Day Trading, Volatility and the Price-Volume Relationship: Evidence from the Taiwan Futures Market

Transcription

1 Day Trading, Volatility and the Price-Volume Relationship: Evidence from the Taiwan Futures Market Ming-Hsien Chen 1, Vivian W. Tai 2, Sheng-Yung Yang 3, Abstract Information reveling is necessary for market transparency; however, that of day trading activities is almost still not available from exchanges. This paper extends the price-volume relationship by incorporating an unexplored day trading volume variable. which is infrequently addressed in the extant literature. Our evidence demonstrates that volatility is asymmetrically negative in price-volume relationship. Moreover, unexpected day trading is negative correlated both with return and volatility, suggesting that the arbitrage activities of unexpected day trading activities may accelerate the movement of futures prices to a new equilibrium; these results are consistent with the findings of prior studies. Finally, based on our findings, we strongly suggest that transaction information about day trading should be released from futures exchanges for the purpose of achieving greater transparency. Keywords: Day trading, Unexpected shocks, Stock index futures JEL Classification: C22, G12 1 Corresponding author. Department of Finance, National Kaohsiung First University of Science and Technology, No. 2, Jhuoyue, Rd., Nanzih District, Kaohsiung 811, Taiwan (R.O.C.). Tel: ext. 4017; fax: ; mhchen@nkfust.edu.tw. Chen would like to thank the National Science Council of Taiwan for its financial support for this study, which is one of the subtopics of a research plan that is funded by grant no H Department of Banking and Finance, National Chi Nan University, No. 1, University Rd., Puli, Nantou 545, Taiwan (R.O.C.). Tel: ext. 4636; fax: ; whtai@ncnu.edu.tw 3 Department of Banking and Finance, National Chung Hsing University, No. 250, Kuo Kuang Road, Taichung 402, Taiwan (R.O.C.). shengyang@nchu.edu.tw.

2 1. Introduction Recently conspicuous empirical regularities to emerge from the literature focus both on modeling the price-volume relationship and on concerning asymmetry return-volatility relationship has frequently been studied in the field of finance over the past two decades. As noted by Karpoff (1987), the price-volume relationship, regarding the contemporaneous and positive relationship between security price changes and trading volume not only enhances the understanding of the structure of financial markets but also provides information that helps to distinguish between competing theoretical models of these markets. The asymmetry return-volatility relationship, concerning both in changes in financial leverage and in volatility feedback effect, also provide the evidence of the formation on price in financial markets. 1 Such a relation is based on theoretical prospects, Epps (1975) and Jennings et al. (1981) for a price-volume relationship based on the mixture of distributions ; Copeland (1976) and Epps and Epps (1976) for a volume-volatility relationship based on sequential arrival information hypothesis ; and empirical evidence is widely documented by Karpoff (1987). However, the literature seemly does not attempt i) to jointly links the price-volume relationship with asymmetry return-volatility relationship together, ii) to consider different volume variables which contain distinct economic meanings, and iii) to forward look in terms of rational expectation, even lots of studies clarify its theoretical or empirical determinants have appeared to be the 1 Black (1976) and Christie (1982) show the asymmetric return-volatility relationship to changes in financial leverage (debt-to-equity ratio); French et al., (1987) and Campbell and Hentschel (1992) explain asymmetric return-volatility relationship based on the volatility feedback effect. If volatility is priced, an anticipated increase in volatility would raise the required rate of return, in turn requiring an immediate price decline to allow for higher future returns. Specifically, the asymmetric return-volatility relationship decrypts positive price shocks (volatility) are associated with larger volume than are negative price shocks. Therefore, the causality underlying the volatility feedback effect runs from volatility to prices, as opposed to the leverage effect that hinges on the reverse causal relationship. 1

3 most promising of these. 2 This paper provides additional empirical evidence for the process both of return and volatility formation by using volume variables, including total volume, open interest, and most important, the day trading activities, jointly on investigating the price-volume relationship and the asymmetry return-volatility relationship by using the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) Futures (TX) prices in the Taiwan Futures Exchange (TAIFEX). Both academics and practitioners have also been interested in the role played by day trading volume in predicting the movements of futures. Because of the design of the trading mechanism in the TAIFEX, day trading orders submitted by an investor involve an ex ante commitment to literally be a day trader ; that is, to resolve these trade orders within a single trading day; thus day trading may provide additional information for explaining price-volume relationship and the asymmetry return-volatility relationship, as the queue of day trading orders constitutes an ex ante mechanism for submitting a trade order. Since day traders and other traders do not always trade simultaneously or in the same quantities; in particular, day trading may represent speculation in the market, based on that open interest is proxied for market depth or liquidity, suggested by Bessembinder and Seguin (1993). 3 Open interest, an important feature of futures contracts, provides an additional measure of trading activity which has been shown to covary with price changes. 2 For example, please see, Schwert (1989), Lamoureux and Lastrapes (1990), Bessembinder and Seguin (1993), Chen et al. (2001), Aragó and Nieto (2005), Koopman et al. (2005), Kalotychou and Staikouras (2006), Büyükşahin and Harris (2009), Chen, et al. (2010), Judd and Leisen (2010), Le and Zurbruegg, 2010, and Tai, et al. (2011), for more detailed. 3 In the literature, liquidity is often synonymous with bid-ask spread; however, bid-ask spread as a measure of liquidity has some limitations. For example, many large trades occur outside the spread, but many small trades often occur within the spread (Lee, 1993). Glosten and Harris (1988) and Brennan and Subrahmanyam (1996) and show that volume variables are major determinants of market liquidity. 2

4 Bessembinder and Seguin (1993) document a positive (negative) relation between price volatility and volume (open interest) and argue that market depth varies with recent trading activity, which is proxied by endogenously determined open interest. When open interest is large, it is expected that observed volatility, conditional on contemporaneous volume, would be lower. 4 Further, open interest is used as a proxy for hedging demand (Change et al., 2000). Although past prices and trading activity, including volume and open interest, are closely watched by futures market participants, the informational role of day trading activities in broader futures markets has not been well studied. Specifically the day trading activities have less concentrated both on the price-volume relationship and the asymmetry return-volatility relationship. We fill the gap in the literature regarding this issue by extending previous research along the three dimensions. First, except for the total trading volume, open interest and day trading are proprietary volume variables in the futures markets. 5 Information about volume and open interest are typically and regularly released by futures exchanges after the close of the market on each trading day; however, there are scarce futures exchanges around the world seemly currently disclose information about day trading activities, despite the fact that a great deal of literature has demonstrated that the day trading of stocks provides information about returns and volatility (Harris and Schultz, 1998; Barber and Odean, 2000 and 2001b; Ip, 2000; Campbell, et al., 2001; and Goldberg and Lupercio, 2004). By correlating day trading data with volume and open interest, insights may be revealed regarding the price effects that are generated 4 Kyle (1985) defines the market depth as the order flow required to move prices by one unit. 5 Margin purchasing and short selling in the stock market operate on a leverage trading mechanism that is similar to the mechanism underlying open interest and day trading in futures markets; however, leverage trading activities in stock markets are different from these activities in futures markets in terms of trading mechanisms, such as mark-to-market, and with respect to the proprietary maturity of contracts in the futures markets. 3

5 by informed versus uninformed traders or by hedgers versus speculators. Open interest reflects primarily hedging activities, serving as a proxy both of the quantity for liquidity, and of market depth. By contrast, most speculators are day traders that do not hold open positions overnight; thus, day traders are typically sophisticated and risk-taking investors (Odean, 1998; Büyükşahin and Harris, 2009) that seek to exploit their information advantages through the use of day trading orders. Second, this paper decompose the three volume variables into expected and unexpected components. Investors are motivated by their expectations and may trade for either informational or liquidity reasons, producing various effects on return, volume and volatility (Wang, 1994; Chen et al., 2001; Lee and Rui, 2002; Kim. 2005). 6 We use TX prices in the TAIFEX to identify the effects of the unexpected components of volume variables on the price-volume relationship and the asymmetry return-volatility relationship. Specifically, the arrival of good or bad news may cause highly asymmetric effects on uncertainty, thereby inducing a volatility shock and producing abnormal changes in trading activities. Büyükşahin and Harris (2009) demonstrate that larger effects on volatility are produced by orders, which may contain hidden information, than by either trading volume or open interest. By decomposing volume variables, we can determine the effects on observed volatility that are produced by each of these separate components; thus, our work may enable academics to learn more about the price-volume relationship and the asymmetry return-volatility relationship in the context of futures contracts. Accordingly, an understanding of how prices are impacted by abnormal changes in unexpected day trading is important, as a degree of market uncertainty may result from day trading 6 For example, Wang s model (1994) links trading volume to stock price volatility under asymmetric information patterns. In light of information asymmetry, the relationship between trading volume and return volatility has also been investigated. 4

6 activities. Finally, empirical methods are employed that explicitly accommodate persistence return, volume and volatility. Given the economic and econometric importance attached to the persistence, we provides a methodological improvement over previous studies to synchronously consider the price-volume relationship and the asymmetry return-volatility relationship by using the exponential general autoregressive conditional heteroskedasticity model (EGARCH), which was derived by Nelson (1991). 7 Unexpected volume, open interest and day trading are not predetermined variables, and their inclusion in this model does not imply that volume shocks and changes in positions necessarily cause changes in prices in either an economic or statistical respect. As Sims (1980) argues, large-scale models do perform useful forecasting and policy-analysis functions despite their incredible identification; however, the restrictions imposed in the usual style of identification are neither essential to constructing a model which can perform these functions nor innocuous. Thus, EGARCH process, including return, volume and volatility variables in model specification, is an alternative style of identification is available and practical. Our major findings are as follows. First, after accounting for both expected and unexpected open interest and day trading variables, we find that trading volume is no longer significant for explaining the price-volume relationship. Unexpected changes in open interest and day trading are the primary factors that explain the price-volume relationship; further, negative coefficient of unexpected market depth, proxied by open interest, indicates unexpected decrease of market depth or liquidity shocks 7 Previous evidence has reported that a positive conditional volatility-volume relationship exists in models involving the Gaussian errors of return processes; however, these findings must be cautiously interpreted because of biases that relate to the simultaneity of returns and volume. 5

7 causes a lower returns. This evidence provides that the open interest activity is used for liquidity. Additionally, significantly positive coefficient of the one-lagged unexpected open interest supports that all else equal, contracts with higher levels of open interest will possess greater liquidity. In contrast, a significantly positive coefficient of unexpected day trading to return provide the evidence that unexpected day trading activities is endowed with information; further, one-lagged unexpected day trading is negatively correlated with TX return, which indicates market absorb new information into price formation and quickly reflect shocks in the market. The so called price-volume relationship partially hold, when the trading volume are classified into three volume variables and are decomposed into expected and unexpected components. Our results are consistent with the findings of Tai et al. (2011) with respect to financial futures contracts and with the conclusions of Büyükşahin and Harris (2009) with respect to crude oil futures contracts. Second, our result of EGARCH (1,1) estimation support the asymmetry return-volatility relationship; the negative impacts are greater than positive impacts with respect to the volatility of TX futures. The negative relationship between expected open interest and volatility indicates that open interest represents uninformed trading by hedgers or hedging activity and is thus an important determinant of market depth. The effect of unexpected day trading shocks on the volatility shows a large quantity of unexpected day trading largely reduce the volatility and shifts market prices closer to equilibrium; however, the persistence of unexpected day trading is insignificant, indicate information of day trading is quickly absorbed by the market but day trading activity less disturbs market volatility. Our results, which show an increase in day trading during the trading day lessens the effect of volume shock on volatility, highlight the importance of unexpected day 6

8 trading in the asymmetry return-volatility relationship, especially for futures markets. Our results are similar to the findings of Watanabe (2001), who demonstrates that the expected open interest of the Nikkei 225 stock index futures is significantly and negatively correlated to volatility, and are also consistent with the expectations of the Bessembinder and Seguin (1993) model. Finally, we use the product of the dummy and the unexpected volume series to estimate the coefficient associated with the unexpected series represents the marginal impact of a negative shock on volatility; while the marginal effect of a positive shock can be estimated by adding the coefficients associated with the unexpected series and the product of the series and the dummy variable. Significant asymmetries exist for both unexpected open interest and day trading variables. Positive shocks from open interest are associated with higher levels of volatility, and further indicates that positive shocks have a larger effect on volatility than negative shocks; however, positive shocks from day trading are associated with lower levels of volatility. We find that an unanticipated increase in open interest is also associated with higher volatility; in contrast, an unanticipated increase in day trading is associated with lower volatility. We contribute to the extant financial literature by examining the effect of the information content of day trading in terms of expected perspectives on the price-volume relationship and the asymmetry return-volatility relationship. Our findings are important to academics and have considerable practical applications, as the abnormal volatility of futures prices affects not only the mark-to-market margins that are required by clearing houses but also hedging strategies, the valuation of futures options, and settlement behaviors in response to abnormal day trading, which 7

9 have been attributed to the cancellation of arbitrage transactions in these types of situations day trading. For example, the desired margin size is a positive function of futures price volatility. Therefore, if this volatility increases, margins must be set to higher levels, and hedging strategies will require monitoring and adjustment. The application of our study will increase trading stability and improve transactional transparency because in the absence of noisy news or information, knowledge regarding certain trading activities that relate to day trading may quickly cause the equilibration of the trading price to an equilibrium. The remainder of this paper is organized as follows. Section 2 provides an overview of day trading in the TAIFEX. Section 3 describes the study data and constructs the models that are used for the analysis. Section 4 presents the empirical results of this investigation, and Section 5 concludes the paper. 2. An Overview of the TAIFEX and Day Trading Activities With all its legal requirements for futures trading in place, the TAIFEX opened for business and launched its first product, the TX, on July 21, In 2011, the trading volume on the TAIFEX totaled 182,995,171 contracts, and the average daily volume of 740,871 contracts; these figures have increased by % and %, respectively since 2007, when the trading volume and average daily volume were 1,181,350 and 5,783, respectively. The transaction volume of index futures has grown steadily in Taiwan. In terms of market structure, individuals accounted for approximately 45.16% of trading in the TAIFEX and institutional investors conducted the remaining 54.84% of trading on this exchange; approximately 9.54% of these institutional investors were foreign institutions. 8

10 Information on trading volume and open interest is typically and regularly released on a daily basis by futures exchanges after the close of the market; however, most futures exchanges do not currently disclose information regarding day trading, despite the fact that the extant literature has demonstrated that day trading data provide certain indicators of returns and volatility. We address this gap by examining how information about trading volume, open interest and day trading affect prices of the index futures that are listed on TAIFEX, which is one of the fastest growing futures markets in emerging countries. In contrast to a buy-and-hold approach, day trading strategies refer to active transaction methods in which traders quickly create and offset their positions during the course of a short trading duration. In testifying in front of the Permanent Subcommittee on Investigations of the Senate Committee on Governmental Affairs in 1999, President of National Association of Security Dealers Regulation, Mary Schapiro said... the term day trading, as follows: 8 An individual who conducts intra-day trading in a focused and consistent manner, with the primary goal of earning a living through the profits derived from this trading strategy. In 1999, the Electronic Trade Association estimated that 4,000 to 5,000 individuals engaged in full-time trading through day trading brokerages (Whitestone and Serafino, 1999); these individuals were thought to account for nearly 15 percent of the daily volume on NASDAQ (Tunick, 1999). Harris and Schultz (1998) analyzed the day trading of Small Order Execution System bandits and determined that the 8 The U.S. Security and Exchange Commission report Report of Examinations of Day trading Broker-Dealer uses a similar definition (February 25, 2000). 9

11 poor returns on U.S. stocks from 2000 to 2002 squelched day trading activity. However, when the U.S. market earned strong returns in 2003, day trading began to mount a comeback (Krantz, 2003). Day trading first began growing in popularity at the end of the last millennium, exploiting the long bull market that occurred in U.S. equities after electronic communication networks (ECN s) were introduced into trading systems. The primary difference in day trading activities between stock markets and futures markets is that leveraged trading (margin purchases and short sales) in stock markets could exist in both intraday trading and across trading days. On October 8 th 2007, the TAIFEX implemented a new margin requirement policy that allows investors to designate their orders as day trade orders and deposit only half of the required margin for these orders. When a day trade order is executed successfully, day trading the futures exchange requires the day trader to offset its initial trading position with an opposite position within a single trading day. In essence, an investor commits ex ante to literally becoming a day trader. In contrast to the definitions in the existing literature, which rely on executed transactions to define day traders, in this study, day traders are identified on the basis of their submission of day trade orders. Thus, this study focuses on explicitly designated day trading orders instead of on investors that merely buy and sell the identical security during the same day. In contrast to much of the extant literature on day trading activities in stock markets, our contribution takes advantage of this new margin rule in the TAIFEX to address the specific effects of day trading in futures markets. 3. Data and Methodology 10

12 3.1 Database The TAIFEX has provided us with the daily transaction records for TX futures from October 8, 2007 to October 29, The data contain the last price quote, remaining time to expiration, and day trading labels for futures contracts, in addition to the total volume, open interest, and day trading volume for each trading day. To avoid maturity effect biases, it is assumed that nearby month contracts and most actively traded contracts will be used on the delivery day. We roll the nearby month contracts into the second nearest contract on the contract maturity date, which is the third Wednesday of each month. 3.2 Descriptive Statistics To obtain a return series, the logarithm return, R t, of futures contracts on the nearby-month contract that is closest to expiration is estimated. R t, the logarithmic difference in the prices of consecutive observations, is defined as follows: Rt 100 ln( Pt / Pt 1), (1) where P t is the closing price of TX futures at date t. The resulting returns series have two desirable properties. They may be realized by traders that follow the simple strategy of rolling their positions into the second nearest contract at the beginning of each delivery month. Moreover, these returns are computed using the prices from the most actively traded contracts and are therefore most likely to be representative of market prices at which reasonable quantities could be transacted. 11

13 Table 1 reports descriptive statistics for TX returns, volume, open interest, and day trading. The average return of TX from 2007 to 2009 is , with a standard deviation of , implying that the TX market is volatile. The TX return also demonstrates a slightly negative skew value of and a leptokurtosis of Trading volumes and day trading activities consistently grew from 2007 to 2009, indicating that the Taiwanese futures market was flourishing during this period. The percentage of day trading to total volume rose from 2.76% in 2007 to 5.33% in 2009; thus, day trading activity became an increasingly important component of the futures market between 2007 and < insert Table 1 about here> Panel A of Table 2 presents augmented Dickey-Fuller (ADF) statistics and Phillips-Perron (1988) statistics that statistically reject the null hypothesis of a unit root in the series of TX returns at a 1% significance level. Similar results are supported by a Kwiatkowski-Phillips-Schmidt-Shin (KPSS, 1992) Lagrange multiplier test. 9 The determination of whether a series contains a unit root represents an important preliminary step in the partitioning of the series in question into expected and unexpected components. The existence of a unit root is rejected for all of the volume series, as revealed by Panel A of Table 2. Panel B of Table 2 indicates the evidence for the existence and persistence of heteroskedasticity in the series of TX returns, based on Ljung-Box (Q and Q 2 ) statistics and Engle s Lagrange multipliers (1982) at 20 lags. These results emphasize the necessity of accommodating the persistence of volatility in our empirical design, the GARCH models. 9 The 36-lag autocorrelation and partial correlation series of statistics in the paper may be provided by the authors upon request. 12

14 < insert Table 2 about here> 3.3 Decomposing Expected and Unexpected Volume Variables The decomposition of volume into expected and unexpected components allows us to investigate the effect of each component on price volatility. In accordance with the approaches of Daigler and Wiley (1999), Watanabe (2001), and Tai et al. (2011), we use an autoregressive (AR) model to decompose the 3 aforementioned volume variables into expected and unexpected components. 10 AR(1) process is not only intuitively applied in practice but allows the empirical works to avoid overspecification problems. The AR(1) model is defined as follows: yt = a0 + a1yt 1 + εt, for yt= Vt, OIt,and DTt, (2) y it, where represents volume (V t ), open interest (OI t ) or day trading (DT t ); is the residual in the equation above. ε it, The unexpected component of each series is defined as ε t, the estimated residual from equation (2), whereas the expected component of each series is defined as a + ay 0 1 t 1, the difference between the actual series and the unexpected component. Thus, the expected component of each volume, open interest, and day trading day 10 Davidian and Carroll (1987), Schwert (1990), and Bessembinder and Seguin (1993) use univariate Box-Jenkins methods to partition volume and open interest into expected and unexpected components that correspond to simultaneously estimated regressors; however, this methodology may induce model over-specification problems because of both the choice of an arbitrarily long set of autoregressive coefficients and the nonstationary volume variables that are present in their samples. Moreover, the standard errors that are associated with lagged volatilities are biased downward due to the generated regressors problem; this issue is addressed by various sources, such as Davidian and Carroll (1987). As demonstrated in Table 3, the three volume variables are stationary in terms of Durbin-Watson s DW tests and LM statistics; moreover, joint F-statistics reveal that an AR(1) process fits the model specifications. 13

15 series is conditioned on one lagged value of the series in question. The results for the expected and unexpected components are reported in Table 3. Table 3, Panel A presents the AR(1) model specification. The estimated coefficients of the lagged variable are 0.60 for volume, 0.86 for open interest, and 0.85 for day trading, and all of these variables are statistically significant at the 1% level, respectively. It is notable that the estimated magnitudes of the lagged coefficients display greater clustering effects for open interest and for day trading than for volume. Both the Ljung-Box Q statistics and the Durbin-Watson statistics for volume (2.13), open interest (2.06), and day trading (2.43) indicate that there is no serial correlation in the residuals; thus, the AR(1) process is a good fit for the model. The F-statistics reported in the regression output significantly reject the hypothesis that all of the slope coefficients (excluding the intercept) in the regressions are zero. Panel B of Table 3 presents descriptive statistics for the expected and unexpected components of volume, open interest, and day trading. From the results for the second moments and ranges of the samples, we infer that the unexpected variables are more volatile than the expected variables. < insert Table 3 about here> 3.4 Methodology In the context of the mixture of distribution hypothesis (Clark, 1973), a serially correlated mixing variable controls the rate at which information arrives at the market, although the probable source of this phenomenon remains theoretically debatable. Moreover, it is not straightforward to directly observe the rate of information flow to 14

16 the market. Further, Lamourerux and Lastrapes (1990) integrated trading volume into the GARCH representation as a proxy for predicting the arrivals of unobservable information. They reported that the volatility persistence (the GARCH effect) in the return series diminishes significantly with the inclusion of trading volume in the conditional variance. Given not only the economic and econometric importance that are attached to the persistence of volatility but also the existence of a strong conditional stochastic volatility effect with respect to the LM statistics (Table 2), both the Schwarz information criterion (SIC) and Akiake information criterion (AIC) are used to determine the fitness of EGARCH models. As illustrated by Panel A of Table 4, EGARCH (1,1) consistently appear to be well-specified model by SIC and AIC. Our empirical models are consistent with the model that was suggested by Tai et al. (2011). < insert Table 4 about here> The EGARCH (1,1) model is specified as follows: R = a + a R + a V + a V + a V + a OI + a OI + a OI e un un e un un t 0 1 t 1 2 t 3 t 4 t 1 5 t 6 t 7 t 1 R = a DT + a DT + a DT + ε e um um t 8 t 9 t 10 t 1 t +, (4) iid... 2 t = t t t P t t 1 = P t ε σν, ν ~ (0, 1), and ( ν ε ) ( ν), (5) ε ε log( σ ) = α + α + α + β log( σ ) + wv + wv + w ( d V ) + 2 t i t 1 2 e un un t t 1 1 t 2 t 3 un V t t σ t i σ t 1 2 e un un e un un log( σ t ) = w4oit + w5oit + w6( d un OIt ) + w7dtt + w8dtt + w9( d un DTt ) OIt DT, (6) 15

17 2 εt k where Rt is the log-return of TX futures; σ t is the conditional variance; is σ e un positive for good news shocks and negative otherwise; and are the V t V t t k e un expected and unexpected volume, respectively; OI t and OI t represent the e un expected and unexpected open interest, respectively; and DT t and DT t are proxies for expected and unexpected day trading, respectively. d, d un, and un V t OI t d un are three dummy variables for indicating the signed unexpected volume DT components. d i equals to one, if unexpected volume component is positive, and zero, otherwise; thus, the cross term, d i products unexpected volume, measure the effect of an unanticipated increase in volume associated with volatility. The coefficients of α 1 and β 1 represent the ARCH and GARCH effects on volatility, and the persistence is equal to the sum of these coefficients. A positive value of the coefficient α 1 indicates that unexpected new information leads to increasing volatility. The parameter, α 2, predicts the asymmetric dynamics of the conditional variance. There are no asymmetric effects if α 2 > 0 by contrast, if α 2 < 0, the leverage effect exists. In addition, there is an error consistency effect if the β 1 estimated is significant. We include one-lagged return variable in equation (4), since several researchers have argued that past (signed) returns must be included in the mean equation for an autoregressive conditional heteroskedasticity process, such as AR(p)-EGARCH-M (i, j), to more accurately model returns that are close to actual results, particularly given the fact that the mean and volatility equations are estimated sequentially For arguments from the literature, see, for example, Schwert (1989), Lamoureux and Lastrapes 16

18 4. Empirical Results Before examining the effects of unexpected shocks on the price-volume relationship and the asymmetry return-volatility relationship, we first assess whether the day trading variable significantly contributes to the explanation of the variations in return and volatility. As suggested by Bollerslev (1986), the likelihood ratio (LR) test is more conservative than the Wald test; thus, LR statistics are used to test a constraint against true parameters. We simply set the unrestricted EGARCH (1,1) model, including day three trading variables both in mean and volatility equations, against the restricted competing model that does not include the day trading variable. As shown in Table 4 Panel A, the result of the LR statistical test is , and the p-value of the comparison between the two models is , indicating that compared with the restricted model, the model that includes the day trading variable provides a 5% statistically significant improvement in fitness. This result implies that day trading information meaningfully contributes towards an explanation of the price-volume relationship and the asymmetry return-volatility relationship. 4.1 The Effects of Volume, Open Interest, and Day Trading on Returns Day trading activity may provide a more sensitive reflection of information shocks than changes in open interest, given that as discussed above, these changes have not been settled for the time period immediately preceding the period of interest. Again, open interest may act as a proxy both for liquidity trading and for market depth, given that most of the open interest that persists at the close of trading likely reflects (1990), and Bessembinder and Seguin (1993), among others, who use the lagged returns to detect autocorrelation in the returns process; however, in our opinion, the AR effect in the returns process should be tested before the empirical model is established. 17

19 liquidity activity. The estimated results of the price-volume relationship from the EGARCH (1,1) model are shown in Table 5, panel A. 12 The lagged returns have insignificant explanatory power. The trading volume has little predictive power for explaining the TX return; instead, the expected and unexpected changes in open interest and day trading are the primary factors that explain the changes in TX returns. Thus, unexpected changes in both day trading and open interest provide more information than the volume variables. Panel A of Table 5 indicates that negative coefficient, , of unexpected open interest at 1% statistically significant level, implying that an unexpected increase of 10,000 contracts in open interest will decrease the futures returns by 0.78%. On the contrary, investors that expect a particular trend of futures prices to occur will keep their open interest positions because open interest is the total number of contracts that are currently open, i.e., contracts that have been traded but have not yet been liquidated by an offsetting trade, an exercise or an assignment. Further, unexpected market depth, proxied by open interest, is negatively correlated with return, indicating unexpected decrease of market depth or liquidity shocks causes a lower returns, which decrease the TX prices. Our result is consistent with the findings of Bessembinder and Seguin (1993), who use that Kyle s (1985) measure of market depth, open interest, as the order flow, unexpected open interest shock, required to move prices by one unit and show a negative relationship between return and unexpected open interest. Further, High levels of open interest indicate greater levels of activity and liquidity for a contract. A lack of open interest for a contract indicates the absence of a 12 We also use the GJR-GARCH (1,1) model as a robustness test. The results of the GJR-GARCH (1,1) and the EGARCH models are consistent. However, as summarized by Hamilton (1994, p. 672), substantial evidence exists to support the use of the EGARCH model. 18

20 secondary market for the contract in question. In other words, if contracts have high levels of open interest, they will have a large number of interested buyers and sellers; thus, an active secondary market will increase the odds of futures orders being filled at attractive prices. Thus, all else equal, contracts with higher levels of open interest will possess greater liquidity. This is supported by the one-lagged unexpected open interest, the proxy for the persistence, has significantly positive coefficient, The results for open interest are similar to the findings of studies by Büyükşahin and Harris (2009) and Tai et al. (2011). The unexpected day trading coefficient, , is significantly at 5% level and positively correlated with returns, implying that an unexpected increase of 10,000 day trading contracts will increase futures' returns by 30%; however, the coefficient, , of one-lagged unexpected day trading is negatively correlated with TX return at 10% statistical level, indicating unexpected day trading activities absorb new information and quickly reflect shocks in the market. Day traders are less likely to suffer from information asymmetry when they may have greater profit-making opportunities. Our result is consistent with the findings of Battalio, et al., (1997), who clearly demonstrates that the behavior of modern day traders is different from that of Small Order Execution System bandits. In terms of absolute coefficients, shocks in open interest and day trading are more influential to TX returns if they are unexpected than if they are expected. < insert Table 5 about here> 4.2 Results of The Asymmetries of Return-Volatility Relationship Panel B of Table 5 reveals that the estimated coefficient, , of asymmetric 19

21 dynamics of the conditional variance, ε t-1 /σ t-1, at 1 % level. The negative estimate for the EGARCH (1,1) model specification support asymmetry return-volatility relationship, which were also indicated by the negative skewness of these distributions (see Table 1). This finding is consistent with evidence from Tai et al. (2011), who also show that the negative impacts are greater than positive impacts with respect to the volatility of TX futures. A significant value of β 1 and an insignificant value of α 1 imply that past volatility information supersedes large market shocks in predictions of current volatility. Additionally, descriptive statistics for LB_Q (20) and the ARCH effect suggest that our empirical model is fitted without autoregression and heteroskedasticity. Thus, the decomposition of both the expected and unexpected effects of day trading provides not only a suitable model with good fitness for representing empirical data but also generates more avenues for elucidating the phenomenon of the price behavior of futures. The coefficient of expected volume in the volatility equation is insignificantly positive, whereas the coefficient, , of unexpected volume is significantly positive at 1% level in TX contracts. Most studies have shown a positive correlation between volume and volatility, on most asset markets (for instance, Schwert, 1989 or Gallant et al., 1992) on stock markets, or Bessembinder and Seguin (1993) on futures markets; however, as suggested in Harris and Gurel (1986) and Karpoff (1987), this correlation is often weak. Our results strongly provide support of the asymmetry return-volatility relationship by decomposing the trading volume into unexpected components, which may be caused from the shocks both on open interest and day trading from total volume. The coefficient, , of expected open interest are statistically significant at 20

22 10% level, and is negatively correlated with volatility. The negative relationship between expected open interest and volatility indicates that open interest represents uninformed trading by hedgers or hedging activity and is thus an important determinant of market depth. Specifically, a significant negative coefficient for the effect of expected open interest on volatility is consistent with the hypothesis that other things being equal, a market becomes deeper as expected open interest increases, leading to smaller price volatility. Our results are consistently with the finding form Bessembinder and Seguin (1993) and Wang and Yu (2004). Our results highlight the importance of unexpected day trading in the asymmetry return-volatility relationship, especially for futures markets. The coefficient of expected day trading, , is economically and statistically significant at 5% level, whereas the coefficient of unexpected day trading, , is significant and negative with volatility. The effect of unexpected day trading shocks on the volatility is about 5.47 times greater than the effect of expected day trading shocks, indicating a large quantity of unexpected day trading largely reduce the volatility and shifts market prices closer to equilibrium. However, the results that the persistence of unexpected day trading is insignificant, indicate information of day trading is quickly absorbed by the market but day trading activity less disturbs market volatility. Contrast to the results of Chung et al., (2009) who provide the results that greater day-trading activity leads to greater volatility by using the intraday transactions Korea stock data, we infer the opposite result is caused from that i) the unique characteristic of an ex ante mechanism for submitting a trade order in TAIFEX, ii) the function, hedge or speculation, of futures contracts, and iii) frequency of sample. Further, the negative coefficients of both the expected and unexpected day 21

23 trading variables imply that an increase in day trading during the trading day lessens the effect of volume shock on volatility. The magnitude of this mitigating effect can be roughly estimated by comparing the coefficient that is associated with unexpected day trading with the coefficient that is associated with unexpected volume. For instance, the marginal effect of an unexpected volume of 10,000 contracts on volatility is ± (or ± percent), depending on whether day trading was reduced or increased. Finally, the results support both the price-volume relationship, the asymmetry return-volatility relationship, (Karpoff, 1987) and the sequential information arrival hypothesis (Copeland, 1976) for the information spillover from day trading to open interest and volume. This implication may indicate that the lagged values of volume and day trading may be used to predict current volatility and that conversely, volatility could be a predictor of volume and day trading 4.3 Results of The Leverage Effect of Unexpected Volume Shocks The effects of unexpected changes in volume, open interest, and day trading on volatility are allowed to vary with the sign of the shock. Dummy variables are defined that equal zero for a negative shock (volume variables below their expected levels) and one for a positive shock (volume variables above their expected levels). The product of the dummy and the unexpected volume series is created; therefore, the coefficient associated with the unexpected series represents the marginal impact of a negative shock on volatility, while the marginal effect of a positive shock can be estimated by adding the coefficients associated with the unexpected series and the product of the series and the dummy variable. 22

24 Significant asymmetries exist for both unexpected open interest and day trading variables, though the natures of the asymmetries differ. The coefficients associated with unexpected shocks of open interest is significantly positive at 10% level; that with unexpected shocks of day trading are significantly negative at 1% level. As above, negative volume shocks are associated with lower levels of volatility. This reinforces the previous finding that positive shocks from open interest are associated with higher levels of volatility, and further indicates that positive shocks have a larger effect on volatility than negative shocks; however, positive shocks from day trading are associated with lower levels of volatility. Implying. A rough guide to the magnitude of the asymmetry is the ratio of the estimated coefficient associated with positive shocks (which is the sum of the unexpected three volume coefficients plus the cross-product coefficients, respectively) to the estimated coefficient associated with negative shocks (which is the three unexpected volume coefficients). The average of these ratios is This ratio indicates little asymmetry for unexpected volume (with a ratio of 1.09). In contrast, unexpected positive open interest shocks (with a ratio of 5.74) have more than three times the effect on price revisions as negative shocks. Further, the coefficient associated with the cross-products is positive and larger in magnitude than the unexpected open interest coefficient. Therefore, the sum of the two, which measures the effect of an unanticipated increase in open interest, is positive, indicating that an unanticipated increase in open interest is also associated with higher volatility. The asymmetry associated with day trading takes a different form. Estimated coefficients associated with unexpected day trading are negative. This suggests that, ceteris paribus, an unanticipated increase in day trading is associated with lower 23

25 volatility. Contrast to the results of unanticipated open interest shocks, the coefficients associated with the cross-products are negative and smaller in absolute magnitude than the unexpected day trading coefficient. Therefore, the sum of the two, which measures the effect of an unanticipated increase in day trading, is negative, indicating that an unanticipated increase in day trading is associated with lower volatility. 4.4 Robustness: Endogeneity of Return and Three Volume Variables In the context of the mixture of distribution hypothesis (Clark, 1973), a serially correlated mixing variable controls the rate at which information arrives at the market, although the probable source of this phenomenon remains theoretically debatable. Moreover, it is not straightforward to directly observe the rate of information flow to the market. Thus, identifying endogeneity among return, volume, and volatility variables is seemly a debate between theoretical models and empirical studies. As Sims (1980) argument that large-scale models do perform useful forecasting and policy-analysis functions despite their incredible identification; thus, the restrictions imposed in the usual style of identification are neither essential to constructing a model which can perform these functions nor innocuous. We use a joint four equation VAR model to account for endogeneity of variables and identification of models to estimate the cross-variable dynamics for a robustness. Specifically, we construct joint four equation VAR (2) process, or seemly unrelated regression (SUR) model, with identical regressors for our analysis on return and three volume variables, and apply econometric tests to investigate interlinkages and causality. We also perform impulse response analysis to see how long a shock may persist, if any. Further, we decompose volume variables, including total trading volume, open interest and day trading, into expected terms and unexpected shocks. 24

26 However, the results is disappointed! The interlinkages among return series and three volume variables are unstable and the results of causality test is statistical significance only for day trading to volume. Thus, empirical procedure for endogeneity identification of open interest is followed as Bessembinder and Seguin (1993). The empirical results are available on requirement. 5. Conclusion This paper decomposes volume, open interest, and day trading activities into expected and unexpected components to jointly investigate the price-volume relationship and the asymmetry return-volatility relationship in Taiwan futures market. The peculiar trading rule governing ex ante day trading orders inspired us to study the effects of unexpected and asymmetric day trading, volume, and open interest shocks on TX contracts in the Taiwan Futures Exchange. As detailed above, the TAIFEX requires day traders to submit designated day trading orders ex ante and manually or automatically close out their day trading positions before market closes on each trading day. The peculiar trading rules of futures markets, which differ from leveraged trading practices in stock markets, require day-traders to either close out their day trading positions or fill the requirement of their margin calls before the close of each trading day. Moreover, for instance, technicians have considered day trading scenarios where there is a price advance with steady increasing volume, or big buying volume without the price going higher, or a slow and steady movement upward with consistent volume etc. It would be interesting to assess how the day trading variable correlates with the price-volume relationship and the asymmetry return-volatility relationship along the lines of several possible trading strategies, including the ones above. 25

27 We contribute to the extant academic literature in the following manner. First, we provide a joint analysis between the price-volume relationship and the asymmetry return-volatility relationship by incorporating the unexplored variable of day trading, which is rarely released from most futures exchanges around the world and has not been well characterized in the literature. Second, we find that high levels of open interest provide greater levels of liquidity for a futures contract; all else equal, contracts with higher levels of open interest will possess greater liquidity. Moreover, consistent with prior studies, our results indicate that volatility is asymmetrically correlated with unexpected day trading, supporting the notion that the arbitrage-seeking activities of unexpected day trading may quickly drive futures prices towards a new equilibrium. Finally, we suggest that both unexpected and asymmetric effects should be carefully considered in a variety of applications that involved the construction of portfolios that include futures positions. In policy application, we emphasize a legitimate concern that market transparency may be meaningfully damaged by the fact that nearly all futures exchanges refrain from providing information regarding day trading activities. As announced by the U.S. Securities and Exchange Commission regulation limits the size of the bandits of Nasdaq s Small Order Execution System; however, the current policy debate on whether day trading exerts negative influences on disrupting the market by increasing the volatility should be re-concerned between regulation and transparency. Reference Aragó, V. and Nieto, L., 2005, Heteroskedasticity in the Returns of The Main World Stock Exchange Indices: Volume versus GARCH Effects, Journal of International Financial Markets, Institutions and Money 15, Barber, B. and T. Odean, 2000, Trading Is Hazardous to Your Wealth: The Common 26