Stock Index Futures Real-time Buying and Selling Decision Making
First Author: CHIN-TSAI LIN
Department of Information Management, Yuanpei Institute of Science and Technology
Second Author: CHIE-BEIN CHEN
Institute of International Business, National Dong Hwa University
Third Author: SHIN-YUAN CHANG
Graduate Institute of Management Science, Ming Chaun University
No. 250, Sec.5, Chung Shan N. Road Taipei Taiwan
Tel: 886-2-28824564 ext. 2401
E-mail：firstname.lastname@example.org or email@example.com
The TAIEX Electronic Sector Index Futures (TAIEX-ESIF) real-time decision making problem-solving
technique is presented in this research. The regression model and partial SPRT are used to construct the
real-time decision support system (RTDSS). TAIEX-ESIF real-time data from Feb. 20, 2001 to Mar. 02,
2001 are used to do empirical experiment. The purpose of this experimental design is used to evaluate the
RTDSS. The achievements of this research not only provide RTDSS for TAIEX-ESIF but also prove that
partial SPRT can be one of decision-making methods applied to financial engineering.
Keyword: stock index futures, regression model, partial SPRT, real-time decision making, financial
1. Introduction 1.1The Motivation of Research
The presence of Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) Futures, TAIEX
Electronic Sector Index Futures, TAIEX Banking and Insurance Sector Index Futures and Singapore Morgan
Stanley Capital International Taiwan Stock Index (SIMEX MSCI TSI) Futures represent several meaningful
progressions for the capital market in Taiwan. First of all, they provide the investors convenient hedging
instrument. Secondly, the Taiwan stock market become more attractive to foreign capital which promote the
internationalization, liquidity and volume of Taiwan stock market. Thirdly, they stimulates the development
of financial engineering and financial instrument, such as warrant, option, negotiable security, asset
Brock et al. (1992); and Gencay and Stengos (1998) used different methods to study and analyze the forecast of investment tools, such as stock, exchange rate, futures…..etc, in the past. Wu and Lee (2000),
Liu and Lee (2000); Chou (2000); and Lin (2000) had shown different models to simulate the trend of Taiwan
Stock Index futures by selecting more than 40 among 400 different stocks. Although these models are
theoretically well, they are not practical for arbitrage, speculation, and hedging on index futures because the amount of investment is limited and the time of making decision is delayed.
The contemporary market consists of the three different kinds of trading strategies, including speculation, hedge and arbitrage. Although there are many various types of finance models to describe the market, but
most of them do have lots hypotheses and limitations. Index futures speculation is one of the most popular
investment strategies to many institution investors. Most investors hope to get exceed revenue from the
stock index futures’ market, however, the investors must consider many factors from capital, policy,
economical to psychological factors. Since it is not an easy thing for an investor to make decision at proper time to buy or sell the index of futures, the motivation of this research is to construct a decision support
system for the investors to help them make decision at proper time in real-time trading system.
1.2 Problem Statement and Objective of Research
In recent, because of the freedom of financial environment and the dynamic changing of the investment, Taiwan is coming a knowledge era of investment. By this trend, there are many decision systems to help
investors to make decision, but most of them are not real-time or online. For example, Lee (2000) applies
data mining techniques on financial statement to forecast the return and the relationship between stock prices and financial statement on electronic listed corporation in Taiwan. Chou (2000) applied neural network
techniques to forecast the stock basis trend. Meanwhile, the output of the trend forecast in that study was used as a guideline to improve the arbitrage strategy. In the existing research, there are even few researches’
studying the speculation, fewer them provide methods for investors to make decision in speculation. In this
research, simple regression in statistics and partial sequential probability ratio test (SPRT) are used as tools to solve stock index futures real-time buying and selling predicting. The simple regression in statistics is
developed for the time point of index futures dealing and partial SPRT is used to test the slope of regression line dynamics. That is, this research will provide a real-time decision support system (RTDSS) to help
investors to make trading decision. From now, there are many applications of SPRT or partial SPRT in
manufacturing engineering, medical engineering and many other areas because of a variety of reasons,
including patient safety, trial efficiency, and cost reduction (Chen, 1989; Chen and Wei, 1998; Kittelson, 1999; Lia and Hall, 1999; Chen and Wei, 2000; Chen 2001). In order to provide real-time suggestions for
investors, the partial SPRT method will be applied to RTDSS. Thus, the objectives of this research is:
to construct a real-time RTDSS by simple regression model and partial SPRT method for investors obtaining exceed revenue from the TAIEX Electronic Sector Index Futures;
to examine the effectiveness of trading to pursuit the net profit by experiment; 1.3The Structure of This Research
The major structure of this research is constructed in Figure 1. Figure 1 illustrates the TAIEX Electronic Sector Index Futures of real-time buying and selling prediction model and evaluating process. The first part
is the system linking the online database of index futures from Taiwan Futures Exchange. The second part is
constructing real-time buying and selling prediction model. The simple regression model and partial SPRT
method are used. The third part is to examine or evaluate the performance of the constructed prediction
model. There are three items will be evaluated the criteria: (1) the accuracy of buying and selling decision
making, (2) the number of buying and selling, (3) the gains or losses. The accuracy of buying and selling
decision-making is the accuracy to suggest buying and selling messages. The number of buying and selling
is the amounts that RTDSS suggests. And the gains or losses is the total profits in one transaction day. The
forth part is empirical experiment. In this part, the orthogonal array will be used. And the next part is result
analysis. Grey relationship analysis method is used to find the “optimal” combination of levels in this part.
The final part is confirmation experiment. T test will be used in this part to verify the effectiveness based on
primal run of experiment.
2. Prediction Model Construction
There are two sections in this chapter for constructing prediction model. The first section discusses the
simple regression model. The second section develops the partial sequential test for testing the slope and
intercept of regression model. The testing limits of slope are used to construct the real time buying and
selling prediction of TAIEX.
Taking Online Stock Index Futures from Database
Constructing 1.Regression Model for
Real-Time Buying ˆ Constructing b1and Selling Prediction Model 2.Partial SPRT Model for
ˆ Testing b1
Result Presentation 1.Accuracy of Buying and Selling 2. No. of Buying The Evaluating 3. No. of Selling Process 4. Gains or losses
Figure 1 The Structure of this Research
2.1 Simple Regression Model
A regression model can be calculated from the sampled points by establishing a best-fitting line
according to the least squares method. This regression line can also be referred to as a prediction mean line.
In a simple regression model wherein there is but one predictor variable X, this function relationship can be expressed as
, (1) YfX??()?iii
where any observed value in the population would be a function of the true mathematical model Yi
plus some residual . The population regression model can be re-expressed as fX()?ii
, (2) YX??????iii01
where the two unknown parameters and are necessary for determining a straight line. is ???010
Ythe true intercept; a constant factor in the regression model representing the expected or fitted value of
XYwhen = 0. is the true slope; it represents the amount that changes (either positively or negatively) ?1
Xper unit change in . Since we do not have access to the entire population, we cannot compute the
parameters and and obtain the population regression model. The objective then becomes one of ??01
ˆˆobtaining estimates (for ) and (for ) from the sample. Usually, this is accomplished by ??bb1010
ˆˆemploying the method of least squares (MLS). With this method the statistics and are computed bb10from the sample in such a manner that the best possible fit within the constraints of the least squares model is
achieved (Mark et al., 1983). That is, we obtain the linear regression equation
ˆˆˆ (3) ??YbbXi01i
nn22ˆsuch that (Y?Y)?e is minimized. ??iiiii?1?1
In using the least-squares method, the following two normal equations are developed:
nnˆˆY?nb?bX (4) ??ii01ii?1?1
nnn2ˆˆXY?bX?bX (5) ???iiii01iii?1?1?1
ˆˆand solving simultaneously for and , we compute bb10
nXY?XY???iiii???i1i1i1ˆb? (6) 1nn22nX?(X)??ii??11ii
G-16 2002年管理創新與新願景研討會 and
ˆˆˆso that the sample regression equation is obtained. ??YbbXi01i2.2 Partial Sequential Probability Ratio Test
In order to determine the quality of straightness of the edge, a hypothesis test and the Sequential
ˆˆProbability Ratio Test for slope of the estimated mean line were used. Partial and intercept bb10
ˆˆsequential tests for two parameters of slope and intercept of simple regression were developed by bb 10
Arghami and Billard (1987).
Let (x, y), i = 1, 2, .... be pairs of peak points. Assume the null hypothesis ii
ˆ H : ? = ? = , (8) b010
and the alternative hypothesis
ˆ H : ? = ? = +, (9) btll1
ˆ or H : ? = ? = , -btl1 1
where, y is independent and i
ˆˆ y? N (x, ?), i = 1, 2, ..... (10) + bb i i102
2ˆˆand is the parameter of interest, while and ? are nuisance parameters. A transformation bb 10
2ˆsimilar to that used in Arghami and Billard (1987) can eliminate the nuisance parameters and ?. Then b 0
Partial SPRT based on the transformed variables can be performed.
To do this, take n (? 3) pairs of initial points (x, y), ....., (x, y) and compute the minimum variance 011nn00
2,unbiased estimator of ?
n0221??ryy?????0i0S2xy2i1? (11) r?S?,0SS2n?xxyy0
where Sxyxxyy???()() ?ii?1i
n0And r is the correlation coefficient of x and y based on the n initial points and , yyn?/?0i000i1?0nx?i i?1n?2 such that x?)Take n additional pairs of points, where n is the smallest integer (01. lln0
*2nS2w?, (12) ?iz1i?1
,where n* = n + n0l
???,,,...,12xxin? 00i , w?i????,,...,*1xxinn00i?
n0 x, ix?,?0n0i1?
*nx i x?.?1n1in1??0
and zis a positive number independent of y, i = 1, 2, ..., which may depend on x, i = 1, 2, ..... l ii
pre-specified way such that However, a set of real numbers p, ..., p can be found in a ln*
n02p is proportional to ww/i = 1,2, ..., n, ?i, ii01i?
px?1, and ?iii?
Next, take n pairs of points where n is the smallest integer (> 2) such that 22
*n?n22S2 (14) ?,w?i*zi?n?12
** w = x -x, i = n+1, ...., n+n ii 22
and z is a positive number independent of y, i =1, 2, ...., which may depend on x, i = 1, 2,..... 2ii
However, a set of real numbers q, ..., q can be found in a predetermined way such that nl2
*nn?q2*iny?i (15) U?.?2z*2in??1
Similarly, compute U, j = 3, 4,..., using positive numbers z, j = 3, 4, ....., which are independent of the y jji
but may depend on the x. i
It can then be shown that the joint density of U, ...., U is lm
/???nm22??0?1m??2?2??n????0 ???U?????2?nu?,?????j???1, ?????????j0jj????2?????j1??
2, ….., m, (16)
??/where z?= 1jj .
To perform a Partial SPRT with levels of risk ? and ? for the hypotheses in upper eauation, proceed as follows:
22/nm????0???; (17) Hthen accept ????0 (1) If ,????1
22/nm????01???? (2) If ??H; (18) then accept ??1,???
2222//nmnm????????00?1?????? (3) If take an additional ??????????? 1???
; (19) observation
nU2???????00jjj1?, ?? 2m
??1 ??,j0j = 1, 2, ......., m, zj
?t??11??,j1j = 1, 2, ......., m. zj
Figure. 1 shows an illustration of m waves and the number of , and , where m = 3, = 5 nnnn1123
points, = 3 points and = 4 points. nn23
Figure 1 The Illustration of the Number of , n, n and nm123
22?1??nm??nm??2(2)00Figure 2 illustrates both limits of ?()() and , where = 0.05, = 0.1 ???1?
and = 30, at different number of clusters, . It is seen that the more clusters, the closer of these two nm0
limits. That is when the number of cluster increases, the upper limit decreases and the lower limit will
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201 is very large, the probability of additional observation is less. mincrease simultaneously. Thus, when
This will accelerate to accept or reject . HH18100
Curve A811Curve Btest value610.95
The No. of waves, m
22?1??nm??nm??2200?Note: curve A: and curve B: , where = 0.05, =0.1 and = 30 ()()n?0??1?
Figure 2 The Relationship of two boundaries at different number of clusters
Theoretical proof is expressed in the following:
??1?00=()?()?1?1?0 (20) ??1?
2.3 Decision Rule and Evaluating Process of RTDSS
ˆFigure 2 illustrates the decision-making flow chart. At first, when is positive and if the test value, b1?, is larger than the boundary of curve B at different , that is fallen into reject area of . At this time, Hm0
ˆRTDSS will send out the message of “selling”. Since the hypothesis is b = and H: b = H:b11101
ˆˆˆ?H- t = -0.2. Therefore, when test value, , is fallen into reject area of , it means is Hbbb10111
accepted and the newest data decline the slope of the regression line.
ˆSecondly, when ? is negative and if the test value, , is larger than the boundary of curve B at b1
different , that is fallen into reject area of . At this time, RTDSS will send out the message of Hm0
ˆˆˆˆ“buying”. Since the hypothesis is bHb = and : = + t = + 0.2. Therefore, H:bbbb11101111
?when test value, , is fallen into reject area of , it means H is accepted and the newest data increase H10
the slope of the regression line.
The RTDSS for prediction or decision-making has been designed. It is then the necessary to determine
whether the model is good or not in comparing with the index of buying and selling.
The main purpose the evaluating process is to evaluate the performance of RTDSS. There are three
steps of the evaluating process in the computer program. The first one is buying and selling index setting,
and the second one is to storage them, the final one outputs, the accuracy of buying and selling, the number of
buying and selling suggestions, and the gains or losses.
Is the slope of
Reject H0Reject H0
Figure 2 The Decision-making Flow Chart
When RTDSS provides “selling” or “buying” messages in sequence, it just suggests to buying or selling
once. Figure 3 illustrates the messages of “buying” and “selling” sent by RTDSS. The investors (users)
could select one index which is suggested by RTDSS to sell (or buy) the index future. The earlier of
“selling” or “buying” points are appeared by RTDSS, the larger of weights are given by evaluating process. Thus, the evaluating process sets the selling or buying index by the following equation.
nk??1th?where ?i and is the continuous selling (or buying) message provided by pkin
RTDSS (see Figure 3).
In the evaluating processes of the computer program, there are two arrays, “buying array” and “selling
array”, used to store the buying index and selling index calculated by Eq. (3.1) individually. The purposes of
these two arrays are used to store the index of buying and selling in one transaction day.
There are three outputs or responses as the evaluating tools. The accuracy of buying and selling is the
number of correct decision-making divided by the total transaction. And the second one is the number of
buying and selling transaction. The final one is gains or losses. And the gains or losses is the total difference
between the elements of buying array and selling array.