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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 E-......

    G-12 2002年管理創新與新願景研討會

    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

    Fax: 886-2-288-9764 or


    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

    2002年管理創新與新願景研討會 G-13


    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

G-14 2002年管理創新與新願景研討會

    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

    2002年管理創新與新願景研討會 G-15


    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

    ˆˆbYbX??01 (7)

    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

    2002年管理創新與新願景研討會 G-17



    n02 Syy??()?yyi0?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?


    p?0, ?ii?


    px?1, and ?iii?

    *nz21p?. ?i2Si?

    Then, let

G-18 2002年管理創新與新願景研討會

    *npyiiU??1zi1?1 (13)

    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




     and qx?1,*?iin?*in??1

    n2z22 q?.?i2Si1?

    Then, let

    *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

     fuuu,.....,;,,.....,??? ??1212,mm

    m?/m?2/n?22??0 ?????funnm;/?222??????????jj00i?1

    /???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:

    2002年管理創新與新願景研討會 G-19

    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

    nU2????01jj??? j1?

    ??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

G-20 2002年管理創新與新願景研討會 221

    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:

    2222limlim11??????m??m??n?m?2n?m?2n?m?2n?m?20000 lim(()())()()???m??11??????

    ??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.

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    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

    regression line



    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.

     (21) Pppp??????????...1122nn

    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.

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