A STUDY OF PROFIT MINING
Yu-Lung Hsieh and Don-Lin Yang
Dept. of Information Engineering and Computer Science, Feng Chia University, No. 100 Wenhwa Road, Taichung, Taiwan
Keywords: Financial data mining, Association rule, Inter-transaction, Profit mining, Risk, Win rate, Trading simulation.
Abstract: In the past decade, association rule mining has been used extensively to discover interesting rules from large
databases. However, most of the produced results do not satisfy investors in the financial market. The
reason for this is because association rule mining simply uses confidence and support to select interesting
patterns while the investor is more interested in the result- trading at high profit and low risk. We propose a
novel approach called Profit Mining which provides investors with trading rules including information
about profit, risk, and win rate. To show the feasibility and usefulness of our proposal, we use a simple
trading model of an inter-day trading simulation. This mining approach works well not only in the stock
market, but also in the futures and other markets.
1 INTRODUCTION
In the last decade, many data mining researchers
focused on the study of association rule (AR)
mining (Agrawal, 1993; Shen, 1999). Especially in
the financial applications, data mining can be used to
make forecast (Boetticher, 2006). Using the
application of AR on the stock market as an example,
one can benefit from the rule: when the price of
ABC stock goes up, the price of XYZ stock goes up
with 70% confidence at the same day. However, this
rule cannot depict the information of when to buy or
when to sell the stock. As a result, the inter-
transaction mining (ITM) was proposed (Lu, 1998)
to improve the usage of AR. The generated rule
from ITM indicates when the price of ABC stock
goes up, then the price of XYZ stock goes up the
next day with 70% confidence.
With ITM we still cannot be sure to have a profit
as illustrated in the next example. Assume an
investor earns 1 dollar from trading one unit of XYZ
stock when both the prices of ABC and XYZ stocks
go up. If the price of XYZ stock goes down today
after the price of ABC stock went up yesterday, the
loss is 3 dollars per unit where tax and trading fee
are taken into account. Since the confidence of the
generated rule is 70%, we can calculate the total loss
of 2 dollars from ten trades. The calculation is 7 * 1
dollars – 3 * 3 dollars = -2 dollars. Although ITM
provides the information of trading time, the chance
of making a profit from simply following the
generated rules is still small. The reason is that a
high confidence rule does not necessary possess the
benefit of high profit.
In the investment market, although every trader
wants to make a profit, taking a loss is still
inevitable and such a loss is called risk. If two
trading approaches have the same profit and risk
with two different winning chances of 1% and 99%,
the investor would prefer the latter over the former.
Here the winning chance is called WinRate.
To satisfy the above expectation of investors in
the financial market, we propose a novel concept
called profit mining (PM). The goal of PM is to mine
the trading rules for the financial investors.
Therefore, PM needs a trading model which can
present various trading strategies used in the trading
rules. The trading results from applying these rules
are acquired by the trading simulation using the
trading model, trading rules, and databases of
historical transactions.
There are various trading rules and trading
results of PM depending on the trading model and
investor’s expectations. In fact, there are a lot of
trading models existed in PM and we only propose a
simple model in Section 3.
The concept of PM is similar to utility mining
(Yao, 2006) which uses a sales manager’s
perspective to reveal the profit that is important to
the miner. Traditional statistical correlations may not
measure how useful an itemset is in accordance with
a user’s preferences. Therefore, PM is a new mining
approach like utility mining.
510
Hsieh Y. and Yang D..
A STUDY OF PROFIT MINING.
DOI: 10.5220/0003691705020506
In Proceedings of the International Conference on Knowledge Discovery and Information Retrieval (KDIR-2011), pages 502-506
ISBN: 978-989-8425-79-9
Copyright
c
 2011 SCITEPRESS (Science and Technology Publications, Lda.)

2 RELATED WORK
Agrawal (1993) proposed the association rule
mining for finding the rule of related itemsets with
high frequency and confidence from transactional
database. Lu (1998) presented the inter-transaction
association rules for mining the timing of stock
prices going up or down. Zhang (2004) revealed “the
fact that data mining in finance is involved with
applications, data, and domain models leads to a
conceptual framework consisting of three-
dimensions.” Boetticher (2006) performed several
studies to mine the information from financial data
in which the result is presented by profit, but lacks
risk information. Risk management in financial
market (Magdon-Ismail, 2004) is critical for the
investors. In the real world applications, many
investment experts use Trade Station (TradeStation,
2011) to build program models that can perform
trading simulation. After the simulation, Trade
Station generates reports to present the profit, risk
and other trading results of the program model.
3 OUR PROPOSED
PROFIT MINING
Profit mining consists of a trading model with the
transactional database (TDB). According to the
trading model and transactional database, the trading
rules and trading results are generated. Using trading
rules we can apply trading model to simulate the
trading for the TDB and generate the trading result.
First, we define a simple trading model called inter-
day model as described below.
3.1 Trading Model – Inter-Day Model
Let MP = {None, Long, Short} be a set of market
positions and TC = {Buy, Sell} be a set of trading
commands. Let TO = {tc, qty, price} be a form of
trading order where tc∈TC, qty∈{1,2}, price∈R and
price>0. For simplification, we limit the values of
qty to 1 and 2. We say that TO is a BuyOrder (BO)
where tc = “Buy”, or a SellOrder (SO) where tc =
“Sell”. Let POS = {mp, hqty, hprice} be a form of
hold position where mp∈MP, hqty∈{0,1}, hprice∈R
and hprice≥0. We say that POS is in a close position
when mp = “None”. Similarly, POS is in a long
position when mp = “Long” or a short position when
mp = “Short”.
Figure 1: The state machine of our trading model.
Figure 1 shows these three hold positions in our
model. A close position means that the investor does
not hold any stock. “Long or Short Position” means
that the investor expects the price of stock in the
future to go up or down. BP and SP stand for Buy
Pattern and Sell Pattern respectively, where sprice is
the selling price and bprice is the buying price.
In the initial trading, an investor holds a close
position. When a BP or SP occurs, the BO or SO is
generated respectively. These orders change the
close position to long or short position as indicated
by the arrowhead lines from the top of Figure 10 to
its left or right respectively.
If a long position POS
t-1
(generated by TO
t-1
)
meets a BP, it is ignored until an SP is met to
generate an SO. Then the long position POS
t-1
is
changed to the short position POS
t
, where the
arrowhead line is drawn from the long position (left)
to the short position (right) in Figure 1. The TO
t-1
is
called a complete trade (CT) in which the POS
t-1
is
changed to the short position by TO
t
. The case
where the short position is changed to the long
position is opposite to the last case.
Table 1: Transactional database (TDB).
3.2 Transactional Database
Table 1 shows an example of transactional database
with three attributes TID, ItemSet and Price. TID is a
transaction ID possessing the time feature, where the
item set (or event set) and trading price recorded at
that time are ItemSet and Price respectively.
A STUDY OF PROFIT MINING
511

N
P
i,j
3.3 Trading Rule
When BP or SP occurs at the close position, there is
a semantic ambiguity because the investor does not
know which trading action to take, Buy or Sell? A
new attribute of Trading Priority (TP) is required to
solve the problem. Then, we have the format of the
trading rule: <TP, BP, SP> where TP∈{BF, SF}. BF
is BuyFirst and SF is SellFirst.
To identify a pattern, we need to specify a
maxspan value indicating the maximal number of
transactions in the TDB containing the pattern. For
example, If maxspan = 2, there are 2 patterns
{{a(0)},{a(0)b(-1)}} at transaction TID 5. The
pattern {a(0)b(-1)} has 2 items (or events) a and b.
The number in the parenthesis of b(-1) is the interval
which describes the distance from the base
transaction TID 5 to the item b at transaction TID 4,
which has a distance value of -1. A negative value
means the backward distance. Since the pattern
{a(0)b(-1)} occurs at TID 5, the trading price 450 of
the pattern {a(0)b(-1)} is set at transaction TID 5,
not at transaction TID 4.
3.4 Trading Results of Profit, Risk and
WinRate
In our PM model one must specify the handling fee
for each trading to cover the fee and tax as in the
real world.
3.4.1 Profit
Let DB
Begin
and DB
End
be two TIDs which represent
the TID of the first and last transactions in the TDB
respectively. Let P be a function for getting the price
at a specific TID, denoted as P(TID). Let T
i
and T
j
be two TIDs, where T
i
<T
j
and T
i
,T
j
∈TID. We
denote that i and j are two trading orders and T
i
and
T
j
are the locations of trading orders i and j,
respectively. Let minP(T
i
, T
j
) and maxP(T
i
, T
j
) be
two functions for getting the minimal and maximal
prices from T
i
to T
j
, where T
i
<T
j
and T
i
,T
j
∈TID.
Then the equation of NetProfit (NP) and profit of
trading rule are as follows:
P(T
j
) – P(T
i
) – 2*fee, if mp
i
= “Long”
P(T
i
) – P(T
j
) – 2*fee, if mp
i
= “Short”
(1)
Profit = ΣNP
i, j
(2)
3.4.2 Risk
To define the risk of trading rule, three variables are
required: Consecutive Loss (CLoss), Draw Down
(DD) and Run Up (RU). Their initial and maximal
values are all 0. CLoss records the consecutive loss
of net-profit by using the following equation:
CLoss at time t: CLoss
t
= CLoss
(t-1)
+ NP
t
(3)
where CLoss
0
= 0 and CLoss
t
= 0 if (CLoss
(t-1)
+ NP
t
) > 0
Figure 2: Computing the risk of trading rule using stock
price vs. trading time curve.
We use Figure 2 to present the calculation of
variables DD and RU which are used to record the
risk during the trading process as MP = “Long” or
MP = “Short”. DD records the difference between
the buying price and the lowest price. One example
is shown in the T
2
point of Figure 2. The L
1
point is
the lowest point between T
2
and T
3
. The equation to
compute DD is shown below:
DD
t-1
= CLoss
t-2
+ minP(T
t-1
, T
t
) - P(T
t-1
) (4)
if MP
t-1
= “Long” and t>0 and T
t
≠Null
However, if the BP at T
t
is next to the DB
End
,
there is no SP to expect and equation (5) is used to
compute DD. Otherwise, the value of DD is 0.
DD
t
= CLoss
t-1
+ minP(T
t
, DB
End
) – P(T
t
) (5)
if MP
(t-1)
= “Long” and t>0 and T
t
≠DB
End
The definition of RU is similar to DD, but RU
works at MP = “Short” and records the difference
between the selling price and the highest price. The
following two equations (6) and (7) corresponding to
equations (4) and (5) are used for RU respectively.
RU
t-1
= CLoss
t-2
+ P(T
t
-1) - maxP(T
t-1
, T
t
) (6)
if MP
t-1
= “Short” and t > 0 and T
t
≠ Null
RU
t
= CLoss
t-1
+ P(T
t
) - maxP(T
t
, DB
End
) (7)
if MP
t-1
= “Short” and t > 0 and T
t
≠ DB
End
The current risk is the maximal absolute value
among the current values of CLoss, DD, RU and the
previous risk. The equation of risk is defined as
follows:
KDIR 2011 - International Conference on Knowledge Discovery and Information Retrieval
512

Ris
k
at time
t
: Ris
k
t
= max[ |CLoss
t
|, |DD
t
|,
|RU
t
|, Risk
(t-1)
] if t > 0 and Risk
0
= 0 if t = 0
(8)
3.4.3 WinRate
The variable WinRate is the ratio between the
number of complete trades with net-profit >0 and the
total number of complete trades (CTs).
The WinRate of trading result is defined below:
(Total # of CT
s
with NP>0) / (Total # of CT
s
) ×
100
%
(9)
3.5 Profit Rule
Let minProfit, maxRisk and minWinRate be user
specified threshold values. We define a profit rule to
be a trading rule R with trading results {Profit
R
,
Risk
R
, WinRate
R
} if minProfit ≥ Profit
R
, maxRisk <
Risk
R
and minWinRate ≥ WinRate
R
.
4 AN EXAMPLE OF MINING
PROFIT RULES
We use a trading rule <BF, a(0), b(0)> from Table 1
to explain the trading simulation. As before, we set
the trading fee to 1. The trading process is shown in
Table 2, where there are fifteen attributes as defined
previously.
At the beginning, the position = {None, 0, 0}.
The first trading order is BuyOrder = {Buy, 1, 500},
because BP and SP occur at TID 1. Since the
semantic ambiguity of trading appears, TP =
BuyFirst is adopted. After trading, the position is
changed from {None, 0, 0} to {Long, 1, 500} as
shown in the Record No. 1 of Table 2. In the second
trade at Record No. 2, BP and SP patterns occur at
TID 3, where BP is ignored and the sell-order =
{Sell, 2, 480} changes the position to {Short, 1,
480}. The NP
1
at Record No. 1 equals to 480 – 500
– 2 * 1 = -22. The value of CLoss
1
= CLoss
0
+ NP
1
=
0 + (-22) = -22. The value of DD
1
equals to minP(1,
3) – P(1) = 480 - 500 = -20. The value of RU
1
= 0
because MP
1
= “Long”. The value of Risk
1
= max(|-
22|, |-20|, |0|, 0) = 22. The value of WinRate
1
is 0
because NP
1
≤ 0.
The next trading order is BuyOrder = {Buy, 2,
450} is at TID 5 and NP
2
equals to 480 – 450 – 2 * 1
= 28 at Record No. 3. Here CLoss
2
= 0 and DD
2
= 0
because CLoss
1
+ NP
2
= -22 + 28 = 6 > 0 and MP
1
=
“Short” respectively. Then we have RU
2
= -22 +
P(3) – maxP(3, 5) = -22 + 480 – 490 = -32 and Risk
2
= max(|0|, |0|, |-32|, 22) = 32. The WinRate
2
is 50%
because NP
2
>0. The last trading order is SellOrder
= {Sell, 2, 440} is at TID 7. After selling two stocks,
NP
3
= 440 – 450 -2*1 = -12. We have CLoss
3
= 0 +
(-12) = -12 and DD
3
= 0 + minP(5, 7) – P(5) = 410 –
450 = -40. Then RU
3
=0 because MP
2
= “Long”.
The WinRate
3
is 33% because NP
3
≤0.
There is no buy pattern BP coming after TID 7.
However, it is not risk free because there are
transactions from TID 7 to DB
End
(i.e., TID 8). We
have RU
4
= -12 + P(7) - maxP(7, 8) = -12 + 440 –
470 = -42 and Risk4 = max(|-12|, |0|, |-42|, 40) = 42.
The Profit of the trading rule is the summation of
NPs = (-22) + 28 + (-12) = -6. Therefore, the trading
result for the trading rule <BF, a(0), b(0)> is {-6, 42,
33%}.
Table 2: The simulated trading of the rule <BF, a(0),
b(0)>.
5 EXPERIMENTAL RESULT
To verify the correctness of our profit mining and
validate the mining results to satisfy the investor’s
expectation in the financial market, we use the
following experiment to show the trading rule and
trading result.
5.1 Our Experiment
In the experiment, we assume that the trading fee is
1, the value of maxspan is 2, and the thresholds of
Table 3: The Mining Results of the experiment.
A STUDY OF PROFIT MINING
513

minProfit, maxRisk and minWinRate are 10, 30 and
30%, respectively. After mining the TDB of Table 1,
we found fourteen profit rules as shown in Table 3.
For Rule No. 8, the BP is equal to its SP meaning
that investors must sell their stocks first when they
hold no stock, or they will lose money. For the rules
No. 2 and No. 3, their BP, SP and trading results are
the same. It means that investors can adopt buy-first
or sell-first since their trading results are the same
either way.
5.2 Discussion
As a preliminary study on financial data mining, we
use a simple trading model of inter-day model for
trading simulation. With different trading models,
one can derive many different trading rules under
specific transaction databases.
In data mining research, one expects to mine the
knowledge of any kind that users might be interested
in. These useful results of knowledge can be
discovered and presented in the forms of rules,
patterns, or any other forms to meet users’
expectation.
Similarly in profit mining, we think more types
of profit rules can be defined and discovered in any
of the financial sectors. Since investors have their
own measurement criteria for mining the preferred
trading rules, there must be more useful models of
financial data mining to be investigated.
6 CONCLUSIONS
In this paper, we present a new data mining in the
financial market, called profit mining, with initial
results showing the feasibility and usefulness of our
proposed model. There still remains much research
to be investigated other than association rule mining
and inter-transaction mining. Currently we are
working on efficient algorithms for profit mining in
various trading models. Our future research also
includes solving the challenge of reducing the search
space and speeding up the mining process with
limited memory space.
ACKNOWLEDGEMENTS
This research was supported by the National Science
Council, Taiwan, under grant NSC 98-2221-E-035-
059-MY2.
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