Discrete Dynamics in Nature and Society

Volume 2018, Article ID 4783214, 13 pages

https://doi.org/10.1155/2018/4783214

## Investor Sentiment and the Basis of CSI 300 Stock Index Futures: An Empirical Study Based on QVAR Model and Quantile Regression

College of Economics and Management, China Agricultural University, No. 17 Qinghua East Road, Haidian Zone, Beijing 100083, China

Correspondence should be addressed to Chen Liu; moc.361@91793912031

Received 5 February 2018; Revised 14 October 2018; Accepted 16 October 2018; Published 13 November 2018

Academic Editor: Filippo Cacace

Copyright © 2018 Chen Liu and Yi An. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The asymmetrical mutual influence of investor sentiment and the basis of CSI 300 stock index futures under conditions in different market situations was investigated using the quantile vector autoregressive model (QVAR). The article also discussed asymmetrical influence of investor sentiment on the basis under conditions in different investor structures using the quantile regression method. On this basis, we obtained several important conclusions: 1 There exists a one-way causal relationship where investor sentiment has a significant impact on the CSI 300 stock index futures basis in China; the investor sentiment is likely to exert stronger influences on the basis in the chaotic period of the stock market and imposes significant asymmetrical effects. 2) The institutionalized development of investors can reduce the influences of investor sentiment on the basis when the stock market is stable, while it does not play its function in stabilizing the capital market when the stock market is in turmoil. 3) The low institutionalization level, the individualization of institutional investors, and the imperfect short-sales mechanism as a whole are still the sticking problems in the immature capital market of China.

#### 1. Introduction

The basis of CSI 300 stock index futures is the difference between the CSI 300 spot index and futures index and plays an important role in the information transfer of the capital market. It does not only provide investors with diverse risk management strategies, but also help to improve the scale and structure of China’s capital market. Its hedging effectiveness is also a direct reflection of China’s capital market operation efficiency and has an important guiding significance deepening of the capital market. Generally in an efficient market, the difference between the futures and spot prices will not have a large systematical deviation. However, the abnormal phenomenon occurs to the price difference under extremely special conditions. For example, the futures index showed substantial discount relative to the stock index and the basis strengthened during the Chinese stock market crash in 2015. Such significant discount is a great problem in the operation of the capital market and needs to be deeply studied and interpreted.

For a long period to come, what the capital market and the theoretical circle both need to systemically consider are the following questions: whether there exists the interaction between the basis of stock index futures and Chinese investors’ sentiment, whether the asymmetrical interaction between investor sentiment and the basis varies in different market situations, and whether the improvement of the institutionalization of the capital market in China is in favor of alleviating the abnormal effects of the investor sentiment on the basis. Studying and answering these questions can comprehensively analyze the relationship between investor sentiment and the basis and sufficiently unveil the hedging and pricing efficiencies of the stock index futures market in China. This is of great reference significance for the formation of market investment strategies and the decision adjustment of the regulatory agencies.

The paper is divided into six parts: Section 1 is the introduction, Section 2 reviews the relevant literatures, Section 3 puts forward the hypotheses to be tested and the research design, the selected sample data and descriptive statistics are provided in Section 4, Section 5 reveals the results of the empirical analysis on the relationship between the investor sentiment and the basis, and Section 6 draws the conclusions and the inspirations.

#### 2. Literature Review

##### 2.1. Research on the Relationship between the Basis and Investor Sentiment

Many factors in the capital market have influences on the trend of the basis, including market liquidity and volatility, risk-free interest rate, and investor structure (Marcinkiewicz, 2014) [1]. It was pointed out by Baker and Stein (2008) [2] that the liquidity can be taken as the investor sentiment index in the market with short-sales constraints. Noise traders generally have irrational buying behaviors when they are in high spirits, and the demand shocks will improve the liquidity of the securities market. A market with high liquidity commonly presents low transaction cost and impacts cost of stock, which further drives the rise in the stock price. Roll et al. (2007) [3] studied the liquidity of the New York Stock Exchange (NYSE) and the futures-spot basis of its component index. They concluded that the two have the Granger causality. Through the impulse response analysis of the bivariate VAR model, they found that the liquidity has greater short-term influences on futures-spot arbitragers. Moreover, among the literatures on the factors affecting the basis, some scholars found the Granger causality relationship between the liquidity and the basis (Lien et al., 2013; Li and Guo, 2017) [4, 5].

As scholars across the world constantly deepen the research on the investor sentiment and the behavioral bias, some literatures begin to focus on the influences of investor sentiment on the securities market. Investor sentiment reflects the expectations of investors for the future of the market. Because investor sentiment cannot be directly measured, previous researchers basically construct investor sentiment index by using single or multiple sentiment factors. Investor sentiment is also responsible for the irrational fluctuations of the stock price. Scholars across the world have found that investor sentiment has a significant relationship with the market volatility, which indicates that the higher the investor sentiment level, the greater the volatility of the stock market (Yang and Gao, 2014; Wang et al., 2017) [6, 7]. Different from the above literatures, Zheng and Lin (2015) [8] found there is no significant relationship between the liquidity and the pricing bias of the CSI 300 stock index futures through the VAR model. Instead, the investor sentiment is the dominating influence factor of the pricing bias in China. On the whole, scholars carried out few studies on the relationship between investor sentiment and the basis. Zou and Sun (2012) [9] obtained a valuable research finding which is worth using to study the relationship between the investor sentiment and the basis. They found that the investor sentiment exerts different degrees of influences on the trade in different market situations, and the investor sentiment also has different impact on the returns and volatility of the stock market. Therefore, it is very necessary to study whether investor sentiment and the basis of stock index are mutually influential or not in different market situations, especially in the time period before and after the capital market turning from the steady operation to the unsteady one in China. If the mutual influence changes, what are the changes and what influences will they bring about?

##### 2.2. Improvement of the Research Methods

Overseas studies on the relationship between the change of the basis and the relevant influence factors mainly use analysis methods including the VAR model and Granger causality test (Roll, 2007; Kadapakkam and Kumar, 2013; Han and Pan, 2016) [3, 10, 11], while investigations into the asymmetrical impacts of the liquidity or the investor sentiment on the basis are hardly seen. The commonly used methods are confined to setting dummy variables or using models (asymmetric GARCH model or piecewise regression model). However, these methods have shortcomings of losing samples and therefore cannot effectively measure the asymmetrical mutual influence between the basis and investor sentiment.

Based on the above literatures, the current research divided the market into the steady and chaotic situations from a new perspective, in order to explore the relationship between investor sentiment and the basis in different market situations. For the first time, we use the quantile vector autoregressive model (QVAR) method to analyze the asymmetrical mutual influence between investor sentiment and the basis. Different from the processing methods used by previous researchers, this method is superior to the VAR model as it can be used to analyze the relationship between two variables at different quantile levels. It is also superior to quantile regression that can provide more robust regression results and avoid endogeneity caused by causal relationship.

#### 3. Hypotheses to Be Tested and Research Design

##### 3.1. Hypotheses to Be Tested

According to the above literature review, we summarize key research issues from three aspects to further analyze the hypothesis: Firstly, the investor sentiment can influence the basis directly through the supply-demand relationship or by indirectly impacting the market liquidity and volatility. When the investor sentiment grows, investors find that the hedging and arbitrage are less attractive but tend to the unilateral speculation for the stock index futures (high-risk assets). The increasing market liquidity and volatility further lessen the basis, which is apt to cause futures premium. On the contrary, as the market sentiment reduces, investors’ pessimistic judgment of index trend will be reflected by the price of the stock index futures, which is likely to propel the discount of stock index futures and strengthen the basis. Therefore, it can be seen that the investor sentiment is the factor leading to the change of the basis which declines with the growing index of the investor sentiment while it increases with the decrease of the index. Meanwhile the degree of basis discount reflects the expectations for futures market, giving the wrong information to the noise trader. Because of Chinese futures market's immaturity and lack of arbitrage trading, insufficient liquidity in the capital market cannot be effectively reflected in investor sentiment. Compared to the impact of investor sentiment on the basis, the impact of the basis on investor sentiment may not be significant.

Secondly, investors’ psychology and behavior are affected by the market environment in different market situations. Meanwhile, the interaction between basis and investor sentiment also varies in different market situations. This is because the market situation can be reflected in the characteristics of capital market prices and volatility. Whether the market is stable or not will affect investors’ judgment on the capital market situation; this subjective judgment will bring about the corresponding trading behavior. It will be reflected in the premium of the stock index futures and the stock index futures basis. In summary, investors will have different trading behaviors due to the different market conditions and investors will also generate different levels of mood fluctuation based on the basis in different market situations. So the impact on the basis will also be different. The mutual influence between investor sentiment and basis changes as the market situation changes.

Thirdly, the asymmetrical short-sales mechanism of the spot market commonly restricts the reverse cash and carry arbitrage, which is the leading cause for the asymmetric effects of the investor sentiment on the basis. In the same way, investors will also generate a different level of mood fluctuation based on the different level of the basis. Moreover, the change of the basis is the result of multiple influence factors. The psychological and behavioral biases of investors in the periods of futures premium and discount also can induce the asymmetrical change of the sensitivity of these factors to the basis.

Fourthly, irrational noise trade is likely to result in the continuous rise of the market price and the theoretical price. From the perspective of trading behavior of different types of investors, Lee et al. (2012) [12] found from empirical research that irrational behaviors of investors in different structures have different influences on the basis. Therefore, the effects of the investor sentiment on the basis can be probably impacted by different investor structures: institutional investors in the market are basically more rational in terms of the investment (Daniel et al., 1997) [13], while individual investors are more likely to behave irrationally while making their investment decisions (Odean, 1998) [14]. When the number of individual investors grows in the market, the soaring investor sentiment can amplify the irrational buying behavior and leads to the continuous increase of the basis. Based on the four aspects, the following four hypotheses (1~4) to be tested are proposed:

*Hypothesis 1. *Under the same market situation, there exists a two-way causal relationship or one-way causal relationship between investor sentiment and basis. The basis decreases with the enlarging index of the investor sentiment and increases with the decline of the index

*Hypothesis 2. *The mutual influence between investor sentiment and basis changes in different market situations

*Hypothesis 3. *Under the same market situation, the mutual influence between the investor sentiment and the basis presents asymmetric character

*Hypothesis 4. *The institutionalization level of the capital market changes the influences of the investor sentiment on the basis

##### 3.2. Variable Construction

###### 3.2.1. Selection of Indicators (Explanatory Variable/Endogenous Variable) of the Investor Sentiment

When selecting the direct indictors of the sentiment, CCTV BSI and some macroeconomic factors (industry prosperity index, consumer confidence index, and economist confidence index included) are generally used in the Chinese capital market. However, these indicator data present poor continuity and consistency and whether the data are compiled rationally remains to be further checked through the practice. In the academic circle, the majority of scholars in China carry out investigations using sentiment proxy variables, such as closed-end fund premium/discount rate, price-earnings ratio (PE), new trading accounts, initial public offering (IPO) shares, IPO initial return, and some indicators of market liquidity. Because the liquidity data are difficult to measure, domestic scholars (Zheng and Lin, 2015) [8] adopted the turnover and the trading volume as the proxy indicators of the liquidity, which are able to reflect the changes of the investor sentiment to some extent. The current research discriminates these sentiment variables, so as to establish the model. The reasons are as follows: Firstly, the IPO shares and the IPO initial return are influenced by many human factors and the increase in the IPO shares of enterprises is a long-term process, so they are not suitable for reflecting the investor sentiment. Secondly, China has comprehensively loosened the restriction that “one person can only have one account” in the A-share market since April of 2015, so the new trading account loses its representativeness as the indicator of investor sentiment. It, however, can be replaced by the number of investors newly participating in the trade. Thirdly, Kumar and Lee (2006) [15] used the ratio of the difference between the buying and selling volumes of stock to the total trading volume to represent the investor sentiment. Their empirical analysis reveals that the indicator more accurately represents the investor sentiment in explaining the stock price change than the closed-end fund premium/discount rate. Therefore, the ratio of the difference of the active buying amount minus the active selling amount to the total trading volume is taken as the active buying rate indicator in the spot market. As the data of active buying and selling are difficult to attain, the net inflow of funds in the CSI 300 block is regarded as the proxy variable for the difference between the active buying amount and the active selling amount. After eliminating the extreme situations such as circuit breakers of the stock market, the weekly average net inflow of funds is used as the indicator of the active buying rate in the spot market. And fourthly, the trading volume and the turnover can describe the variation of the investor sentiment and further affect the liquidity of the futures and spot markets, so the ratio of the trading volume to the circulated stock value is taken as the turnover of the market.

Based on the above considerations, the research selects the number (num) of investors newly participating in the A-share trade in the end of a phase closed-end fund premium/discount rate (prem), market turnover (turnover), average price-earnings ratio (PE) of A shares, and the active buying rate (buyrate) in the spot market as the original indicators for the composite index of the investor sentiment.

We consider that the composite index of the investor sentiment proposed by Huang et al. (2015) [16] using the partial least squares (PLS) has higher accuracy and stronger predictive ability than those constructed using other methods. PLS can be implemented by the following two steps of OLS regressions. In the first step, for each original investor sentiment proxy is the number of investors newly participating in the A-share trade in the end of a phase closed-end fund premium/discount rate, market turnover, average price-earnings ratio of A shares, and the active buying rate in the spot market, we run a time-series regression of on a constant and realized stock return.

The coefficient in the first-stage estimation can describe how each sentiment index depends on the true investor sentiment. captures the sensitivity of each sentiment proxy to investor sentiment instrumented by future stock return that expected excess stock return explained by investor sentiment as the following standard linear relation:

In the second-stage regression, we run a cross-sectional regression of on the corresponding loading estimated in (1),where is the estimated investor sentiment and can be regarded as investor sentiment of the capital market in China. By using the complete-sample information, we obtain the vector of composite index of the investor sentiment. is the linear composition of the indicators of the investor sentiment and also the expression of the composite sentiment index using the PLS method.

where R is the vector of the spot return of the CSI 300 stock index and X= is the order matrix composed of single original indicator variables of the investor sentiment, in which N represents the number of the selected original indicators of the sentiment. Then, there are matrixes , , where and are the T- and N-dimensional identity matrix, and are the T- and N-dimensional vectors of ones.

###### 3.2.2. Futures-Spot Basis (Explained Variable/Endogenous Variable)

To study the mutual influence between the investor sentiment and the futures-spot basis of the CSI 300 stock index, the weekly basis of the CSI 300 index is used as the explained variable and the basis at the moment t is defined as . Therein, and are the CSI 300 index price at t and the futures price obtained via weighting in accordance with the positions.

###### 3.2.3. Moderator Variable

The quarterly data in the Wind database are used as the structure data (structure) of the investors. The “structure” represents the proportion of the CSI 300 component stock held by institutional investors. The current research also assumes that the investor structure does not change in a quarter. It needs to be noted that although the assumption is likely to lead to the sequence correlation, the corresponding shareholding ratio of institutional investors is not absolutely identical due to the different weights of CSI 300 component stock every day. Moreover, the quantile regression method relaxes the restriction for the assumption of the error term, so the assumption does not impact the results of regression analysis.

###### 3.2.4. Control Variables

*(**1) Market Interest Rate (Holding Cost)*. The market interest rate r influences the flow of the market funds, as well as the cost for investors to invest in the spot and the futures markets. When the market interest rate rises, the financing cost grows, which shrinks the futures-spot arbitrage opportunities and further influences the basis. To uniformly match with other weekly variables in real time, the weekly interest rate of bond repurchase is adopted as the risk-free interest rate.

*(**2) Arbitrage Cost. * Arbitrage cost consists of direct cost and indirect cost. Therein, the direct cost of the stock market includes the commission and the stamp tax while that of the futures market merely involves the commission. Although the CSI 300 and the SSE 50 stock index futures contracts have risen the trade security deposit and the service charge to different extents for the nonhedging positions since the stock market disaster in 2015, the direct arbitrage cost is still fixed because the trade in the spot market follows the “T+1” trading rule. So, we need to pay more attention to the influences of the variable indirect arbitrage costs on the adjustment of the basis. Indirect transaction costs mainly include the impact cost and the waiting cost. The impact cost can not only measure the part of transaction cost with liquidity premium but also estimate the risk brought about by the development of the price to the unfavorable orientation in the waiting process. Among the overseas researches on the impact cost, Harris (1990) [17] proposed the statistical measurement index based on tick-by-tick trade, and others put forward price impact models based on the econometric model (Glosten and Harris, 1988; Hasbrouck, 1991) [18, 19]. As the high-frequency tick-by-tick trade data needed in these methods are hard to attain and need complex computation, we refer to the impact cost model put forward by Almgren (2005) [20] to calculate the impact cost. Moreover, the CSI 300 stock index futures market has different impact costs of arbitrage with its component stock and CSI 300ETF. Therefore, it is necessary to calculate the impact costs (“impact-F,” “impact-S,” and “impact-ETF”) of the CSI 300 stock index futures, component stock, and CSI 300 ETF, respectively. The waiting cost is represented by the volatility (“rsigma”) of the return of the CSI 300 index and the volatility (“frsigma”) of the return of the CSI 300 stock index futures.

Then use the following steps to calculate impact costs. Based on the nature and characteristics of the perpetual impact and the temporary impact costs, we firstly define the impact cost referring to the research (Wei and Liang, 2013) [21] conclusion as follows: where IC is the impact cost and I and J are perpetual impact and the temporary impact costs, respectively. We assume that the impact cost function is of linear form; and are perpetual and temporary impact factors, respectively. Suppose a single transaction volume for any stock; we choose the standardized daily market volume (N) to obtain the standardization of its trading speed (). Transaction speed “v” is in line with the trading direction. We use “NT” to present the average volume of transactions from time to , which avoids directly estimating T. So the econometric model to calculate the impact cost is as follows:where is the intraday volatility calculated by the price of stock index futures; is the daily market trading volume calculated by the average market trading volume over the past 10 trading days, through the net capital flow of the average price, a period of time and the prices when corresponding impact disappears to obtain the price perpetual impact and the temporary impact costs . represents the stock at the beginning of the transaction and represents the stock price at moment t. Then we can get the impact and the temporary impact costs to estimate parameters and.

In this paper we use the above method to compute the impact costs (impact-F, impact-S, and impact-ETF) using the estimated parameter values and.

*(**3) Mean-Reversion Characteristic (Reversion)*. The arbitrage mechanism in the market allows stock index futures to have a long-term equilibrium relation with the spot commodity. If the basis is beyond the risk-free arbitrage interval, the presence of large amounts of arbitrage activities will lead to the mean reversion. Numerous studies of Chinese scholars (Theobald and Yallup, 2001; Monoyios and Sarno, 2002; Yi et al., 2010) [22–24] have proved that the basis of the stock index futures shows the nonlinear mean-reversion characteristic. Due to the constraint of the short-sales mechanism of the stock spot market in China, the mean reversion has more significant asymmetry. In the research, suppose the basis subject to the following stochastic processes:where is the basis of SCI 300 stock index futures and meets the condition . are the parameters for risk neutral market. is the long-term equilibrium value of the basis. We should do mathematical expectations on both sides of the formula and get the long-term equilibrium value of the basis () and combined with the first formula of (9), can be used to interpret the mean-reversion characteristic by dividing the difference between the basis and the mean using the relative volatility between the SCI 300 stock index futures and the spot index.

##### 3.3. Quantile Regression Model and Quantile Vector Autoregressive Model

Before we test the influence of the investor sentiment on the basis, the endogenous problems caused by mutual causality between sentiment and basis should be considered. In addition to the simple Granger causality test, the quantile vector autoregressive model (QVAR) [25] can measure the causal relationships. We can first investigate the asymmetrical mutual influence of investor sentiment and the basis of CSI 300 stock index futures under conditions in different market situations using the quantile vector autoregressive model. The quantile vector autoregressive model of order p is shown as follows:

where is the basis of the CSI 300 stock index futures in the th week and is the composite index of the investor sentiment in the th week. and are endogenous variables and is the N-dimensional intercept term vector at the level of division . The lag coefficient matrix with dimension size and represents the error term vector with dimension size. This model can consider the interrelationships between the endogenous variables at different quantile levels, simultaneously.

Then the influence of investor sentiment on basis under different investor structures is discussed using the quantile regression method. The quantile regression model is applied to test the influences of the investor sentiment on the basis, and the model is shown as follows:

Lagging the control variable by one order can avert the occurrence of the endogeneity in the regression model. To more favorably compare the influences of different factors on the basis, all variables except for the explained variable are standardized. This way, the influences of per-unit change of each factor on the basis can be more easily compared.

In the robustness test, the control function method is used to establish the semiparameter quantile regression model, which is shown as follows:

where and represent the basis of the CSI 300 stock index futures and the composite index of the investor sentiment in the th week, respectively. is an endogenous explanatory variable while is the instrumental variable of . Lagging the control variable by one order can avoid the endogeneity in the regression model and can be regarded as an exogenous explanatory variable. and are unobservable real-valued random variables. In the regression, formula (14) is subjected to the quantile regression at first, and then the obtained residue term is substituted in formula (13) to carry out the quantile regression to attain the estimates of the parameters.

#### 4. Sample Data and Descriptive Statistics

##### 4.1. Sample Data

The sample data used in the research were the daily trading data of the CSI 300 stock index futures from July 26, 2013, to July 15, 2016. Because the majority of the proxy variables for the investor sentiment are weekly data, data of 155 weeks were used for the research. Based on the distinguishing method for the bull market and the bear market proposed by Pagan and Sossounov (2003) [26], the volatility three months before and after the th week was calculated to differentiate the market situations. It is regarded that the stock market becomes chaotic when the volatility of the th week and in the subsequent period (lasts no less than 4 months) keeps exceeding 20% of the volatility before the th week. In this way, the market is divided into a steady period (July 26, 2013~March 27, 2015) and a chaotic period (April 3, 2015~July 15, 2016). The explained variable, explanatory variables, control variables, and moderator variable were all calculated by the original data which were collected from the Wind database and underwent quantile regression analysis using R3.3.0.

##### 4.2. Descriptive Statistics and Variance Analysis

Table 1 lists the detailed descriptions of each variable and the descriptive statistics in different market situations. The descriptive statistics and variance analysis unveil that the growth rate (num) of investors newly participating in the trade, closed-end fund premium rate (prem), market turnover ratio (turnover), average price-earnings ratio (PE) of the A share, and the active buying rate (buyrate) in the spot market are taken as the original indicators for the composite index of the investor sentiment. Except for the number of investors newly participating in the trade and the active buying rate (buyrate), other indicators have significant differences in the two market situations. It can be seen from the results of the variance analysis that the composite sentiment index presents significant difference in the two market situations. The basis also has significant difference in the two market situations (significant at the 1% level), which indicates that the premium/discount degree of the stock index futures varies in the two market situations and has a mean value of 0.2 in the chaotic stock market, implying an apparent premium phenomenon. The moderator variable and the control variables present different significant levels in the two market situations, which suggests that the above division of the two time periods truthfully reflects different market situations.