Data and Empirical Model

III. Data and Empirical Model

Daily data on the SP 500 cash index, which includes open, high, low and closing values, and monthly and weekly data relating to the CFTC-compiled Commitments of Traders COT on the SP 500 futures index were obtained from Pinnacle Data Corporation, Webster, New York. The data spans 11986 –395 for the daily SP 500 cash index data 2,347 observations, from 11986 –31995 for the monthly COT data 111 observations, and from 1092–32895 for the weekly COT data 131 observations. 3 The COT reflects the contractual commitments of four futures trading groups, of which commercial traders, noncommercial traders, and small traders are relevant to this paper. Commercial traders are defined by the CFTC guidelines as hedgers, or those who hold positions representing a substitute for transactions to be made at a later time in the cash market. Their positions exceed the established reporting levels, i.e., the number of contracts which makes declaration of positions mandatory 300 contracts for the SP 500 contract. Noncommercial traders are speculators, either short or long, whose holdings exceed the reporting levels. Small-trader positions do not exceed the reporting levels, and no distinction is made regarding the traders’ motives. The fourth trader group is spreaders, defined as traders who simultaneously hold positions in the cash and futures markets. The proportion of futures traders who are spreaders has been negligible for the SP 500 index. Hence, this group was not included in the analysis of the impact speculation on cash market behavior. Prior studies have employed a variety of variability measures for the purpose of examining the cash volatility–trading activity relationship. We deployed four accepted formulations which capture a range of cash market behaviors thought to be of interest to market observers. The first three are normal measures of volatility, while the fourth captures nonnormal or extreme variability in cash markets. The proxy of interday price variability is uP t 2 P t 21 uP t 21 where P t is the level of SP 500 index at the close of day t. This variable is a modified version of the absolute price change measure employed in Ying 1966, among others. The standardization by P t 21 here is intended to control for biases which may arise from trends in the price index. The proxy for intraday price variability is P t H 2 P t L 1 ⁄ 2 P t H 1 P t L , where P t H , P t L and 1 ⁄ 2 P t H 1 P t L represent the high, low, and mean price levels, respectively. The numerator of this price-range measure for intraday volatility has been considered by Rutledge 1979, among others. The standard- ization by 1 ⁄ 2 P t H 1 P t L , is intended to control for the trends in the level of the SP 500 index. A third volatility measure is the adjusted price range, ADJR, employed in Garcia et al. 1986. This measure is constructed as follows: in the event that P t L . P t 21 , the difference P t L 2 P t 21 is added to the numerator of the intraday volatility formula. Similarly, if P t H , P t 21 , the difference P t 21 2 P t H is added to the numerator of the intraday volatility measure. This adjustment is aimed at controlling for the patterns of overnight price jumps that will not otherwise be reflected in measures of intraday variation. The fourth measure, jumps or jump-volatility, is described in Becketti and Sellon 1989, and is designed to measure the frequency of jumps over an interval. Jumps are identified as the frequency of SP 500 cash returns which are less than R L 2 1.5R Q , or greater than R u 1 1.5R Q , where returns 5 P t 2 P t 21 P t 21 ; R L and R U , represent the 25th and 75th percentile of returns, and R Q 5 R U 2 R L is the interquartile range. The values for R U and 3 The CFTC compiled the COT report once a month prior to 1991, bimonthly from 11991 to 101992, and weekly from 101992 to date. 326 A. Chatrath et al. R L were .0046 and 2.0037, respectively, so that R L 2 1.5R Q 5 2.01615 and R U 1 1.5R Q 5 .0171. The Jumps measure captures the occasional and extreme changes in stock prices, which are arguably of greatest concern to regulators and traders. The volatility series derived from the daily SP 500 index data are averaged over each month, and alternately, each week in the sample to match the monthly and weekly COT series. The commitments pertain to contracts of all expirations, March, June, September and December; thus, any concerns over a maturity effect in the level of trading are bypassed. To examine the influence of speculative commitments relative to the open interest, we estimated the model: s t 5 a 1 O i 50 2 b i s t 2i 1 O j 5 22 2 g j DSPEC t 2j 1 O k 5 22 2 j k DOI t 2k 1 e t , 1 where s t represents alternate cash market volatility measures; SPEC t represents the commitments of large speculators; OI t is the open interest, and a and e are the constant and random error terms, respectively. The model employs the differenced SPEC and OI series due to nonstationarity in the level of commitments. 4 SPEC, OI, and the other speculative measures employed in this study numbers of speculators and average contract size were found to be near-random walk variables. 5 Thus, the differenced variables are interpreted as shocks to speculative participation activity. The lag lengths in equation 1 were selected to satisfy the autocorrelation criterion as provided by the standard Durbin h [Durbin 1970] statistics. 6 Following the popular models relating to the market impact of speculation, we also investigated the role of both the number of speculators, as well as their average commit- ments size of holdings in the volatility of the cash index. We did not attempt to distinguish between risk aversion and speculative intensity, an issue which may be intractable [see for instance, Driskill et al. 1991 and Osler 1995]. Rather, the study relied on a joint hypothesis that the number of traders and their average holdings risk aversion or speculative intensity will influence spot volatility. The empirical model relating market volatility to speculator numbers and contract size is similar to equation 1 and is given by: s t 5 a 1 O i 50 2 b i s t 2i 1 O j 5 22 2 g j DN t 2j 1 O k 5 22 2 j k DSIZE t 2k 1 e t , 2 where N t represents the number of speculators, and CSIZE t is the average size of contracts held by speculators. 7 4 Traditional causal models are strictly appropriate only when the variables are stationary. For nonstationary variables, they may be valid only approximately, or not at all [for instance, see Charemza and Deadman 1992]. 5 For instance, the regression of SPEC t on SPEC t 21 provided a coefficient of .99, statistically indistinguish- able from 1. 6 Equation 1 was alternately estimated with changes in non-speculative commitments the difference between DOI and DSPEC in place of changes in open interest as explanatory variables. The results from the alternate specification were very similar. 7 The model was also estimated with contemporaneous, lagged and leading changes in open interest as explanatory variables. The implications of the results remain unchanged. Speculative Activity and Stock Market Volatility 327 An alternate measure of trading, Working’s 1960 speculation index SPI, was also considered, to examine the impact of excessive speculation activity on cash market volatility. Specifically, SPI 5 1 1 NCLCML 1 CMS if CML CMS, and SPI 5 1 1 NCSCML 1 CMS if CML , CMS, where NCL and NCS are noncommercial long and short contracts, respectively, and CML and CMS are the commercial long and short contracts, respectively. The index reflects speculative activity over and above that which is required to fill hedging imbalances. Following Ward and Behr 1983, we also constructed the upper and lower levels of this index. The upper level of the index, USPI, was constructed by assuming that the nonreporting small traders are speculators. The lower level, LSPI, was constructed by assuming that all small traders are hedgers. The examination of such indexes has regulatory implications, as regulators are mainly con- cerned about speculative activity which does not serve to address the imbalances in long and short hedging contracts. 8

IV. Empirical Results