of
time on the buy trades and the maximum
given in a period for the short trades. It is ex-
pected today, due to higher volatility on the
markets, the system to give us a lower profit.
The fact is proved by the statistics. Even so,
starting from the Turtle trading system some
trading strategies can be developed and
adapted for algorithmic trading to be used in
the electronic trading environment today.
Some of these trading strategies will be pre-
sented in the next chapter.
3 Trading signals
The AT in the ET environment represents the
automation of trading decisions and orders.
Computers using mathematical algorithms,
based on the real-time price time series build
the trading orders and send them with low-
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latency to the brokerage companies in order to
be executed. Regardless of the algorithm used
to build the trading decisions, in AT the
trading signal is related with a Boolean
variable which is true when a trade can be
opened and false when no trade must be
opened. Once the market was chosen and the
trading volume computed by an exact
methodology, the buy and sell orders will be
generated depending on so-called signal
variables. We note them here as a buy signal
and sell signals. These variables will be
calculated for each (i) time interval. For the
Turtle system, the trading signals are given
by:
k
Ni
ik
ii
k
Ni
ik
ii
LowMinpSellSignal
HighMaxpBuySignal
(3.1)
where N is the number of days considered for
the turtle strategy (20 days for the shorter term
strategy or 50 days for the longer term
system), and Highi and Lowi are the highest
respectively the lowest value of the price level
for each i time interval in the N number of
days considered. For any market in ET the
time price series give the values of Highi and
Lowi and the maximal and minimal valued of
these series can be computed to find the values
of the trading signals in real-time.
3.1 Additional Limit Conditions
Trading the signals given by (3.1) in the new
market conditions can give us low results es-
pecially in those periods when the price is on
overbought or oversold intervals. In these sit-
uations, the price can exceed the maximum of
20 or 50 days period and reversed strongly in
the other direction after the signal is present
and the trade is executed. The price movement
in the reversed direction can be important and
a high-frequency trading (HFT) strategy for
AT can give a lot of losing trades. The over-
bought and the oversold intervals must be
avoided in order to open new trades.
It was found that additional condition to avoid
the extreme price will significantly improve
the trading results and will increase the
efficiency of the trading system. A proper
mode to avoid these intervals is to use the
“Price Cyclicality” function presented in [6].
Noting with PCYi the price cyclicality
function value for each i time interval, the
original Turtle trading conditions became:
 
 
ik
Mi
ik
ii
ik
Mi
ik
ii
PCYLowMinpSellSignal
PCYHighMaxpBuySignal
(3.2)
where ξ and φ are two functional parameters
that can be optimized for each market in order
to avoid opening orders into overbought and
oversold intervals. In relation (3.2) it was
changed the N interval with M specifically, in
order to draw attention to the fact that the
number of days M in AT and HFT can be
different than the number of days N
considered in the original Turtle system. It
was found that the trading signals given by the
relations (3.2) can generate reliable trades for
different time interval than 20 respectively 50
days, considering the breakout for different
time periods, depending on markets and the
timeframe used.
More than that, it was found that trading for
the small profit target, as is the case for HFT,
the signals given by the relations (3.2) can be
traded consistently, without to skip the signal
if the last trade was a profitable trade, as in the
original turtle system. The relations (3.2) can
be traded each time when the conditions give
us a true buy or sell signal. With a proper
optimization for ξ and φ, the M interval can be
also considered a parameter specific to each
market. And more than that, it was found that
running the trading signals given by (3.2) can
be also made with good results for different
timeframe than the daily interval. The signals
can also be optimized for four hours
Informatica Economică vol. 23, no. 2/2019 29
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timeframe (4H) or for hourly timeframe if the
trades are made in markets with strong
liquidity and the target is small. Decreasing
the time interval lower than 4H timeframe can
imply a significant growth of the drawdown,
but the 4H interval can give in some cases
even better results than the daily interval for
some markets. Trading results will be
presented in the next chapter considering all
these improvements.
The PCY function used to build the modified
Turtle signals in (3.2) has also a functional
parameter that can be optimized in order to
improve the results. This parameter is the
period considered to build the cyclicality
function. More considerations about it can be
found in the author source [6]. The signals
(3.2) can be used for both AT and HFT.
3.2 The Power of the Trend
Trading the signals (3.2) will give us good
results in most of the cases especially for HFT
with a small profit target. However, there are
cases when the signal can open a losing trade
even for s very small profit target. These cases
are related to the situations when the price
exceeds the maximum level but the trend is
not strong enough to continue the movement.
A reversed price continuation will occur and
the trade will generate a loss. A case like this
is presented in Figure 3.1.
Fig. 3.1. Turtle signals on strong and weak trends.
As we can see in Figure 3.1, the first Turtle
signal occurs in a strong trend and the trades
were profitable. In the second situation, the
trend was weak and the trades produced
losses. Not the amplitude of the price
movement can indicate if the price trend is
strong or weak. It was found that can be found
strong local price movements in a weak trend.
It was found also statistically that a good
Turtle signal can be also followed by another
good and strong trend, the measure to skip the
next signal if the last trade was profitable is
not a productive measure in AT and HFT.
In Figure 3.1. it is presented the “Price
Prediction Line” [7], which is a trend line built
using a trigonometric interpolation. More
details about how to compute the PPL
together with code samples are presented in
[8]. As it is presented in the author paper, the
gradient of this line is a good indicator of the
power of the trend. A high distance between
two consecutive points of the price prediction
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(PP) line indicates a strong trend. A small
difference between two consecutive points of
the PP line will indicate a weak trend. This can
give us the possibility to make additional limit
conditions in order to filter the trading signals.
With this filter, the trading signals will be:
 
 
1
1
iiik
Mi
ik
ii
iiik
Mi
ik
ii
PPPPPCYLowMinpSellSignal
PPPPPCYHighMaxpBuySignal
(3.3)
where δ is the minimum gradient of the PP
line for the trend is considered strong enough
in order to initiate a new trade. The measure
of δ is a functional parameter that can be
optimized for each market.
3.3 Two days channel
A particular form of the modified Turtle
trading signals presented in subsection 3.1. is
obtained for the case when the price makes a
particular pattern. It was found that when the
yesterday high did not exceed the previous
day high and the yesterday low is higher the
previous day low and the current price level
exceeds the last two days high, the trading
signals can give significant results. In these
situations, the buy trading signal given by
(3.3) can be rewritten as:
 
   
12
2121
iiiii
iiiii PPPPPCYHighp
LowLowHighHighBuySignal
(3.4)
It was found that the trading signals given by
relation (3.4) can be also built with good re-
sults for 4H timeframe, not only for daily in-
tervals. The sell signal can also be built simi-
larly with (4) for those markets where short
trades can be considered.
3.4 Three days channel
It was found that extending the (3.4) relation
for an interval of three days we can obtain a
significant return. For this case the trading
signal can be automatically built with the
formula:
 
   
 
1
33231
3231
iii
iiiiii
iiiii
PPPPPCY
HighpLowLowLowLow
HighHighHighHighBuySignal
(3.5)
The parameters ξ and δ can be also optimized
for good results using daily and four hours
timeframes. The formula (3.5) can be also
extended for more days intervals, but this case
is not so numerous.
3.5 The limit of the price
The relations (3.3), (3.4) and (3.5) can be used
with good results for AT and HFT. For HFT
where the profit target is close, the signals can
generate a significantly high number of trades.
For HFT an additional condition must be im-
posed in order to avoid opening trades on a
much higher price level. It was found that us-
ing a limit condition for the price not to exceed
a specified distance from the PP is a good and
functional solution. With the additional condi-
tion, the HFT signals can be adapted starting
from the previous signals as:
(3.6)
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where λ is a functional parameter that can be
optimized for each traded market. For HFT
the parameter λ will permit to automate the
process of waiting for a better price level in
order to make the next trade in HFT. Because
the target in HFT is small, the λ parameter will
assure that the price is close enough to the PP
line in order to complete the target until the
next new local maximum point. Trading re-
sults with all these signals will be presented
below. For HFT the buy signals (3.6) can also
be compbined with the Fisher function limit
conditions. Additional information about
computational models and trading signals us-
ing Fisher function for AT and HFT can be
found in [9].
4 Trading results
In this section, we will see trading results
obtained with the signals presented above.
These results were obtained using
TheDaxTrader [10], an automated trading
system that uses modified Turtle trading
signals in order to generate buy trades for
Frankfurt Stock Exchange Deutscher
Aktienindex DAX30 [11].
The results presented in table 1. were obtained
for HFT of DAX30 the period 01.06.2015
30.06.2018 using a fixed target of 10 points
for each trade. The DAX30 index market was
traded as a contract for differences (CFD)
with a spread of 1 point. The exposed capital
involved and the risk management were made
using the “Global Slot Loss Method” [12].
The modified Turtle trading signals were built
for daily and four hours timeframe interval.
An additional condition was imposed regard-
ing the hourly intervals of the executed trades
between 8:00 and 16:00 coordinated universal
time (UTC) in order to ensure the liquidity on
the market. In table 1. are presented the trad-
ing results for cyclicality limit ξ =99.9, power
of the price trend δ=5 and the limit price λ=10.
The trading signals (3.3) were optimized for
M=5 in the daily timeframe and for M=10 in
the H4 timeframe. The signals were repeated
one time in four hours. For the trading signals
(3.4) and (3.5) the signals were repeated one
time per one minute. In all trading process,
only one opened trade was accepted at a time.
Table 1. Trading results of different breakout strategies with additional limit conditions
Trading signal
and timeframe
Number
of trades
Profit
Drawdown
Risk to
reward ratio
(3.4)+(3.6) M=2 D1
132
19,574
3,687
1:5.31
(3.5)+(3.6) M=3 D1
7
1,061
388
1:2.73
(3.3)+(3.6) M=5 D1
64
9,269
2,890
1:3.21
(3.3)+(3.6) M=10 H4
67
9,764
2,888
1:3.38
All above signals to-
gether
150
22,302
3,693
1:6.03
For all modified Turtle signal presented, good
optimization for the parameter set can assure
a positive income with a reasonable risk to re-
ward ratio (RRR). The lowest capital expo-
sure is obtained for the signals made with (3.5)
and (3.6). The best individual RRR was ob-
tained using (3.4) and (3.6) but all signals
traded together produced a RRR of 1:6.03 in a
period of 30 months. The capital evolution in
this interval trading all modified Turtle signals
with HFT is presented in Figure 4.1.
32 Informatica Economică vol. 20, no. 1/2016
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Fig. 4.1. Capital evolution due to the trades made by modified Turtle signals
5 Conclusions
The breakout turtle trading system can be
adapted for AT and HFT in ET for today’s
markets.
The first improvement must be made in order
to avoid the overbought and oversold price
intervals. For this purpose, we used the price
cyclicality function [6]. The second
improvement must be made in order to avoid
opening trade in weak price trends. For this
second purpose, we used the price prediction
line [7] in order to measure the trend power
and to limit the trading signal.
With all these conditions, the modified Turtle
trading signal can produce a significant
number of trades with positive profit
expectancy. The new trading methodology
can be optimized based on some functional
parameters in order to be traded on different
timeframe intervals. A different number of
days can be used than the original Turtle
system, in order to increase the number of
trades and to grow the trading efficiency.
The modified Turtle trading signals were
traded for 5 days interval and 10 intervals of
H4 with good returns. A particular form of the
modified Turtle signals was found using two
days interval when yesterday high and low are
lower respectively higher than the days before
high and low. This particular trading signal
generated the highest number of trades with a
RRR of 1:5.03. All presented trading signals
traded together generated a RRR of 1:6.03.
Starting these results it can be said that the
modified Turtle trading signals are reliable for
AT and HFT.
The optimization process of the functional
parameters of the trading signals presented
can be made using a time price series of the
historical price for any market with good
liquidity. These signals can be also optimized
for AT with longer profit target for automated
trading or investment systems.
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on Fisher Transform for algorithmic Trad-
ing. Timișoara, Romania: Timisoara Jour-
nal of Economic and Business, Vol. 11, Is-
sue 1:2018. ISSN: 2286-0991. West Uni-
versity of Timișoara. DOI: 10.2478/tjeb-
2018-0006 Available at: https://tjeb.ro
[10] C. Păuna, TheDaxTrader. Automated
trading system, 2010. Online software
presentation. Available at:
https://pauna.biz/thedaxtrader
[11] Börse, Frankfurt Stock Exchange
Deutsche Aktienindex DAX30 Compo-
nents, 2018. Available at: http://www.bo-
erse-frankfurt.de/index/dax
[12] C. Păuna, Capital and Risk Manage-
ment for Automated Trading Systems,
Iași, Romania: Proceedings of the 17th In-
ternational Conference on Informatics in
Economy, 2018, pp 183-188. Alexandru
Ioan Cuza University. Available at:
https://pauna.biz/ideas
Cristian PĂUNA graduated the Faculty of Cybernetics, Statistics and
Economic Informatics of the Bucharest Academy of Economic Studies in 1999
and he is also a graduate of the Aircraft Faculty from the Bucharest Polytechnic
University in 1995. He got the title of Master of Science in Special Aerospace
Engineering in 1996. In the last decades, he had a sustained activity in the
software development industry, especially applied in the financial investment
domain. Based on several original mathematical algorithms, he is the author of several
automated trading software for capital markets. At present, he is the Research and Development
Manager of Algorithm Invest company and he is involved as a Ph.D. student in the Economic
Informatics Doctoral School of the Bucharest Academy of Economic Studies.
... A particular approach for risk management techniques that can be used in automated decision-making systems for capital investments can be found in (Vince, 1992). Mathematical models especially designed and optimized for algorithmic trading with proved and sustained results in real capital investments can be found in (Păuna & Lungu, 2018), (Păuna, 2018a), (Păuna, 2018b), (Păuna, 2018c), (Păuna, 2019a), (Păuna, 2019b), (Păuna, 2019c), (Păuna, 2019d), (Păuna, 2019e), (Păuna, 2019f), and (Păuna, 2020). ...
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Capital investment is a sustained activity nowadays. After the worldwide release of the electronic trading systems, automated decision-making investment software is the new trend in financial speculation. A significant part of capital trading is fully computerized today. The buying and selling orders are made and sent automatically, almost in real-time. The price evolution is analyzed by servers using advanced mathematical algorithms. This paper will present one of these models named Price Probability Predictor. It is a method to build a probability field based on the price history and the real-time price action. The revealed function will generate the current probability of a price growth in the next time intervals. Automated entry and exit signals and market limit conditions will be built using the new indicator, in order to automate the whole investment process. Capital investment results will also be included in the current paper to qualify the presented trading methodology and to compare it with other similar models. In conclusion, it was found that the Price Probability Predictor is a reliable mathematical algorithm that can assist any trading decisions, in both ways, manual or automatic capital investments.
... For the currency and commodity markets, reliable trading models that can be automated can be found in [8], [9], and [10]. Original investment models and methodologies especially optimized for automated capital investment software can be found in [11], [12], [13], [14], [15], and [16]. Essential psychological strategies that can be used for better adaptation to the context of actual markets can be found in [17], [18], and [19]. ...
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ABSTRACT Algorithmic capital investment procedures became the essential tools to make a profit in the volatile price markets of the 21st century. A large number of market participants, private traders, companies, or investment funds are buying and selling on thousands of markets every day to make a profit. After the 2010 year, algorithmic trading systems became a significant part of the capital investment environment. The price evolution is analyzed today in real-time by powerful computers. To buy cheap and to sell more expensive is a simple idea, but to put it on practice is not easy today in very volatile price markets. The orders are built and set almost instantly today by artificial intelligence software using special mathematical algorithms. These procedures automatically decide the best moments to buy and to sell on different financial markets depending on the price real-time movements. This paper will present a specific methodology to analyze the time price series of any capital market. The model will build reliable trading signals to enter and to exit the market to make a profit. The presented method uses trigonometric interpolation of the price evolution to build a significant trend line called here the Trigonometric Trend Line. It will be mathematically proved that this function is in a positive and direct correlation with the price evolution. The Trigonometric Trend Line will be used to build and automate capital investment signals. Besides, the introduced function will be used in order to qualify the actual price trend and to measure the trend power in order to decide if the price makes an important evolution or not. Limit conditions will be imposed in the financial market to avoid trading in non-significant price movement and to reduce the risk and capital exposure. Comparative trading results obtained with the presented methodology will be included in the last part of this paper to qualify the model. Each trading signal type presented in the paper was traded separately to have a qualitative image. Also, all capital trading signals built with the Trigonometric Trend Line were traded together in order to obtain a better risk to reward ratio. To classify the presented methodology, the presented results were compared with real trading profits obtained with the other three well-known capital investment strategies. With all of these, it was found that using the Trigonometric Trend Line reliable automated trading procedures can 7 th International Symposium "SOCIO-ECONOMIC ECOSYSTEMS " January 22-24, 2020 University of Alicante , Spain Please send to: abstract-submission@bslab-symposium.net be made and optimized for each financial market to obtain good results in the capital investment. Being exclusively a mathematical model, the Trigonometric Trend Line methodology presented in this paper can be applied with good results for any algorithmic trading and high-frequency trading software. The functional parameters can be optimized for each capital market and for each timeframe used in order to optimize the capital efficiency and to reduce the risk. The optimization methods will use the historical time price series in order to catch the price behavior and specificity of each market. The reduced number of parameters and the simplicity of the presented method recommend the Trigonometric Trend Line model to be used in any advanced algorithmic trading software.
... 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]. ...
Conference Paper
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In the first decades of the 21st century, in the electronic trading environment, algorithmic capital investments became the primary tool to make a profit by speculations in financial markets. A significant number of traders, private or institutional investors are participating in the capital markets every day using automated algorithms. The autonomous trading software is today a considerable part in the business intelligence system of any modern financial activity. The trading decisions and orders are made automatically by computers using different mathematical models. This paper will present one of these models called Price Prediction Line. A mathematical algorithm will be revealed to build a reliable trend line, which is the base for limit conditions and automated investment signals, the core for a computerized investment system. The paper will guide how to apply these tools to generate entry and exit investment signals, limit conditions to build a mathematical filter for the investment opportunities, and the methodology to integrate all of these in automated investment software. The paper will also present trading results obtained for the leading German financial market index with the presented methods to analyze and to compare different automated investment algorithms. It was found that a specific mathematical algorithm can be optimized and integrated into an automated trading system with good and sustained results for the leading German Market. Investment results will be compared in order to qualify the presented model. In conclusion, a 1:6.12 risk was obtained to reward ratio applying the trigonometric method to the DAX Deutscher Aktienindex on 24 months investment. These results are superior to those obtained with other similar models as this paper reveal. The general idea sustained by this paper is that the Price Prediction Line model presented is a reliable capital investment methodology that can be successfully applied to build an automated investment system with excellent results.
... 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]. ...
Article
Full-text available
In the first decades of the 21st century, in the electronic trading environment, algorithmic capital investments became the primary tool to make a profit by speculations in financial markets. A significant number of traders, private or institutional investors are participating in the capital markets every day using automated algorithms. The autonomous trading software is today a considerable part in the business intelligence system of any modern financial activity. The trading decisions and orders are made automatically by computers using different mathematical models. This paper will present one of these models called Price Prediction Line. A mathematical algorithm will be revealed to build a reliable trend line, which is the base for limit conditions and automated investment signals, the core for a computerized investment system. The paper will guide how to apply these tools to generate entry and exit investment signals, limit conditions to build a mathematical filter for the investment opportunities, and the methodology to integrate all of these in automated investment software. The paper will also present trading results obtained for the leading German financial market index with the presented methods to analyze and to compare different automated investment algorithms. It was found that a specific mathematical algorithm can be optimized and integrated into an automated trading system with good and sustained results for the leading German Market. Investment results will be compared in order to qualify the presented model. In conclusion, a 1:6.12 risk was obtained to reward ratio applying the trigonometric method to the DAX Deutscher Aktienindex on 24 months investment. These results are superior to those obtained with other similar models as this paper reveal. The general idea sustained by this paper is that the Price Prediction Line model presented is a reliable capital investment methodology that can be successfully applied to build an automated investment system with excellent results.
Thesis
Full-text available
After several attempts to publish my Ph.D. thesis with different prestigious publishers, I have decided to make this work public and free of charge for anyone. Enjoy! Cristian Păuna
Chapter
Capital investment is a sustained activity nowadays. After the worldwide release of the electronic trading systems, automated decision-making investment software is the new trend in financial speculation. A significant part of capital trading is fully computerized today. The buying and selling orders are made and sent automatically, almost in real-time. The price evolution is analyzed by servers using advanced mathematical algorithms. This chapter will present one of these models named Price Probability Predictor. It is a method to build a probability field based on the price history and the real-time price action. The revealed function will generate the current probability of a price growth in the next time intervals. Automated entry and exit signals and market limit conditions will be built using the new indicator, in order to automate the whole investment process. Capital investment results will also be included in the current paper to qualify the presented trading methodology and to compare it with other similar models. In conclusion, it was found that the Price Probability Predictor is a reliable mathematical algorithm that can assist any trading decisions, in both ways, manual or automatic capital investments.
Conference Paper
Full-text available
Using automated capital investment software systems is a common task today. At the beginning of the third millennium, modern investors are using artificial intelligence resources and methods to find the best investment opportunities on capital markets and to process the trading orders. One of the most important aspects of this activity, besides the buying and selling decisions, is to stay away from the market risk in specific conditions. For this purpose, in the current doctoral research, the notion of limit conditions in capital markets was introduced by the authors. On the high price volatility markets, when the economic or geopolitical background is changing fast, real-time decisions for earlier investment closing, or filtering decision not to open new positions in specific market states, will contribute together to the risk reduction and will provide a higher capital efficiency a the long time run. In the real-time investment software systems, the limit conditions method's implementation presumes particular aspects in order not to introduce additional time delays for the trading orders. This paper will present the way how to include additional limit conditions procedures into automated algorithmic trading software systems. It was found that any investment strategy can be improved by using the limit conditions methods presented in this paper. Based on particular data-mining methods applied to real-time price series of any market, these methods can be automated and included in any capital investment informatics systems in order to improve the results and to reduce the allocated capital risk.
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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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Trading the financial markets is a common idea nowadays. Millions of market participants, individuals, companies or public funds are buying and selling different equities in order to obtain profit from the buy and sell price difference. Once the equity was established, the main question marks are when to buy, when to sell and how long to keep the opened positions. This paper will present a mathematical model for the cyclicality of the price evolution. The model can be applied for any equity in any financial market, using any timeframe. The method will gives us information about when is good to buy and when is better to sell. The price cyclicality model is also a method to establish when the price is approaching to change its behavior in order to build limit conditions to stay away the market and to minimize the risk. The fundamental news is already included in the price behavior. Being exclusively a mathematical model based on the price evolution, this method can be easily implemented in algorithmic trading. The paper will also reveal how the cyclicality model can be applied in automated trading systems and will present comparative results obtained in real-time trading environment.
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After the introduction of the electronic execution systems in all main stock exchanges in the world, the role of the automated trading software in the business intelligence systems of any financial or investment company became significant. Designing of reliable trading software to build and send automated orders based on quantitative mathematical models applied in the historical and real-time price data is a challenge for nowadays. Algorithmic trading and high-frequency trading engines become today a relevant part of any trading system and their specific characteristics related with the fast execution trading process and capital management involves specific measures to be used. Smart integration of the trading software in the business intelligence systems is also a sensitive theme for any financial and investment activity, a plenty of functional, control and execution issues being subjects of researches for future improvements. This paper wants to gather together more particular aspects on this subject, based on the experience of last years, opening the way for future topics.
The Original Turtle Trading Rules. Fighting the Scams, Frauds and Charlatans
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C. M. Faith, 'The Original Turtle Trading Rules. Fighting the Scams, Frauds and Charlatans', 2003. Available at: http://originalturtles.org/turtlerules.pdf
Way of the Turtle. The Secret Methods that Turned Ordinary People into legendary Traders
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C. M. Faith, 'Way of the Turtle. The Secret Methods that Turned Ordinary People into legendary Traders', McGraw-Hill, 2007 ISBN: 978-0-07-148664-4, pp. XX
Trend Detection with Trigonometric Interpolation for Algorithmic Trading, under final review at Scientific Annals of economics and Business
  • C Păuna
C. Păuna, (2018), Trend Detection with Trigonometric Interpolation for Algorithmic Trading, under final review at Scientific Annals of economics and Business, ISSN: 2501-3165
Online software presentation
  • C Păuna
C. Păuna, TheDaxTrader. Automated trading system, 2010. Online software presentation. Available at: https://pauna.biz/thedaxtrader
Frankfurt Stock Exchange Deutsche Aktienindex DAX30 Components
  • Börse
Börse, Frankfurt Stock Exchange Deutsche Aktienindex DAX30 Components, 2018. Available at: http://www.boerse-frankfurt.de/index/dax
Capital and Risk Management for Automated Trading Systems
  • C Păuna
C. Păuna, Capital and Risk Management for Automated Trading Systems, Iași, Romania: Proceedings of the 17th International Conference on Informatics in Economy, 2018, pp 183-188. Alexandru Ioan Cuza University. Available at: https://pauna.biz/ideas