Frontiers in Business, Economics and Management 
ISSN: 2766-824X | Vol. 5, No. 1, 2022 

 

94 

Correlation	Analysis	between	Stock	Index	and	Spot	
Index	
-- An Empirical Study Based on VECM Model 

Yixuan Liu 

Guangzhou Huashang College, Guangzhou, China 

 

Abstract: Since the reform and opening up, with the continuous strengthening of China's economic strength, the continuous 
improvement of the financial market, and the increasing appeal of investors to avoid market risks. Since China's first stock index 
futures contract was listed and traded, the research on the relationship between this financial derivative and the corresponding 
spot market has been a hot spot in academic circles. It refers to the hot events triggered by the futures market, and it has also 
been widely concerned by the media, the government and the people. China's financial derivatives market is still in its infancy, 
the market system is not yet perfect, and the professional quality of institutions and individuals engaged in trading still lags far 
behind that of investors in western mature markets. How to improve the futures index market mechanism and maintain the stable 
operation of the market deserves the government's in-depth consideration. China's financial futures market supervision 
authorities should continue to vigorously promote the improvement and development of China's stock index futures market. 
Specific measures include: speeding up the introduction of institutional investors to participate in futures trading and cultivating 
mature market trading subjects; Establish an investor suitability management system to lower the entry threshold of the stock 
index futures market; Perfecting the risk management system of the futures market will provide the necessary risk barrier for the 
healthy and stable development of China's financial market. 

Keywords: Stock index futures, Spot index, Correlation analysis, VECM model. 
 

1. Introduction 
Although the history of stock price index futures contract 

trading has been more than 30 years, the stock index futures 
trading in China has just started due to the lagging 
development of China's securities market [1]. As early as 
1970s, with the announcement of the abandonment of the 
"gold standard" by the American government, the fixed 
exchange rate system completely collapsed with the collapse 
of the Bretton Woods system, and the floating exchange rate 
system in the world began to take shape gradually [2]. Under 
the floating exchange rate system, the currency price is 
completely determined by the relationship between market 
supply and demand. Because the basis of exchange rate 
determination has become very unstable, and the factors 
affecting the relationship between foreign exchange supply 
and demand are complicated, the exchange rate changes 
frequently, which brings great price risks to the foreign 
exchange market. The high leverage, low cost, hedging and 
short selling of stock index provide investors with effective 
tools to avoid market risks, and at the same time broaden their 
investment channels [3]. Nowadays, the trading scope of 
futures contracts is not limited to physical goods and 
monetary bonds, such as commodity price index futures 
contracts with consumer price index as the target. Morton 
Miller, the Nobel laureate in economics, even praised that 
"financial futures are the biggest financial innovation in the 
past twenty years" [4]. 

The birth of financial futures, especially stock index futures, 
is the need of the times. It not only achieved rapid 
development and great success in the United States, but also 
quickly spread to all parts of the world, providing safe haven 
for investors all over the world [5]. At the same time, the birth 
of stock index futures has become the most effective right-

hand man of modern portfolio theory. Information 
transmission in an efficient financial market is unimpeded, 
and the reception of new information in all markets is 
consistent [6]. This is not the case. In reality, the securities 
market has friction, and there are differences in the degree of 
friction in different markets. Therefore, the reaction speed of 
the two cities to new information is also different, that is, there 
is a leading lag phenomenon [7]. There is a strong correlation 
between the two cities. Therefore, it is of far-reaching 
significance for Chinese investors and regulators in theory 
and practice to study the lead-lag relationship and volatility 
spillover effect between the two cities. Modern portfolio 
theory can avoid non-systemic risks to the greatest extent by 
putting eggs in different baskets, but it is helpless to systemic 
risks. The emergence of stock index futures just makes up for 
this defect [8]. 

2. Method 

2.1. Related Theories of Stock Index-Based on 
VECM Model 

Stock price index refers to stock price index, stock index or 
stock index for short. It is usually compiled by stock 
exchanges or financial service institutions to measure the 
market average price level and changes of all the stocks 
contained in the stock index [9]. Generally, the stock price 
index refers to "stock index point" to measure the price level 
of the whole stock market or a certain industry or plate stock. 
According to the number of sample stocks, the stock price 
index includes comprehensive stock price index and 
component stock price index. The comprehensive stock price 
index generally includes all the listed stocks of a stock 
exchange, such as the Shanghai Composite Index; Sample 
stocks of components are usually some listed stocks of a stock 



 

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exchange [10]. Divided according to the market value of 
circulation, including big market index, middle market index 
and small market index; In addition, stock exchanges or 
financial institutions will compile special industry indexes for 
listed companies with obvious industry characteristics. 

VECM model test includes the stationarity test of VAR 
model (first-order difference) and the independence test of 
residual error. The independence test of residual error needs 
to analyze the autocorrelation diagram, and if there is no 
autocorrelation in the residual error, it means that the residual 
error is independent. The stationarity test is the unit root test, 
which observes whether the heels of the characteristic 
equations of the model fall in the unit circle. If the 
characteristic roots are all in the unit circle, the model is stable. 
First, the independence test of residual error is carried out, as 
shown in Table 1. 

 
Table 1. VECM model correlation test 

Lag Chic2 df Prod<chi2 
1 6.6235 38 0.67239 
2 29.5698 38 0.77519 

 
The original hypothesis of "no autocorrelation" is accepted 

at 5% significance level. Secondly, the stability of VECM 
system is tested, and the results show that all the roots of the 
system fall within the unit circle, which satisfies the stability 
condition of the system. The precondition of VECM model 
analysis is that "all the roots of the equation fall in the unit 
circle, that is, the stationary process". However, some 
effective information will be lost in the process of using data 
difference to get the data stationary, and more attention will 
be paid to the short-term change process between variables, 
often less attention will be paid to the long-term change 
process. In order to keep the original appearance of data and 
get the long-term equilibrium relationship between time 
series, VECM model can be established to investigate the 
long-term equilibrium relationship between time series 
vectors. When the spot index changes by one unit, its own 
influence is positive, showing a trend of first decreasing and 
then stabilizing; The impact on stock index futures is 
gradually increasing. 

With the development of economy, financial futures 
contracts are emerging, and their development momentum is 
particularly fierce, accounting for 80% of the futures market 
and becoming an important part of the futures market. The 
stock index contract is one of the financial futures contracts, 
which came into being late, but developed rapidly. Since it 
came into being on February 24, 1982, it quickly seized the 
market and occupied a pivotal position. Since the birth of the 
stock index, its scale has developed rapidly. We can divide the 
whole process into birth stage, growth stage, downturn stage 
and prosperity stage. With the deepening of academic 
research on financial market volatility, in the 1990s, more 
foreign scholars turned their focus to the mean spillover and 
volatility spillover between securities markets. That is to say, 
the research angle has shifted from the one-way fluctuation 
influence of the futures market on the spot market to the 
fluctuation relation between the two markets. This means that 
the academic circles have started to study the volatility of the 
futures and spot markets in various directions. China's 

securities market has not experienced big twists and turns in 
more than 20 years, and its development is relatively smooth. 
The market has begun to take shape, and it has a certain 
buffering capacity even if it is impacted by the outside world. 
In addition, in recent years, China has carried out a series of 
reforms aimed at the financial and securities markets, which 
has gradually pushed China's securities market to the 
international market. The establishment of the stock index 
market not only brings valuable practical experience for the 
follow-up development of financial derivatives in China, but 
also allows relevant scholars in China to study their own 
futures market. 

2.2. Correlation Analysis of Stock Index and 
Spot Index 

A futures contract is a standardized contract formulated by 
a futures exchange, which stipulates that an agreed number of 
subject matter will be delivered at a certain time and place in 
the future. The subject matter, also called basic assets, can be 
physical commodities, such as gold, crude oil, agricultural 
and sideline products, or virtual indexes, such as stock price 
index. Futures exchanges provide a place for people who need 
to buy or sell an asset at some point in the future. With the 
development of modern computer information and network 
technology, the trading mode of securities and futures has 
gradually evolved from the previous open bidding auction to 
today's electronic trading. 

Due to the unique trading form of forward delivery of 
futures contracts, the price between futures contracts and spot 
prices is often inconsistent due to factors such as holding costs 
and market participants' expectations. When the time is very 
close to the last trading day of the futures contract, the traded 
futures contract will be faced with physical delivery or 
hedging liquidation, so the price of the futures contract will 
fluctuate strongly around the spot price and be consistent 
before the last trading day stops. Therefore, in general, 
although there is a price inconsistency between the futures 
price and the spot price, the futures price will not deviate from 
the spot price indefinitely due to the inherent delivery 
requirements of the futures contract. In addition, generally 
speaking, the futures and spot prices of the same commodity 
are affected by both supply and demand. 

The futures market is born out of the spot market, but the 
differences between the two are far more than the similarities. 
Generally speaking, the two parties to the spot transaction of 
bulk commodities often have to negotiate and sign a legally 
binding contract, the specific content of which includes the 
price and quantity agreed by both parties. Spot transactions 
are generally transactions of one-handed payment and one-
handed delivery. In the spot market, the purpose of buyers and 
sellers is to obtain commercial profits by acquiring or 
transferring the ownership of commodities. In the futures 
market, it is not always the case. Generally speaking, futures 
trading does not want to acquire the ownership of the real 
thing at the expiration date, but to close the position before 
the expiration date. Hedgers avoid market risks through 
futures trading, arbitrageurs hedge their positions to obtain 
risk-free profits, while speculators seek risk profits through 
futures trading. The similarities and differences between the 
two markets are shown in Table 2. 

 
 
 
 



 

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Table 2. Comparison between spot and futures 
Contract details Spot contract Futures contracts 
Trading variety All circulating commodities Limited commodity 

Trading place Any place 
Futures Exchange & Some Commodity 

Exchanges 
Contract format Non-standardized contract Standardized contract 

Settlement method Pay off the loan Daily mark-to-market settlement 
Delivery method Physical delivery Daily liquidation 

Credit risk Uncertain credit risk The credit risk is minimal 
 

Academic relevance is defined as not only a certain degree 
of relationship between two objects, but also a certain degree 
of linkage. Linkage or linkage effect is the key point to 
examine the relationship between them. Academics agree that 
there is a linkage effect in the financial market, whether it is 
a mature market or a developing market. This effect is 
developing rapidly today, and the innovative global financial 
market is becoming more and more prominent. The pace of 
global securities markets is becoming more and more 
convergent, and the mutual influence is much more obvious 
than before. With the rapid development of science and 
technology, the academic circles think that the IT technology 
applied in the securities market makes the correlation between 
the two markets much higher than before. The information 
transmission speed is extremely fast, resulting in an increase 
in the frequency of arbitrage transactions by arbitrageurs. 
Once the risk-free arbitrage space between markets is found, 
the arbitrageurs will immediately seize the opportunity to 
carry out arbitrage operations. Moreover, due to effective 

trading, the price difference between futures and cash will be 
narrowed, and the prices of both markets will surely move in 
one direction, and the arbitrage space will eventually 
disappear. Although the price difference may increase, the 
futures price may have different trends in a certain period of 
time, but the futures price and the spot price finally converge 
and converge with each other.  

3. Analysis and Discussion of Results 
Impulse response function can be used to describe the 

impact of a standard deviation on the random error term, 
reflecting the current and future impact on endogenous 
variables. (a) ~ (e) are impulse response functions 
representing the impact of GDP, Internet development level, 
cost-income ratio, net interest margin and non-performing 
loan ratio on the average return on assets, respectively. Figure 
1 depicts the changes of implied volatility of call options in 
different value states. 

 

 
Figure 1. Changes of implied volatility of call options in different states 

 
The change trend of implied volatility of call options in 

different value states is very close. For OTM, NTM and 
ITMH groups, the correlation coefficient between two groups 
is as high as 0.89W. The assimilation OTM group and NTM 
group are particularly close, and the average values in the 
sample interval are 40 and 0.39 respectively. Compared with 
ITM group, the ITM group was 0.33. The lowest value in ditm 
group is 0.22. 

An impact of the development of the Internet has a positive 

impact on the average return on assets of commercial banks, 
which can also be verified by the regression results of VECM 
modified equation. This is mainly because the development 
of Internet technology has driven the development of Internet 
financial industry, providing more profit channels and ways 
for commercial banks. Commercial banks use the 
development of Internet technology to innovate financial 
products, thus reducing their dependence on the difference 
between deposits and loans in traditional businesses. In 



 

97 

addition, commercial banks use Internet technology to make 
financial transactions more convenient, save customer 
business costs, enhance customer attachment, make the stock 
of customers more stable, and indirectly increase profits. 
Therefore, the more developed the Internet degree of 
commercial banks, the more it will help to improve the 
average return on assets of commercial banks. 

4. Conclusions 
Since the listing of China's stock index futures, China's spot 

market has been in a low state for a long time, so the 
correlation between the function of stock index futures and 
the fluctuation of the spot market has always been a research 
hotspot in academic circles. At present, China has entered the 
"innovation period" of digital finance, and digital technology 
has pushed Internet finance to a new height. In the new period, 
commercial banks should face new opportunities and 
challenges, make full use of digital technology to establish 
more business channels, innovate more business models, and 
enhance their own operating efficiency. From the results of 
Vecm model, the price equilibrium relationship between 
futures index and stock index spot index has existed for a long 
time, and when the price equilibrium between them is broken, 
ECM correction can adjust the current price of the subject 
matter in both directions. There is a long-term equilibrium 
relationship between the logarithmic price series of the two 
cities. Once the prices of the two cities deviate from the 
equilibrium state, they can quickly return to the long-term 
equilibrium level under the action of arbitrage mechanism. 
However, due to the fact that the market is not completely 
efficient, that is, there is friction in the market, so there is a 
basis difference between the two cities, and the basis 
difference may gradually decrease due to the influence of the 
delivery date and other factors. 

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