futures trading vol determinant prices hodgson

8/13/2019 Futures Trading Vol Determinant Prices Hodgson

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2Futures trading volume as a determinant of prices3in different momentum phases

4Allan Hodgsona, A. Mansur M. Masihb,*, Rumi Masihc

5aSchool of Accounting, Banking and Finance, Griffith University, Nathan, Brisbane 4111, Australia

6bDepartment of Finance and Economics, King Fahd University of Petroleum and Minerals,

7KFUPM P.O. Box 1764, Dhahran 31261, Saudi Arabia

8cGlobal Economic Research, Goldman, Sachs & Co., New York, NY 10004, USA

9

10Abstract

11Recent studies contend that trading volume has predictive power for ex ante stock prices,

12particularly small stocks that do not react quickly to macroeconomic information. This study13postulates that a significant amount of macro-information that flows on to stock markets is derived

14from derivative markets. We examine the impact of short-term futures trading volume and prices

15on cash stock prices using a case study of 15-min data from the Australian stock index futures

16market which reports actual trading volume. After applying vector error correction modelling

17(VECM), variance decomposition and impulse functions, we conclude that futures prices provide a

18short-term information lead to stock prices that dominates trading volume effects. We also observe

19asymmetric changes in the impact of trading volume between bull and bear price momentum

20phases and after large trading volume shocks. These results suggest that, in future, studies on

21trading volume should control for the cross-correlation impact from derivative prices and the

22differential impact of trading phases.

23D 2004 Published by Elsevier Inc.

24JEL classification:G15; C52

25Keywords:Futures trading volume; Stock and futures prices; Multivariate causality; Price momentum phases

26

1057-5219/$ - see front matterD 2004 Published by Elsevier Inc.

doi:10.1016/j.irfa.2004.10.014

* Corresponding author. Tel.: +966 3 860 2135; fax: +966 3 860 2585.

E-mail address: [email protected] (A.M.M. Masih).

International Review of Financial Analysis xx (2004) xxxxxx

FINANA-00222; No of Pages 18

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271. Introduction

28The objective of this paper is to investigate the role of index futures trading volume

29in terms of the information it contains about ex ante futures and stock prices. More

30specifically, we are interested in the power of trading volume, over and above own and

31cross-price autocorrelations in predicting ex ante prices during different bull and bear

32price momentum phases. The paper is primarily motivated by claims that trading volume

33is a primary vehicle for predicting ex ante stock prices. Secondary motivations are

34provided by concerns posed by the dramatic increase in trading volume in futures

35markets,1 whether trading volume has additional information for prices, whether different

36price momentums affect the impact of trading volume, and in extending previous research

37in futures that has concentrated on the relationship between trading volume and price

38volatility (seeBessembinder & Seguin, 1992, 1993; Karpoff, 1987; Locke & Sayers, 1993;39Rutledge, 1986). This research is important with an obvious advantage the ability of

40investors to profit from such research. More generally, exchange organisation, regulation,

41portfolio and investment risk management could all be improved by knowledge of the

42factors that influence price formation, hedging activities and information transfer. Finally,

43a better understanding of these determinants should increase investor confidence in

44financial markets and thereby enhance the efficacy of corporate resource allocation

45(Chordia, Roll, & Subrahmanyam, 2001,p. 501).

46Previous research concerned with predicting prices has concentrated on stock markets

47and has uncovered persistent cross-autocorrelation patterns in prices. Explanations vary

48but mainly encompass (i) time varying expected returns, (ii) microstructure bias such as49thin trading, and (iii) the tendency of prices to adjust more slowly to economy wide

50information (the speed of adjustment hypothesis). More recent research has determined

51trading volume is also a significant determinant of the cross-autocorrelation patterns in

52price returns and the volume of trading plays a significant role in the dissemination of

53market wide information. Moreover, the fundamental importance of trading volume is

54exemplified by the specific relationship between liquidity, trading volume and the

55corporate costs of capital (the liquidity hypothesesAdmati & Pfleiderer, 1988; Chordia

56et al., 2001); learning information by jointly observing past prices and trading volume

57metrics (the information hypothesisBlume, Easley, & OHara, 1994; Chordia &

58Swaminathan, 2000); and the impact of speculative trading on prices (the speculative59hypothesisGrossman, 1977).2

60The above indicates a number of competing hypotheses for the impact of trading

61volume on prices. For example, Chordia and Swaminathan (2000) find that high trading

62volume portfolio returns significantly predict low trading volume portfolio returns and

63this is caused by the tendency of low volume stocks to respond more slowly to

1 For example, in Australia in 1980 less than 3% of contracts traded on the Sydney futures exchange (SFE)

were financial derivatives. By 2000, over 99% of annual futures trading volume were in financial futures or

options. At the same time, total trading volume on the SFE increased from 617,800 contracts to over 31 million(in 2000), and in the SPI from 180,000 (1983) to 3.8 million (in 2000).

2 Embedded within the speculative hypothesis is the volume price momentum hypothesis (Jegadeesh &

Titman, 1993) and the volume overreaction hypothesis (Lee & Swaminathan, 2000).

A. Hodgson et al. / International Review of Financial Analysis xx (2004) xxxxxx2


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64marketwide information. In a similar vein, Gervais, Kaniel, and Mingelgrin (2001) find

65that unusually high trading volume stocks outperform low trading volume stocks in the

66short term. They attribute this to trading volume causing higher market visibility for the

67stock, thus leading to subsequent price increases caused by: (i) a larger set of potential

68buyers compared to sellers being limited to current shareholders, (ii) short selling

69constraints, and (iii) the arrival of additional analysts and traders who reduce estimation

70risk, facilitate risk sharing and increasing information flow (see also Merton, 1987;

71Miller, 1977). These authors basically argue information or structural theories for the

72impact of trading volume.

73On the other hand, others argue that high trading volume indicates the presence of

74speculative trading, psychological factors or market inefficiency. Cooper (1999)

75concludes that periods of high trading volume indicate the presence of speculative

76trading, Hong and Steins (1999) behavioural model states that increased trading by one77class of agents produces momentum in stock prices, and Gervais et al. (2001) observe

78that knowledge of trading volume metrics leads to positive economic returns of 11% per

79annum. Additionally, Lee and Swaminathan (2000) state that abnormal trading volume

80causes divergence from fundamental value and partly reconciles the long-term under-

81and over-reaction price effects. They further conclude that initial price momentums

82observed by others3 is caused by abnormal trading volume and past trading volume

83predicts the magnitude, persistence and reversion coefficients of ex ante prices.4 In turn,

84related to market misperceptions of future earning prospects with analysts providing over

85(under) optimistic earnings forecasts for high (low) volume stocks.

86In this paper, we pose two main incremental refinements to the above research. First,87we postulate that part of the high trading volume premium is related to macroeconomic

88information obtained from futures prices. Second, we examine the impact of trading

89volume in different momentum phases. The first extension is manifestly important because

90of the theoretical role that futures markets play in disseminating information and in

91providing liquidity to spot cash markets. It is well established that futures prices provide an

92information lead to stock prices (Abhyankar, 1995; Chan, 1992; Cheung & Ng, 1990;

93Garbade & Silber, 1983; Kawaller, Koch, & Koch, 1987; Stoll & Whaley, 1990).5

94Theoretically, this information externality is a result of lower transaction costs (Brorson,

951991), incentives to collect and first trade macroeconomic information in futures markets,

96increased financial leverage, and higher liquidity in futures markets (Grossman, 1977;97Subrahmanyam, 1991). These features, in theory, attract new and differentially informed

98investors to futures markets. The resulting increase in trading activity, together with the

99inextricable arbitrage linkage between stock and futures markets, implies an increase in

3 Jegadeesh and Titman (1993) andGervais et al. (2001) reported a short-term volume return premium

stocks that experience unusually high (low) trading volume outperform (are outperformed by) stocks that have

normal trading volume.4 High (low) volume winners (losers)experience faster momentum reversals and lower (higher) future returns

(see alsoDatar, Naik, & Radcliffe, 1998).5 Garbade and Silber (1983) concluded that approximately 75% of new information first affected futures

prices and then flows to stock prices and Chan (1992) found that futures prices consistently led cash price

movements by 10 to 45 min, with cash stock prices rarely leading futures by more than 1 min.

A. Hodgson et al. / International Review of Financial Analysis xx (2004) xxxxxx 3


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100market information (Stephan & Whaley, 1990).6 Conversely, individual stocks of the cash

101market are more likely to react only to firm specific information, which in turn, reduces

102market wide transparency and inhibits trading.

103Hence, if futures prices are a reflection of macroeconomic data and the underlying

104asset is an index of stocks, then the use of derivative prices (partially) controls for the

105impact of macroeconomic data. In addition, the mixture of distributions hypothesis

106(MDH) of Epps and Epps (1976), hypothesises that trading volume provides a lead to

107absolute price changes and in the sequential information model (SIC), the arrival of

108new information to the market generates both trading volume and price movements,

109leading to positive leadlags between prices and volume in either direction (Jennings,

110Starks, & Fellingham, 1981). Moreover,Roll (1984) empirically observed that informed

111futures investors brought own private information into the market through their trading

112volume. We thus add futures trading volume as a potential metric that reveals macro-113data. Within this context, our paper is in the spirit of Chordia et al. (2001) who analyse

114the time series behaviour of trading volume across the aggregate market and Blume et

115al. (1994) who argue prices and trading volume are jointly determined by the same

116market dynamics. Consequently, we analyse the impact of macroeconomic data through

117the cross-correlations of both futures prices and trading volume.

118Additionally, concern has been expressed that futures trading is based upon speculation

119and driven by psychological factors. For example, Grammatikos and Saunders (1986)

120argue that most trading in futures is speculative in nature and that interval-to-interval

121variations in trading volume may be a proxy for interval-to-interval variations in

122speculative activity (see also Garbade & Silber, 1983; Rutledge, 1986; Schwarz &123Laatsch, 1991).7 Previous trading volume research has concentrated on examining the total

124volume of trading or extracting an abnormal volume metric. We provide a different focus

125by examining the impact of trading volume (also abnormal trading volume) on prices

126during bull and bear trading phases. Evidence that trading volume has differential effects

127during each phase may suggest a psychological explanation or that the information impact

128of prices declines in different phases (Fabozzi, Ma, & Linkstey, 1988).8 Finally, for

129technical analysts who favour the psychological approach, the volume/price relationship

130may be used to extract the current dmoodT of the market.

131The inclusion of futures market metrics also provides us with the opportunity to control

132for some other structural problems raised by previous studies. For example, there are no

7 The role of futures market trading has been the focus of substantial recent attention in the US, including

studies by the New York Stock Exchange, the Commodity Futures Trading Commission, the Securities and

Exchange Commission, the United States General Accounting Office and a Presidential Task Force (the Brady

Commission). In Australia, the Australian Securities Commission released a report on over the counter derivative

trading in May 1994 with a major focus being the impact of derivative trading volume on price setting in futuresand cash markets.

8 A reported example of asymmetric behaviour is that institutions act as momentum traders when they enter

markets and act as contrarian traders when they exit (Badrinath & Wahal, 2002).

6 The Australian financial press has reported that the ranks of private security traders have swelled as

technology and market access has become cheaper, more sophisticated and accessible. The bulk of private

traders are seen to be information traders who take advantage of short-term opportunities offered by futures

markets.



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133asymmetries in the ability of futures traders to short sell and the pool of potential traders is

134not confined by current share ownership. Hence, there should be no behavioural trading

135distinctions suchas a steeper demand curve for dbullsTcompared to dbearsTas hypothesised

136by Epps (1975). Additionally, previous studies on intraday futures trading (for example

137Chan, 1992) used recorded number of transactions as a proxy for actual trading volume

138because of the unavailability of intraday futures trading volume in the US. This problem is

139controlled by the use of actual intraday futures trading volume obtained from the Australian

140futures market. We also check for long- and short-term Granger causality by the application

141of cointegration and vector error correction techniques (VECM).

142The findings in this paper confirm that futures price cross-correlations have a statistically

143significant and substantial predictive impact on the underlying stock market. We also

144observe subtle changes in the explanatory power of trading volume with a stronger

145influence in bear markets and opposite impacts from sudden jumps in trading volume146during the bull and bear momentum phases. The paper now proceeds as follows. We

147concentrate on short-term futures trading volume as an explanatory metric and apply a 15-

148min intraday data set from the Sydney futures exchange as a case study illustration. The

149next section describes the data, Section 3 outlines the methodology, Section 4reports the

150results and the paper is concluded in Section 5.

1512. Data

152The data used consists of a case study of 15-min interval dsnapshotT derived from an153online service of Australian all ordinaries (AOI) and share price futures index (SPI)

154prices and SPI futures trading volume over a 1-year period from 1 April 1992 to 30

155March 1993. This data was further checked for integrity against 15-min intraday price

156data on the AOI in hard copy form and tick-by-tick data on the SPI, obtained from the

157stock and futures exchanges. The nearest traded SPI futures contract was used to match

158against the AOI.

159In Australia, the SPI trades from 0950 to 1610 each day (with a break for lunch from

1601230 to 1400), and the shares which constitute the AOI trade continuously from 1000 to

1611600. The observations for the first and last 10 min of trading were excluded for the SPI

162and the lunch time trades from 1245 to 1345 excluded for the AOI. Three days were163deleted from the sample3 August 1992 because no trading data could be obtained for the

164SPI, 24 August 1992 because there was no trading on the stock market during the

165morning, and 9 February 1993 because prices were extremely erratic and deemed to be

166aberrant. This gave 20 matched intraday observations for 249 complete trading days with a

167total of 4980 observations over the research period.

168Raw 15-min data was transformed by taking natural logarithms and the rate of change

169(or first difference) in prices was calculated as:

DXtln X

t ln X

t1

170171where Xt is the observed variable at time t, Xt1 is the previous periods price or futures

172trading volume and ln is the natural logarithm.



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173The data displayed two distinct bull and bear phases. The bear phase coincided with the

174first half of the data set from 1 April 1992 to 30 September 1992 when the value of the

175AOI index consistently declined by some 6.3% from 1584.4 to 1485. During this period,

17657.8% of intraday price changes were negative, which represented 37% more price

177decreases than increases. The bull period equated with the second half of the data set when

178the AOI increased by 12.3% to close at 1667.4 on 31 March 1993. During this phase, the

179ratio of relative intraday price changes was reversed with price increases outnumbering

180price decreases by 33%.

181The application of intraday futures data from the Australian market also allows the

182opportunity to examine the contentions that the pricevolume relation is strongest in

183markets in which price volatility is highest9 (Karpoff, 1987). Further, if trading volume is a

184proxy for information flow, then its value would be stronger in markets driven by thin

185trading (Conrad, Hameed, & Niden, 1994). The Australian market employs a continuous186trading mechanism which when combined with thin trading theoretically implies (i) the

187depth of the market will be further reduced, and (ii) that differential forms of information

188(such as trading volume) may have greater impact.

1893. Econometric method

1903.1. Cointegration and vector error-correction modelling (VECM)

191Two or more variables are cointegrated if they exhibit long-run equilibrium relation-192ship(s) that is they share common trend(s) (Engle & Granger, 1987). As long as two

193variables have a common trend, causality in the Granger sense, must exist in at least one

194direction either unidirectional or bidirectional. Evidence of cointegration among variables

195also rules out the possibility that the estimated relationship is dspuriousT. However,

196although cointegration indicates the presence or absence of Granger-causality, it does not

197indicate the direction of causality between variables. The direction of Granger causality

198can be detected through the vector error correction model (VECM) derived from the long-

199run cointegrating vectors.

200Engle and Granger (1987)demonstrated that once a number of variables (say,x tand y t)

201are cointegrated, there always exists a corresponding error-correction representation (ECM).202This in turn implies that changes in the dependent variable are a function of the level of

203disequilibrium in the cointegrating relationship as well as changes in other explanatory

204variables. A consequence of ECM is that eitherDxtorDytor both must be caused by Et1205(the equilibrium error) which is itself a function ofx t1,yt1. Intuitively, ify tand x thave a

206common trend, then the current change inxt(say the dependent variable) is partly the result

207of xt moving into alignment with the trend value of yt (the independent variable). The

208Granger-causality (or endogeneity of the dependent variable) can be evidenced either

209through the statistical significance of thet-test of the lagged error-correction term(s) and/or

210theF-test applied to the joint significance of the sum of the lags of each explanatory variable.

9 In the data set used in this study, the relative SPI/AOI price variance ratio was 2.96. This ratio was

consistent across the trading day.



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211In addition to indicating the direction of causality amongst variables, the VECM

212approach allows the researcher to distinguish between dshort-runT and dlong-runT forms

213of Granger-causality. When the variables are cointegrated, then in the short-term

214deviations from the long-run equilibrium will feed back on the changes in the dependent

215variable in order to force the movement back towards long-run equilibrium. If the

216dependent variable is driven directly by this long-run equilibrium error then it is

217responding to this feedback. If not, it is responding only to short-term shocks to the

218stochastic environment. TheF-tests of the ddifferencedT explanatory variables provide an

219indication of the dshort-termT causal effects (i.e. the joint cross-autocorrelations) whereas

220the dlong-runT causal relationship is implied through the significance or otherwise of the

221t-test(s) of the lagged error-correction term(s).

222This point is important. If the variables are cointegrated, then causality tests which

223incorporate differenced variables will be misspecified unless the lagged error-correction224term is included (Toda & Phillips, 1993). Second, standard tests that establish stationarity

225by mechanically differencing variables eliminate the long-run information embodied in the

226original level form of the variables. The VECM derived from the cointegrating equation(s)

227overcomes these problems by including the lagged error-correction term that reintroduces

228the long-run information lost through the differencing procedure and opens up an

229additional channel of Granger causality. This is an important statistical innovation given

230that it accounts for short-term dynamics whilst still preserving the long-run structural

231relationship inferred by the arbitrage cost-of-carry model.

2323.2. Variance decompositions (VDCs) and causal relativities

233The VECM, F- and t-tests may be interpreted as within-sample causality tests. They

234can indicate only the Granger-exogeneity or endogeneity of the dependent variable.

235They do not provide an indication of the dynamic properties of the system, nor do they

236allow us to gauge the relative strength of the Granger-causal chain or degree of

237exogeneity amongst the variables beyond the sample period. VDCs by partitioning the

238variance of the forecast error of a variable into proportions attributable to innovations (or

239shocks) in each variable in the system including its own, can provide an indication of

240these relativities. Alternatively, VDCs provide a literal breakdown of the change in the

241value of the variable in a given period arising from changes in the same variable in242addition to the changes in other variables in previous periods. A variable that is

243optimally forecast from its own lagged values will have all its forecast error variance

244accounted for by its own disturbances (Sims, 1982).10

10 The results based on VARs and VDCs are generally found to be sensitive to the lag length used and the

ordering of the variables. A considerable time was spent in selecting the lag structure by using FPE criterion. FPE

is based on an explicit optimality criterion of minimising the mean squared prediction error. The criterion tries to

balance the risk due to bias when a low order is selected, and the risk due to the increase in the variance when a

higher order is selected. By construction, the errors in any equation in a VAR are usually serially uncorrelated.However, there could be contemporaneous correlations across errors of different equations. These errors were

orthogonalised through Choleski decomposition with a pre-determined triangular ordering in the following order:

[SPI, CSH, VOL]. The results were not sensitive to alternative ordering of the variables.



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2453.3. Response to unanticipated shocks: impulse response functions (IRFs)

246The information contained in the VDCs may also be equivalently represented by

247IRFs, as both are obtained from the moving average (MA) representation of the original

248VAR model. IRFs essentially map out the dynamic response path of a variable (say, the

249cash stock prices) due to a one-period standard deviation shock to another variable (say,250futures trading volume).

251The impulse response functions like the variance decompositions were also obtained

252from the unrestricted VAR form of the model, although they could be computed via a

253dynamic multiplier analysis of VAR systems with cointegration constraints (see

254Lutkepohl & Reimers, 1992). To trace the dynamic effects of various shocks, the

255estimated VECM was reparameterised to its equivalent formulation in levels. With this

256reparameterisation, the error-correction terms were incorporated into the first period

257lagged terms of the autoregression. The model was then inverted to obtain the impulse

258response functions that capture the effects of deviations from long-run equilibrium on

259the dynamic paths followed by a variable in response to initial shocks. Intuitively, IRFs

260trace the response over time of a variable, due to a unit shock given to another

261variable.

t1.1 Table 1

Tests of the unit root hypothesist1.2

Aug DickeyFuller PhillipsPerront1.3

sl ss Z(a) Z(ta) Z(U1) Z(a*) Z(ta*) Z(U2) Z(U3)t1.4

Bear market periodt1.5

Levelst1.6

SPI 0.03 2.18 0.11 1.06 1.20 1.43 2.55 3.41 5.87***t1.7CSH 1.13 1.37 1.93 1.15 1.66 4.55 1.44 1.42 1.14t1.8VOL 1.99 2.00 4.28 2.00 3.18 7.73 2.09 2.55 2.66t1.9

First differences (D)t1.10

SPI 2.87*** 4.71* 25.47* 11.78* 69.02* 22.37* 11.87* 46.69* 70.04*t1.11CSH 4.11* 4.21* 24.14* 11.51* 66.16* 25.52* 11.57* 44.51* 66.77*t1.12VOL 3.33** 3.49* 24.19* 10.71* 57.32* 32.17* 10.73* 38.32* 57.48*t1.13

t1.14

Bull market periodt1.15Levelst1.16

SPI 0.21 0.11 1.58 1.25 0.60 1.22 1.98 3.21 4.41t1.17CSH 1.51 0.25 1.87 1.35 1.54 3.34 1.65 2.27 2.98t1.18VOL 1.65 1.25 3.03 1.88 2.97 3.54 1.85 1.27 1.95t1.19

First differences (D)t1.20

SPI 4.87* 6.22* 12.10* 10.84* 57.21* 31.10* 13.20* 25.67* 52.41*t1.21CSH 4.11* 5.42* 24.19* 10.28* 24.31* 25.41* 12.57* 35.74* 45.88*t1.22VOL 3.33** 4.26* 32.28* 9.87* 31.02* 24.74* 11.98* 35.01* 45.61*t1.23

The optimal lag used for conducting the Augmented DickeyFuller test statistic was selected based on an

optimal criteria (Akaikes Final Prediction Error), using a range of lags. The truncation lag parameter l used

for the PhillipsPerron tests was selected using a window choice of w(s,l)=1[s/(l+1)] where the order is thehighest significant lag from either the autocorrelation or partial autocorrelation function of the first differenced

series. The symbols *** , ** and * indicate significance at the 10%, 5% and 1% levels, respectively.t1.24



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2624. Results

2634.1. Prerequisites for cointegration: unit root tests

264A necessary but not sufficient condition for cointegration is that each of the variables

265should be integrated of the same order (more than zero) or that all series should contain

266a deterministic trend. A wide range of unit root tests was applied in order to test the

267order of integration of the variables and the results appear in Table 1.

268Basically, if a time series is trend-stationary and no account is made of this fact when

269implementing the testing procedure, this may lead to high probabilities of making a type II

270error (seeTaylor, 1993).11 The results inTable 1indicate that for all variables concerned,

271the variables were nonstationary at the dlevelTform but stationary after dfirst-differencingT

272I(1). The results were robust to both the bull and bear market samples.

2734.2. JohansenJuselius (JJ) maximum likelihood multivariate tests for cointegration

274We apply the JJ procedure (Johansen & Juselius, 1990) to test for cointegra-

275tion.12 The results based on the JJ multivariate cointegration tests are presented inTable 2

276and indicate that these three variables are bound together by two separate long-run

277equilibrium relationships (i.e. r=2). Note that both maximum eigenvalue (K) and trace

278statistics reject the null of rV1 in favour ofrN1, but cannot reject the null ofrV2 at the

27995% critical values.

280These results mean that there is a unique common long-term trend which binds281together AOI cash prices, SPI futures prices and SPI trading volume. Economically, it is

282expected that AOI and SPI prices would be related in a long-term trend because of the

283nature of the arbitrage relation between cash and futures markets. However, what is

284more interesting is the cointegration of futures trading volume and cash and futures

285prices. This means that as price levels increase so does the level of trading volume. This

286could be related to a richer information environment or a result of factors unrelated to

287information, such as an increased demand for risk transfer trading supplied by hedging

288and insurance strategies.

289Having established the two cointegrating vectors, the Johansen and Juselius procedure

290allows us to test several hypotheses on the coefficients by way of imposing restrictions

12 The JJ procedure has several advantages: (i) it explicitly tests for the number of cointegrating relationships;

(ii) it assumes all variables to be endogenous; (iii) the JJ procedure avoids the arbitrary choice of the dependent

variable used in the EngleGranger approach, and is insensitive to the variable being normalised; (iv) itestablishes on a unified framework for estimating and testing cointegrating relations; and (v) JJ provide the

appropriate statistics and the point distributions to test hypothesis for the number of cointegrating vectors and tests

of restrictions upon the coefficients of the vectors.

11 The following sequence was applied with details of test equations appearing in Appendix A1: (i) apply

Z(ta*), Z(U2) and Z(U3), respectively, and if the unit root hypothesis is rejected then the procedure should be

halted at this point; (ii) if the unit root hypothesis cannot be rejected then the greatest power may be obtained by

estimating equations associated with the PhillipsPerron transformations of the relevantt- andF-statistics,Z(ta*),

andZ(U1). Due to the fact that these two tests are not invariant to the constant term, this is only valid if the drift

term (l*) used in test equations applied in (i) was zero. In this respect, these two tests should only be used if

Z(U2) cannot be rejected.



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291and likelihood ratio tests which are, asymptotically, chi-square distributed with one292degree of freedom. Further, the scrutinising of the cointegration vector in each model

293provides us with a measure of the relative importance of each component in terms of its

294relative weight in comparison to the remaining components. Estimates of these tests are

295also presented in Table 2 for the bull and bear samples. Results indicate each of these

296restrictions are rejected, at conventional levels, which in turn implies that each of the

297variables enters into the cointegrating vectors at a statistically significant level.

2984.3. Temporal causality and vector error-correction modelling

299The presence of a two cointegrating vector(s) in each of the bull and bear three-

300dimensional VARs used in the JJ cointegration tests provides us with two error-

301correction term(s) for constructing models. In order to determine the direction of

t2.1 Table 2

Johansen and Juselius tests for multiple cointegrating vectorst2.2

Long-run cointegrating vector Hypotheses Test statisticst2.3


H0: H1: Max eigenvalue (K) Tracet2.5

r= 0 rN 0 271.386** 306.239**t2.6

rV1 rN1 24.816** 34.853**t2.7

rV2 r= 3 0.037 0.037t2.8

t2.9

Coefficients of normalised cointegrating vector and tests of restrictionst2.10

Vector 1 Vector 2 Chi-square test [v2]t2.11

SPI 1.000 1.000 51.371*t2.12

CSH 0.8466 0.9390 49.911*t2.13

VOL 0.0211 0.0009 71.284*t2.14t2.15

Bull market periodt2.16

H0: H1: Max eigenvalue (K) Tracet2.17

r= 0 rN0 185.251** 227.161**t2.18

rV1 rN1 38.407** 41.915**t2.19

rV2 r=3 3.508 3.508t2.20

t2.21

Coefficients of normalised cointegrating vector and tests of restrictionst2.22

Vector 1 Vector 2 Chi-square test [v2]t2.23

SPI 1.000 1.000 37.001*t2.24

CSH 0.896 0.957 36.970*t2.25VOL 0.048 0.0002 81.507*t2.26

The optimal lag structure for each of the VAR models was selected by minimising the Akaikes FPE criteria.

Critical values are sourced from Johansen and Juselius (1990). The test statistic under the null is distributed as

chi-square with two degrees of freedom, ** indicates rejection at the 95% critical values and * indicates rejection

of zero restriction at least at the 1% level of significance.t2.27



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302causality, we now turn to the results based on the VECM formulation presented in Table

3033. As previously discussed, the long-run equilibrium is driven by the theoretical cost-of-

304carry arbitrage relationship between cash AOI and SPI futures prices and long-term

305levels in trading volume. When the error correction term (ECT) term is significant, this

306implies that this term contains information over and above that implied by only short-

307term lagged changes in the explanatory variables and has a significant feedback effect on

308the changes in the dependent variable. In futures markets, if futures prices lead cash

309prices then this is taken as evidence that futures are used by informed traders to re-

310establish fundamental values. If stock prices lead futures prices then this suggests that

311futures are used to hedge cash prices.

312With respect to the ECT for the bear market period, the results indicate at least one

313ECT is significant for each of the equations in the VECM. In econometric terms, this

314indicates that when there is a deviation from any long-term equilibrium cointegrating315relationship, each variable endogenously adjusts to clear the disequilibrium. In terms of

316a leadlag, it means that no individual variable leads or lags in the long-term and that

317neither information nor hedging activities dominate in the long term.

318During the bull market period, the situation is different. The ECT term in the trading

319volume equation is significant at the 1% level together with weaker evidence of

320significance in futures prices. In contrast to the bear period, the ECT is no longer

321significant for the cash AOI index equation. Econometrically, this means that after an

322exogenous shock to the long-term equilibrium, trading volume and futures prices adjust

323back to long-term equilibrium. This indicates that the AOI is the leading long-term

t3.1 Table 3

Summary results of multivariate temporal causality among SPI, CSH and VOL, based on vector error-correction

model (VECM)t3.2

Dep variable DSPI DCSH DVOL ECT1[ni,t1] ECT2[ni ,t1]t3.3

F-statistics t-statisticst3.4


DSPI 1.109 1.099 2.921* 0.450t3.6

DCSH 4.997* 1.010 2.796* 2.334**t3.7DVOL 0.768 0.731 6.584* 0.450t3.8

t3.9


DSPI 1.367 0.865 1.205 1.772***t3.11

DCSH 4.279* 0.826 0.291 0.203t3.12DVOL 1.107 0.843 6.275* 0.699t3.13

The ECTs (nit1fori=1) for each model were derived by normalising the cointegrating vectors on SPI resulting in

rnumber of residuals. Optimal lag structures for each model were selected by minimising Akaikes FPE criteria.

This procedure filters out the infrequent trading component in the AOI and bid-ask bounce in the SPI. Figures that

appear in the final column are estimated t-statistics testing the null that each lagged-ECT is statistically

insignificant. All other estimates are asymptotic GrangerF-statistics. The residuals used in constructing the ECTs

(from each JJ VAR) were also checked for stationarity by way of unit-root testing procedures applied earlier andinspection of their autocorrelation functions, respectively. The VECM was estimated using an optimally

determined criteria (Akaikes FPE) lag structure for all lagged difference terms and a constant. The symbols ***,

**, and * indicate significance at the 10%, 5% and 1% levels.t3.14



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324variable providing the anchor price for arbitrage purposes with futures prices being used

325more often as a long-run hedging vehicle.

326Having filtered out the longer-term leadlag relationships, we are now able to

327determine, in a more rigorous statistical manner, the short-term leadlag effects by

328referring to the asymptotic Granger F-statistic. Reading down the columns in Table 3

329shows that the lagged terms for the DSPI have a significant short-term impact on the

330DCSH but not on DVOL. Short-term movements in cash prices and futures trading volume

331do not exert any influence. These equations strongly indicate that futures prices provide

332the short-term lead to the cash stock index and that the results are robust across both bull

333and bear markets.

334To summarise our results in terms of leadlag relations. During the bear market period,

335there is no long-term leadlag relationship from any variable. In the short term, futures

336prices exert a strong leading impact on cash prices with short-term futures trading volume337not statistically significant. During the bull market, cash AOI prices provide the long-term

338lead, but are still strongly affected in the short term by changes in futures prices. These

339observations are consistent with the results ofChan (1992) and reinforce that SPI prices

340consistently provide a short-term information lead to the AOI regardless of the

341psychological state of the market. In terms of the aim of this paper, the results confirm

342that short-term cross-autocorrelations in futures prices are significant explanators of cash

343stock prices.

344Further, after controlling for price cross-correlations results show that trading volume

345does not significantly affect futures or cash prices. There may, however, be a potential

346research design flaw because raw trading volume is applied and not unexpected trading347volume. As a test of the robustness of our results, and given the emphasis on

348differentiating the effects of anticipated and unanticipated information on prices, measures

349of expected trading volume based on the day of the week and time of the day were

350constructed by fitting polynomial functions to intraday trading volume. We then analysed

351the impact of surprises from expected trading volume in the VECM model. Results were

352not qualitatively different from those obtained from raw volume.13 Consequently, at first

353pass, raw and unexpected futures trading volume appear to be exogenous and provide very

354little incremental predictive or information to prices.

3554.4. Variance decompositions (VDCs) and causal relativities

356In order to gauge the relative strength of prices and raw trading volume or to

357dquantify our temporal causality resultsT, the system of financial variables is now

358shocked and the forecast error variance of each of the variables is partitioned. The

359decomposition results are presented in Table 4 for both bear and bull periods for five

360alternative accumulative 15-min periods. Those results pertaining to 40 periods (2 days

361trading) after the shock are only discussed. By observing the main diagonal, we can

362ascertain the extent to which each variable is exogenous since the diagonal represents

363how much of a variables own variance is being explained by movements in its own

364shock over the forecast horizon.

13 Results can be obtained from the authors on request.



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t4.1 Table 4

Decomposition of variancet4.2

Percentage of forecast variance explained by innovations in:t4.3

DSPI DCSH DVOLt4.4


Periods Relative variance in:t4.6

1 DSPI 100.00 0.00 0.00t4.7

4 97.57 0.22 0.21t4.8

8 96.24 0.37 3.39t4.9

20 95.69 0.62 4.07t4.10

40 94.07 1.29 4.64t4.11


1 DCSH 59.09 40.91 0.00t4.13

4 60.99 35.20 3.81t4.14

8 60.12 34.54 5.35t4.1520 59.57 34.23 6.20t4.16

40 58.77 34.25 6.98t4.17


1 DVOL 0.08 0.01 99.91t4.19

4 0.17 0.07 99.76t4.20

8 0.34 0.15 99.51t4.21

20 0.47 0.47 99.06t4.22

40 1.18 0.86 97.96t4.23

t4.24



1 DSPI 100.00 0.00 0.00t4.27

4 99.00 0.96 0.03t4.28

8 98.27 1.13 0.59t4.29

20 97.20 1.46 1.32t4.30

40 96.01 2.15 1.85t4.31


1 DCSH 58.62 41.38 0.00t4.33

4 59.87 40.10 0.03t4.34

8 59.46 40.17 0.37t4.35

20 59.24 39.57 1.19t4.36

40 58.61 39.54 1.86t4.37

Periods Relative variance in:t4.381 DVOL 0.00 0.01 99.99t4.39

4 0.39 0.05 99.57t4.40

8 0.75 0.26 98.99t4.41

20 1.48 1.20 97.32t4.42

40 2.10 1.58 96.32t4.43

Figures in the first column refer to horizons (i.e. number of 15-min intervals). All other figures are estimates

rounded to two decimal placesrounding errors may prevent a perfect percentage decomposition in some

cases. Several alternative orderings of these variables were also triedsuch alterations, however, did not alter

the results to any substantial degree. This is possibly due to the variancecovariance matrix of residuals being

near diagonal, arrived at through Choleski decomposition in order to orthogonalise the innovations across

equations.t4.44



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365What is clearly highlighted inTable 4is the relative endogeneity of the cash AOI prices

366and the impact of futures prices. For example, after 2 days trading following the shock,

367about 58.77(58.61)% of the shock to the cash index is explained by innovations in the

368futures prices for the bear (bull) market periods. That is, cash stock prices become more

369dependent on futures prices as the time frame is increased. This result further confirms the

370importance of futures prices in explaining and predicting ex ante stock prices.

371In contrast, both futures prices and trading volume are exogenous in the short run.

372Trading volume has minor impacts on futures and cash stock prices and we attribute

373this to the fact that we have controlled for the cross-autocorrelations in own and related

374market prices. However, there are some subtle changes. In bear (bull) market phases,

375the importance of trading volume is higher (lower) in predicting subsequent price

376movements. For example, in the bear phase 4.6% (7%) of the variance in futures (cash

377share) prices is explained by trading volume with the proportion much lower in the378bull phase.

379Decomposition analysis also serves as a tool to assess the behaviour of the relative

380information dynamics of this system across bull and bear markets. For example, during

381the bull market the cash AOI index appears to be slightly more exogenous compared to

382the bear market, since in the former 39.54% of the own shock is explained as compared

383to 34.25% explained in the case in the bear market. This suggests stock markets generate

384increased internal information in bull markets which may be related to heightened

385analyst interest.

3864.5. Impulse response analysis

387In this section, we utilise impulse response analysis which outlines the dynamic

388response of each variable to innovations from other individual variables in the system.

389Impulse response functions indicate the extent that a shock of one variable is transitory

390(or persistent) in terms of its effect on other variables. From our system of three

391variables, we could construct illustrations of up to nine possible scenarios (for each of

392the bull and bear market periods) of impulse response paths. However, we wish to

393further explore the asymmetric volume theories which suggest that trading volume will

394have differential information effects in bear and bull markets. To this end, reliance is

395placed on the empirical observations of Bessembinder and Seguin (1993) who396documented that positive shocks in futures trading volume were associated with 76%

397greater price volatility. We therefore analyse the response paths of cash AOI and SPI

398futures prices to a large (one standard deviation) shock in increased futures trading

399volume in the separate bear and bull periods.

400Impulse response paths illustrating these scenarios are presented in Figs. 1 and 2 and

401demonstrate the difference in the dynamic response paths of the cash and futures prices

402across bear and bull periods. During the bear market, a large shock to futures trading

403volume has a negative transitory path dependent effect. The increased trading volume

404has the effect of initially lowering price volatility with cash and futures prices reverting

405back to their pre-shock level within about 15 periods. Of further interest is that the

406impulse response paths appear to have a cyclical effect with the path repeating itself

407after 1 day (20 lags), albeit with a reduced impact. In contrast, during the bull market a



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408sudden increase in futures trading volume is associated with higher initial price volatility

409which lasts about 11 periods. Similarly, the bull market impulse response paths also

410appear to have a decaying 1-day memory lag with price volatility again increasing at 20

411periods after the volume shock. A further observation is that there is a greater absolute

412volatility reaction in futures prices compared to cash AOI prices, but they generally

413follow similar response paths.

414

These results both confirm and modify previous theoretical predictions and 415observations. Large increases in futures trading volume have an asymmetric

416information impact across bear and bull days and a memory lag of 1 day which is

417not related to current trading volume. In bull markets, sudden increases in trading

418volume may provide information content that is associated with or indicates further

419speculative activity (per Rutledge, 1986), with the subsequent higher price volatility a

420reflection of the increased uncertainty induced by noise trading. During bear periods,

421the information of increased trading volume may be perceived as positive reinforcement

Fig. 1. Impulse responses of CSH and SPI from a one-standard deviation shock to VOL during bear period.

Fig. 2. Impulse responses of CSH and SPI from a one-standard deviation shock to VOL during bull period.



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422with traders interpreting this as signalling greater confidence. This in turn results in an

423inverse feedback relationship with the dgood newsT of increased trading interpreted as

424less uncertainty and reflected in lower price volatility. The above conjectures may be

425contentious but offer the possibility of further research into the information importance

426of futures trading volume.

4275. Summary and conclusions

428This paper places the empirically controversial issue of the predictive relationship

429causality between cash share prices, SPI futures prices and futures trading volume within

430a multivariate cointegrated Granger-causal framework. This is done by analysing the

431ddynamic

T Granger-causal chain or leadlag relationship amongst the three variables

432using 15-min data, with an additional focus on the impact that bear and bull momentum

433phases have on the dynamics of the system. Overall, our case study results support the

434contention that macroeconomic information flows from futures prices and they, in turn,

435are a statistically significant predictor of ex ante share prices.

436On the other hand, futures trading volume was statistically exogenous in the short term

437and was dominated by futures prices. That is, when jointly estimated, futures trading

438volume added very little predictive power to that already impounded in prices. There are,

439however, some qualifications. The predictive power of trading volume increased during

440the bear phase and large increases in trading volume induced lower (higher) initial price

441volatility during the bear (bull) phase.442Overall, this research adds to previous short-term research in the stock market which

443attributes excess trading volume as the provider of incremental macro-information. The

444results confirm that substantial macro-information flows in from futures price changes and

445predict subsequent movements in stock prices. Second, we also uncovered asymmetric

446impacts from trading volume to prices during different price momentum phases and this

447signals subtle changes in the predictive and information value of trading volume. We

448suggest that researchers control for cross-autocorrelation effects from related markets

449(especially derivatives markets) and market psychology when analysing the predictive

450power of trading volume.

4516. Uncited references

452Chan & Chung, 1993

453Hong, 2000

454Acknowledgments

455We gratefully acknowledge Robert Brooks, Robert Faff and Pradeep Yadav for

456insightful comments. The views contained in this paper do not necessarily reflect those of

457Goldman, Sachs and Co. or any of its affiliated offices.



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