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Option volume and stock price behavior: some evidence from the Chicago Board Options Exchange.

Introduction

Since stock options began trading on the Chicago Board Options Exchange (CBOE) in 1973, a number of studies have investigated whether information reaches and is acted upon by option and stock market participants simultaneously or whether one market's activity leads that of the other. Conventional wisdom seems to suggest that, if anything, option market activity leads stock market activity. Option trading typically involves lower transaction costs, less stringent restrictions on short selling, and greater liquidity than does stock trading [Chance, 1991]. For these reasons, informed investors may be attracted to the option market over the stock market, implying that the former will react first as new information arrives.

On the other hand, options derive their values from the underlying stocks. As such, option traders may not react based on how they expect the underlying stock to respond to new information but how, in fact, the stock does respond. If this is the case, the option market will follow the stock market.

A further possibility is that differences in transaction costs, short selling opportunities, and liquidity notwithstanding, information will reach the two markets simultaneously and be reflected in bid and ask prices, if not actual trades. If so, prices in one market will not lead those in the other and no systematic volume-price change relationship will exist.

Evidence on the subject is mixed but on balance suggests that trading activity and price adjustments in the option market lead those in the stock market. However, most of this evidence has been obtained using daily data. Lead-lag relationships may well involve much shorter periods. In the present paper, the options volume-stock price relationship for selected CBOE options is examined using intraday data. In order to measure volume, both the number of option transactions and the number of contracts traded are considered. However, before proceeding to the analysis, previous studies of stock option market relationships will be reviewed briefly.

Previous Studies

Most previous studies have investigated the data for relationships between prices in the two markets. Initially, the particular concern was whether closing option prices were leading indicators of closing stock prices. Using a response surface methodology, Panton [1976] concluded that call option prices could not be used to predict the underlying stock prices one and two months in advance. This result is not surprising in view of the long time period used. Manaster and Rendleman [1982], using daily closing option prices and stock prices implied by the Black-Scholes model, concluded that option prices lead and, therefore, reveal information not reflected in stock prices for periods of up to 24 hours. Chiras and Manaster [1978], also using the Black-Scholes model, found that closing option prices could be used to predict future stock prices and earn abnormal returns, even after allowing for transaction costs.

The studies based on closing prices were criticized by a number of authors, among them Bhattacharya [1987] and Stephan and Whaley [1990], who suggested that much of the apparent "lead" of the option market could be explained by differences in the timing of trades in the two markets. In their view, closing option prices on the CBOE, which is open for trading 10 minutes after the close of trading on the New York Stock Exchange (NYSE), capture information not reflected in closing stock prices. Bhattacharya [1987], using data supplied at 15-minute intervals, concluded that there was some information in option prices not present in contemporaneous stock prices but that it was insufficient to be used profitably. Stephan and Whaley [1990], in contrast, found that stock price changes led call option price changes by an average of 15 to 20 minutes.

There has also been a limited amount of work examining the relationship between the trading volumes in the stock and option markets. Anthony [1988], using daily call and stock volume data, reports weak evidence suggesting that option volume leads stock volume by one day. However, he notes that the apparent lead in the option market may be attributable to the later closing of the CBOE relative to the NYSE. He goes on to suggest that because the supply of stock is fixed, while the option supply is not, issuing new options may cause hedgers to trade stocks in order to maintain their optimal hedged positions. In contrast to Anthony's [1988] findings, Stephan and Whaley [1990], using intraday data, report that stock volume leads call volume by 20 to 30 minutes.

A further line of inquiry is founded in trading rules based on put-call ratios. Market participants using these rules believe that information on option trading volumes can be used to predict stock price changes. High put volumes are taken as indicative of an expectation that stock prices will fall, while high call volumes are associated with an expectation that stock prices will rise. If, indeed, this view does prevail among stock traders, then call and put option volume and put-call ratios may be leading indicators of stock price movements.

Chance [1990] examined the relationship between the S&P 100 Index (OEX) put-call ratio and the return on the index itself as well as between the put-call ratio for all CBOE options and the S&P 500. He reports weak evidence, suggesting that put-call ratios can be used to predict stock price changes. However, the information gleaned from put-call ratios is insufficient to be used profitably once transaction costs are considered. Similarly, Billingsley and Chance [1988], using a similar methodology but employing data for an earlier sample period, find that put-call ratios lead stock price changes.(1)

Data Selection

CBOE transaction data together with contemporaneous stock prices were obtained from the Berkeley Options Tapes for the period January 3, 1989 to January 31, 1989. The data were filtered in a series of four steps in order to satisfy various criteria. First, spread and straddle transactions were eliminated since such transactions incorporate some degree of hedging behavior. As such, they do not provide clear information on a trader's expectations concerning the future direction of stock prices.

Second, all transactions after 3:00 p.m. Central Time were eliminated since the NYSE closes at that time. New information that comes to the option market between 3:00 and 3:10 p.m., when the CBOE closes, can be acted upon immediately, whereas the corresponding change on the NYSE will not occur until the next trading day. Eliminating these transactions should provide a more exacting test of causality since a trading time inconsistency will foster a lead in the option market.

Third, all options with a time to expiration greater than four months were discarded on the grounds that long-term options are unlikely to provide very much short term information. In addition, all options traded on the day they expired (that is, on January 20, 1989) were dropped since investors would be closing out profitable positions and little additional information would likely be obtained from transactions data.

Finally, only near- and at-the-money options were retained for analysis. Stephan and Whaley [1990] found that transactions involving options more than 10 percent in or out of the money accounted for only 3 percent of the total number of transactions in their 60-day sample period. In addition, deep in- and out-of-the-money options have a low time value and are priced close to their intrinsic values. As such, they are unlikely to provide very much information about future stock price movements. Stephan and Whaley [1990] defined at-the-money options to be those for which the stock price differed from the exercise price by no more than 2 percent. In the present paper, the benchmark for inclusion was taken to be at- or near-the-money options with exercise prices within 5 percent of the stock price.

The filtered data were then separated into puts and calls, and the 40 most heavily traded firms (in terms of numbers of transactions) for both puts and calls on each of the 21 days were identified for possible inclusion in the sample. The resulting lists were then inspected and the firms that ranked in the top 40 for both put and call trading on each day chosen for the sample. This produced five firms and one index option. To increase the sample size, firms that ranked in the top 40 on all days for either put or call transactions and in the top 40 for at least 80 percent of the days for the other option's transactions were then included. This expanded the sample size to 12, including 10 firms (Boeing, Dow Chemical, Eastman Kodak, Ford Motor, General Electric, General Motors, IBM, Merck, RJR Nabisco, and Exxon)(2) and two indices (S&P 100 (OEX) and S&P 500 (SPX)).

The final stage of filtering involved eliminating transactions in which options violated boundary conditions. Dividend data were collected for each of the 10 firms to identify those firms that paid dividends prior to expiration.(3) The lower bound for each call option, S - [D.sub.t][(1 + r).sup.-t] - E[(1 + r).sup.-T], and for each put option, E[(1 + r).sup.-T] - (S - [D.sub.t][(1 + r).sup.-t]), where [D.sub.t] = the dividend at time t, r = the three-month U.S. T-bill rate, T = the time to expiration of the option, S = the current stock price and E = the exercise price, was calculated. All transactions which violated these conditions were eliminated from the sample.

The next step was to choose the intraday sampling interval. The interval had to be large enough so that trading was sufficiently heavy in each interval to provide useful information but small enough to capture a short-term causal relationship. After inspecting the data, an interval of 15 minutes was chosen. The data were then aggregated for each firm based on this 15-minute time interval to give the total number of put and call contracts traded as well as the total number of put and call transactions in each interval. If in any interval there was no trading in either puts or calls, a value of zero was assigned to that volume or transaction variable. If neither a put nor a call was traded, a value of zero was assigned to each volume variable and the original data were reexamined by time of day to find the stock price in that interval. In those cases in which no transaction or bid-ask record was available for a particular time period (45 of 6,552 total intervals), the stock price was taken to be the average of the preceding and following quotes.

The final step involved combining the firm volume and transaction data into price-weighted (greatest weight to highest priced stock) and average return (equal weight to one period returns of each firm) portfolios. The returns of these two portfolios were found to be highly correlated (p = 0.9994). Hence, the subsequent analysis was done using the price-weighted portfolio only (denoted TFX).(4)

Methodology

Testing for Causality

Two similar, yet distinct, methods of testing for causal relationships between economic time series are widely used in the causality literature. The first, proposed by Granger [1969], is the one adopted here. Granger shows that given two stationary time series, [X.sub.t] and [Y.sub.t], with zero mean, a causality test can be performed by estimating the coefficients of the model specified by equations (1) and (2):

[X.sub.t] + [b.sub.0] [Y.sub.t] = [summation of] [a.sub.j][X.sub.t-j] where j = 1 to m + [summation of] [b.sub.j] [Y.sub.t-j] where j = 1 to m + [[Epsilon].sub.1t], (1)

[Y.sub.t] + [c.sub.0][X.sub.t] = [summation of] [c.sub.j][X.sub.t-j] where j = 1 to m + [summation of] [d.sub.j] [Y.sub.t-j] where j = 1 to m + [[Epsilon].sub.2t], (2)

where [[Epsilon].sub.1t] and [[Epsilon].sub.2t] are uncorrelated series. According to the model specified in (1) and (2), [Y.sub.t] is causing [X.sub.t], with a lag of j periods if some [b.sub.j] is nonzero, [X.sub.t] is causing [Y.sub.t] with a lag of j periods if some [c.sub.j] is nonzero, and feedback is occurring between the two series if some [b.sub.j] and [c.sub.j] are simultaneously nonzero. The choice of m is arbitrary and can be of any length up to infinity. However, because the data set is finite, m should be chosen to be equal to or shorter than the length of the time series.

The model in (1) and (2) is said to be an instantaneous model since it includes not only lagged values of the independent variables but also the current value of the nondependent variable with coefficients [b.sub.0] and [c.sub.0]. If [b.sub.0] or [c.sub.0] is nonzero, the causal relationship is said to be instantaneously signaling that either the sampling interval chosen might have been too long or that the two variables react immediately and simultaneously to the arrival of new information. For sampling periods which are short relative to what is believed to be the true length of the lag in a causal relationship, one can reduce the instantaneous causal model to the simple causal model shown in (3) and (4) by setting [b.sub.0] = [c.sub.0] = 0.

[X.sub.t] = [summation of] [a.sub.j] [X.sub.t-j] where j = 1 to m + [summation of] [b.sub.j] [Y.sub.t-j] where j = 1 to m + [[Epsilon].sub.1t], (3)

[Y.sub.t] = [summation of] [c.sub.j] [X.sub.t-j] where j = 1 to m + [summation of] [d.sub.j] [Y.sub.t-j] where j = 1 to m + [[Epsilon].sub.2t]. (4)

The choice of whether or not to use a simple causal model is again somewhat arbitrary and depends on what is perceived to be the speed with which information is disseminated as compared to the sampling period. According to Granger [1969], a simple causal model can show feedback when in fact none exists if the sampling period is chosen to be too long to detect the actual causal relationship. In this case, it is difficult to ascertain whether the fifteen minute interval is short enough to find a relationship, if, indeed, one exists.

According to Granger and Newbold [1986], if X and Yare taken to be the actual levels of the economic variables, the time series may not be zero-mean random processes. This may cause large cross-correlations, thereby invalidating conventional test statistics. To avoid spurious regressions, Granger and Newbold [1986] suggest that the time series be initially identified and estimated.

Several methods of series identification have been proposed in the literature. Anthony [1988] fitted each of the stock volume time series in his study with an autoregressive integrated moving average (ARIMA) model and used the residuals from the estimation phase as the inputs to Granger's [1969] simple causal model. In using residuals from the estimation process as inputs to the model, he ensures that the series are uncorrelated since the residuals indicate only unexplained variations in the data. The ARIMA model considers both the autoregressive and moving average characteristics of a time series and also corrects for nonstationarity. Although Anthony [1988] found that the majority of the volume time series in his sample could be described by a low-order autoregressive (AR) model, there were cases in which low-order moving average (MA) components contributed to the explanatory power of the model and, in one case, nonstationarity was present. The probability of having both MA and AR components as well as nonstationarity and even seasonality in the data is greatly increased when intraday data are used. Hence, instead of using a strictly AR, MA, or ARMA approach, ARIMA seemed to be the most appropriate model in the present study.

Time Series Identification and Estimation

In order to use the ARIMA methodology, it was first necessary to identify whether the sample autocorrelation coefficient, [Mathematical Expression Omitted], for the function was mean stationary at lags k = 1, ..., n:

[Mathematical Expression Omitted], (5)

where the choice of n depends on the sampling interval. Because a time of day effect was expected, in light of Stephan and Whaley's [1990] finding that options trading starts slowly, then rapidly peaks shortly after the opening, sags around noon, peaks again before the close, and then drops off shortly after the close of the spot market. [Mathematical Expression Omitted] was calculated up to lag n = 4s, where s = length of the intraday interval.

For a strictly mean stationary series, [r.sub.k] = 0 for k [greater than] 0. Therefore, to determine whether the series were mean stationary, [Mathematical Expression Omitted] was calculated up to a lag of 105, since a seasonal cycle of length 26 (based on 6.5 hours of trading with four 15-minute intervals in each hour) was expected and plotted for each price and volume series. The series were identified as nonseasonal, nonstationary if the autocorrelation coefficients at lags above k = 5 were still significantly different from zero at 5 percent but gradually became insignificant. Seasonal nonstationarity was taken to be present if at intervals corresponding to the season there were autocorrelation coefficients significant at the 5 percent level for at least five consecutive lags.

If it is determined that a series is nonstationary, it can be repeatedly differenced until a stationary series results. Most of the market price and option volume series required first-order nonseasonal differencing. This was expected because of the comparatively short time period used. Plots of the data showed that for the month of January 1989, the market price level was trending consistently upwards as shown by all three indicators. The only volume series that did not require first-order nonseasonal differencing were those associated with the S&P 500 Index options. This may be attributed to the fact that these options had very low and highly variable and dispersed trading patterns, which showed no identifiable trend over time.

The problem of heteroskedasticity was much more difficult to identify and correct. This proved to be an especially troublesome problem where volume series were observed to be extremely variable from one period to the next. Although periods of high and low volume tended to be clustered together, there was no consistent pattern to the clusters or to the volume levels within them. In an effort to identify whether the high variability was due to increased activity or was simply due to the presence of large block trades, the correlations between volume and transactions were calculated for both puts and calls for the portfolio of 10 firms as well as the two indices. While the correlation coefficients ranged as high as 0.8697, it would appear that block trades can account for at least some of the variability. Therefore, the transaction series were retained to be used in tests for causality to determine if larger traders are also more informed. In addition, the correlations between call and put volume and call and put transactions are included. If a high level of correlation is found between put and call activity, the calculation of a put-call ratio may remove a considerable amount of the variation.

In time series which show increasing variability with increasing mean, heteroskedasticity can often be corrected using a logarithmic transformation. Each of the series in this study was plotted and examined to identify candidates which might require transformation. It was found that in many cases, a log transformation would be needed to smooth the data. To confirm whether or not heteroskedasticity was present, a number of diagnostic tests were run based on the actual and log transformed data on lagged regressions of the form:

[X.sub.t] = [summation of] [a.sub.j] [X.sub.t-j] where j = 1 to m. (6)

Heteroskedasticity was found to be present in most of the raw volume and transaction series but was completely removed from all but two of the series by log transformations. Those series for which a transformation could correct for heteroskedasticity were log transformed prior to differencing the series in order to avoid taking logs of negative numbers.

After the degree of nonseasonal and seasonal differencing, d and D, had been determined and heteroskedasticity removed, as required, the MA values, p and P, and AR values, q and Q, had to be specified. Values for p, q, P, and Q were obtained by comparing plots of theoretical autocorrelation functions and partial autocorrelation functions with the autocorrelation functions and partial autocorrelation functions of the series under consideration. In the present case, in order to obtain p, q, P, and Q, several specifications had to be tried and evaluated, using typical patterns in the published literature [Pankratz, 1983]. Once identified, a model or series of possible alternative models had to be estimated. In addition, where series had been differenced, the constant had to be suppressed whenever the mean of the differenced series was not significantly different from zero. A model was considered to be an accurate specification if the estimated coefficients were significant and the residuals from the estimation were serially uncorrelated.

The Ljung-Box-Pierce, or modified Box-Pierce, Q-statistic:

[Mathematical Expression Omitted] (7)

was used to determine whether the residuals of the estimation procedure were uncorrelated. The Q-statistic is approximately chi squared with m (the number of coefficients being tested) degrees of freedom, with the null hypothesis of serially uncorrelated residuals not rejected if the statistic falls below the critical value for nt. Various models were estimated until the residuals were found to be uncorrelated. Often several models would represent a given series. If so, in the interest of parsimony, the lowest order one was used. Once it was determined that the model had been correctly specified, the residual series became the inputs for the causality test. In several cases, the estimated coefficients were close to one. If a t-test showed that an estimate was different from one, the model was reestimated with the corresponding series deleted.

Results

Table 1 gives details of the estimated coefficients, as well as adjusted [R.sup.2], t-, and Q-statistics for the THX series.(5) The results confirm Anthony's [1988] finding that the volume series can be specified by low-order models. Strong seasonality present in this series, as well as in the OEX series, is a direct result of the use of intraday data. While there is a high correlation between option volume (that is, number of contracts) and number of transactions, the relationship is not consistent. This suggests that volume variability may be at least partly due to block trades. A causal relationship between price change and number of contracts traded may arise because the largest traders are also the best informed. To see if trader size has any effect on a possible causal relationship, causality tests were undertaken using market price and option transaction series in addition to the tests of market price and option volume. If a causal relationship is found between volume and price, but not transactions and price, one can conclude that there is a size-information connection.

Causality tests to determine the relationship between option activity and market level were undertaken using the model shown in (8) and (9):

[X.sub.t] = [summation of] [a.sub.j] [X.sub.t-j] where j = 1 to 13 + [summation of] [b.sub.j] [Y.sub.t-j] where j = 0 to 13 + [[Epsilon].sub.1t], (8)

[Y.sub.t] = [summation of] [c.sub.j] [X.sub.t-j] where j = 1 to 13 + [summation of] [d.sub.j] [Y.sub.t-j] where j = 0 to 13 + [[Epsilon].sub.2t], (9)

[TABULAR DATA FOR TABLE 1 OMITTED]

where [X.sub.t] and [Y.sub.t] are residual series from the ARIMA estimation phase of the market level (price indices) and options activity measures (volume and transactions), respectively. The tests were first performed on the stock price-option volume relationships (call volume, put volume, and the put-call ratio) by running regressions up to a lag of 13, which corresponds to one half-day of trading. The results for the TFX series indicated the following. First, prewhitening of the series by initial identification and estimation was quite successful in that only two of 234 of the estimated coefficients, [a.sub.j] and [c.sub.j], were significantly different from zero, while in all cases, the t-statistic for the 13 lags indicated that the estimates as a whole were not significant. Second, as expected, the instantaneous causal model was required for the TFX index with the coefficients [b.sub.0] and [d.sub.0] significant in the tests of causality for both call volume and put-call ratio versus stock price. A 15-minute interval proved to be quite adequate for both the OEX and SPX options, which showed no evidence of significant zero lag coefficients. Overall results are summarized in Table 2 with arrows denoting the direction of causality (note: [if and only if] denotes feedback).

[TABULAR DATA FOR TABLE 2 OMITTED]

Table 2 shows evidence of feedback occurring between the stock price level and option volume measures in five out of nine cases, in two cases causal relationships were observed but they differed in the direction of causality, and in two cases (OEX and SPX), put-call ratios were found to have no relationship to stock prices. These results seem to indicate that the two markets are dominated by feedback.

The same procedure was followed in testing for causal relationships between market price and option transactions. However, using the number of transactions rather than the number of contracts traded produced very similar results. The main difference was that transactions data gave a stronger indication that the 15-minute time interval was too long since, in addition to the TFX transaction series, the OEX transactions series indicated significant coefficient estimates for b and d at lag zero. Overall results are summarized in Table 3.

Though the relationships differ somewhat, Table 3, like Table 2, indicates that feedback is present, with six out of nine cases showing that market price is causing options volume and vice versa. In the case of SPX, however, there is evidence that stock prices may lead options trading activity by as much as one to two hours. A strong feedback relationship between stock price and option volume suggests that movements in stock prices are quickly followed by increased options activity and vice versa. There is little evidence to suggest that either market consistently leads the other.

[TABULAR DATA FOR TABLE 3 OMITTED]

Many of the significant coefficients were found to occur at low lags, suggesting that activity in one market signals similar activity in the very near future in the other. The presence of significant zero lag terms suggests that information is disseminated and acted upon very quickly in both option and stock markets with a feedback relationship between the two present at intervals of less than 15 minutes. There was also no indication that trader size was related to access to information. However, the validity of this test depends on a proportional relationship between size and information.

Conclusion

Informed investors may be drawn to the option market rather than the stock market because of lower transaction costs and less stringent trading regulations. If so, one would expect the option market to lead the stock market, providing investors are investing strictly on the basis of new information. However, speculative trading only accounts for a portion of the activity in the option market and its impact, relative to that of other motives for trading, is difficult to gauge.

The results of the present study suggest that the relationship between the price level of the stock market and volume and transaction activity in the option market is characterized by feedback with option volume causing stock price changes and vice versa. Adjustments in one market are quickly reflected in the other and it appears that neither market can be used as a benchmark to predict activity in the other. In contrast to some previous work, the option market showed no evidence of being a leading indicator of stock price movements. The difference in results may be explained by the fact that the present study used intraday data, whereas previous studies used daily data with no adjustments for timing inconsistencies between the two markets.

Footnotes

1. See also Detemple and Seldon [1991], Easley et al. [1994], and Finucane [1991]. In addition, information flows between futures and spot markets have been examined by Chan et al. [1991], Schwarz and Laatsch [1991], Schroeder and Goodwin [1991], and Stoll and Whaley [1990], among others.

2. These 10 firms accounted for 51.4 percent of total nonindex at- and near-the-money (943,426 of 1,835,734) contracts and 45.2 percent of total (62,973 of 139,409) transactions in the same options for the month of January.

3. Dividend yields were not collected for the index options since the likelihood of having boundary conditions violated for these options is very low.

4. Causality tests at the individual firm level could not be effected because of extreme variability in the firm volume data.

5. Results for the SPX and OEX series are available from the authors. Generally, they parallel those obtained for the TFX series. Likewise, the detailed causality test results, discussed below, are available upon request.

References

Anthony, J. H. "The Interrelation of Stock and Options Market Trading Volume Data," Journal of Finance, 43, September 1988, pp. 949-64.

Bhattacharya, M. "Price Changes of Related Securities: The Case of Call Options and Stocks," Journal of Financial and Quantitative Analysis, 22, March 1987, pp. 1-15.

Billingsley, R. S.; Chance, D. M. "Put-Call Ratios and Market Timing Effectiveness," Journal of Portfolio Management, 15, Fall 1988, pp. 15-28.

Chan, K.; Chan, K. C.; Karolyi, G. A. "Transmissions of Volatility Between Stock Index and Stock Index Futures Markets," Review of Financial Studies, 4, 1991, pp. 657-84.

Chance, D. M. An Introduction to Options and Futures, 2nd ed., Chicago, IL: Dryden Press, 1991.

-----. "Option Volume and Stock Market Performance," Journal of Portfolio Management, 17, Summer 1990, pp. 42-51.

Chiras, D. P.; Manaster, S. "The Information Content of Option Prices and a Test of Market Efficiency," Journal of Financial Economics, 6, 1978, pp. 213-34.

Detemple, J.; Seldon, L. "A General Equilibrium Analysis of Option and Stock Market Interactions," International Economic Review, 32, May 1991, pp. 279-302.

Easley, D.; O'Hara, M.; Srinvas, P. S. "Option Volume and Stock Prices: Evidence on Where Informed Traders Trade," Cornell University Working Paper, May 1994.

Finucane, T. "Put-Call Parity and Expected Returns," Journal of Financial and Quantitative Analysis, 26, December 1991, pp. 445-57.

Granger, C. W. J. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, 37, July 1969, pp. 424-38.

Granger, C. W. J.; Newbold, P. Forecasting Economic Time Series, 2nd ed., Orlando, FL: Academic Press, 1986.

Manaster, S.; Rendleman, Jr., R. J. "Option Prices as Predictors of Equilibrium Stock Prices," Journal of Finance, 37, September 1982, pp. 1043-47.

Pankratz, A. Forecasting with Univariate Box-Jenkins Models, New York, NY: John Wiley, 1983.

Panton, D. "Chicago Board Call Options as Predictors of Common Stock Price Changes," Journal of Econometrics, 4, January 1976, pp. 101-13.

Schroeder, T. C.; Goodwin, B. K. "Price Discovery and Cointegration for Live Hogs," Journal of Futures Markets, 11, December 1991, pp. 669-84.

Schwarz, T. V.; Laatsch, F. E. "Dynamic Efficiency and Price Leadership in Stock Index Cash and Futures Markets," Journal of Futures Markets, 11, December 1991, pp. 669-84.

Stephan, J. A.; Whaley, R. E. "Intraday Price Change and Trading Volume Relations in the Stock and Stock Option Markets," Journal of Finance, 45, March 1990, pp. 191-219.

Stoll, H. R.; Whaley, R. E. "The Dynamics of Stock Index and Stock Index Futures Returns," Journal of Financial and Quantitative Analysis, 25, December 1990, pp. 441-68.

Michael J. Boluch and Trevor W. Chamberlain, McMaster University - Canada. Data for the study were generously provided by Itzhak Krinsky and Jason Lee of the DeGroote School.
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Author:Boluch, Michael J.; Chamberlain, Trevor W.
Publication:Atlantic Economic Journal
Date:Dec 1, 1997
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