CHAPTER 1 Introduction
1.2 Investor Sentiment
In this study, we discuss the timing of trading stock portfolio. In practice, investors are not just following the basic information of the stock trading; more investors will use their preferences and emotions as the basis for judging stock. However, this does not meet the assumptions of traditional investment theory, so we are closer to the reality of choice to investor's sentiment as the decision to buy and sell stock timing. Besides, referencing to investor sentiment can solve the problem of investors not being able to cope with the above-mentioned major events. The following describes the background and impact of investor sentiment.
In 1970, Fama proposed a theory called Efficient Market Hypothesis (EMH) [14]. The study assumed that the market is efficient, investors are rational, and stock prices can respond quickly and entirely to all real-time information. The EMH is one of the most important theories in finance. Under this assumption, scholars examine how the market evaluates stock or return rates and then use their findings to predict stock prices to get the high excess. However, EMH cannot explain the problem of the overreaction of stock price.
The overreaction problem means that when the bull market comes, the stock will continue to rise, far exceeding the investment value of listed companies; and when the bear market
comes, the stock will continue to fall, and it will fall to the extent of being unacceptable. The overreaction problem resulted from the many uncertainties concerning the company's future value. It is precisely this uncertainty that caused the irrational and psychological factors of investors, and the absurd attitude common among investors led to the plunge or surge of the stock market [11]. Besides, there are some noise traders who will react to non-fundamental news, and that will have an impact on stock prices and transactions [10]. In other words, it is not just the fundamentals and overall economic factors that affect the stock price; other trading activities such as noise traders will also do so.
Investor sentiment is one of the irrational factors that cause the transaction of noise. It represents the subjective judgment of an investor’s mentality to the volatility of the stock market. The phenomena derived from investor sentiment includes stock price overreaction, closed-end fund discount, and other events, which will challenge the efficiency of the market hypothesis. These phenomena can be used to predict future rewards of company stocks [31].
This study combines DGSP with investor sentiment. The rest of this paper is organized as follows. Related work and background knowledge are described in Section 2. The data processing elements of the proposed approach, algorithm and example are stated in Section 3.
Extensive experiments on real datasets are stated in Section 4. Conclusions and recommendations for future work are in Section 5.
CHAPTER 2
Related Work and Background Knowledge
2.1 The M-V Model
In 1952, Markowitz proposed the mean-variance (M-V) model and conducted a systematic, in-depth and fruitful study; he won the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. M-V model uses an efficient frontier to describe the risk in a portfolio and to help investors decide asset combinations [28] [30]. Markowitz established two basic assumptions for the model. The first assumption is that investors are risk averse and pursue the desired utility maximization. The second assumption is that the investor chooses the portfolio based on expected rate of return and the variance of return. The third assumption is that the investor's investment period is the same. In other words, the model is to find the portfolio (asset allocation) with the highest return and the lowest risk in the same investment period.
In the M-V model, the total return of the portfolio is expressed as a weighted average of the expected returns of each asset, and the risk of the portfolio is expressed as the variance or standard deviation of the gain. The M-V model is as follows:
cov( , ),where rp is the return in the portfolio p, σ2(rp) is the risk value which depends on the variance value in the portfolio, n is the number of assets in the portfolio, wi and wj are the weights of assets i and j, cov(ri, rj) is the covariance value for assets i and j, and E(rp) is the expected value of return in the portfolio. In the different expected benefits, the M-V model gets the corresponding variance of the smallest combination of assets. The combination of the expected rate of return and the corresponding minimum variance forms the return-risk curve. On the curve, investors can choose the optimal portfolio based on their earnings goals and risk appetite.
2.2 Grouping Genetic Algorithm and Grouping Problem
The genetic algorithm (GA) was first proposed by Holland in 1975 [22]. Holland used the principle of biological inheritance and natural selection to develop the operations of GA. The components of GA contain chromosome representation, genetic selection, genetic crossover, and genetic mutation. GA can provide feasible solutions within a limited time or within a limited number of times. GA has been applied to many fields, e.g., fuzzy logic controllers, machine learning [19]. There are some research used to optimize GA like [19]. With the advantages of fast operation, it often used to solve problems which are difficult to be solved [20]. In 1994, Falkenauer proposed group genetic algorithm (GGA) based on GA for solving the grouping problem [15]. There were many researches related to GGA [16] [17] [26]. The grouping problem is attempting to divide n elements into K groups and make the number of objects in groups as similar as possible. The structure and process of the GGA are the same as GA, but the components are different.
In Falkenauer’s GGA representation, a chromosome consists of object part and group part.
The object part stores the information about how the objects are grouped, and the group part is an ordered list of the groups. An example of a complete chromosome is shown below:
ABBAC | ABC
In this example, the object part is located before the vertical bar, and the group part is after it. In the object part, there are five objects partitioned into three groups. In the group part, the names of the groups are recorded as a sequence. This chromosome represents that the objects o1 and o4 belong to group “A”, the objects o2 and o3 belong to group “B”, and the object o5
belongs to group “C”. There are three genetic operations of GGA including crossover, mutation, and inversion.
The crossover operation in GGA is different from GA. For instance, we assume that chromosome C1 is base chromosome and chromosome C2 is insertion chromosome, two chromosomes are shown as follows:
C1: A: {o1, o4}, B: {o2, o3}, C: {o5}, C2: a: {o1, o2}, b: {o3}, c: {o4,o5}.
First, we randomly select the positions of the base chromosome in the group part. Then assume that the position of the insertion in the base chromosome is between groups B and C.
And, the insertion group selected from C2 is group b. After crossover, the result shows as follows:
C1': A: {o1, o4}, B: {o2, o3}, b: {o3}, C: {o5}.
In chromosome C1', it has four groups and objects o3 are duplicated. Obviously, C1' should be adjusted. The objects o3 are removed from groups B. Then, the adjusted chromosome is as follows:
C1'': A: {o1, o4}, B: {o2}, b: {o3}, C: {o5}.
One group will be selected to remove because the number of groups in C1'' is four and the desired number of groups is three. Assume the group C being picked and the object o5 in group
C being moved to group B, the final result shows as follows:
C1''': A: {o1}, b: {o4, o5}, C: {o2, o3}.
In the mutation operation in GGA, we randomly move an object in a group to another group. Using C1''' for example, if the selected object is o3 and moves to group A, the C1''' will become C1'''' after mutating. The chromosome C1'''' shows as follows:
C1'''': A: {o1, o3}, b: {o4, o5}, C: {o2}.
In the mutation operation in GGA, we randomly change the order of the groups in the chromosome. Take chromosome C2 as an example. If two groups a and b are selected to exchange, after inversion, the result is shown as follows:
C2': b: {o3}, a: {o1, o2}, c: {o4, o5}.
There are many approaches using to deal with various grouping problems based on GGA.
Hong et al. proposed an algorithm for improving the performance of attribute clustering by using GGA [25]. Quiroz-Castellanos proposed GGA with controlled gene transmission (GGA-CGT) for bin packing [33]. Pankratz used the adaptation of the GGA to solve the vehicle routing problems [32]. Rekiek employed the GGA for the handicapped person transportation problem [34].
2.3 Maximally Diverse Grouping Problem
In the previous chapter, we describe the grouping problem. The goal of the grouping problem is to divide n elements into K groups, with numbers of objects in groups as similar as possible, and each element belonging to a group. There is a research discussing the effect of diversity in grouping problem [29]. Therefore, the maximally diverse grouping problem (MDGP) starts to be discussed. The MDGP considers the diversity in the traditional grouping
problem. MDGP is to get maximal diversity among the elements in each group. Formally, the formulas of MDGP is as follows:
, between each pair of objects.
There is a research used to prove that MDGP is the NP-hard problem [4]. Therefore, there are many heuristic approaches proposed to solve MDGP [3] [4] [9] [18] [29] [35] [40] like the hybrid genetic algorithm [18], the variable neighborhood search [3], and the artificial bee colony algorithm [35]. Then, Chen et al. proposed an algorithm for mining stock portfolio for solving MDGP [9].
2.4 The Proposed Method for Stock Portfolio
In this section, we explore the literature on the stock portfolio. In 1952, Markowitz proposed the M-V model to lay the foundation for the theory of stock portfolio [28]. After the M-V model has been proposed, there are many studies carried out on the selection of portfolio.
Although this issue has been raised for a long time, there are still many studies to explore it until now. The following describes the recent discussion of the stock portfolio of literature.
The theory of stock portfolio is roughly divided into two categories depending on whether a model is used or not. Some research with a stock portfolio model is first introduced below [12] [21] [22] [37] [38]. Escobar et al. proposed a model for closed-form solutions that was for optimal allocation and value functions [12]. With the model, they pointed out that the stock return predictability significantly affects the optimal bond portfolio and the hedge components were larger in bond portfolio than the respective hedge components in stock portfolio. Sun and Liu established the empirical cross-correlation matrices to improve portfolio optimization by combining the Pearson’s correlation coefficients (PCC) method and the detrended cross-correlation analysis (DCCA) method. In the experiment, the stability analysis of portfolio weights demonstrates that the PCC method matrix has a greater effect than the DCCA method matrix on the portfolio weight stability [37]. Yu et al. developed two CVaR-based robust portfolio models. The first one is worst-case conditional value-at-risk (WCVaR) model, and the second one is relatively robust conditional value-at-risk (RRCVaR) model. They find that when required return is fixed, the RRCVaR model brings higher returns, lower trading costs, and higher portfolio diversity than the WCVaR model [38]. Then, some research without a stock portfolio model is introduced below [1] [5] [7] [13] [24] [42]. Baralis et al. presented an itemset-based approach to automatically identify promising sets of high-yield but diversified stocks to investors. They investigated the usage of itemsets to generate appropriate stock portfolios and recommend them to investors from historical stock data [1]. Thakur et al. used the fuzzy Delphi method to identify the critical factors in input data. They then used critical factors and historical data to rank the stocks by the Dempster– Shafer evidence theory [24].
There are still many approaches in progress.
2.5 Investor Sentiment Index
In 1990, DeLong et al. proposed the noise trader model [10]. The model considers that in the market there are some noise traders who give not only excessive response but the low response to information, which directly affects the stock price equilibrium and result to market risk rise. Investor sentiment is one of the irrational factors that cause the transaction of the noise. It represents the subjective judgment of the investor based on his attitude to the future stock price rising or falling. Hence, many studies have begun to look for emotional factors that can reflect the future changes in the stock market for traders. Schmeling used a new data set on investor sentiment to show that institutional and individual sentiment proxy for smart money
and noise trader risk.
In 2001, Brown et al. indicated that if investors believe that the actual value of the stock is higher than (below) the current price, their mentality will tend to be optimistic (pessimistic) [2]. The authors also found that investor sentiment will be affected by past stock returns and the degree of emotional volatility is also highly correlated with the stock returns in the same period. Schmeling used a new data set on investor sentiment to show that institutional and individual sentiment proxy for smart money and noise trader risk [36]. Lee et al. found that there is a close relationship between investor sentiment, market volatility and excess return [27].
The following describes the research related to investor sentiment indices. In 1998, Neal et al. researched the three investor sentiment indices including the degree of closed-end funds discount, odd-lot ratio, and net redemptions for forecasting stock returns [31]. They found that the degree of closed-end funds discount and net redemption are predictable for small companies, and the odd-lot ratio has no predictability for either large or small company. In 2000, Barber et al. considered that there is a strong negative relationship between the IPO rate and the following year's market returns [6]. This relationship can provide a stronger market return prediction. In 2012, Wang et al. pointed out that there is a high correlation between the three retail sentiment variables including the buy-sell imbalance, the individual investor turnover and the proportion of day-trades [41]. This result indicated that these three variables are likely to capture similar retail investment behaviors.
CHAPTER 3
Proposed Approach
In this section, we will introduce our proposed approach, which uses two investor sentiment indices in the grouping genetic algorithm to obtain a diverse group stock portfolio. We first design some rules based on two sentiment indices to decide the buying and selling points of all the input stocks. These stock price data with buying and selling points are then sent to the proposed based approach for obtaining a best group stock portfolio. The proposed GGA-based approach will use the sentiment indices and the other factors in its fitness to evaluate the chromosomes (possible group stock portfolios). After a predefined number of generations, the chromosome with the best fitness value at the last generation is output as the diverse group stock portfolio. The flowchart of the proposed approach is given in Fig. 1.
Fig. 1. The flowchart of the proposed approach.
Fig. 1 shows that the input data is preprocessed by trading strategy generated from investor sentiment index and trading signal. And, it puts the preprocess data into the grouping genetic algorithm to produce the best derived diverse GSPs with investor sentiment index. The components of the proposed approach are described as follows.
3.1 Data Preprocessing: Trading Strategy
For considering the sentiment factor in the proposed GGA-base approach for finding a good group stock portfolio, we first transform the input stock price sequences to the ones with sentiment considered. We design some rules based on two sentiment indices to decide the buying and selling points of all the input stocks.
Most of the portfolio research topics focus on how to find a high-risk and low-risk portfolio; however, little research is proposed to provide users with trading time points of the stock portfolio. In this study, we provide users with trading timings for each trading period. For instance, we assign the trading period from 2014 to 2016. With this research, we accurately informed consumers to buy the stock on February 3, 2014, and sell it on December 24, 2016.
What is more, this study still retains the advantages of high-risk and low-risk of traditional stock portfolios.
In this study, the decision rules for determining the timing of buying or selling the stocks are based on the investor sentiment index. In the previous chapter, there are many indices that can reflect the investor's sentiment, called investor sentiment index. After filtering, we choose the research [41] to provide investor sentiment indicators as the basis for this study. There are three reasons for selecting the investor sentiment indices. First, the sentiment indices provided by the paper apply to the Taiwan stock market and it consists with the data used in this paper.
Due to the different rules of the transaction, the floating price of the stock in different regions
will be different, and the impact of investor sentiment indices will also be affected. Therefore, selecting the same range of research as our paper is important. Second, the formulas for investor sentiment indices are clear and easy to understand. Too complicated formulas not only difficult to directly express its meaning but also cause the overlong operation time. Third, the indices are designed based on the behavior of retail investors. In Taiwan, retail investors' trading volume accounts for 70% of Taiwan's overall trading volume for the stock market. Therefore, studying Taiwan's retail investors' behavior is more meaningful and persuasive. Next, we introduce the two investor sentiment indices used in this paper to reflect the investor's sentiment.
The first index is called Buy-Sell Imbalance (BSIt), which is defined as follows:
,
The parameters in this formula are as follows: BMLt is the balance of margin loan of the stock on the day t; BSLt is the balance stock loan of the stock on the day t; Vt is the trading volume of the stock on the day t; BIt is the buying volume of institutional investors of the stock on the day t; and SIt is the selling volume of institutional investors of the stock on the day t.
With these defined parameters, BSIt means the value of buy-sell imbalance of the stock on the day t, VBt means the retail investors' buying volume of the stock on the day t, and VSt means the retail investors' selling volume of the stock on the day t.
Then we explain the proper terms used. The margin loan is an investor’s behavior which means investor borrows money from securities dealer to buy the stock. In Taiwan, the securities
dealer will borrow 60% of the value of the stock to investors with good credit to purchase the stock. For example, we assign that the price of the stock is one hundred, and the value of the stock is one hundred thousand. It means that investors can only use forty thousand to hold the stock by margin loan. In general, investors expect that stock price will rise in the future, but the hands of the funds is not enough; then they pay a part of the margin to securities dealer to borrow money for buying stock, and then wait for an opportunity to sell the stock at high prices and earn low selling low spreads. In contrast to a margin loan, the stock loan means investors borrow stock from securities dealer to sell it. If investors expect that stock price will fall in the future, they can borrow stock from securities dealer to sell by the stock loan. The trading volume represents the total number of transactions including institutional investors and retail investors, where institutional investors include foreign investment institutions, investment
dealer will borrow 60% of the value of the stock to investors with good credit to purchase the stock. For example, we assign that the price of the stock is one hundred, and the value of the stock is one hundred thousand. It means that investors can only use forty thousand to hold the stock by margin loan. In general, investors expect that stock price will rise in the future, but the hands of the funds is not enough; then they pay a part of the margin to securities dealer to borrow money for buying stock, and then wait for an opportunity to sell the stock at high prices and earn low selling low spreads. In contrast to a margin loan, the stock loan means investors borrow stock from securities dealer to sell it. If investors expect that stock price will fall in the future, they can borrow stock from securities dealer to sell by the stock loan. The trading volume represents the total number of transactions including institutional investors and retail investors, where institutional investors include foreign investment institutions, investment