The innovations of e-mini contracts and futures price volatility components: The empirical investigation of S&P 500 stock index futures

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1 Int. Fin. Markets, Inst. and Money 17 (2007) The innovations of e-mini contracts and futures price volatility components: The empirical investigation of S&P 500 stock index futures Anthony H. Tu a,, Ming-Chun Wang b a Department of Finance, National Chengchi University, 64 Sec. 2, Zhi-nan Rd., Wenshen, Taipei 11605, Taiwan b Department of International Business Management, Wufeng Institute of Technology, Chia-yi 621, Taiwan Received 19 August 2005; accepted 2 November 2005 Available online 19 December 2005 Abstract The effect of the initiation of e-mini stock index futures (ESIFs) on the volatility components of S&P 500 stock index futures is herein investigated. The study decomposes S&P 500 stock index-related observed volatilities into unobserved fundamental volatility and transitory noise and utilizes the decomposition to test two hypotheses: the clientele factor hypothesis and the information adjustment hypothesis. The first hypothesis proposes that the ESIFs attract more noisy traders who prefer trading the friendly-size futures contracts. The second one proposes that the innovations of ESIFs improve the information flow of the futures markets. Using a stochastic volatility model, the empirical results are consistent with both of our proposed hypotheses Elsevier B.V. All rights reserved. JEL classification: G13; G15 Keywords: Stock index futures; Kalman filter; Stochastic volatility model 1. Introduction For each index future, the involved exchange must select a contract multiplier. In some cases, an exchange has established two index futures on the same underlying index, but with different contract multipliers. The original MMI futures had a multiplier of $100, but, in August 1985, a maxi version was introduced with a multiplier of $250. In September 1986, the original (mini) Corresponding author. Tel.: ; fax: address: atu1106@yahoo.com.tw (A.H. Tu) /$ see front matter 2005 Elsevier B.V. All rights reserved. doi: /j.intfin

2 A.H. Tu, M.-C. Wang / Int. Fin. Markets, Inst. and Money 17 (2007) Table 1 Contract specifications for the S&P 500 futures the terms of an S&P 500 futures contract effective as of 9 September 1997 S&P 500 futures E-mini S&P 500 futures Contract unit $250 S&P 500 index $50 S&P 500 index Minimum price 0.10 Index point 0.25 Index point Fluctuation (tick) (or $25.00 per contract) (or $12.50 per contract) Trading hours 8:30 a.m. to 3:15 p.m. (plus overnight hours on GLOBEX) 3:30 p.m. to 3:15 p.m. next day on GLOBEX Position limits 5000 contracts net long or net short in all contracts 100,000 net over all contracts months combined Delivery months March, June, September, and December Delivery Cash settlement to the final settlement price Daily price limits, trading halts, and others a Sources: Chicago mercantile exchange. a All remain unchanged. For complete details of the rule, please contact the CME research division. MMI contract was discontinued. From 11 October 1993, the multiplier of all ordinaries index futures decreased from $100 to $25 in order to boost volume. On 9 September 1997, the CME introduced e-mini S&P 500 stock index futures (ESIFs, hereafter), which are one-fifth the size of regular S&P 500 index futures. The ESIFs are smaller, more investor-friendly in size, and they trade exclusively on an electronic trading system (named GLOB EX). In contrast, the larger contract is pit-traded during the day (8:30 a.m. to 3:15 p.m. central time) and trades on GLOBEX when the pits are closed. Moreover, the minimum price fluctuation for ESIFs is $12.50 (0.25 index point times the multiplier $50), which is only one-half that of S&P500 futures. The contract specifications of S&P500 index futures and e-mini S&P500 index futures are detailed in Table 1. For investors, the disadvantage of ESIFs is the higher trading cost as the percentage of underlying contract value in comparison with trading cost of equity index futures. In contrast, the ESIFs have several advantages. First, the margin requirements of ESIFs are only one-fifth of the regular equity index futures. The lower margin requirements allow more small investors to qualify to trade in index futures market. Second, investors who wish to make small adjustments in their portfolio prefer to use e-mini contracts rather than regular equity index futures. Third, electronic trading system used by ESIFs is more convenient for small investors and is optionally more efficient than open out-crying trading system adopted by regular equity index futures. By October 1996, the value of the S&P500 index futures contract had grown to five times its value at its inception in April The purpose of introducing the ESIFs is to make the S&P500 index futures contract more accessible to investors and to smooth out trading, because investors can use the regular S&P500 index futures, and the new ESIFs or both. The observed volatility for S&P 500 index futures shows a significant increase coinciding with the initiation of ESIFs (as shown in Section 5). This study seeks to understand whether the increasing volatility is more due to the information or it is more due to the noise, since this issue has important policy implications. As the ESIFs bring more traders who trade on the basis of noise rather than information, it may lead to futures prices being driven away from fundamental equilibrium prices. Thus, if futures prices volatility is driven by noise, then further regulation may be warranted. However, if information is the driving force, then regulatory changes may not be

3 200 A.H. Tu, M.-C. Wang / Int. Fin. Markets, Inst. and Money 17 (2007) justified. 1 In this study, we propose new tests to examine how the initiation of ESIFs affects the volatility components of S&P 500 stock index and/or futures. The new tests decompose stock index-related volatilities into transitory noise and unobserved fundamental volatility and utilize the decomposition to investigate the effect of the initiation of ESIFs on the volatility components. We define the volatility caused by information as fundamental volatility and the volatility caused by noise trading as transitory noise. Observed volatility series may be regarded as a combination of transitory noise and permanent fundamental volatility. When information arrives, the permanent components of volatilities of both the stock index and futures will move in the same way. On the other hand, transitory components of volatilities caused by noise trading may not behave in the same fashion. We shall assume that there is only one true permanent component for all volatilities which are related to one underlying asset, while there are multiple transitory noises. The effect of the initiation of ESIFs on the original S&P 500 index futures can be treated similar to that of stock splits on outstanding stocks. Since empirical studies on futures splits are rare, we have to rely on the split experience of the equity market to understand whether the initiation of ESIFs affects S&P500 index futures price volatility. 2,3 We propose the following hupotheses: Hypothesis 1. The greater post-esif volatility may be due to the activity of relatively ignorant noisy traders who prefer trading the friendly-size futures contracts (this clientele factor hypothesis is first attributed to Black (1986)). 4 As the hypothesis is true, the transitory noise of the observed volatility increases. Since the ESIFs, as mentioned above, traded on an electronic trading system and with a smaller size, the initiation of ESIFs provides a more convenient way for information traders to reflect the arrival of new information. The increased liquidity makes futures prices move back toward their fundamental value more quickly. In other words, the innovations of e-mini contracts improve the information flow of the futures market. Thus, we also propose 1 Holmes and Tomsett (2004) examine that extent to which futures price changes are driven by noise or information for U.K. futures contracts by utilizing the Anderson s (1996) specification of the mixture of distributions hypothesis. They found that the link between futures volume and volatility can be attributed to the flow of information. It is shown that price movements are dominated by informed rather than noise trading for the FTSE-100, the Long Gilt and the Brent Oil futures contracts. They suggest that further regulation based on the notion that noise traders dominate futures trading is unwarranted. 2 Two exceptions are the studies by Martini and Dymke (1995) and Karagozoglu and Martell (1999). They, however, analyze the relation between contract size and liquidity using the respecificaiton of Sydney futures exchanges (SFE) shares price index (SPI) and 90-day bank accepted bill (BAB) futures contracts. In 1993, SFE decreased the size of SPI futures by a factor of four while increasing its minimum tick. The BAB contract was doubled in size with the minimum tick size left unchanged. They found, after controlling for market factors, that the respecification of the SPI futures resulted in higher trading volume, while that of BAB futures decreased trading volume. Recently, Bollen et al. (2003) measures changes in the trading environment as the CME doubled tick size of its S&P 500 futures contracts and halved the denomination on 3 November They examined empirically whether and how the contract redesign affects the expected profits of its members. 3 Ohlson and Penman (1985) provide evidence that NYSE stock returns variances increase subsequently to ex stock distribution days for splits that are 100% or greater. They increase in volatility is independent of the size of the split and the post-split price. Their study also spurred subsequent work on small-sized distributions and reverses splits (Dravid (1984)), on return variances (Park and Krishnamurti (1995)) and on split-related beta shifts (Brennan and Copeland (1988) and Wiggins (1992)). However, the source of the relationship between volatility and stock split still remains a mystery. 4 Black (1986) suggests that noise trading increases after stock splits because noise traders prefer low-priced to highpriced stocks. He also argues that the increase in noise traders causes an increase in volatility. If noise traders trade small trades, our proposals for e-mini futures are consistent with Black s model.

4 A.H. Tu, M.-C. Wang / Int. Fin. Markets, Inst. and Money 17 (2007) Hypothesis 2. The volatility persistence after ESIFs is lower than that before ESIFs (we refer to this as the information adjustment hypothesis ). In the next section, we decompose the S&P 500 stock index-related volatility into transitory noise and fundamental volatility. We then proceed, in the third section, by introducing the stochastic volatility model (SVM). Section 4 describes the data and the methodology employed in this study, while Section 5 presents and discusses the empirical results. The Section 6 summarizes the article. 2. Fundamental and noisy component of volatility The efficient market hypothesis views price volatility as a result of the random arrival of new information, which changes returns. However, empirical studies such as Shiller (1981), Schwert (1989), and French and Roll (1986) suggest that volatility cannot be explained only by changes in fundamentals. A significant amount of volatility in asset prices comes from noise trading by irrational traders. 5 From this point of view, an observed volatility series may be regarded as a combination of transitory noise (θ) and permanent fundamental volatility (f). 6 We define the volatility caused by information as fundamental volatility and the volatility caused by noise trading as transitory noise. Observed volatility series may be regarded as a combination of transitory noise and permanent fundamental volatility. In a futures market, two different volatility series, which are related to one underlying asset can be calculated: underlying asset return volatility (RV) and futures return volatility (FV). When information arrives, the permanent components of all volatilities will move in the same way. On the other hand, the transitory components of volatilities caused by noise trading may not behave in the same manner. We shall assume that there is only one permanent component, which is related to one underlying asset, while there are two transitory noises. It is natural to assume that there is only one fundamental volatility defined over the underlying asset and its futures. This is because information, which affects the fundamentals of the underlying asset is the same across the underlying asset and its futures and, thus, results in the same fundamental volatility. The return volatility of an underlying asset at time t is RV t = f t + θ R,t (1) The relationship between the return volatility of an underlying asset and that of its futures can be easily derived from the cost-of-carry model. The no-arbitrage equilibrium futures price can be denoted by F t = S t exp (r f,t d t )τ, where F t is the futures price at time t, S t is the underlying asset price at time t, d t is (if it exists) the dividend yield rate, r f,t is the risk-free rate at time t, and τ is the time-to-maturity. Upon taking logarithms of the above no-arbitrage futures price equation and differencing, we obtain the futures return volatility (FV) having the following relationship 5 A plentiful amount of theoretical models examines irrational noise trading in the stock market and helps to explain why stock prices might deviate from their fundamental value for substantial periods and why stock prices might be excessively volatile. These models include Shleifer and Summers (1990), De Long et al. (1990), Shleifer and Vishny (1990), and Kirman (1993). 6 Empirical studies such as Shiller (1981), French and Roll (1986), and Schwert (1989) show that changes in the fundamental value cannot explain all of the price movements in financial markets. In other words, the observed volatility series has noise.

5 202 A.H. Tu, M.-C. Wang / Int. Fin. Markets, Inst. and Money 17 (2007) with the underlying asset return volatility (squared return) at time t: FV t = f t + θ F,t (2) and θ F,t = θ R,t + Var(r f,t ) + Var(d t ) Cov(r f,t,d t ) Therefore, RV and FV have the same common unobserved fundamental volatility as in Eqs. (1) and (2). The above setting can be expressed as a multivariate model V t = f t θ t (3) Here, V t = [RV t, FV t ]isa(2 1)vector of observed volatilities which are related to one underlying asset, is 1 - isa(2 1) vector of ones, and θ t = [θ R,t,θ F,t ]isa(2 1) vector of transitory noises of observed volatilities. 3. Stochastic volatility model A decomposition of volatilities into fundamental volatility and noises can be carried out with GARCH models or stochastic volatility models (SVMs). However, the two models are different in the sense that SVMs have been developed in terms of information arrival and are known to be consistent with diffusion models for volatility, while the GARCH models have been predominantly used to describe some stylized facts of volatility (Taylor (1994) and Ghysels et al. (1996)). 7 In addition, changes in the level of the fundamental volatility which are used for the investigation of the effects of initiation of ESIFs, are difficult to identify in GARCH models, because a nonnegative time trend included in the conditional volatility equation of GARCH models is usually not significantly different from zero. 8 The SVM employed in this study can be represented by u t = σ t ε t, σ t = σ exp {0.5FVP t } FVP t = φfvp t 1 + η t where u t denotes observed random residuals of a series; σ is a positive scale factor; ε t is an independent, identically distributed random disturbance series; FVP t is an unobserved fundamental volatility process; η t is a series of independent disturbances with mean zero and variance ση 2. Introducing the innovation η t substantially increases the flexibility of the model in describing the evolution of σt 2. The difficulty in estimating a SVM is also understandable because, for each shock u t, the model uses two innovations ε t and η t. Jacquier et al. (1994) provides some properties of the above SVM. It is assumed throughout this paper that FVP t and η t are uncorrelated. 9 When we take logarithms of the squared residuals, the SVM can be represented as V t log u 2 t = log σ 2 + FVP t + log ε 2 t = μ t + FVP t + e t (4a) 7 We expect that there is no significant difference in our analysis between the two models since consistent estimates of a stochastic volatility model can be obtained with GARCH models under certain conditions; see Nelson and Foster (1994) and Nelson (1996) for details. 8 For more discussions on stochastic volatility models, see Taylor (1994), Harvey et al. (1994), and Harvey and Shephard (1996). 9 You might refer to the discussion in Hwang and Satchell (2000) for the rationality of this assumption.

6 A.H. Tu, M.-C. Wang / Int. Fin. Markets, Inst. and Money 17 (2007) FVP t = φfvp t 1 + η t (4b) where log u 2 t is a logarithmic value of the squared residual at time t; μ t = log σ 2 + E(log ε 2 t ) denotes the volatility level. e t = log ε 2 t E(log ε 2 t ) is a noise with zero mean. In an SVM for (4), the logarithm of σt 2 is modeled as a stochastic process. As with EGARCH, working in logarithms ensures that σt 2 is always positive, but the difference is that it is not directly observable. Eq. (4) is the natural discrete-time approximation to the continuous-time Ornstein Uhlenbeck process used in finance theory. For more discussions on SVMs, see Taylor (1994). Eq. (4) assumes that the fundamental volatility process follows an AR(1) process without a trend. Instead of a trend, we introduce a constant, μ, which represents the level of expected volatility in the measurement equation. Thus, the fundamental volatility in Section 2 can be further decomposed into a volatility level (μ) and a fundamental volatility (mean zero) process (FVP) as in Eq. (4). Note that we have only one fundamental volatility process, while volatility levels are different across the two volatility series used later in this study. In the following analysis, we present results for AR(1), AR(2), and ARMA(2,1) extensions. A natural extension of (4) is the bivariate SVM model, which is V t = μ t + FVP t 1 + e t FVP t = φfvp t 1 + η t (5a) (5b) Here, V t, μ t and e t are 2 1 vectors. Term 1 is 2 1 vector of ones. 4. Data and model estimation 4.1. Data description Two daily volatility series, S&P 500 stock index return volatility and S&P 500 futures return volatility, are used in this study. To investigate the possible changes in the unobserved fundamental volatility and transitory noise resulting from the initiation of ESIFs, we divide the entire sample period into two subperiods: the first subperiod (before the initiation of ESIFs) is from 3 May 1993 to 8 September 1997 and the second subperiod (after the initiation of ESIFs) is from 9 September 1997 to 13 January The S&P 500 stock index series and futures series are obtained from Datastream. Table 2 reports the statistical properties of each logarithmic volatility series. Note that futures and index logreturn volatilities show negative skewness, because of close-to-zero return volatilities. Although most of the log-return volatilities are far from normal (for the normality test, a critical value of 5.99 at the 5% significance can be used for the Jarque and Bera (1980) (J&B) statistics in the table), the application of logarithms makes the raw volatility series closer to normality. Thus, the statistical properties in Table 2 suggest that log-volatilities might be better used in a linear modeling framework than the volatilities themselves Quasi-maximum likelihood estimation of the SVM model Estimations of the univariate SVM model (4) using the S&P 500 stock index and futures log-variances are presented in Table 3. The table reports the Quasi-maximum likelihood (QML) estimates of stochastic volatility models for the daily S&P 500 stock index and

7 Table 2 Summary statistics for the daily logarithmic return volatilities of the S&P 500 stock index and futures Mean S.D. Skewness Kurtosis J&B statistics a Autocorrelation Portmanteau statistics (1) (3) (5) (8) (10) (30) (50) (100) (200) Q(10) Q(100) S&P 500 stock index log-return volatility Entire period Subperiod Subperiod S&P 500 futures log-return volatility Entire period Subperiod Subperiod a For the normality test, a critical value of 5.99 at 5% significance can be used for the Jarque and Bera (1980) (J&B) statistics in the table. 204 A.H. Tu, M.-C. Wang / Int. Fin. Markets, Inst. and Money 17 (2007)

8 Table 3 Estimates of univariate SVM models for S&P 500 stock index- and futures-related volatilities Coefficients of state equations Subperiod 1 (before ESIFs 3 May 1993 to 8 September 1997) Subperiod 2 (after ESIFs 9 September 1997 to 13 January 2002) AR(1) AR(2) ARMA(2,1) AR(1) AR(2) ARMA(2,1) S&P 500 stock index μ (0.0450) (0.0452) (0.0469) (0.0416) (0.0412) (0.0434) θ (0.0010) (0.0004) φ (0.0590) (0.0573) (0.0565) (0.0609) (0.0576) (0.0582) φ (0.0616) (0.0618) (0.0573) (0.0598) σ e σ η STN ratio = ση 2/σ2 e Skewness Kurtosis Normality Q(10) Q(50) MLE S&P 500 futures μ (0.0443) (0.0486) (0.0467) (0.0428) (0.0440) (0.0436) θ (0.0004) (0.0033) φ (0.0604) (0.0575) (0.0583) (0.0609) (0.0585) (0.0580) φ (0.0617) (0.0608) (0.0622) (0.0602) σ e σ η STN ratio = ση 2/σ2 e Skewness Kurtosis Normality Q(10) Q(50) MLE Note: The table reports the Quasi-maximum likelihood estimates of stochastic volatility models for the daily log-variances of S&P 500 stock index and futures. Estimates are obtained using the BFGS optimization algorithm provided by RATS. State equations are assumed to follow the ARMA(p,q) process. The state-space representation for ARMA(2,1) is; V t = μ + FVP t +e t ; FVP t = φ 1 FVP t 1 + φ 2 FVP t 2 + η t + θ 1 η t 1 ; where V t and FVP t are observed and unobserved fundamental volatilities, respectively. Term μ is the level of fundamental volatility, and e t and η t are the transitory noise and permanent error, respectively. Numbers in parentheses are standard errors. A.H. Tu, M.-C. Wang / Int. Fin. Markets, Inst. and Money 17 (2007)

9 206 A.H. Tu, M.-C. Wang / Int. Fin. Markets, Inst. and Money 17 (2007) futures log-variances. 10 Estimates are obtained using the BFGS optimization algorithm provided by RATS. State equations are assumed to follow AR(1), AR(2), and ARMA(2,1) processes. The first subperiod shows little difference in the fundamental volatility process compared with that of the second subperiod. The fundamental volatility processes for S&P 500 stock index and futures in both subperiods all show mean reversion (φ 1 are, respectively, and for subperiods 1 and 2 in AR(1) for the stock index and are, respectively, and for subperiods 1 and 2 in AR(1) for futures). In addition, the permanent innovation in both subperiods is a little bit larger than the transitory noises and thus, the signal-to-noise ratios (STN = ση 2/σ2 e ) for AR(1), AR(2), and ARMA(2,1) are around one for S&P 500 stock index and futures. Notice that maximum likelihood values are not significantly different between models over two subperiods. Thus, an AR(1) model will be used for the state equation for the rest of this study. Table 4 reports the estimated bivariate SVM model. Although the coefficients of the fundamental volatility processes in the bivariate SVMs are different from those of the univariate SVM, all fundamental volatility processes exhibit very strong persistence (φ 1 are, respectively, and for subperiods 1 and 2 in AR(1)) Kalman filter and unobserved fundamental volatility We now investigate the changes in the unobserved fundamental volatility resulting from the introduction of ESIFs. The decomposition of observed volatility into fundamental volatility and transitory noise gives a new perspective on the investigation of the effect of ESIFs introduction on volatility. The Kalman filter is a recursive procedure for computing the optimal estimate of the unobserved state vector, based on the appropriate information set. It provides a minimum mean squared error estimator, given the appropriate information set. To obtain the unobserved fundamental volatility, FV i, we use a smoothing algorithm. 11 An inference about FV i using the full set of information, defined as FV i t/t, is called the smoothed estimate of FVi, which can be represented as ( FV FV i i ) t/t = E t ΩT i where ΩT i = (V i,t,v i,t 1,,V i,1 ) denotes the information set; V t = log u 2 t ; and i = S&P 500 or its futures. Using the smoothing technique for the AR(1) plus the noise model, we obtain smoothed estimates of FV i for each period and thus a transitory noise series. Note that the S&P 500 index and futures return volatilities have the same fundamental volatility process, but the levels of the fundamental volatility are different across the two volatility series. 10 Ruiz (1994) suggests that the QML for the SVM model has a good finite sample property and is usually to be preferred to the corresponding method of moment estimator. 11 This is a fixed-interval smoothing algorithm. See Harvey (1989, p ). Depending upon the information set used, the Kalman filter has two algorithms: basic filter and smoothing. The basic filter refers to an estimate based on information available up to time t, and smoothing refers to an estimate based on all the available information in the sample through time T. Smoothing provides us with a more accurate inference on unobserved fundamental volatility, since it uses more information than the basic filter.

10 Table 4 Estimates of bivariate SVM models for S&P 500 stock index- and futures-related volatilities Coefficients of state equations Subperiod 1 (before ESIFs 3 May 1993 to 8 September 1997) Subperiod 2 (after ESIFs 9 September 1997 to 13 January 2002) AR(1) AR(2) ARMA(2,1) AR(1) AR(2) ARMA(2,1) Stock Futures Stock Futures Stock Futures Stock Futures Stock Futures Stock Futures S&P 500 stock index μ (0.0349) (0.0300) (0.0431) (0.0285) (0.0433) (0.0299) (0.0419) (0.0293) (0.0215) (0.0273) (0.4462) (0.0331) θ (0.0003) (0.0033) φ (0.0000) (0.0577) (0.0756) (0.0034) (0.0196) (0.0007) φ (0.0577) (0.0478) (0.0000) (0.0094) σ η σ e STN MLE Note: The table reports the maximum likelihood estimates of bivariate stochastic volatility models for the S&P 500 stock index and futures. Estimates are obtained using the BFGS optimization algorithm provided by RATS. State equations are assumed to follow ARMA(p,q) models. The state-space representation for ARMA(2,1) is; V - t = μ - + FVP t e - t; FVP t = φ 1 FVP t 1 + φ 2 FVP t 2 + η t + θ 1 η t 1 ; where V t and FVP t are observed and unobserved fundamental volatilities, respectively. Term μ is the level of fundamental volatility, and e t and η t are the transitory noise and permanent error, respectively. Note that V t, μ, FVP t and e t are 2 1 vectors. Numbers in parentheses are standard errors. A.H. Tu, M.-C. Wang / Int. Fin. Markets, Inst. and Money 17 (2007)

11 208 A.H. Tu, M.-C. Wang / Int. Fin. Markets, Inst. and Money 17 (2007) Empirical results of ESIFs effects By decomposing observed volatility into fundamental volatility and noise, we can further analyze changes in volatility resulting from the introduction of ESIFs. The effects of the initiation of ESIFs on fundamental volatility are reported in Table 5. As explained previously, the fundamental volatility is decomposed into a volatility level (μ) and a fundamental volatility process (FVP t ). Panel A of Table 5 investigates the effects of the initiation of ESIFs on the level of the fundamental volatility using the following intervention model: level = μ + dd t, where D t is a dummy variable which is zero before the initiation of ESIFs and one after the introduction of ESIFs. Since d is positive and significant (at the 5% level) for both the univariate model (4) and bivariate model (5), the initiation of ESIFs seems to increase the level of fundamental volatility. Panel B of Table 5 reports the results for the effects of the introduction of ESIFs on the persistence of fundamental volatility process (FVP t ). A higher persistence results in a longer delay for the conditional variance to converge to its unconditional value. The intervention model used here is FVP t =(φ + dd t )FVP t l + η t, where D t is a dummy variable which is defined the same as above. The persistence of the fundamental volatility process for S&P 500 stock index volatility decreased significantly (d is negative and significant at the 10% level) after the initiation of ESIFs. However, the fundamental volatility process for S&P 500 futures volatility decreased, but not significantly (d is negative but not significant at the 10% level). For the bivariate model, the persistence of fundamental volatility process is lowered significantly (d is positive and significant at the 5% level), because φ is negative. We have considered two types of volatility changes: changes in levels and changes in the underlying dynamic fundamental process that correspond to a change in the overall persistence Table 5 The effects of the initiation of the ESIFs on the unobserved fundamental volatilities Univariate model Bivariate model μ d μ d (A) Changes in volatility level S&P 500 stock index ** (0.0431) ** (0.0609) ** (0.0217) ** (0.0558) S&P 500 futures ** (0.0435) ** (0.0620) ** (0.0242) ** (0.0369) Univariate model Bivariate model φ d φ d (B) Changes in fundamental volatility process S&P 500 stock index S&P 500 futures ** (0.0666) ** (0.0664) * (0.1066) (0.1009) ** (0.0441) ** (0.0507) Note: The fundamental volatility is decomposed into a volatility level (μ) and a fundamental volatility process (FVP t ). Note that the volatility levels are different across the two volatility series used in this study, although we have only one fundamental volatility process. The univariate model refers to Eq. (4) and the bivariate model refers to Eq. (5). Panel A investigates the effects of the initiation of ESIFs on the level (μ) of the fundamental volatility using the following intervention model: level = μ + dd t ; where D t is a dummy variable which is zero before the initiation of ESIFs and one after the initiation of ESIFs. Panel B reports the results on the effects of the initiation of ESIFs on the fundamental volatility process (FVP t ). The intervention model on the fundamental volatility process is; FVP t =(φ + dd t )FVP t 1 + η t where D t is defined the same as above. Numbers in parentheses are standard errors. * Significance at the 10%. ** Significance at the 5%.

12 A.H. Tu, M.-C. Wang / Int. Fin. Markets, Inst. and Money 17 (2007) Table 6 The effects of the initiation of the ESIFs on the transitory noise Univariate model Bivariate model δ d δ d S&P 500 stock index ** (0.0100) (0.0141) ** (0.0263) * (0.0372) S&P 500 futures ** (0.0090) ** (0.0128) ** (0.0264) ** (0.0374) Note: The table reports the effects of the initiation of ESIFs on the transitory noise using the following intervention model; e t = δ + dd t + ν t ; where D t is a dummy variable which is zero before the initiation of ESIFs and one after the initiation of ESIFs. Term e t is from Eqs. (4a) and (5a) in the univariate and bivariate models, respectively. Numbers in parentheses are standard errors. * Significance at the 10%. ** Significance at the 5%. of all markets, which both are interesting to regulators. We feel that large changes in the latter should be of particular interest as they reflect the fact that information shocks may accumulate rather than die away. As we consider the futures and spot separately (in a univariate model), we cannot, due to the absence of statistical significance, reach a firm conclusion on the effect of the initiation of ESIFs on the fundamental volatility process. When we consider futures and spot jointly (in the bivariate model), the above result seems to suggest that persistence of the fundamental volatility process is reduced as a result of the initiation of ESIFs. On the other hand, following the initiation of ESIFs, we find that the level of fundamental volatility is enhanced in both univariate and bivariate models. Table 6 reports the effects of the initiation of ESIFs on the transitory noise using the following intervention model e t = δ + dd t + ν t, where D t is defined the same as above and e t is from Eqs. (4a) and (5a) for the univariate and bivariate models, respectively. The transitory noise of volatility for S&P 500 futures increased significantly (d is positive and significant at the 5% level) by the initiation of ESIFs. On the other hand, the transitory noise of volatility for the S&P 500 stock index exhibits an unsignificant change (at the 5% level). Following the initiation of ESIFs, the observed volatility for S&P 500 index futures shows a significant increase, as we observe an increase in the level of fundamental volatility and transitory noise. We also found that the persistence of the fundamental volatility process is reduced; implying that the effect of information shocks dies away more quickly than before. The results support our proposed information adjustment hypothesis. In contrast, the transitory noise of volatility for S&P 500 stock index and futures is enhanced significantly. Consistent with our proposed clientele factor hypothesis, the smaller size of futures contracts attracts relatively ignorant noise traders and brings more price fluctuations caused by noise trading. 6. Conclusions On 9 September 1997, the CME introduced e-mini S&P 500 index futures (ESIFs), one-fifth the size of the regular S&P 500 index futures. In addition, the ESIFs are traded on an electronic trading system, named GLOBEX. To understand whether the ESIFs attract more noisy (or informed) trading and whether the innovations of ESIFs improve the information flow of the futures market, we investigate how the introduction of ESIFs affects the volatility components of the S&P 500 index futures.

13 210 A.H. Tu, M.-C. Wang / Int. Fin. Markets, Inst. and Money 17 (2007) Using a stochastic volatility models, we decomposed two related volatilities, S&P 500 index return volatility and futures return volatility, into what we call unobserved fundamental volatility and transitory noise. We then utilized the decomposition to investigate the effect of the initiation of ESIFs on the volatility components by performing new tests for two hypotheses: the clientele factor hypothesis and the information adjustment hypothesis. The overall findings presented in the study are consistent with both of our proposed hypotheses. The persistence of the fundamental volatility process is reduced, while the transitory noise in the S&P 500 futures is enhanced significantly. The evidence presented here suggests that further regulation based on the notion that noise traders dominate futures markets is warranted. Acknowledgements We thank for the helpful comments from participants on the 2004 Asian Finance Conference in Taipei and the seminar in Xiamen University, China. All remaining errors are clearly our own. References Anderson, T., Return volatility and trading volume in financial markets: an information flow interpretation of stochastic volatility. Journal of Finance 51, Black, F., Noise. Journal of Finance 41, Bollen, N.P.B., Smith, T., Whaley, R.E., Optimal contract design: for whom? Journal of Futures Market 23, Brennan, M.J., Copeland, T.E., Beta changes around stock splits: a note. Journal of Finance 43, De Long, J.B., Shleifer, A., Summers, L.H., Waldmann, R.J., Noise trader risk in financial markets. Journal of Political Economy 98, Dravid, A.R., The behavior of returns around ex-dates for splits and stock dividends. Working Paper, Stanford University. French, F., Roll, R., Stock return variances: the arrival of information and the reaction of traders. Journal of Financial Economics 17, Ghysels, E., Harvey, A.C., Renault, E., Stochastic volatility. In: Maddala, G.S., Rao, C.R. (Eds.), Handbook of Statistics, vol. 14. Elsevier, North-Holland, Amsterdam. Harvey, A.C., Forecasting Structural Time Series Models and the Kalman Filter. Cambridge University Press. Harvey, A.C., Ruiz, E., Shephard, N., Multivariate stochastic variance models. Review of Economic Studies 61, Harvey, A.C., Shephard, N., Estimation of an asymmetric stochastic volatility model for asset returns. Journal of Business and Economic Statistics 14, Holmes, P., Tomsett, M., Information and noise in U.K. futures markets. Journal of Futures Markets 24, Hwang, S., Satchell, S.E., Market risk and the concept of fundamental volatility: measuring volatility across asset and derivatives markets and testing for the impact of derivatives markets on financial markets. Journal of Banking & Finance 24, Jacquier, E., Polson, N.G., Rossi, P., Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics 12, Karagozoglu, A.K., Martell, T.F., Changing the size of a futures contract: liquidity and microstructure effects. Financial Review 34, Kirman, A., Ants, rationality and recruitment. Quarterly Journal of Economics 108, Martini, C.A., Dymke, R.J., Liquidity in the Australian SPI futures market following a redenomination of the contract. Working paper, University of Melbourne. Nelson, D.B., Asymptotically optimal smoothing with ARCH models. Econometrica 64, Nelson, D.B., Foster, D.P., Asymptotic filtering theory for univariate ARCH models. Econometrica 62, Ohlson, J., Penman, S., Volatility increases subsequent to stock splits: an empirical aberration. Journal of Financial Economics 14, Park, J., Krishnamurti, C., Stock splits, bid-ask spreads and return variances: an empirical investigation of NASDAQ stocks. Quarterly Journal of Business and Economics 34,

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