Download Trading Decision Maker: Stock Trading Decision by Price Series

Trading Decision Maker: Stock Trading Decision by
Price Series Smoothing and Tendency Transition Inference
Hsin-Tsung Peng1, Hahn-Ming Lee2 and Jan-Ming Ho3
Institute of Information Science, Academia Sinica, Taipei, Taiwan1, 3
Department of Computer Science and Information Engineering,
National Taiwan University of Science and Technology, Taipei, Taiwan2
{m91150131, hoho3}@iis.sinica.edu.tw, [email protected]
Abstract
Financial engineering, such as trading decisionmaking, is a major topic for research and also has
commercial applications. The stock price series has a
series of change-points, and accurate prediction of its
movements is the key to successful trading. However,
making correct trading decisions is difficult because of
the influence of embedded noise and price fluctuations
that confuse the interpretation of stock trends. This
paper proposes a novel stock trading method, called
the Trading Decision Maker (TDM), based on price
series smoothing to reveal important change-points,
which reflect changes in stock trends more precisely.
Tendency transition inference is used to identify these
important change-points effectively. We demonstrate
the usefulness of TDM in evaluating profitability
capacity, and prove that its accumulated rate of return
performed 199.05% better than other buy-and-hold
strategies used by open-ended mutual funds on the
Taiwan Stock Exchange Capitalization Weighted Index
(TAIEX) from 2001 to 2003.
1. Introduction
The stock market is a complex and dynamic system.
The stock price series, therefore, is inherently noisy,
non-stationary and chaotic [1] [2]. Modeling stock
market behavior is a challenging task for financial
experts because it is always complex, but artificial
intelligence techniques [3] [4] can make the task easier.
In recent years, various theories and methods have
been developed to help investors earn higher profits.
The stock price series is affected by a mixture of
deterministic and random factors [5], and accurate
prediction of its movements is the key to successful
trading. Although random factors, such as embedded
noise, make the stock price series unpredictable,
deterministic factors like political events, institutional
investors, foreign investors and governments, have a
direct influence on the stock market. Therefore, we
can conjecture that there is a series of change-points in
stock trends. Obviously, investors want to sell stocks
at the top of the range and buy stocks at the bottom of
the range within the stock trends [6]. Thus, only a
couple of important change-points, which reflect more
precisely the changes in stock trends, are the key to
helping investors reach their goals.
In this paper, we propose a novel stock trading
method, called the Trading Decision Maker (TDM),
based on price series smoothing to smooth out price
fluctuations. Important change-points are identified
through tendency transition inference.
The
combination of price series smoothing and tendency
transition inference will help investors optimize their
investment decisions.
The remainder of paper is organized as follows:
Section 2 presents TDM in detail. Section 3 gives the
environment and assumptions of the experiments. In
Section 4, we conduct an experiment to compare the
trading performance of TDM with some open-ended
mutual funds from 2001 to 2003. Finally, in Section 5,
we present our conclusion.
2. The Trading Decision Maker
2.1. Architecture of Trading Decision Maker
The system architecture of TDM is comprised of
four components: namely, the smoothing unit, the
Discrete Difference Equation Prediction Model
(DDEPM) [7], which is a time series prediction model
derived from the grey prediction model, the tendency
transition inference unit and the trading mechanism.
The architecture of TDM is shown in Figure 1.
On each trading day n, the smoothing unit reads the
closing price Cn and transforms it into the smoothing
value Sn. At the same time, Sn is buffered d time-steps
by the time delay block, which saves the smoothing
values of the pervious d trading days. TDM uses
DDEPM predicts the next k-day’s smoothing value
Ŝn+k using the saved smoothing values {Sn, Sn-1, …, ŜnTo identify changes in the stock trend, the
d+1}.
tendency transition inference unit uses the predicted
results, which cover the period from trading day j in
the past to trading day k in the future, to calculate the
inference score Tn j , k on trading day n. Finally, the
trading mechanism is based on the inference score to
make a trading decision for investors.
Figure 1: Architecture of TDM.
The stock price series has a number of changepoints, of which only a few can precisely reflect the
changes in stock trends. Most change-points cause
embedded noise and price fluctuations, and provide
very little information to investors. Furthermore, the
information that they do provide can mislead investors
about effective stock trading strategies.
It is essential, therefore, to reveal important changepoints from the stock price series. Smoothing out price
fluctuations and embedded noise will reflect changes
in stock trends in the stock price series more precisely,
and thereby help investors earn higher profits in the
long-term. In order to filter out price fluctuations and
embedded noise, we assign a lower weight to each
closing price in the stock price series.
The smoothing function based on an exponential
moving average curve [8], is defined as follows:
r = 2 (1 + m) ,
2.3. Discrete Difference Equation Prediction
Model
By smoothing out the stock price series, each
change-point in the smoothing series plays an
important role in determining changes in the stock
trend. It is essential, therefore, to enhance the
prediction performance at the change-points. For this
purpose, DDEPM [7] is applied to the prediction
module in TDM.
The concept of DDEPM is derived from the grey
prediction model, which uses a mathematical
hypothesis and approximation to transform a
continuous differential equation into a discrete
difference equation. We can summarize the properties
of DDEPM as follows: 1) It is computationally simple
and few data items are needed. 2) It can serve as a
chaotic time series prediction problem. 3) It has good
prediction performance at change-points.
2.4. Tendency Transition Inference Unit
2.2. Smoothing Unit
S n = S n−1 ⋅ (1 − r ) + Cn ⋅ r ,
with
and can be more sensitive in reflecting the stock price
changes and emphasizing the direction of stock trends.
As mentioned previously, the key to earning high
profits in stock trading is to determine a suitable
trading decision before the direction of the stock trend
changes. Hence, identifying the changes in the stock
trend is very important for investors.
We construct an inference function to obtain the
position of the smoothing value for the current trading
day in a consecutive period. If it appears that the
future stock trend will develop strongly in the future,
the position of the smoothing value for the current
trading day will be near the bottom of a consecutive
period, and vice versa. Thus, each investor can adjust
the trading strategy based on individual confidence and
risk endurance capacity.
The inference function, which is derived from the
Williams overbought/oversold index (WMS%R) [9], is
defined as follows:
(1)
(2)
where Sn is the smoothing value of trading day n, Cn is
the closing price of trading day n, r is the weight
function and m is the smooth constant.
In Equations (1) and (2), the smoothing function
gives the lower weight to the latest closing price Cn
depending on the definition of the smooth constant m
Tnj , k
⎧
Maxin=+nk− j Sˆi − Sˆ n
⎪
n+k
n+ k
⎪ Maxi = n − j Sˆi − Mini = n − j Sˆi
n+ k ˆ
⎪
ˆ
S n − Mini = n − j S i
⎪
= ⎨−
n+k ˆ
n+k ˆ
Max
i = n − j S i − Mini = n − j Si
⎪
⎪
0
⎪
⎪⎩
if ( Sˆn + k − Sˆn − j ) > 0
if ( Sˆn + k − Sˆn − j ) < 0
otherwise
,
(3)
where Tn j ,k is the inference score of trading day n, and
ranges from 1 to -1; j is the backward scoring range,
and k is the forward scoring range.
In Equation (3), the inference score identifies the
changes in the stock trend on trading day n. When the
stock trends change its behavior in the future, the
inference score will be zero, which helps each investor
define a trading strategy based on individual
confidence and risk endurance capacity.
2.5. Trading Mechanism
The trading mechanism is responsible for generating
the trading decision based on the inference score. As
mentioned previously, when the inference score is zero,
the direction of the stock trend will change in the
future.
Herein, we introduce the following two
concepts to develop our trading mechanism: 1) When
Tn j ,k is zero and Tn j−,1k is greater than or equal to zero,
the stock trend is expected to indicate a bearish market
in the future; hence, we sell holding stocks and borrow
stocks to sell. 2) When Tn j , k is zero and Tn j−,1k is
smaller than or equal to zero, the stock trend is
expected to indicate a bullish market in the future, so
we buy stocks to repay the previously borrowed stocks
and buy new stocks using our own money.
3. Setting of Experiments
In our experiments, we use the Taiwan Stock
Exchange Capitalization Weighted Index (TAIEX)
price series from 1995 to 2003. The experimental data
set collected from 1995 to 2000, was used in the
parameter selection procedure, while other data
collected from 2001 to 2003 was used in the trading
performance evaluation of TDM. At the end of the
experimental period, the stock held is sold and the
accumulated rate of return is calculated together with
other trades. To evaluate the trading performance, all
the rates of return are calculated after considering the
actual transaction cost for each trade.
In the parameter selection procedure, we define
d=20 in the time delay block and k=1 in the inference
function. In addition, two important parameters need
to be selected in the following experiments; one is the
smooth constant m, which determines the weight
function in the smoothing function; and the other is the
backward scoring range j, which determines the
backward length of scoring data sequence in the
inference function. We define a parameter selection
algorithm, which considers the balance between profits
and risks, to retrieve the pair of parameters (m, j) as the
recommended pair, and finally choose a pair of
parameters (30, 1) to evaluate the trading performance.
4. Experiments
The trading performance of TDM was evaluated
from January 2001 to December 2003. To assess the
trading performance of TDM, the evaluation criteria
[10] were taken into the consideration. To prove that
TDM can be applied to the real Taiwan stock market,
we compare its trading performance on the TAIEX
with three open-ended mutual funds that use buy-andhold trading strategies. The selection procedure is as
follows: the open-ended mutual funds, which are
equity funds, are ranked by their accumulated rate of
return for the period 2001 to 2003, and the top three
are selected. The funds selected are: SHINKONG Fu
Kuei Fund, SHINKONG Competitiveness Fund and
PRESIDENT TRUST SHIN Fund.
Figures 2, 3 and 4 show the experiment results of
buying/selling timing for the period 2001 to 2003. We
can see that the buying/selling timing suggested by
TDM can help investors identify the changes in the
stock trend. To avoid higher losses, TDM revises the
wrong trading decisions immediately. For example,
when TDM suggested that investors take a long
position on 2001/06/06, TDM considered that the
future stock trend indicated a bullish trend. However,
since the bearish trend lasted until September, TDM
revised its suggestion on 2001/06/07 to avoid higher
loss.
Specifically, in the period 2003/03/18 to
2003/05/23, the TAIEX price series seems to be nonstationary and causes successive losses. As shown in
Tables 1, the maximum draw-down is -12.01%
compared to the annual rate of return of 35.00%,
which is high enough to cover losses. Finally, Table 2
shows that the accumulated rate of return obtained by
TDM is superior to the TAIEX and all the open-ended
mutual funds.
Figure 2: Experiment result of buying/selling timing in
2001.
Figure 3: Experiment result of buying/selling timing in
2002.
identify these important change-points effectively. We
assume that the important change-points reflect the
changes in the stock trend more precisely; in other
words, profits in the long-term will be kept in the stock
price series between successive important changepoints. Identifying these important change-points will
help investors make profitable trading decisions by
selling at the top of the range and buying at the bottom
of the range within the stock trends. Experiment
results show that TDM can help investors earn high
profits in the long-term. It also has a higher trading
performance than the open-ended mutual funds used in
the benchmark.
In the future, we will continue to refine TDM,
including the design of parameter selection algorithm
and trading mechanism for short-term investment.
References
[1]
Figure 4: Experiment result of buying/selling timing in
2003.
Table 1: Trading performance evaluation of TDM
Experimental Period
Total Number of Trades
Total Number of Profitable Trades
Maximum Number of Consecutive
Unprofitable Trades
Average Rate of Return per
Profitable Trade
Average Rate of Return per
Unprofitable Trade
Maximum Rate of Return per
Profitable Trade
Maximum Rate of Return per
Unprofitable Trade
Maximum Draw-Down
Annual Rate of Return
2001
13
6
2
2002
11
6
2
2003
13
5
6
12.49%
8.28%
9.38%
-3.29%
-2.23%
-1.72%
40.50%
16.21%
19.63%
-13.68%
-4.75%
-5.11%
-14.50%
52.97%
-6.80%
43.12%
-12.01%
35.00%
Table 2: Comparison of TDM with mutual funds based on
the accumulated rate of return from 2001 to 2003
Comparative Units
TDM
SHINKONG Fu Kuei Fund
SHINKONG Competitiveness Fund
PRESIDENT TRUST SHIN Fund
TAIEX
Accumulated Rate of Return
199.05%
128.46%
78.89%
70.70%
24.30%
5. Conclusion
In this paper, we have proposed the Trading
Decision Maker (TDM), based on price series
smoothing, to reveal important change-points in the
stock price series; and tendency transition inference to
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