VOLUME CYCLICALITY. RELIABLE CAPITAL INVESTMENT SIGNALS BASED ON TRADING VOLUME INFORMATION

Abstract

Capital investment is a sustained activity nowadays. The buy and sell decisions are usually made in technical analysis using the price quote evolution in time. Another useful information provided by any stock exchange is the trading volume for each time interval. The volume information is usually hard to be included in a trading or investment strategy, having an unstable and discontinued evolution in time. Some obsolete ideas indicate a favorable entry period after a maximal traded volume value interval, but today, on the high price volatility markets, when a maximal value is detected, usually is too late for a convenient price entry on that market. This paper presents a mathematical model specially designed for fast and instant market entry decisions based only on the traded volume information. It was found that even the traded volume variation in time is discontinued, a cyclical phenomenon is present in all markets. With the proper mathematical method, the Volume Cyclicality function can be computed in real-time in order to build reliable capital investment signals. The model presented in this paper fills an essential gap in the literature, and it was tested for more than ten years on the most important stock exchanges in the world. Investment results are also included in this paper to prove the efficiency and utility of the presented method. The Volume Cyclicality function is an exclusively mathematical model, and it can be applied in any automated investment software system to improve capital efficiency.

Full text

Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31 -44
VOLUME CYCLICALITY.
RELIABLE CAPITAL INVESTMENT SIGNALS BASED ON
TRADING VOLUME INFORMATION
Cristian PĂUNA¹
DOI: 10.2478/tjeb-2020-0003
Capital investment is a sustained activity nowadays. The
buy and sell decisions are usually made in technical
analysis using the price quote evolution in time. Another
useful information provided by any stock exchange is the
trading volume for each time interval. The volume
information is usually hard to be included in a trading or
investment strategy, having an unstable and discontinued
evolution in time. Some obsolete ideas indicate a
favorable entry period after a maximal traded volume
value interval, but today, on the high price volatility
markets, when a maximal value is detected, usually is too
late for a convenient price entry on that market. This paper
presents a mathematical model specially designed for fast
and instant market entry decisions based only on the
traded volume information. It was found that even the
traded volume variation in time is discontinued, a cyclical
phenomenon is present in all markets. With the proper
mathematical method, the Volume Cyclicality function can
be computed in real-time in order to build reliable capital
investment signals. The model presented in this paper fills
an essential gap in the literature, and it was tested for
more than ten years on the most important stock
exchanges in the world. Investment results are also
included in this paper to prove the efficiency and utility of
the presented method. The Volume Cyclicality function is
an exclusively mathematical model, and it can be applied
in any automated investment software system to improve
capital efficiency.
Keywords:
Capital investment, Technical analysis, Trading volume, Volume cyclicality, Trading strategy,
Algorithmic trading
JEL Classification:
M15, O16, G23, M21
1 Economic Informatics Doctoral School, Academy of Economic Studies, Bucharest, Romania

DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
32
1. Introduction
Financial trading and capital investment are everyday activities nowadays. With the single
purpose of making a profit, millions of individuals or companies are participating every day in
the free markets. The buy and sell decisions are usually founded on the technical analysis of
the time price evolution. A considerable number of strategies to analyze the price action are
published in the specialized literature. This paper will treat a less discussed and developed
subject, and this is about how to build a reliable investment decision based on the trading
volume information.
Any stock exchange is providing today the real-time price quotes, and the trading volume on
a specific time interval. Both are valuable pieces of information that can be used to build a
buy or sell decision. The trading volume is “the number of shares exchanged between buyers
and sellers during a given period of time, typically a day.” (Dormeier, 2011) The trading
volume information is less used in common algorithmic trading strategies. The main reason
is that the variation of the traded volume in time is a discontinued and unstable function.
This fact can be easily seen in figure 1. Under the price graph of the DAX30 Frankfurt Stock
Exchange Deutscher Aktienindex daily price evolution, the trading volume for each day is
plotted. As can be seen, there are days with a higher traded volume and days when the
investment appetite decreases, without any rule or significant trend.
The question this paper will answer to is how to use the traded volume information to build
reliable investment decisions and how to combine trading volume with price evolution to
increase investment capital efficiency. A new function will be introduced: Volume Cyclicality
function (VOC), which is computed using only the traded volume information, without any
dependence with the price quotes. The general study of the cyclic behavior of any time-
evolving phenomena is essential, giving us the possibility to find the minimal and maximal
points in real-time and clearly define the ascending and descending periods. In this way,
important decisions can be made based on cyclical behavior over time. This research has
found that the Volume Cyclicality function has a significant correlation with the price
evolution, and it can be used with outstanding results to include the volume information in
trading and investment decision strategies and to build buying and selling signals depending
on the trading volume information. The importance of the Volume Cyclicality function analysis
is highlighted by the results obtained in a joint study with the Price cyclicality function. These
two functions can significantly improve the performance of any trading or investment strategy
to increase capital efficiency.

DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
33
Figure 1. Volume, average volume, and Volume Cyclicality function for DAX30 Index.
2. Literature review
In 3087 trading books and 2811 published articles about technical analysis, strategies, and
algorithmic trading studied to write a literature review, no paper is presenting a mathematical
model to study the cyclic behavior of the trading volume. The present paper fills this important
gap.
In the literature, many investments or trading strategies “involve investigating patterns based
on historical trading data (past price data and trading volume) to forecast the future
movement of individual stocks or the market as a whole.” (Focardi & Fabozzi, 2004) However,
many found strategies do not include the trading volume information accurately. Usually, the
volume is linked with a price evolution pattern that conducts an entry decision if the traded
volume is growing up, thinking that many other investors are making the same decision in
that interval. “A huge pickup in volume can propel the stock into its next trading range.”
(Shkolnik, 2003) On a price market bottom interval, “a high-volume spike often occurs.”
(Appel, 2005) “Volume confirms the trend.” (Monte & Swope, 2008)

DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
34
Some authors link a decreased trading volume to an up-pricing movement by a bear long time
trend, once the investors seeing the weakness “will not be participating in the current up-
move.” (Williams, 2005). Some strategies are using a moving average of the trading volume,
transforming in this way the discontinued volume function into a more convenient evolution.
No author can identify the idea of using volume averages instead of the nominal value of the
traded volume. Some authors recommend empirical relations between volume, price, and
trading decisions, as can be found in (Chordia, Roll & Subrahmanyam, 1998).
Other authors indicate a proper market entry when “the volume trend diminishes over time
until the breakout.” (Bulkowski, 2005) A receding trading volume trend can signify that the
majority of investors have already entered that market, and a significant movement is likely
to come. A different approach is presented in (Barclay & Hendershott, 2003) analyzing the
low trading volume after hours, and considering as a significant signal the measure of the
traded volume of US stocks listed on foreign exchanges outside the US, stocks that are traded
outside the regular trading hours of the major US stock exchanges. An intraday analysis of
the intraday trading volume is also made (Chan, Chockalingam & Lai, 2000). Other authors
are studying the idea to link the trading volume of specific time intervals, a particular day of
the week, or weekend as in (Brooks, 1997). Other authors link the trading volume patterns
with specific hour intervals to fundament a trading decision (Foster & Viswanathan, 1993).
Analyzing the trading volume information is a sustained criterion for an investment portfolio
selection. In the stock market, the high volume criteria are well considered by the
professionals. “Where there is volume, there will be trends.” (Pruitt & Hill, 2003) “By analyzing
trading volume, a technician could more easily detect whether a price movement represented
true commitment.” (Dormeier, 2011) In commodities markets, there is a “positive relationship
between the trading volume of the large hedge funds and market volatility” (Gregoriou,
Karavas, Lhabitant & Rouah, 2004). On the long-term profitability, the volume information
seems to be a strong criterion. “Markets nearly always behave better technically when they
are moving on higher volume. The lower the volume, the more unpredictable they become
because it does not take as much volume.” (Norris & Gaskill, 2011)
The trading volume information can also be used to fundament an exit decision. Some
authors indicate to build an exit decision after a maximal volume interval, considering that
many other investors are closing their investments in that specific interval for a particular and
right reason. “Trading volume decreases as the (wedge) formation develops. This is an
important condition because declining volume during up trends suggests a reduction in
buying pressures.” (Appel, 2005). An exit decision can be made “when volatility suddenly
expands on high volume after a sustained trend.” (Katz & McCormick, 2000)

DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
35
The general idea is that the trading volume is essential information provided by the stock
exchange that must be included in the trading or investment decisions to improve capital
efficiency. The question is, how? Very disappointing answers to this question can be found in
the literature papers using terms as <after an unprecedented volume value>, <proper trading
volume value>, or <not enough volume> without presenting any substantial or coherent
measurement method or a mathematical approach for trading volume information usage.
Intentionally the citations of these terms were excluded from this paper. How to analyze the
volume information in real-time? How to include this data into reliable investment decisions?
How to integrate the trading volume information in algorithmic trading strategies? And how
to automate a trading decision based on the trading volume information? All of these are
questions this paper will answer.
3. Volume Cyclicality
There is a trading volume cyclicality in time in any market. This is the main hypothesis of this
paper that will be confirmed or not by the results. By cyclicality, we understand that periods
with increasing and decreasing volume values can be clearly identified. On a low volume
values market, with the proper market conditions changes, more and more investors will add
orders to the market, and the trading volume will be increased. Based on this natural human
behavior, the market will begin to evolve with higher prices that will also attract more
investors. This will conduct to a time period with a higher volume values on average, even the
volume value from one day to another will also be discontinued and unstable. After a time
when the market is evolving well, the current trend usually meets some maximal points
accompanied by maximal trading volume values. Depending on the market conditions or on
the economic or geopolitical news, the investor's appetite can be changed. Once the investors
start to know that the market made a maximal point, in lack of positive news or in the
presence of negative news, the traded volume starts to decrease, once that market becomes
less attractive. A decreasing investment enthusiasm will produce a descending trading
volume period for the market. After a while, once the negative economic factors are solved,
positive aspects will increase the investment attractiveness for the market again, and the
cycle will be repeated.
This paper proposes a mathematical model that can be used to analyze the volume cyclicality.
An analytical function will be built in order to transform the unstable volume function into a
continuous function with a cyclical behavior. This function will be in direct correlation with the
trading volume values and will permit us to analyze the volume change. Minimal and maximal
points will be clearly identified, and the analysis of ascending and descending periods of the
Volume Cyclicality function will allow us in a precise manner to include the volume information
into the trading decisions. Moreover, the introduced function can be computed in real-time
and can be implemented in any automatic capital investment software system.

DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
36
A reliable mathematical model to study the cyclical behavior of the price market was
introduced in (Păuna & Lungu, 2018). This paper will apply the same model for trading volume
information. The first step to build the volume cyclicality function is to use two moving
averages of the trading volume. We will note with i
M
and i
m
the series values of two moving
averages of trading volume, with different periods
P
and
p
. The index i denotes the time
interval. If the
P
is the period of
i
M
, and
p
is the period of
i
m
, and
pP >
, than, on an
ascending period of the trading volume, we will have
i
i
m
M<
. On a descending volume
period, the high period moving average we will have
ii
mM >
.
The cyclical behavior of the trading volume can be assessed if we analyze the evolution of the
two moving averages above. To do that, we will use a specific mathematical conform
transformation between the normal trading volume space and a particular space limited into
the interval [0;1]. On a specific n number of time intervals, the maximal and minimal distance
between the two moving averages can be computed using:
( )
ii
n
i
ik
i
mMmin −=
−
=
min
and
( )
ii
ni
ik
imMmax −=
−
=
max
(1)
The transformation mentioned above is built using:
ii
ii
i
minmax
max
−
−
=∆
ξ
where
iii
mM −=
ξ
(2)
In order to build the function that will describe the Volume Cyclicality, we will use a first-order
Spline functions (Berbente, Mitran & Zancu, 1997) given by:
( )
11 −−
+−∆=
iiii
VOCVOCVOC
α
where
0
0=VOC
(3)
The Volume Cyclicality function obtained with formulas (1), (2), and (3) for
10=n
,
10=
p
,
30=P
, and
33.0=
α
is drawn in figure 1.C. The functional parameter α determines the
gradient of the VOC function, and can be optimized for each traded market. In figure 1.B.,
over the volume function drawn with bars is represented the moving average of trading
volume with period
10=p
.

DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
37
As can be seen in figure 1, the Volume Cyclicality function is a periodic one. This fact confirms
the hypothesis made, according to that the trading volume has a cyclical behavior. The VOC
function has minimal and maximal points and clear ascending and descending periods, and
it is computed using only the volume information. The price quotes are not used in this model.
The parameter values used above are, of course, an example. The VOC function can be built
for any market with the proper parameters set in order to obtain the maximal efficiency and
the minimally involved risk. The optimal parameter set can be found for each case using the
historical volume series of the traded market and an optimization method. The author uses
the gradient method (Berbente, Mitran & Zancu, 1997) to complete this step.
An important note about the VOC function is that the model can be built using the trading
volume of any time period. In figure 1 is represented the Volume Cycaliclity using the daily
time volume series, but i
M
and
i
m
moving averages can be computed using the volume
values for other intervals. Relevant studies can be found using one-hour (H1), four-hours (H4),
and even one-week (W1) volume series data. In these cases, the VOC function is given by
unchanged formulas (1), (2), and (3).
The cyclicality of the VOC function has different analysis criteria than PCY function (Price
Cycaliclity Function). An increasing VOC period will determine a strong price evolution, but this
is not meaning that the price will go up. Also, a descending price trend can be accompanied
by an ascending VOC period. Usually, the VOC is ascending when more participants are joining
the markets, and more buy and sell orders are substantially increasing the trading volume. A
descending period of the VOC function denotes a small investment interest.
After a stable price trend, a maximal VOC point can indicate a change in investor behavior.
That can be assimilated with an exit opportunity. Moreover, after a descending VOC period, a
minimal point will occur. This will indicate an increase in the investors' interest in the current
market and can be confirmed with a low-risk entry signal. Usually, after a minimal VOC point,
a new trend is defined, a pattern that can also exist in both directions (upward or downward).
A particular interest is shown for a special pattern of thinking from the investment point of
view. After a price downward trend, any investor searches for an answer to the question when
that trend is over, and the price will be bottom out. The VOC function gives us this information
in an exact manner. After a clear price downward trend the VOC function will make a minimal
point and will start to ascend. That is one of the lowest risk signals that can be found.
Investment results will be presented in the next section.

DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
38
Figure 1 presents the evolution of the DAX30 index during the pandemic Coronavirus crisis in
2020. This choice is not accidental. The DAX30 decreased as never before in history, by
42.24%, from the maximal 13796 Euro on 17th February 2020 to the minimal value of 7968
Euro on 19th March 2020. During this unprecedented crash, any investor asks the question
of when the market will stop falling and start to recover, and when it will be a safe point to
start to buy. This moment is clearly defined by the Volume Cycaliclity function in figure 1. On
6th April 2020, the VOC function starts to ascend, and the market begins to recover,
confirmed by the future evolution. Remember that the VOC function is built only based on the
volume information; the price quotes are not included in the VOC computation formulas.
The Volume Cyclicality function is tested by the author starting with December 2010 on all
equities included in the most important stock exchanges in the world: Frankfurt Stock
Exchange 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), NASDAQ Index (NASDAQ100),
Standard & Poor’s Index (S&P500), and Small Capitalization US Index (Russell2000). A
clustering method in time price series was used in two parallel ways for this purpose. In the
first case, a cross-validation optimization method was tested with the historical price series
of all mentioned stock exchanges. After the clustering validation, a real capital test was
performed using periods of two months back in the time price series to generate real
investment signals for one month further. All results obtained in the above capital markets
are similar to the results presented in this paper. The Volume Cyclicality Method has been
included in live trading since August 2011 through DaxTrader (Păuna, 2010) software
included in theServer automated capital investment system.
Computing the Pearson correlation coefficient (Andrei, 2003) for all these markets, it was
found that there is a strong and direct correlation between the minimal points of the VOC
function and a stable and precise price movement in the ascending interval of the VOC
function. The values of the computed correlation coefficient are situated between 0.712 and
0.862 for the study made on the 4-hours timeframe, and between 0.833 and 0.951 in the
study processed with the daily timeframe data series. The results indicate a strong correlation
that can be successfully used to build reliable capital investment signals, as it will be
presented in the next section.
4. Investment signals with Volume Cyclicality
This chapter will answer the question of how to build capital investment signals using the
Volume Cyclicality function? As it was already presented, the logic behind the usage of the
VOC function is based on the idea that in an uncertain period, the investor's interest is

DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
39
decreasing, producing a decrease in the invested volume and, by consequence, a decreasing
period for the VOC function. When proper market conditions appear, the investors will start
to add more and more orders onto the market, producing a volume increase. This fact will
produce a minimal point for the VOC function, a specific point after the VOC evolution will
have an increasing period. With the strong correlation between the minimal point of the VOC
function and the stable evolution of the price in the ascending period, we can build a buy
signal:
() ( )
i
ii
i
iVOCVOC
VOCVOC
BuySignal <
∧>
=−
−− 1
12
(4)
Practically, the signals built with the formula (4) will generate a buy entry in the market after
a minimal VOC point. In the old fashion investments, the entry decision is usually made after
a maximal value of the volume. It was found that many times, after a maximal point of the
volume, the prices can be even lower for a small period of time. Even the minimal values of
the VOC function have a slight lag when we compare with the maximal volume point, and the
practice proved that the entry price using the minimum VOC points, according to the signals
(4) lower than the entries triggered by the maximal volume interval in many cases, this
meaning that the VOC function will generate entries with a lower risk.
An important observation is that the formula (4) defined a BuySignal. We have mentioned
before that after a descending period of the VOC function, depending on the market
conditions, the price will register a stable evolution. This evolution is not necessary to be
considered as price growth. Depending on the fundamental market conditions, the price
quotes can also start a descending trend. The formula (4) was defined as BuySignal thinking
that, after a representative descending price period, a price increase is more probable. On
the analyzed markets mentioned above, the statistics showed us a probability of 1:30
chances as after a descending price trend, a new descending price trend to follow after a
minimal VOC point, built with the daily time price series.
Figure 2 presents the capital evolution due to the signals (4) applied to the Frankfurt
Deutscher Aktienindex DAX30 between 20.04.2019 and 19.04.2020 using the daily time
price series. The trades were executed using DaxEqualizer software included in theServer
automated capital investment system (Păuna, 2010). The risk management was made using
the “Global Stop Loss” method (Păuna, 2018) with a global risk level of 1% of the current
capital.
The signals (4) have generated 149 trades in the period mentioned above, with only five
losing trades. These losing trades were made in those cases when after a descending period
of the VOC function, a descending price trend was met. The entry signals made with (4) were
built with no other price evolution condition. Using only the trading volume information, it was

DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
40
obtained in this case, a risk to reward ratio of 1:2.08, meaning each 1 Euro risk has produced
a profit of 2.08 Euro.
Figure 2: Capital evolution due to buy signals made with Volume Cyclicality
5. Investment signals with Volume Cyclicality and Price Cyclicality
The VOC function does not include information about the price direction; it is computed only
on the trading volume information. The first optimization idea is to combine the signals
provided by the minimal VOC points with some market conditions that will filter only those
cases when the price registers an upward trend. This way, an investment signal will avoid the
cases that produced losses in the example presented in the previous section.
During this time, more price-related conditions are tested to filter the VOC signals. Good
results are obtained using the monotony of an exponential or weighted price moving average
(Cox, 1961) or the Relative Strength Index (Wilder, 1978). Each of these additional price
conditions was filtering the losing trades, but a significant number of winning trades from the
example above were also excluded.
The best solution was found by using the Price Cyclicality function (Păuna & Lungu, 2018). The
ascending periods of the PCY function are in a strong and direct correlation with the price
evolution, as the authors proved in the introduction paper of the Price Cyclicality model.
Combining the ascending periods of the VOC function with the ascending periods of the PCY
function, the signals can be automated using the formula:
( ) ( ) ( )
1112 −−−− >∧<∧>= iiiiiii PCYPCYVOC
VOCVOCVOCBuySignal
(5)
The asymptotic evolution of the PCY function is giving us the possibility to impose additional
conditions in order not to enter in the market near a maximal price level. To avoid these cases,

DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
41
the signals will include a limitation condition, meaning that the PCY function not to exceed a
specific limit value:
( ) ( ) ( ) ( )
ξ
<∧>∧<
∧>
=−−−− PCYPCYPCYVOC
VOCVOC
VOCBuySignal i
i
iiiii 1
112
(6)
Figure 3. Capital evolution due to buy signals made with Volume Cyclicality and Price Cyclicality
In figure 3, is plotted the capital evolution due to the signals (6) applied for DAX30 between
20.04.2019 and 19.04.2020 using the daily time price series and the same traded volumes
as in the case presented in the previous section. As can be observed, the number of trades
is significantly lower. Also, the net profit recorded is lower due to this fact, but the capital
drawdown, in this case, was three times less than the case above. Using the signals made by
formula (6), it was obtained a risk to reward ratio of 1:4.62.
The signals (4), (5), and (6) were written for capital investment systems. On these particular
strategies, after entry on the market is made, the position is kept open a long period of time
until the market conditions dictate an exit decision. The investment strategies make a
reduced number of trades and try to produce a higher profit on each position. The method of
using the trading volume information can also be included in high-frequency trading systems.
These strategies make a significantly higher number of trades and produce a small profit for
each position. The signals (6) especially adapted for high-frequency trading systems will be
built with the formula:
( ) ( ) ( )
ξ
<∧>∧<= −− PCYPCYPCYVOCVOCBuySignal iiiii 11
(7)
A significant improvement can be made imposing an additional limitation condition in the VOC
value. It is well known that, after an extended price trend, when the price is approaching the
maximal values, the volume starts to decrease, a fact that produces a reduction in the VOC
function gradient before the maximal point. To avoid the case to entry in the market when the
volume starts to decrease significantly, the buy signals will be made using the formula:

DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
42
( ) ( ) ( ) ( )
λξ
<∧<∧>∧
<= −− VOCPCYPCYPCYVOC
VOCBuySignal iiii
i11
(8)
The ξ and λ parameters are at the technical analyst disposal. These functional parameters
will be optimized for each traded market using the historical price and volume series to
maximize profitability and to increase capital efficiency. Due to the large market volatility and
fast-changing economic and geopolitical conditions, it was observed that the optimal
parameters are changing for all markets from time to time. A machine-learning procedure
that will adapt the optimal functional parameters periodically to the new market conditions
will significantly improve the results.
Figure 4. Capital evolution made with Volume Cyclicality and Price Cyclicality in high-frequency trading
The results presented in figure 4 are obtained using the trading signals made by formula (8)
in high-frequency trading of DAX30 index between 20.04.2019 and 19.04.2020. Risk
management was the same as in the examples above. The results were obtained using
DaxRazor trading software included in theServer automated capital investment system
(Păuna, 2010). The risk to reward ratio obtained in this case has a remarkable value of
1:7.66. Excluding the commissions, spreads, and taxes paid for all 1575 trades executed,
the net risk to reward ratio obtained has a value of 1:6.82.
The signals presented in this paper can be combined with any exit strategy. The exit decisions
can also include conditions in VOC function values, similarly with those included in the
formula (8). The theory of the exit decisions optimized for each type of market entry is not a
subject of this paper. Still, the right choice for closing the opened trades has a significant
impact on capital efficiency.
6. Conclusions
The trading volume has a periodical evolution in time in all studied markets. The periodicity
is variable in time and can be analyzed using the Volume Cyclicality function introduced in
this paper. This function can be computed in real-time and uses only the trading volume

DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
43
information. The minimal points of the VOC function have particular importance; after a
minimum point, the function is making an ascending interval when the investor's interest is
increased. This will produce an essential and strong price movement compared to the
descending periods of the VOC function. Identifying the minimal point of the VOC function can
provide a reliable capital investment signal to entry in the markets. Once the VOC function
does not include any information about the price direction, the VOC trading conditions can be
assembled together with additional price-related conditions.
The questions raised at the beginning in this paper have been answered: How should the
volume information be analyzed in real-time? By studying the VOC functions periodicity to find
the minimal and maximal points and to define the ascending and descending periods. How
should trading volume information data be included into reliable investment decisions?
Trading volume information is generating the time values of the VOC function, which is used
to build real-time trading signals. How should the trading volume information be integrated in
algorithmic trading strategies? By using VOC function together with PCY function to limit the
functionality of any strategy, as presented. And how should a trading decision be automated
based on the trading volume information? By building signals similarly with those shown in
the 5th section, including the VOC and PCY functions as efficiency filters.
The combination of the Volume Cyclicality and Price Cyclicality functions gives us an
outstanding risk to reward ratio. The volume information can also be included in the high-
frequency trading systems using the ascending periods of the VOC function. The model
presented in this paper can be automated and included in any trading or investment software
system. Also, the Volume Cyclicality function can be used with excellent results for capital
investment decisions made by human analysts.
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DOI: 10.2478/tjeb-2020-0003
PĂUNA C. (2020).
Volume Cyclicality. Reliable capital investment signals based on trading volume information
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2020 | Volume 13 | Issue 1 | Pages: 31–44
44
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