stock index futures real-time buying and selling decision

2002年管理創新與新願景研討會 G-12

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

E-mail：[email protected]

Second Author: CHIE-BEIN CHEN

Institute of International Business, National Dong Hwa University

E-mail: [email protected]

Third Author: SHIN-YUAN CHANG

Graduate Institute of Management Science, Ming Chaun University

E-mail: [email protected]

No. 250, Sec.5, Chung Shan N. Road Taipei Taiwan

Tel: 886-2-28824564 ext. 2401

Fax: 886-2-288-9764

E-mail：[email protected] or [email protected]

ABSTRACT

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

engineering

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

swap….etc.

mailto:[email protected]





G-13 2002年管理創新與新願景研討會

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

Taking Online Stock Index Futures from Database


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.

RTDSS

ConstructingReal-Time Buying and Selling Prediction Model

1.Regression Model for

Constructing

2.Partial SPRT Model for

Testing

Result Presentation

The Evaluating Process

1.Accuracy of Buying and Selling2. No. of Buying3. No. of Selling4. 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 , this function relationship can be

expressed as

, (1)

where any observed value in the population would be a function of the true mathematical model

plus some residual . The population regression model can be re-expressed as

, (2)

where the two unknown parameters and are necessary for determining a straight line. is the

true intercept; a constant factor in the regression model representing the expected or fitted value of when

= 0. is the true slope; it represents the amount that changes (either positively or negatively) per 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 obtaining estimates

(for ) and (for ) from the sample. Usually, this is accomplished by employing the method of

least squares (MLS). With this method the statistics and are computed from 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

(3)

such that is minimized.

In using the least-squares method, the following two normal equations are developed:

(4)

(5)

and solving simultaneously for and , we compute

(6)

and

XbYb 10ˆˆ

(7) so that the sample regression equation

Conclusions


is obtained.

2.2 Partial Sequential Probability Ratio Test

In order to determine the quality of straightness of the edge, a hypothesis test and the Sequential

Probability Ratio Test for slope and intercept of the estimated mean line were used. Partial sequential

tests for two parameters of slope and intercept of simple regression were developed by Arghami and

Billard (1987).

Let (xi, yi), i = 1, 2, .... be pairs of peak points. Assume the null hypothesis

H0 : = 0 = , (8)

and the alternative hypothesis

Hl : = l = + , (9)

or Hl : = 1 = - ,

where, yi is independent and

yi N ( + xi, 2), i = 1, 2, ..... (10)

and is the parameter of interest, while and 2 are nuisance parameters. A transformation similar

to that used in Arghami and Billard (1987) can eliminate the nuisance parameters and 2. Then Partial

SPRT based on the transformed variables can be performed.

To do this, take n0 ( 3) pairs of initial points (x1, y1), ....., (xn0, yn

0) and compute the minimum

variance unbiased estimator of 2,

(11)

where

And r0 is the correlation coefficient of x and y based on the n0 initial points and ,

. Take nl additional pairs of points, where nl is the smallest integer ( ) such that


(12)

where n* = n0 + nl ,

,

,

and zl is a positive number independent of yi, i = 1, 2, ..., which may depend on xi, i = 1, 2, .....

However, a set of real numbers pl, ..., pn* can be found in a pre-specified way such that

is proportional to , i = 1,2, ..., n0,

and

Then, let *

11 1

ni i

i

p yU

z

(13)

Next, take n2 pairs of points where n2 is the smallest integer (> 2) such that

(14)

where

wi = xi - , i = n*+1, ...., n*+n2

and z2 is a positive number independent of yi, i =1, 2, ...., which may depend on xi, i = 1, 2,.....

However, a set of real numbers ql, ..., qn2

can be found in a predetermined way such that


and

Then, let

(15)

Similarly, compute Uj, j = 3, 4,..., using positive numbers zj, j = 3, 4, ....., which are independent of the yi

but may depend on the xi.

It can then be shown that the joint density of Ul, ...., Um is

j1,

2, ….., m, (16)

where j

= .

To perform a Partial SPRT with levels of risk and for the hypotheses in upper eauation, proceed as

follows:

(1) If ,then accept ; (17)

(2) If , then accept ; (18)

(3) If take an additional

observation; (19)

where


j = 1, 2, ......., m,

j = 1, 2, ......., m.

Figure. 1 shows an illustration of m waves and the number of , and , where m = 3, = 5

points, = 3 points and = 4 points.

Figure 1 The Illustration of the Number of , , and

Figure 2 illustrates both limits of and , where = 0.05, = 0.1 and

= 30, at different number of clusters, . It is seen that the more clusters, the closer of these two limits.

That is when the number of cluster increases, the upper limit decreases and the lower limit will increase

simultaneously. Thus, when is very large, the probability of additional observation is less. This will

accelerate to accept or reject .


Note: curve A: and curve B: , where = 0.05, =0.1 and = 30

Figure 2 The Relationship of two boundaries at different number of clusters

Theoretical proof is expressed in the following:

= (20)

2.3 Decision Rule and Evaluating Process of RTDSS

Figure 2 illustrates the decision-making flow chart. At first, when is positive and if the test value, ,

is larger than the boundary of curve B at different , that is fallen into reject area of . At this time,

RTDSS will send out the message of “selling”. Since the hypothesis is = and : = - t =

-0.2 . Therefore, when test value, , is fallen into reject area of , it means is accepted and the

newest data decline the slope of the regression line.

Secondly, when is negative and if the test value, , is larger than the boundary of curve B at

different , that is fallen into reject area of . At this time, RTDSS will send out the message of

“buying”. Since the hypothesis is = and : = + t = + 0.2 . Therefore, when test

value, , is fallen into reject area of , it means is accepted and the newest data increase 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.

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)

where and is the continuous selling (or buying) message provided by 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.


Figure 3 The Messages of Selling and Buying Sending by RTDSS

3. Empirical Experiments

3.1 Source Data

In recent years the total trading volume in Taiwan stock market has concentrated in two sectors, the

electronic industry and financial industry. Especially, the trading price of electronic industry is the most

active and volatile sector in Taiwan Stock Exchange (See Figure 5.1). However, the average capitalization of

financial firms is larger than other sectors in Taiwan Stock Exchange. Both electronic and financial industries

are high influential to the Value Weighted Index of Taiwan Stock Exchange. Therefore, the experimental data

of TAIEX-ESIF is selected and started from Feb. 20 2001 to Mar. 2 2001, 8 transaction days.

3.2 Experimental Results

DNBS, GL and TT are used to evaluate the performance of the RTDSS. And the parameters, the

constraint of , , , the hypothesis of and the sample size , are set in the table 1. And table 2

illustrates the raw results of seven transaction days and the average results.

Table 1 The value of five parameters

the constraints

of

the hypothesis

of

the sample size

0.005 0.03 0.25 0.225 35

4. Conclusion

The presence of TAIEX Futures, TAIEX Electronic Sector Index Futures, TAIEX Banking and Insurance

Sector Index Futures and SIMEX MSCI TSI Futures represents several meaningful progressions for the

capital market in Taiwan. The contemporary market consists of the three different kinds of trading strategies,

Table 2 The raw results of seven transaction days and the average outputs

The number of

transaction daysDNBS GL TT


1 1 18883 4

2 0 2257 2

3 1 6470 4

4 0 4362 2

5 1 4455 4

6 1 -1401 2

7 1 2563 4

ave 0.63 4311.28 3.5

including speculation, hedge and arbitrage. 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 purpose 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. Thus, in order to provide real-time

suggestions for investors, the partial SPRT method has been applied to RTDSS. Thus, the achievements of

this research are:

(1) a real-time RTDSS by simple regression model and partial SPRT method for investors obtaining

exceed revenue from the TAIEX-ESIF has been constructed;

(2) the effectiveness of trading to pursuit the net profit by experiment has been conducted;

In this research, the upper four objectives are certainly reached. The research results not only provide an

real-time support system but prove Partial SPRT is one of decision-making methods on financial engineering.

That is SPRT method applies on only manufacturing and medical engineering but financial engineering. In

this research, we use the TAIEX Electronic Sector Index Futures for empirical data. In fact, we could also

apply Partial SPRT on many other financial areas such as warrant, option, negotiable security, asset swap.

REFERENCE

[ 1 ] Arghami, R. R. and Billard, L., “Partial Sequential Test for the Parameters of Simple Regression,” New

Perspectives in Theoretical and Applied Statistic, 1987, pp. 413-418.

[ 2 ] Baxt, W. G. and White, H., “Bootstrapping Confidence Intervals for Clinical Input Variable Effects in a

Network Trained to Identify the Presence of Acute Myocardial Infarction,” Neural Computation, Vol. 7,

1995, pp624-638.

[ 3 ] Brock, W., Josef, L. and Black, L., “Simple Technical Trading Rules and the Stochastic Properties of Stock

Returns,” Journal of Finance, Vol. 47, 1992, pp. 1731-1764.

[ 4 ] Chen C. B., Wei C. C., “Efficient sampling for Computer Vision Straightness Inspection”, Computer

Integrated Manufacturing Systems, Vol. 11, No. 3, 1998, pp. 135-145.

[ 5 ] Chen, C B, “Efficient Sampling for Computer Vision Inspection in Automated Quality Control”, Master


Thesis. University of Missouri-Columbia, 1989.

[ 6 ] Chen, C. B. and Wei, C. C., “Efficient Sampling for Computer Vision Roundness Inspection”,

International Journal of Computer Integrated Manufacturing, Vol. 10, NO. 5, 1997, pp. 346-359.

[ 7 ] Chou, S. C., Chen A. P., “Using Artificial Intelligence Techniques to Improve the arbitrage Strategy in the

Taiwan Stock Market”, Master Thesis, University of National Chiao Tung University, 2000.

[ 8 ] Gencay, R. and Stengos, T., “Moving Average Rules, Volume and the Predictability of Security Returns

with Feedforward Networks,” Journal of Forecasting, Vol 17, 1998, pp. 401-414.

[ 9 ] Hsu T. Z. et al., “An Investigation of the Spread and Arbitrage of the TAIMEX stock Index Futures,”

Master Thesis, National Cheng Kung University, 1999.

[ 10 ] JOHNSON N. L, A Simple Theoretical Approach to Cumulative Sum Control Charts, JASA, 1961, pp.

835-840

[ 11 ] Wald, A. (1947).　Sequential Analysis.　New York, NY: John Wiley & Sons, Inc.

[ 12 ] Wu, Y. C. and Lee C. Y., “A Decision Support System for the Arbitrage on Index Futures for Taiwan Stock

Price Index Futures”, Master Thesis , Chinese Culture University, 2000.

[ 13 ] Yang, Y. H., Chiang, Y. M. and Tsaih, R., “Applying run technical analysis in investment: experiment of

NASDAQ index,” Master Thesis , National Chengchi University, 2000.