Futures Trading and Spot Price
Volatility:
New Evidence from the S&P 500
Index and Futures
Yong Zhao, 1372114
University of Groningen
Faculty of Management and Organization
Master Thesis
MSc Business Administration
Specialization Finance
Abstract
This paper investigates the direction of causality between the futures market and the spot market, and then re-examines the lead-effect of futures trading on spot price volatility. The data of the S&P 500 index and the relevant futures contracts in the period from March 1992 to September 2002 are used. The results of the Granger-causality test show that the futures market leads the spot market by one to two days. An EGARCH (1, 1) model is applied in the lead effect analysis and the conclusion is that the futures trading activity destabilizes the spot markets, represented by the increased spot price volatility. This finding appears to be robust even when the model is modified and the representative variables are tested separately.
Table of Contents
Chapter 1 Introduction
Chapter 2 Theory and literature review
2.1 Market depth, information dissemination and spot price volatility
2.2 Speculative effect and spot price volatility
2.3 Lead-lag relationship between spot volatility and futures trading volume
2.4 Review of empirical studies
Chapter 3 Analysis framework and method
3.1 Causal direction test and the Granger-causality method
3.2 Test of the lead-effect of futures trading on the spot index volatility
Chapter 4 Data and results
4.1 Data description and preprocessing
4.2 Results
4.2.1 Results of the Granger-causality test
4.2.2 Results of the test of the lead-effect of the futures trading on spot price
volatility
4.2.3 Robustness test
Chapter 5 Discussion
5.1 Implication of the results
5.2 Limitation of the study
Chapter 6 Discussion
Acknowledgement
References
1. INTRODUCTION
Surrounded by a growing body of theoretical and empirical literature, the debate of the effect of futures trading on commodity prices has continued for several decades. For many years, it has been widely accepted that the futures trading destabilizes the spot prices of the underlying assets, and regulators have enacted bundles of policies that forbid extreme activities on futures markets. However, no consistent conclusions concerning the relation of futures trading and spot price variability have ever been reached. Many economists compared the price volatility of particular commodities when there were no corresponding futures and when the futures exist. Given different commodities and data sets, some find evidence that the activity of futures trading stabilizes or destabilizes spot prices, whereas others do not discover any relationship at all.
Equity futures (S & P 500 index futures) were initiated and first traded in April 1982 at the Chicago Mercantile Exchange. During the same period, the application of computer techniques that facilitates price monitoring and trigger trades between markets fueled the process of futures’dispersion. As a result, equity futures became more and more popular and nowadays they are actively traded at the main futures exchanges all over the world. Like the situation of commodity futures, the role of equity futures was studied and argued ever since the time when they were born. One prevailing opinion is that the introduction of futures trading enlarges or reduces the spot price volatility, and the opponents believe that there is no significant linkage between these two markets. Both sides have provided rational explanations and empirical research for their arguments, whereas given the fact that the framework employed in each study varies and the level of development of concentrated market differs largely, there is lack of consistent conclusions on the relationship up to the present.
futures markets? The first question is answered through systematically reviewing the theory and literature, and the second is solved by an empirical study on a particular market and data set. Finally, a discussion on the third question is expanded based on the empirical results. The carrier of this study will be limited to the equity index futures since historically the controversy in the field of equity futures is much fiercer than that of commodity futures. In addition, little attention has been paid to the possible lead-effect of spot price volatility on the futures trading activities, though there is a financial meaning from an arbitrageur point of view that the futures trading volume could be influenced by the level of spot price volatility. According to the theory, when the spot prices become more volatile, larger futures positions are needed to hedge the increased risk exposure on the spot market. It is not complete to simply investigate if the futures trading stabilizes or destabilizes the spot volatility and leave the reverse causality direction between the two variables behind. This paper will test this reverse causality as well.
Most of the earliest studies have focused on the US stock market. For instance, the Dow Jones Industry Average (DJIA) and the Stand and Poor’s indices futures were most frequently used. Recently, other authors paid attention to the equity markets outside the USA, like the FTSE of the UK, the Hang Seng of Hong Kong and the Nikkei of Japan, etc. These studies help to create a relatively complete cognition on the issue. Recently, some economists refocus on the US market in their studies, since the studies based on the most developed market can be more persuasive and representative. Therefore, this paper will re-examine the issue by applying a totally new method, the modified EGARCH (1, 1) model, to an updated data set of the S&P 500 index and its futures for the period from March 1992 to September 2002. The ten-year period from 1992 to 2002 is selected since during this period the futures markets has become quite mature in the US, and the US equity markets have experienced a complete cycle consisting of recessions and prosperities.
2. THEORY AND LITERATURE REVIEW
Many people believe that the volatility of stock prices has increased substantially in recent years, especially after the initiation of equity futures. Some economists even assert that the trading of index futures increased the stock market volatility during the crash of October 1987 (NYSE, 1990). However, Schwert (1990) indicates that there is little evidence that can link the rising spot price volatility with the activities of futures trading. This is a simple example presenting how diverse the conclusions are upon the topic. Historically, there have been two main branches of theory source, which are derived from a “market depth”and information dissemination point of view and from a “speculative effect”of futures trading point of view, respectively. Each of them provides a rational way of understanding the relationship between the futures trading and spot price volatility.
2.1 Market Depth, Information Dissemination and Spot Price Volatility
Many economists argue that greater market depth is associated with the introduction of index futures trading. This notion is based on three aspects regarding the influence of futures trading. These aspects include the lower trading and transactional costs, more information flows, and more market makers. First, compared with the direct trading of the shares within the spot equity index, the transaction costs of trading the index futures are relatively lower. It helps to establish a larger position with lower margin requirements than is possible when establishing an equivalent position in the spot index, which means that both arbitrageurs and speculators can generate larger order flows with lower costs. After the introduction of futures markets, a trader has been able to take a larger position, and/or trade more frequently than before. According to McKenzie, Brailsford and Faff (2001), new positions and the expanding of existing positions are significantly cheaper after the futures contracts are introduced, so that the market depth is enhanced.
more frequent trading activities lead to more information flows into both spot and futures markets, and thus enlarge the market depth. However, the role of information flowing is still ambiguous both in a theoretical and an empirical sense. The reason is that the information associated with order flows includes both effective news and “noise”. Market participants who have advanced information and trade rationally bring valuable information onto the market, and this helps other informed investors to adjust their responses to the market fluctuation. On the other hand, the noise is brought on the market via the uninformed speculating activities that lower the informativeness of the market.
According to Arditti & John (1980), Breeden & Litzenberger (1978), Hakansson (1978) and Ross (1977), the introduction of futures contracts leads to an information dissemination effect that improves the investment opportunities faced by investors and thus the market is more integrated. Moreover, McKenzie, Brailsford and Faff (2001) indicate that the futures contracts facilitate hedging motivations, which means less reliance is needed to be placed on the spot hedging strategies. Chan (1991) re-handles this issue from the viewpoint of the arbitrage linkage. He argues that index arbitrage should reinforce the information linkage between the spot and futures market. Since the futures price should not deviate far from the costs of buying the component stocks and holding them to maturity, there is no reason to suggest a lead effect of futures trading on the spot volatility. However, many empirical studies [for instance, MacKinlay and Ramaswamy (1988), Chung (1989)] report that there exist significantly large differences between the theoretical and the real futures price, implying that the arbitrage between the two markets could be profitable.
In addition, market depth is increased by the introduction of futures since the overall market liquidity is enhanced when there are more market makers on the markets. Besides, the increased amount of market makers enhances the buying power of the group as a whole. Grossman (1988) describes this mechanism using the NYSE market as an example and concludes that the market makers on the futures markets enhance the liquidity level of the overall equity markets, and that they have a significant influence on the buying power on both spot and futures markets.
is still inconclusive. Stein (1987) argues that more “noise” information is brought on the market via poorly informed speculators entering into the markets and their activities of futures trading; thus, the activity of futures trading may destabilize the spot prices. In contrast, Danthine (1978) suggests that the existence of futures markets increases the market depth and reduces the spot price volatility, since it reduces the cost of responding to price changes for the informed traders.
2.2 Speculative Effect and Spot Price Volatility
For many years, there has been a stabilization-destabilization debate with respect to the role of speculative activities on the futures markets. Regulators are likely to express the futures and derivatives markets as price destabilizing and welfare reducing. In contrast, economists such as Danthine (1978) and Turnovsky (1983) establish models that approve the stabilization effect of futures trading on the spot price volatility. In the literature, the futures markets are considered as a “conduit through which a greater number of speculators can flow into an
already existing spot market” (Stein 1987, pp. 1124). The effect of speculative activities on
the futures markets is further distinguished to two aspects: risk sharing and information transmission. Markets can benefit from the risk sharing effect when some speculators who initially stay on the spot market transfer to the futures markets, releasing the speculative pressure on the spot market and reduce price volatility. Besides, new market makers who establish positions on the futures markets lower the aggregate risk aversion of the whole system, thus strengthening the arbitrage force that stabilizes price volatility. For instance, a risk-averse investor who takes a long position in a particular index can hedge the risk exposure by taking a corresponding short position on the index futures market. The hedging strategy enables him to respond to price changes more quickly and effectively, while if the spot price volatility will increase or decrease is still ambiguous.
accurate and effective news is embodied in the activities of well-informed speculators, which serves to stabilize the spot price volatility. In contrast, noise information is often associated with the trading activities of the poorly-informed speculators, which may destabilize the spot volatility.
Based on Stein (1987), Harris (1989) proposes a more complete understanding of the activities of both well-informed and uniformed traders. He agrees that the noisy trading of the uniformed speculators destabilizes the spot markets. However, the increase in well-informed speculative trading activities may offset the destabilizing effect caused by the uniformed traders, since the well-informed trading provides liquidity to the market. Whereas at the same time, the well-informed trading that carries new fundamental information can also increase the spot price volatility, since the arrival of new information is reflected in the price more quickly. David (1987) states that the futures markets encourage risk taking and speculative behavior; but whether the speculative activities stabilize or destabilize the spot markets is ambiguous.
2.3 Lead-lag Relationship between Spot Volatility and Futures Trading Volume
Most of the previous studies have concentrated on the lead effect of futures trading on the spot volatility and its economic and financial meaning; little attention has been paid to the lag effect of it.
the assets on the spot markets. Therefore, it is reasonable to expect a positive effect of the index volatility on the daily futures trading volume.
The empirical studies on the direction of causality of the two variables are not as fertile as the studies on the lead-effect of futures trading on the spot price volatility. However, most of these studies suggest that the futures’trading is more likely to be the lead factor. For instance, Stoll and Whaley (1990) shows that the S&P 500 and the Major Market Index futures lead the spot market by 10 minutes. Teppo et al. (1995) tests the direction of causality between the Finnish Stock Index futures and the stock index using the one-year data from 1989 to 1990. The results show that predictive information can be derived from the futures market for both frequently and infrequently traded stocks, whereas the information of stock index trading seem to have little effect on the index futures trading.
2.4 Review of Empirical Studies
Previous parts indicate that according to the theory and literature, there is no consistent conclusion on the relationship between futures trading and spot price volatility. Therefore, it becomes an empirical issue to be tested. Many economists have made empirical efforts on the topic and the gains are fertile.
Edwards (1988) investigates whether there is a destabilization effect of the stock index futures on the spot volatility in the long run. He focuses on the S&P index futures and Value Line futures during June 1973 to May 1987 and concludes that there is no significant change of the index volatility after the introduction of futures in long run. However, he finds some evidence of a destabilization effect on the spot volatility around the futures expiration days. Aggarwal (1988) focuses on the S&P futures as well and finds that there is no significant lead-lag effect of the futures trading.
index fund could influence the market volatility as well. Furthermore, Mabery, Allen and Gilbert (1989) find a significant destabilization effect of the S&P futures trading on the index volatility. Focusing on the same market, Becketti and Robert (1990), however, report that no evidence exists for the relationship.
Hodgson and Nicholls (1991) study the influence of futures of All Ordinaries Share Index (AOI) on the AOI index of the Australian Stock Exchange using data from 1981 to 1987. He finds no evidence supporting the opinion that the introduction of futures would affect spot volatility.
Bessembinder and Seguin (1992) re-examine whether greater futures-trading activity (trading volume and open interest) is associated with greater equity volatility. They divide each trading activity into expected and unexpected components, and verify that spot volatility covaries positively with unexpected futures trading volume, while covarying negatively with the expected trading activity. Their findings are consistent with the theory stating that active futures markets enhance the liquidity and depth of equity market.
Jegadeesh and Subrahmanyam (1993) employ the bid-ask spread of individual stocks listed at the NYSE as a measure of the S&P index volatility. They find that the average spread has increased after the introduction of S&P 500 index futures. They repeat the test by controlling factors such as price and volume of trade, and the results still show a bigger spread in the post-futures period. Moreover, the bid-ask spread is used as a measure of liquidity in the study of Hong Choi, et al. (1994). The authors use the intraday data of the S&P 500 and the Major Market Index for a period of one year to examine the impact of futures trading on spot volatility and liquidity. Their results show that the average intraday bid-ask spread has increased in the post-futures period, while no significant change of the spot volatility is observed.
premium have no impact on the volatility.
Antoniou and Holmes (1995) tests the relationship between information and volatility of the FTSE-100 index. They find that the spot index volatility has increased in the post-futures period, and they attribute it to the benefit of the information dissemination effect of futures trading.
The most remarkable studies on this issue in recent years includes Dennis and Sim (1999), McKenzie, Brailsford and Faff (2001), Shang (2001) and Spyrou (2005). Dennis and Sim (1999) examine the impact of the introduction of individual stock futures on the volatility of underlying stocks using data from the Sydney Stock Exchange. The results show that the introduction of futures has very little influence on the stock price volatility. In contrast, McKenzie, Brailsford and Faff (2001) use data of ten Individual Stock Futures (ISF) contracts and the corresponding stocks in the Australia Stock Exchange, the results are more complex. Their findings include a general reduction in systematic risk of individual stocks and a significant decrease in unconditional volatility after the launch of futures. They also conclude that the impact of the introduction of futures on the spot markets does exist, though the exact direction of the impact is stock-specific. Shang (2001) investigates and compares the relationship for several countries. His findings suggest that following the introduction of index futures, the stock volatility of markets in the USA, France, Japan and Australia rises significantly, whereas no impact is found on the markets of the UK and Hong Kong. Finally, Spyrou (2005) expands the examination on the issue to an emerging market : the Athens Stock Exchange and the evidence of the impact is ambiguous. Table 1 summarizes most of the empirical studies on this issue, including the ones mentioned already.
Table 1. Summary of Empirical Studies
Author Market Index Volatility After
the Introduction of Index Futures
Statistical
Significance Level
Santoni (1987) S&P 500 No influence 5%
Edwards (1988a, 1988b) S&P 500 Value Line
Decrease No influence
5%
Harris (1989) S&P 500 Increase 5% Mabery, Allen and
Gilbert (1989)
S&P 500 Increase N.A.*
Fortune (1989) S&P 500 No influence N.A.
Beckatti and Robert (1990)
S&P 500 No influence N.A.
Lockwood and Linn (1990)
DJIA Increase 1% and 5%
Brorson (1991) S&P 500 Increase N.A.
Chan and Karolyi (1991) Nikkei 225 No influence 1%
Laatsch (1991) MMI No influence N.A.
Gerety and Mulherin (1991)
S&P 500 No influence 5%
Hodgson and Nicholls (1991)
Australian AOI
No influence 5%
Baldauf and Santoni (1991)
S&P 500 No influence N.A.
Bessembinder and Seguin (1992)
S&P 500 Decrease 5%
Board and Sutcliffe (1992)
FTSE 100 No influence N.A.
Lee and Ohk (1992) Australian AOI Hang Seng US, UK, Japan No influence Ambiguous Increase N.A. Jegadeesh and Subrahmanyam (1993) S&P 500 Increase 5%
Bacha and Vila (1994) Nikkei 225 No influence 1% and 5% Choi and
Subrahmanyam (1994)
MMI No influence N.A.
Robinson (1994) FTSE 100 Decrease N.A.
Antoniou and Holmes (1995)
FTSE 100 Increase 5%
Chen, Jarrett and Rhee (1995)
TOPIX No influence N.A.
Kumar, Sarin and Shastri (1995)
Nikkei 225 Decrease 1%, 5% and 10%
Kan (1996) Hang Seng No influence N.A.
Reyes (1996) CAC KFX (Denmark) Decrease No influence 1%, 5% and 10%
Pinegar (1999)
Dennis and Sim (1999) ASX No influence 10%
McKenzie, Brailsford and Faff (2001)
ASX Ambiguous 10%
Rahman (2001) DJIA No influence N.A.
Shang (2001) USA, France,
Japan and Australia UK and Hong Kong Increase No influence 5% and 10%
Spyrou (2005) ATHEX Ambiguous 5%
Note: Resource is Mayhew (2000) and Spyrou (2005).
As shown in Table 1, most of the early studies paid attention to the S&P 500 index and the futures, while as the index futures widely introduced to other markets around the world, the issue has attracted more and more attentions for the economists. Another trend is that some recent studies focus on the comparison of different markets rather than sticking to a single market. Generally, the conclusions are mixed, given different markets and data sets, testing methods, and models used.
3. ANALYSIS FRAMEWORK AND METHOD
There are two main objectives in this paper. First, it investigates the causality direction between the spot market and the futures market. In other words, what is the direction of the information flow? Second, it re-examines the prevailing lead-effect of futures trading on the spot price volatility. A Granger-causality technique in a simple Ordinary Least Squares (OLS) model is employed to test the two-way causal relationship, and a GARCH/EGARCH model is used in the test of the lead-effect of futures trading. Throughout this study, spot and futures returns are used instead of the prices of spot index and futures, which is common in this field of study.
The Granger-causality test in this paper follows the way Teppo et al. (1995) used it, in which two variables, for instance the spot index returns and the futures returns, are focused. The conclusion which variable is the trigger factor can be obtained by comparing the corresponding parameters of the Granger OLS regressions, given the same statistical significance level.
According to Granger (1981) and Engel and Granger (1987), a causal relationship can be generated by a common trend or equilibrium between two stationary or non-stationary variables X and Y. Furthermore, if the variables X and Y are non-stationary and the error term produced in the cointegration regression between them is stationary, it must be included in the causality regression as an additional variable. Thus, the Granger-causality test is usually a two-step process: the stationary and cointegration test and the causality test itself1. However,
the variables to be test in this paper are price and return time series, which are stationary under most circumstances. Therefore, the stationary and cointegration tests are omitted and the main body here is the causality test.
The direction of information flows between the spot and futures markets is detected by comparing the corresponding parameters of the causality regressions. Two basic variables are the daily spot index returns
R
st and the daily futures returnsRft, which are calculated as:
1log
t t stS
S
R
(1)
1log
t t ftF
F
R
(2)Where:
S
t andS
t1 are the spot index prices for day t and t-1.F
t andF
t1 are the1
Specifically, if one or both of the two variables are non -stationary, a cointegration test is necessary to determine if the error term produced in the cointegration regression needs to be included in the causality test. The cointegration test applies an augmented Dickey-Fuller (ADF) test to the residual of cointegration equation:
t t
t
X
Y
futures prices for day t and t-1.
The number of lags included will be determined by the Vector Autoregression (VAR) test with the Schwarz Information (SC) criterion, and the causality regression model consists of a couple of regression equations:
k i i st i k i i ft i st a bR p R R 1 1 (3)The null hypothesis (
H
0): The information derived from the futures returns do NOT “Granger cause”the fluctuation of the spot index returns; the futures market does NOT lead the spot market.H
0 is rejected when and only when for all theb
i
0
at a 5% significancelevel.
k i k i i ft i i st i ft c d R q R R 1 1 (4)The null hypothesis (
H
0): The information derived from the spot index returns do NOT “Granger cause”the fluctuation of the futures returns; the spot market does NOT lead the futures market.H
0 is rejected when and only when for all thed
i
0
at a 5% significancelevel.
3.2 Test of the Lead Effect of Futures Trading on the Spot Index Volatility
The methods applied in previous studies on this issue can be summarized into three distinguishing categories. The first and most popular method is to compare the spot price volatility of the pre- and post-futures periods. The volatility can be compared by directly calculating it from the historical spot prices, or by indirectly testing it in an ARCH/GARCH model (see e.g. Antoniou and Holmes, 1995). Secondly, one can compare the price volatility of index stocks with the price volatility of non-index stocks for the same period (e.g. Kumar etc, 1995). Thirdly, one can directly investigate the relationship between the spot price and futures trading volume or open interest (e.g. Bessembinder and Seguin, 1992).
However, directly comparing the spot price volatility of pre-and post-futures periods ignores the interdependence of time series of the spot and futures markets. Thus, it is more appropriate to apply the Autoregressive Conditionally Heteroscedasticity (ARCH) model, which is a standard tool in testing the relationship between financial time series; it takes into account the time varying variance in the analysis process. Furthermore, a general ARCH (GARCH) model, developed by Bollerslev (1986) and Taylor (1986), is more useful, because it allows the conditional variance to be dependent on previous own lags. In this case, the GARCH (1, 1) model is applied.
The null hypothesis (
H
0): There is no positive or negative lead-effect of the futures tradingactivity on the spot price volatility.
t k i i st i st a a R R
1 0 ,
2 , 0 ~ t t u
(5)
k i i ft i k i i ft i t t t V O 1 1 2 1 2 2 1 1 0 2
(6)Where:
R
st is the daily spot index return calculated by equation 1;R
sti is the previousday’s daily spot index return; Vfti is the previous day’s futures trading volume in natural
logarithm form; Ofti is the previous day’s futures open interest in natural logarithm form;
t
is the error term of equation 5, and
t2 is the conditional variance of
t.The null hypothesis
H
0 is rejected when and only when for all
i
0
and for all
i
0
at a 5% significance level.
The GARCH model applies a symmetric treatment of volatility to positive and negative shocks. However, many economists and researchers argue that a negative shock is likely to cause volatility to increase by more than a positive shock with the same magnitude does; consequently, an asymmetric model fits the financial time series better than the symmetric GARCH model. Therefore, the test will finally use an exponential GARCH (1, 1) model proposed by Nelson (1991), as follows:
k i k i i ft i i ft i t t t t t t V O 1 1 2 1 1 2 1 1 2 1 2 2 ) log( ) log(
(8)In equation 8, the lead effect of futures trading is examined by regressing the trading volume and open interest of previous trading days to the conditional variance. If the parameters of
i ft
V are significantly positive, it means that futures trading is destabilizing the spot volatility,
and vice versa. Note that throughout the analysis the open interest is included, since it represents futures market depth, which probably has influence on the volatility of the spot market. Including the open interest as a control variable will make the model more complete and close to reality. Finally, the number of lags used for the previous daily spot index return
i st
R
, futures trading volume Vfti and open interest Ofti will be determined by thesmallest Schwarz Criterion (SC) statistics in the EGARCH test.
4. DATA AND RESULTS
4.1 Data Description and Preprocessing
The data of the S&P 500 index futures from
March 1993 to September 2002 is downloaded from the Internet2, including the variables of daily futures open price, the highestprice, the lowest price, the closing price, trading volume and open interest. The “trading volume”is the number of contracts traded at each day and is a proxy for market activity. The “open interest” is the number of futures contracts outstanding on a certain day and is a measure of the market liquidity and depth.
The h
istorical S&P 500 index price data for the same period is collected from
DataStream
. Instead of using the nominal closing price, the adjusted closing price is used. The S&P 500 index futures contracts are issued four times every year in March, June, September and December, named by the expiration month; totally, there are 40 contracts available from March 1993 to September 2002. Table 2 gives the basic information about the2
S&P 500 index futures contracts issued in 1992 as an example. Complete information about the 40 futures contracts is summarized in Table A1 in the Appendix.
Table 2. Four
S&P 500 Index Futures Contracts Issued in 1992Contract Starting Date Ending Date Number of Observations
SP93M March 23, 1992 March 18,1993 251
SP93J June 22, 1992 June 17, 1993 251
SP93S September 18, 1992 September 16,1993 251
SP93D December 18, 1992 December 16,1993 251
As shown in Table A1 in the Appendix, most of the contracts have a lifespan of less than 24 months, or, less than 500 observations. The observations are far too few when using the EGARCH model. Fortunately, there is a processing method which links the price series of the individual contracts through time to compose an aggregated time series of the futures prices, see Akin (2003). Specifically, the linkage is implemented by tracking the first contract until the last day of the pre-expiration month, and then switching to the next nearby contract. All the 40 S&P500 index futures contracts are linked in this way through time and a new time series is generated. Moreover, given the fact that the trading activities during the early period of the first contract (SP93M) are inactive, the data of the period from March 23, 1992 to June 30, 1992 are excluded. In addition, the futures trading volume and open interest are used in natural logarithm form in the EGARCH model shown by equation 7 and 8, implying that the days when there is zero trading volume and/or open interest must be excluded from the sample as well. Table A2 in the Appendix indicates the 10 excluded days with either zero trading volume or open interest. Table 3 gives the basic information and the descriptive statistics of the processed data including the futures daily returns, trading volume and open interest, together with the spot prices and returns of the S&P 500 index starting from July 1 1992.
Spot Price Spot Returns Futures Returns Trad. Volume Open Interest Mean 878.4913 0.000121 0.000122 4.682336 5.297626 Median 894.1700 0.000147 0.000192 4.823940 5.294581 Sta. Dev. 358.1711 0.004640 0.004913 0.589274 0.452619 Minimum 402.6600 -0.030890 -0.033710 0.000000 2.796574 Maximum 1527.460 0.024209 0.024993 5.348268 5.771522 Skewness 0.149488 -0.177400 -0.176318 -4.223058 -3.095020 Kurtosis 1.551877 7.140447 7.358674 24.08942 14.73777
No. of Observations No. of Contracts Data Period
2574 40 July 1, 1992 ~ October1, 2002
Note: The spot returns and futures returns are calculated by equations 1 and 2. Both trading volume and open interest are in natural logarithm form.
Note that the mean of the futures returns (0.00022) nearly equals to the spot index returns (0.000121), showing that the in the long run, the investments on the spot index and the futures of the index have relatively the same returns. However, the risk on the futures market is higher than in the spot market, shown by the greater standard deviation of the futures returns (0.004913).
Table 4. The Correlogram Test Q-Statistics
) 6 ( Q Q(12) Q(18) Q(36) Spot Returns 14.350** 25.699** 33.085** 66.660*
)
6
(
2Q
2(
12
)
Q
2(
18
)
Q
2(
36
)
Q
Squared Spot Returns 448.23* 687.39* 855.32* 1129.5*
Note: Significance levels: *=1%, **=5%
squared spot returns series. In order to avoid the problem of not detecting serial correlation at high-order lags caused by choosing too small a lag and the problem of lowering test power caused by choosing too large a lag, the test repeats at 6, 12, 18 and 36 orders of lags to give a relatively completed conclusion. As can be seen from the table, all the Q-statistics are significant at 1% or 5%, implying that the non-normality of the spot returns variable is due to leptokurtosis, and using a GARCH/EGARCH model is more appropriate than using a standard OLS model in the test.
4.2 Results
All the analysis and tests in this paper are conducted in the econometrics software Eviews (version 5.0), and the Microsoft Excel (2000) is used in the results summarizing process.
4.2.1 Results of the Granger-causality Test
Before the main tests of the causal equations 3 and 4, the stationary tests are performed on spot index returns and the futures returns. Table 5 presents the results of the unit root test.
Table 5. Results of the Unit Root Test of the Spot and Futures Returns
Spot Returns
R
st Futures Returns RftADF Test Statistic -49.94671 -51.1607
Critical Value at 5% Level -3.411555 -3.41156
R-squared 0.492662 0.50467
Adjusted R-squared 0.492267 0.504284
Durbin-Watson Stat 1.993365 1.994372
F-statistic 1247.343 1308.718
almost no first-order serial correlation for these variables. Thus, the variables of spot and futures returns are stationary and can be directly used in the causal equations 3 and 4 without a cointegration test.
What specific causal regression is used, i.e. how many lags are included, is determined by comparing the Schwarz information Criterion (SC) statistics of the lag length test in the Vector Autoregression (VAR) estimates, in which a maximum of 10 lags are given as endogenous intervals3. Table 6 indicates the VAR lag order selection criteria of the lag length
test.
Table 6. The VAR Lag Order Selection Criteria of the Lag Length Test
Lag FPE AIC SC HQ
0 3.52E-11 -18.39428 -18.38972 -18.39263 1 2.90E-11 -18.5864 -18.57271 -18.58144 2 2.74E-11 -18.64351 -18.62069 -18.63523 3 2.68E-11 -18.66522 -18.63327 -18.65364 4 2.65E-11 -18.67712 -18.63604** -18.66222 5 2.64E-11 -18.68087 -18.63066 -18.66267 6 2.63e-11** -18.68637** -18.62704 -18.66486** 7 2.63E-11 -18.68519 -18.61672 -18.66036 8 2.64E-11 -18.68297 -18.60538 -18.65484 9 2.63E-11 -18.68385 -18.59713 -18.65240 10 2.63E-11 -18.68414 -18.58829 -18.64939
Note: ** indicates the lag orders selected by the criteria (each at 5% significance level). “FPE”stands for Final prediction error. “AIC” stands for Akaike information criterion. “SC”stand s for Schwarz information criterion. “HQ”stands for Hannan-Quinn information criterion.
Table 6 reports the statistics for four different selection criteria, namely final prediction error, Akaike information, Schwarz information and Hannan-Quinn, respectively. Among them, the AIC and SC are the most frequently used criteria by empirical studies, whereas the FPE and
3
HQ are automatically generated by the EViews’program and are not so important as AIC and SC criteria in practice. Moreover, the SC is an alternative criterion to the AIC; the main difference is that it imposes a larger penalty for additional coefficients. There is no essential difference of the conclusion reached by AIC and SC criteria. For simplicity, this paper will adopt the SC as a unique criterion. As suggested by the smallest SC statistics, the model is in the most appropriate form when there are four lags included for both causal regressions 3 and 4. Detailed results of the VAR estimates are shown in table A3 in the Appendix. Table 7 indicates the results of the Granger-causality test.
Table 7. The Results of the Granger-causality Test Information Flows from the Futures Market
to the Spot Market
Information Flows from the Spot Market to the Futures Market.
t k i i st i k i i ft i st a bR p R R
1 1
k i t k i i ft i i st i ft c d R q R R 1 1
0H
:R
st is not Granger caused by RftiH
0: Rft is not Granger caused byR
sti1
b
b
2b
3b
4d
1d
2d
3d
40.424925* 0.366186* 0.114715 -0.040072 0.111085 -0.132371 0.025803 0.137573 [5.2096] [3.9786] [1.2510] [-0.4935] [1.2064] [-1.2904] [0.2543] [1.5376]
R-squared 0.0159 R-squared 0.008327
Adjusted R-squared 0.012825 Adjusted R-squared 0.005228
Durbin-Watson Stat 1.993523 Durbin-Watson Stat 1.993714
Note: The test includes 2569 observations after adjustment. Significance levels: *=1%, **=5%. Values in the [ ] are the t-statistics. For both tests, 4 lags are included, suggested by the results of the VAR estimate and the corresponding SC statistics.
significant), suggesting that the futures’information older than two days has no significant impact on the spot price.
4.2.2 Results of the Test of the Lead-effect of the Futures Trading on Spot Price Volatility
The specific form of the EGARCH (1, 1) model presented by equation 7 and 8 is determined by comparing the Schwarz information criterion (SC) statistics given different combinations of lags of spot returns, trading volume and open interest, as shown in Table A4 in the Appendix. Note that the maximum number of lags of the trading volume and open interest is two since the results in the Granger-causality test prove that the influence of information from the futures market lasts less than two trading days on the spot market. As can be seen from the table, the model is the most appropriate when there is only one lag for both trading volume and open interest in the conditional variance equation, which gives the smallest SC statistic (-8.239849).
Table 8 reports the test results of the EGARCH (1, 1) model. Given the suggestion of the SC criterion that only previous one trading day’s volume and open interest should be included in the conditional variance equation, the results show that there is no significant evidence (insignificant
1with a z-statistic of -1.162846) that the futures trading volume has influence on the spot price volatility. In other words, the synthetic effect of futures trading on the spot price volatility is mixed. However, the parameter of last trading day’s open interest (0.036634) is positive at a 5% significance level, suggesting a positive relationship between the market depth of the futures market and the spot price volatility.4.2.3 Robustness Test
Table 8. Results of the Test of the Lead Effect of Futures Trading
Mean Equation Conditional Variance Equation
0
a
a
1
1
1 0.000101 0.054544** -0.534397* 0.972700* -0.117951* 0.134026* -0.013790 0.036634** [1.521145] [2.522746] [-6.493947] [250.6978] [-12.75577] [8.7941444] [-1.162846] [2.188782] R-squared Adj. R-squared SC Stat Durbin-Watson-0.001498 -0.004232 -8.239849 2.071119
Note: The specific EGARCH model consists of the following equations: The mean equation:
t st st
a
a
R
R
0
1 1
,
2 , 0 ~ t t u
, The conditional variance equation:1 1 1 1 2 1 1 2 1 1 2 1 2 2 ) log( ) log( ft ft t t t t t t
V
O
Included observations: 2572 after adjustments
volume is not the unique measure of the futures trading activity. Futures open interest is a market depth concept, and can be a dimension of the trading activity as well. In other words: if the futures trading volume is a direct measurement, then open interest is the indirect and complementary measurement of trading activity. This point can be proven by the fact that the correlation between the futures trading volume and open interest is as high as 0.89977, reported by the correlation test, see table 9. Therefore, the positive parameter of the open interest in the results suggests that the positive lead effect of futures trading could still exist. In order to verify the correctness of the conclusion, a robustness test is necessary.
Table 9. The Correlation between the Futures Trading Volume and Open Interest Trading Volume Open Interest
Trading Volume 1 0.89977
Open Interest 0.89977 1
Note: Both variables are in natural logarithm form.
The logic that the robustness test follows is to re-examine the relationship between trading activity measurements and the spot price volatility by simplifying the conditional variance equation of the EGARCH model. Specifically, the variables of trading volume and open interest will be included into the equation separately, which simplifies the equation and makes the relationship stronger, with fewer disturbances from other variables. Equation 9 and 10 present the simplified forms of equation 8.
k i i ft i t t t t t t V 1 2 1 1 2 1 1 2 1 2 2 ) log( ) log(
(9)
k i i ft i t t t t t t O 1 2 1 1 2 1 1 2 1 2 2 ) log( ) log(
(10)Table 10. Results of the Modified EGARCH (1, 1) Model 9
Relationship between Futures Trading Volume and Spot Price Volatility
1 st
R
0.053295** [2.487334] 0.053160** [2.476324] 0.053291** [2.478739] 0.053151** [2.468918] 2 stR
0.004936 [0.251204] 0.004816 [0.243360] 1
0.010552* [3.086921] 0.011342* [3.294461] 0.012438 [0.127380] 0.026137 [0.273223] 2
-0.001874 [-0.019356] -0.014725 [-0.155098] SC stat -8.241743 † -8.238247 -8.238690 -8.235200 Durbin-Watson 2.068754 2.066898 2.068746 2.066899Note: The specific EGARCH model consists of the following equations:
The mean equation: t i i st i st a aR R
2 1 0 ,
2 , 0 ~ t t u
, The conditional variance equation:
2 1 2 1 1 2 1 1 2 1 2 2 ) log( ) log( i i ft i t t t t t t
V
Significance levels: *=1%, **=5%. Values in the [ ] are the z-statistics. “†” shows the best model suggested by the SC statistic.
Table 11. Results of the Modified EGARCH (1, 1) Model 10
Relationship between Futures Trading Volume and Spot Price Volatility
1 st
R
0.053939** [2.508115] 0.054046** [2.508638] 0.053966** [2.505513] 0.054010** [2.503692] 2 stR
0.005775 [0.292699] 0.005742 [0.290416] 1 ft
0.017523* [3.454154] 0.018733* [3.655801] 0.019427 [0.122177] 0.022780 [0.143242] 2 ft
-0.001845 [-0.011683] -0.004020 [-0.025456] SC stat -8.242587 † -8.239138 -8.239534 -8.236084 Durbin-Watson 2.069974 2.068434 2.070024 2.068371Note: The specific EGARCH model consists of the following equations:
The mean equation: t i i st i st a aR R
2 1 0 ,
2 , 0 ~ t t u
, The conditional variance equation:
2 1 2 1 1 2 1 1 2 1 2 2 ) log( ) log( i i ft i t t t t t t
O
Significance levels: *=1%, **=5%. Values in the [ ] are the z-statistics. “†” shows the best model suggested by the SC statistic.
5. DISCUSSION
5.1 Implication of the Results
The results of the analysis advocate the viewpoint that the futures market leads the spot market by one to two trading days, and the futures trading activity, expressed by the trading volume and open interest, destabilizes the spot price volatility. Given the updated data set and newly contributed method by this paper, the findings are consistent with the results of Harris (1989), Mabery, Allen and Gilbert (1989) and Brorson (1991), and are opposite to those findings of Edwards (1988a, 1988b) and Bessembinder and Seguin (1992).
simply regard the increased volatility as a “bad”thing. However, increased volatility may be a straight reaction of the increased information that flows onto the market. The effect of the increased information flow can be mixed, as explained in Chapter 2. The results from this study prove the hypothesis of information dissemination proposed by Arditti & John (1980), Breeden & Litzenberger (1978), Hakansson (1978) and Ross (1977), which states that the futures market provides more information for the investors through the activity of futures trading.
In this paper, the futures open interest that presents the market depth of the futures market is included as a control variable in the model. A positive relationship with spot price volatility is obtained from the test, implying that in the case of the S&P 500 index, the synthetic effect of futures market depth is to destabilize the spot price volatility. The reason could be that as more speculators entering the futures markets and take positions, the spot price can be distorted by the noise information caused by the irrational trading activities of the futures trader. The destabilizing effect is greater than the stabilizing effect that is caused by the inflow of valuable information from the futures market. As a result, mis-pricing happens more frequently and it takes longer time for the price to adjust to the equilibrium level in the spot market, thus the price volatility increases.
in the futures markets. The temporary halt of trading may prevent the spot market from price crashing sometimes, but on the other hand, the spot market can also suffer from the halt with severe mis-pricing. In a word, further study is necessary to discover the synthetic effect of these restrictive regulations on the futures market.
5.2 Limitation of the Study
The availability of data limits the depth of this study to some extent. First, high-frequency data are more appropriate in the causality direction analysis. Because of the lack of intra-day data, only daily data are used in this paper. The main conclusion from that part is that the futures market leads the spot market by one to two days. In fact, using the intra-day data, Stoll and Whaley (1990) finds that the S&P 500 index futures price leads the spot index by 10 minutes during the period April 1982 to March 1987. Second, this study is limited to the US futures market and only the S&P 500 index futures is investigated, which may lead to narrow application problems for the conclusion. If more data are available, a comparison study would generate more valuable insights on the topic.
In addition, this paper ignores the fact that the futures traders can be divided into two groups according to their offensive or defensive motivations. The information released can correspondingly be grouped as good news and bad news. The spot market price should react to good and bad news asymmetrically, thus the analysis of the lead effect of futures trading should be differentiated further, which goes beyond the scope of this study and l eaves possible space for future studies.
6. CONCLUSION
main analysis that tests the lead effect, an exponential GARCH (1, 1) model is applied, referenced from Nelson (1991). The results confirm the argument that the futures trading activity measured by daily trading volume and open interest destabilizes the spot price volatility, given the data of the period from March 1992 to September 2002. The results are robust and consistent even when the EGARCH model is modified and the two variables are tested separately.
Generally, the conclusion of this study is consistent with several earliest studies on the S&P 500 index futures, including Harris (1989), Mabery, Allen and Gilbert (1989) and Brorson (1991). However, opposite or ambiguous results also exist, given different research targets and periods. Anyway, this paper provides some new evidence on the issue, based on a relatively up-to-data data set and a newly-developed test method. In the end, it gives some expandable space for the interested researchers.
ACKNOWLEDGEMENTS
REFERENCES
Abhyankar, A. H. (1998), Linear and nonlinear Granger causality: evidence from the UK stock index futures market, Journal of Futures Markets, Vol. 18, No. 5, pp. 519-540.
Abhyankar, A. H. (1995), Return and volatility dynamics in the FT-SE 100 stock index and stock index futures markets. Journal of Futures Markets, Vol. 15, No. 4, pp. 457-488. Admati, A. R. and P. Pfleiderer (1988), A theory of Intraday Patterns: Volume and Price
Variability, Review of Financial Studies, Vol. 1, pp. 3-40.
Antoniou, Antonios, and P. Holmes (1995), Futures trading, information and spot price volatility: evidence for the FTSE -100 stock index futures contract using GARCH.
Journal of Banking and Finance, Vol. 19, No. 1, pp. 117-129.
Bessembinder, H. and P. J. Seguin (1992), Futures trading activity and stock price volatility,
Journal of Finance, Vol. 57, No. 5, pp. 2015-2034.
Chan, K., Chan K. C. and G. A. Karloyi (1991), Intraday volatility in the stock index and stock index futures market, Review of financial studies, Vol.4, No. 4, pp. 657-684.
Chan, K. (1992), A further analysis of the lead-lag relationship between the cash market and stock index futures market. Review of Financial Studies, Vol. 5, No. 1, pp. 123-152.
Darrat, A.F., and S. Rahman (1995), Has futures trading activity caused stock price volatility?
Journal of Futures Markets, Vol. 15, No. 5, pp. 537-557.
Edwards F. R. (1988 a), Does Futures trading increase stock market volatility? Financial
Analysts Journal, Vol. 44, No. 1, pp. 63-69.
Gregory, K. and Michael, T. (1996), Temporal relationships and dynamic interactions between spot and futures stock markets, Journal of Futures Markets, Vol. 16, No. 1, pp. 55-69.
Grossman, S. J. (1988), An analysis of the implications for stock and futures price volatility of program trading and dynamic hedging strategies, Journal of Business, Vol. 61, No. 3, pp. 275-298.
Herbst, Anthony F. and E. D. Maberly (1990), Stock Index futures, expiration day volatility and the “special”Friday opening: A note, Journal of futures market, Vol. 10, No. 3, pp. 323-325.
Hodgson, A. and D. Nicholls (1991), The impact of index futures on Australian share-market volatility, Journal of Business Finance & Accounting, Vol. 18, No. 2, pp. 267-280. Choi H. and A. Subrahmanyam (1994), Using intraday data to test for effects of index futures
on the underlying stock markets, Journal of Futures Markets, Vol. 14, No. 3, pp. 293-322.
Hung-Gay F., Wai-Chung L. and E. P. John (1994), Examining the dependency in intra-day stock index futures, Journal of Futures Markets, Vol. 14, No. 4, pp. 405-419.
James, T. W. (1993), How price discovery by futures impacts the cash market, Journal of
Futures Markets, Vol. 13, No. 5, pp. 469-496.
Jegadeesh, N. and A. Subrahmanyam (1993), Liquidity effects of the introduction of the S&P 500 index futures contracts on the underlying stocks, Journal of Business, Vol. 66, No. 2, pp. 171-187.
Kumar P. and D. J. Seppi (1994), Information and index arbitrage, Journal of Business, Vol. 67, No. 4, pp. 481-509.
MacKinlay, A. C. and K. Ramaswamy (1988), Index Futures Arbitrage and the behavior of Stock Index Futures Prices, Review of Financial Studies, Vol. 1, No. 2, pp. 137-158. Roll, R. (1984), A Simple Implicit Measure of the Effective Bid/Ask Spread, Journal of
Finance, Vol. 39, No. 4, pp. 1127-1139.
Ross, S. A. (1989), Information and volatility: The no-arbitrage martingale approach to timing and resolution irrelevancy, Journal of Finance, Vol. 44, No. 1, pp. 1-17.
Schawrz, T. V. and E. L. Francis (1991), Dynamic efficiency and price leadership in stock index cash and futures markets, Journal of Futures Markets, Vol. 11, No. 6, pp. 669-683. Stephan, J. A. and R.E. Whaley (1990), Intraday Price Changes and Trading Volume Relations
in the Stock and Stock Options Markets, Journal of Finance, Vol. 45, No. 1, pp. 191-220.
Stoll, H. R. and R. E. Whaley (1987), Program trading and expiration day effects, Financial
Stoll, H. R. and R. E. Whaley (1990b), The dynamics of stock index and stock index futures returns, Journal of Financial and Quantitative Analysis, Vol. 25, No. 4, pp. 441-468. Stoll, H.R. and R. E. Whaley (1990c), Stock market structure and volatility, The Review of
Financial Studies, Vol. 3, No. 1, pp. 37-71.
Teppo, M., Jukka, P. and P. Vesa (1995), On the dynamics of stock index futures and individual stock returns, Journal of Business Finance and Accounting, Vol. 22, No. 1, pp. 87-100.
