Economic and Political Studies Vol. 1, No. 2, July 2013, 40-54
Price Discovery Function of Index Futures in China: Evidence from Daily Closing Prices SHIQING XIE and JIAJUN HUANG * Abstract: Price discovery is one of the main functions of stock index futures. Using the daily closing prices of the CSI 300 index and its index futures from April 2010 to April 2012, this paper applies a vector error correction model (VECM) and an impulse response function to conduct an empirical analysis on the price discovery function of index futures in China. This paper has the following four findings: (1) a solid cointegration relationship between the CSI 300 index and its index futures exists in the long run; (2) when prices deviate from the longterm equilibrium, the stock index reverses weakly, while the reversal of index futures is much stronger; (3) the daily lead-lag relationship between the prices of the CSI 300 index and its index futures contracts is not significant in the short run; (4) shocks from the spot market have a lasting impact upon the futures market, but not vice versa, due to the limited short-term adjustment ability of the spot market. Keywords: price discovery, CSI 300, index futures, vector error correction model, impulse response functions
I. Introduction
P
RICE DISCOVERY IS ONE OF the main functions of stock index futures. Theoretically, due to its relatively lower transaction costs and higher leverage, the index futures market is much more sensitive to new information and is thus supposed to lead price changes in the underlying spot market. Due to the crucial role of the index futures market, much research has been conducted with the aim of detecting price discovery in the market. The majority of this research verifies that the futures market leads the spot market in the price discovery process. However, the existing studies mainly focus on the developed markets and little attention is paid to the * Shiqing Xie is from the Department of Finance, School of Economics, Peking University; e-mail:
[email protected]. Jiajun Huang is from Bank of China Macau Branch. We thank the anonymous referees for their helpful comments and suggestions.
Price Discovery Function of Index Futures in China
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rapidly growing Chinese capital market. Dramatic changes have been witnessed in the Chinese capital market in recent years. On April 16, 2010, after several years of prudent preparation by the Chinese government, Shanghai-Shenzhen 300 Index (CSI 300 index) futures contracts were officially launched on the China Financial Futures Exchange. Prior to the introduction of these stock index futures in China, investors could only participate in one-sided transactions and could not short sell, which gave rise to violent fluctuations and pricing inefficiency in the stock market. Therefore, many professionals believed that the newly established index futures market would improve the price formation and transmission mechanism and thus stabilize the stock market by virtue of its price discovery function. However, some scholars also raised concerns over the immaturity of the futures market and the overinvestment by irrational investors. These factors could hinder the effectiveness of the expected price discovery function, or even increase the volatility of the spot market. At the time of writing, index futures had been traded in China for more than two years. This paper attempts to analyze whether the index futures market has played a more significant role than the spot market in the price discovery process during this period, as evidenced in developed markets. Compared to previous studies, we contribute to the existing body of literature in the following three ways. First, despite the abundance of the existing literature, little attention has been paid to the index futures market in China. As the second largest economy in the world, China is now playing an increasingly important role in the world economy. China’s worldwide influence has been seen in the 2008 global financial crisis and the recent European sovereign debt crisis. Moreover, China is also increasing its efforts to promote the RMB’s internationalization, which will further increase its influence around the world. Therefore, when analysing price discovery in the index futures market, China, as a fast-developing economic giant, cannot be ignored. Second, we extend the sample period to incorporate long-run trends. Previous studies only investigate the short-term price adjustment process using high-frequency data covering a short timespan. The data used in these studies were obtained soon after the launching of index futures in China. For this reason, the credibility of their findings must be doubted and confirmation must be sought in further research. In this paper, we instead use the daily closing prices from the past two years (April 2010 to April 2012) to perform our empirical analysis. From this we intend to obtain more accurate results and investigate whether the price discovery function of index futures exists in the long run.
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Third, we adopt a daily perspective on the lead-lag relationship between the spot index and index futures prices in the short term. High-frequency data are normally used to investigate this issue (e.g., Martens, Kofman, and Vorst, 1998; Booth, So and Tse, 1999; Covrig, Ding, and Low, 2004), on the grounds that information is transmitted very promptly in the market and price adjustment occurs within several seconds. However, an investigation into the existence of the daily lead-lag relationship can provide an alternative examination of market efficiency. This paper applies a vector error correction model (VECM) and an impulse response function to conduct an empirical analysis on the price discovery function of index futures in China. The evidence in this paper indicates that there is no significant price discovery in the futures market in terms of the daily lead-lag relationship, although a solid cointegration relationship is revealed between the CSI 300 index and its futures in the long run. This result is in line with our expectations that both the Chinese equity market and index futures market are efficient, in spite of the overall underdevelopment of the Chinese capital market. The rest of this paper is organized as follows. In Section 2, we review some selected studies on both developed markets and the Chinese market; then we describe the empirical methods and data in Section 3; we present the results of the empirical analysis and our main conclusions in Sections 4 and 5 respectively.
II. Literature Review There is a large body of research dedicated to investigating the relationship between prices in the futures market and the spot market. Most of these studies focus on the American capital market and attempt to find a lead-lag relationship between the stock index price and the underlying prices of futures contracts. Herbst, McCormack, and West (1987) investigate the lead-lag relationship between the prices of two differently constructed spot indices, Value Line and S&P 500, and their respective futures contracts. They find that the prices of both the index futures tend to lead the spot prices. Chan (1992) and Martens, Kofman, and Vorst (1998) find similar evidence and come to similar conclusions about the S&P 500. Tse (1999) studies price discovery, as well as volatility spillovers, in the Dow Jones Industrial Average (DJIA) index and its futures contracts. His findings also suggest that the futures market dominates in the price discovery process. These is also a wealth of literature that derives the price discovery function of index futures for markets other than those in America. Lihara, Kato, and
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43
ToKunaga (1996) find that the returns of Nikkei Stock Average (NSA) futures strongly lead the underlying spot returns, whereas this leadership diminishes when strict trading regulations are imposed. Covrig, Ding, and Low (2004) explore the price discovery of the NSA futures on the Tokyo Stock Exchange, Osaka Securities Exchange and the Singapore Exchange, and confirm the significant role of the futures markets in the price discovery process in all these three markets. Booth, So, and Tse (1999) compare the ability of the futures and option contracts in the Deutscher Aktien index (DAX) to affect price discovery and find that the futures and spot markets contribute almost equally to the price discovery process, followed by the options market. Ryoo and Smith (2004) also find evidence of price discovery in the Korea Stock Price Index 200 (KOSPI 200) futures. Since the official launch in 2010, some research has been done on the price discovery function of CSI 300 futures. Hua and Liu (2010) examine the contribution of the CSI 300 index and its futures contracts to the price discovery process from April 16 to June 11, 2010 and find that index futures take a dominant role during this period. The price of CSI 300 index futures has a strong and persistent impact on the spot price, with a lead of about seven minutes on the spot market. Ren (2010) and Zhang and Liu (2010) draw similar conclusions that index futures lead in the price discovery process. However, some scholars have also come to the opposite conclusions. Li and Lin (2010) find that the spot market rather than the futures market leads in the price discovery process and that there is no bidirectional volatility spill over between these two markets in China. The only paper published recently in English that focuses on the Chinese index futures market is by Yang, Yang, and Zhou (2012) and examines the intraday price discovery and volatility transmission between the CSI 300 index and its underlying futures. With respect to the price discovery, they surprisingly find that the spot market rather than the futures market plays a dominant role in the price discovery process. They argue that this partially results from the higher barriers to entry in the index futures market, excluding many informed domestic and foreign individual investors. Overall, the majority of the studies discussed so far verify the price discovery function of the index futures, including in China. However, the studies focused on Chinese markets usually base their analysis on a very short time period, specifically the period immediately after the index futures were launched, without considering the immaturity and instability of this infant market. Consequently, their conclusions are worthy of reconsideration. In this paper, we make two innovations to distinguish our analysis from the existing studies. First, we extend the data sample period to two years, which
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contributes to the validity of our results. Second, we adopt a new perspective through examining the daily lead-lag relationship in order to enrich the current understanding of the price discovery function of index futures.
III. Methodology and Data 1. Methodology The most common model for bivariate time series analysis is the vector autoregressive model (VAR). However, it requires that the time series is stationary to avoid the problem of spurious regression. For non-stationary time series, Engle and Granger (1987) conceived the notion of cointegration and proposed a vector error correction model (VECM) based on the idea of error correction raised by Davidson et al. (1978). Considering two non-stationary series, spot index prices St and index futures prices Ft , they are integrated if they have a long-term relationship of: St = a0 + a1Ft + et ,
(1)
where et is a stationary sequence. We refer to this long-term equilibrium equation as the cointegration equation. Given that the long-term equilibrium relationship between the stock price index and stock index futures does exist, we can therefore derive the VECM as follows: p
p
i =1
j =1
p
p
i =1
j =1
∆St = µ1 + λ1et -1 + ∑αs , i ∆St - i + ∑ β s , j ∆Ft - j + ε s , t ,
(2)
and
∆Ft = µ 2 + λ 2 et -1 + ∑α f , i ∆Ft - i + ∑ β f , j ∆St - j + ε f , t ,
(3)
where µ is a constant term and et1=St – 1– a0– a1Ft –1 is the error correction term. The VECM is able to depict the dynamic relationship between the stock index futures price and the spot price both in the short and long term. The sign and magnitude of the coefficients on the error correction terms in Equations (2) and (3) represent the direction and speed of the adjustment when the prices deviate from the long-term equilibrium within each market respectively. Whereas, the coefficients of the lagged terms, namely α and β , show the interaction and feedback between the two prices in the short run. More specifically, if the parameter β in Equation (2) is significantly different
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45
from zero, then the stock index futures price leads the spot price; and if the parameter β in Equation (3) is significantly different from zero, then the spot price leads the futures price. It is difficult to quantify the lead-lag relationship between the spot market prices and those of the futures market merely by interpreting the coefficients of the VECM. Thus the impulse response function is utilized to further analyse the lead-lag relationship. Based on the VAR or VECM, the impulse response function aims to investigate and quantify the impact of a shock from one variable on the other variables, ceteris paribus. Therefore, if we let ε1, m 1 ε2, m = 0 , m=t , ξ m= ε1, m 0 ε2, m = 0 , m≠t
(4)
then through an iterative approach we can calculate the responses ∆S and ∆ F, i.e., the impulse response function of ε1, m. In a similar way, the impulse response function of ε2, m can also be obtained. 2. Data We select the time period from April 16, 2010 to April 13, 2012 as the sample period. This represents exactly two years since China officially launched index futures. Two sample time series are employed in our analysis. One consists of the daily closing prices of the CSI 300 index and the other consists of the daily closing prices of the closely related CSI 300 futures contract, which are characterised by high liquidity and activity. The data are obtained from CSMAR and 483 daily observations are collected in total. In accordance with the common approach to avoid potential heteroscedasticity, we take the natural logarithm of the two closing price series to gain the St and Ft series. The yield sequences ∆St and ∆Ft are also obtained by first-order differencing:
and
1
∆St = St - St -1 ,
(5)
∆Ft = Ft - Ft -1 .
(6)
For more details of CSI 300 index and its futures contracts, please refer to Yang, Yang, and Zhou (2012).
Economic and Political Studies
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Spot
8.2 8.1
8.1
8.0
8.0
7.9
7.9
7.8
7.8
7.7
II
III IV 2010
I
II
Futures
8.2
III 2011
IV
I II 2012
7.7
II
III IV 2010
I
II
III 2011
IV
I II 2012
FIGURE 1. CSI 300 Index Prices and the Prices of Its Futures Contract
The spot prices and future prices are plotted in Figure 1. It can be observed that the prices are almost the same in the two markets at any given point in time and they share the same trend. Moreover, after having tried to merge the two series in one graph, we found them to frequently overlap, which made distinguishing between them very difficult. Table 1 presents the descriptive statistics for the CSI 300 index prices and the index futures prices as well as their yield series. It’s not hard to notice that the means and standard deviations of the prices are very similar, which gives rise to the conclusion that the daily price level and daily volatility in the two markets maintain a high level of consistency. Although the standard deviations of the yield series in the spot and futures markets are close, the means of the two yield series are quite different. In addition, the leptokurtic and fat tail features of the yield series are consistent with the common characteristics of financial return series.
TABLE 1 Descriptive Statistics of the CSI 300 Index and Its Futures Contract Mean
Standard Deviation
Skewness
Kurtosis
Jarque-Bera
St
7.966
0.101
-0.187
2.152
17.282***
Ft
7.969
0.102
-0.135
2.178
15.052***
∆St(%)
0.047
1.417
-0.128
4.247
32.602***
∆Ft(%)
-0.106
1.451
-0.124
4.997
81.480***
Note: *** p
