An Analysis on the Intraday Trading Activity of VIX Derivatives

Transcription

1 An Analysis on the Intraday Trading Activity of VIX Derivatives ABSTRACT We investigate the relationship between trading activity in the VIX derivative markets and changes in the VIX index under a high-frequency framework, with our results revealing significant relationships between the signed volume of VIX derivatives and the contemporaneous changes in the VIX index. The net signed volume of VIX futures is also found to be a significant predictor of future changes in the VIX index. However, our results provide no clear evidence of the changes in the VIX index being led by trading activity in VIX options. Keywords: VIX index; VIX futures; VIX options; Trading activity; Price impact. JEL Classification: G12, G14. 1

2 1. INTRODUCTION In a perfectly efficient market where all information is immediately incorporated into asset prices without any delay, trades should not convey any information; as a result, investors should be unable to make any inferences from such transactions. However, in the real world financial markets, trades can have an impact on market prices when certain investors take advantage of private information to successfully engage in trading activity more rapidly than prices can be adjusted to such information; this is particularly so in the case of institutional investors who are commonly regarded as informed traders. 1 The arrival of new information prior to the adjustment of quotes imposes significant costs on other market participants, essentially because the suppliers of market immediacy actually provide free options to informed traders (Copeland and Galai, 1983) or because of the existence of adverse selection in the market. 2 Despite their relatively stable price dynamic, information asymmetry is even found to exist in the case of US government bonds, particularly with regard to announcements of 1 Institutional trades have been a major area of research ever since Kraus and Stoll (1972) found that block trades could affect market efficiency. Chakravarty (2001) subsequently confirmed that medium-sized trades provided support for the stealth-trading hypothesis. Analyses of the information content of institutional trades are provided by Saar (2001) and Chiyachantana, Jain, Jiang and Wood (2004), whilst Dasgupta, Prat and Verardo (2011) provided a theoretical equilibrium model to confirm the association between institutional herding and both short- and long-term returns. 2 See Kyle (1985), Easley and O Hara (1987) and Glosten (1994); the reciprocal of the price impact is the Kyle (1985) measure of market depth. Two very recent studies provide specific focus on the effects of adverse selection costs, with Ryu (2013) suggesting that large trades provide more information than small trades, thereby implying the existence of adverse selection in the futures market, and Brogaard, Hendershott and Riordan (2014) showing that high-frequency traders give rise to adverse selection costs among other investors. 2

3 macroeconomic news events (Green, 2004). The prior research into the trading behavior of informed traders in the derivative markets is both contradictory and inconclusive. As noted by Black (1975), lower transaction costs and higher financial leverage encourage informed investors to initially engage in trading in the derivatives markets; thus, derivatives trading will tend to lead to price discovery of underlying assets. 3 However, subsequent studies have been unable to provide any confirmatory evidence; for example, both Amin and Lee (1997) and Cao, Chen and Griffin (2005) demonstrated that options trading activity was only informative immediately prior to the release of details on certain corporate events, such as earnings and takeover announcements. 4 We set out in the present study is to extend the existing literature on the newly established and rapidly growing VIX derivatives markets by exploring trading activity in VIX derivatives and its informational role on the underlying asset, the CBOE volatility index (VIX), which is also referred to as the investor fear gauge. 5 As compared to the straddle and strangle strategies adopted in the S&P 500 index 3 See for example, Bhattacharya (1987), Easley, O Hara and Srinivas (1998), Chakravarty, Gulen and Mayhew (2004),, Ni, Pan and Poteshman (2008), Cao, Yu and Zhong (2010), Xing, Zhang and Zhao (2010), Johnson and So (2012), Chang, Hsieh and Lai (2013), Frijns, Tourani-Rad and Webb (2013) and Chiang (2014). 4 See Vijh (1990), Chiang and Fong (2001) and Chan, Chung and Fong (2002). Chiang (2014) also noted that large deep ITM calls on stocks tended to lead to lower stock returns on the option expiration date due to selling pressure from buyers exercising their call options. 5 The launch of VIX futures (options) took place on the Chicago Board Options Exchange on 26 March 2004 (24 February 2006). Since then, as a result of the increasing demand for practical market risk management, these instruments have become the most successful new product launches in the history of the CBOE. 3

4 options market, the VIX derivatives examined in this study (including both VIX futures and VIX options) offer investors a direct way of trading market volatility; hence, it is important to have a good understanding of the transmission of the volatility information across VIX derivatives and the VIX index. The main issue addressed in our study of the association between trading activity in VIX derivatives and changes in the VIX is whether it can provide an ideal channel for investigating not only the informational role of VIX derivatives trading on the price dynamic of the underlying asset, but also the information dissemination mechanism across the three highly related markets (the VIX index, VIX futures and VIX options). 6 We also complement the recent works of Shu and Zhang (2012) and Frijns et al. (2013) with our analysis of different types of trading activity in VIX futures and VIX options under an intraday setting. 7 As argued by Schlag and Stoll (2005), informed trading will have a permanent impact on the market prices of the underlying assets, whereas the price impact of liquidity trading is only temporary in nature. Following the idea of Schlag and Stoll (2005), if investors wish to act on volatility information, regardless of whether it 6 Given that friction is found to exist in most, if not all, financial markets, and since such friction has different levels of impact on the speed of information flow across such markets, over shorter horizons, one market may process new information more rapidly than another; therefore, the impact of order imbalances in VIX derivatives on the VIX levels conveyed by S&P 500 index options may induce either a contemporaneous or lead-lag phenomenon. 7 From their analysis of the daily market prices of VIX futures, Shu and Zhang (2012) concluded that bi-directional causality existed between the VIX and VIX futures prices. Such bi-directional causality was also identified by Frijns et al. (2013) using intra-day prices on the VIX and VIX futures during the period from 2 January 2008 to 31 December

5 is public or private, they may choose to trade directly in the VIX derivative markets. As such, we would expect to find VIX derivative volume conveying the information and having an impact on the change in the VIX index. Furthermore, unlike most asset returns, which are generally proven to be a random walk, volatility is highly predictable, particularly with regard to the measure compiled from options trading; 8 and indeed, this is the main advantage of investigating information content in the VIX derivative markets. 9 Our empirical analysis uses tick data on VIX futures and options between January 2008 and March We measure the information by analyzing three different types of trading activity in VIX derivatives, namely total number of transactions, trading volume and dollar volume. For each type of information source, we investigate the information content not only of the aggregate variables, but also the signed variables (all of which are explained in detail in Section 3) compiled from buyer- and seller- initiated trading activities using the Lee and Ready (1991) algorithm. Our major findings are summarized from the following three aspects. Firstly, we find significant relationships between the signed volume in VIX derivatives and contemporaneous changes in the VIX index, particularly when using the total 8 See for example, Christensen and Prabhala (1998), Fleming (1998), Andersen, Bollerslev, Diebold and Ebens (2001), Blair, Poon and Taylor (2001), Ederington and Guan (2005), Andersen, Bollerslev, Diebold and Labys (2003), Jiang (2005), Giot and Laurent (2007) and Taylor, Yadav and Zhang (2010). 9 In the present study, we are able to identify only relatively minor microstructure issues, such as the problems of non-synchronized trading and stale prices, essentially because both the S&P 500 index and VIX options are traded with satisfactory liquidity on the same exchange, i.e., the CBOE. 5

6 number of transactions as the information source, thereby providing support for the price impacts attributable to VIX derivative trading. Secondly, in addition to the contemporaneous association, we test the predictability of VIX derivative trading on changes in the VIX index and find that only the signed volume of VIX futures has any predictive power on future changes in the VIX, thereby implying that informed traders tend to act on volatility information to initially trade in the VIX futures market, rather than the VIX options market. Finally, we run Granger causality tests between VIX futures trading, VIX options trading and changes in the VIX, from which bi-directional causality is evident between VIX futures trading and changes in the VIX, whereas VIX options trading is not found to have any causal effect on VIX futures trading or changes in the VIX. The finding that VIX futures trading and changes in the VIX both tend to lead the changes in VIX options trading implies that VIX options are being used for hedging purposes by investors in response to changes in the VIX. Our results echo the findings of Shu and Zhang (2012) who showed that VIX futures prices tend to lead the VIX index, whilst also providing further strong evidence of bi-directional causality between the VIX and VIX futures prices. The contemporaneous associations between VIX futures trading and changes in the VIX documented in our empirical results are also in line with the theoretical findings of 6

7 Easley, O Hara and Srinivas (1998), who predicted that when markets were in a pooling equilibrium, the effects of the contemporaneous coefficients on the positive (negative) derivative trades on the price changes in the underlying asset would be significantly positive (negative). 10 We also show that both VIX futures trading and changes in the VIX Granger-cause VIX options trading, as opposed to the reverse. The remainder of this paper is organized as follows. Details of our hypothesis development are provided in Section 2, followed in Section 3 by descriptions of the data and empirical methodology adopted for our empirical analysis. Our empirical results are subsequently discussed in Section 4, with Section 5 providing robustness analyses of these results. Finally, the conclusions drawn from this study are presented in Section HYPOTHESIS DEVELOPMENT It is well known that in perfect markets, all public information is instantaneously available to all market participants, such that securities prices are immediately adjusted to such public information. Under such a perfect market setting, trading activity will convey no additional information relating to price changes, and thus, there is no discernible relationship between trading activity and price movement. However, as noted by Stoll, when the information becomes known, informed 10 Although informed traders cannot trade directly on the VIX, volatility information contained in the market prices of S&P 500 index options is quickly reflected in the changes in the VIX level because the VIX index is updated every 15 seconds during each trading day. 7

8 traders gain at the expense of suppliers of immediacy (Stoll, 2000: 1482). In other words, if certain types of traders are able to react to publicly-available information more quickly than the speed at which the quote is updated to such public information, or indeed, if a number of investors possess private information on which they then actively trade in the markets, then trading activity will have a permanent price impact; that is, the so-called information hypothesis (Schlag and Stoll, 2005; Chang, Hsieh and Lai, 2013). Although the price impact of trading activity can also be the result of liquidity shocks, such price impact should only be temporary; for example, whilst larger selling volume will temporarily bring down the price, the price is immediately reversed as a result of market makers adjusting the price in order to induce buyers to provide liquidity. Such a situation leads to trading activity having only a temporary impact on price change; that is, the so-called liquidity hypothesis. These two hypotheses apply to the relationship between trading activity in derivatives and price movements in the underlying asset when both the spot and derivatives markets are efficient; and indeed, Schlag and Stoll (2005) explored these hypotheses in the German DAX index, including both futures and options, with their empirical findings providing support for the information hypothesis. Our primary aim in the present study is to contribute to the extant related 8

9 literature by investigating the abovementioned hypotheses in the VIX index and the associated derivatives. Since the construction of the VIX is based upon the prices of S&P 500 index options, the VIX, and its futures and options derivatives, provide not only a channel for exploring the relationship between trading activity in these derivatives and the price movement of the underlying asset, but also a means of examining whether there is an efficient flow of information between S&P 500 index options and the VIX derivatives markets. 11 Our first two hypotheses in this study are therefore constructed as follows: Hypothesis 1: (The information hypothesis) trading activity in VIX derivatives has a permanent price impact on the movement of the VIX index. Hypothesis 2: (The liquidity hypothesis) trading activity in VIX derivatives has a temporary price impact on the movement of the VIX index. Motivated by the work of Black (1975), it was subsequently demonstrated by Easley et al. (1998) and Pan and Poteshman (2006) that informed traders will initially tend to trade in the options markets, rather than in the spot markets, in order to realize the profits from their privileged information, essentially because options offer them greater opportunities for leverage at lower transaction costs. Further evidence was subsequently provided to show that certain types of 11 Numerous explorations of cross-market information transmission are provided within the extant literature; for example, Hotchkiss and Ronen (2002), Longstaff, Mithal and Neis (2003), Norden and Weber (2004), Blanco, Brennan and Marsh (2005) and Roll, Schwartz and Subrahmanyam (2014). 9

10 informed investors will realize their volatility information by trading in the options markets (Ni et al., 2008; Chang et al., 2013), whereas the empirical investigations of Shu and Zhang (2012) and Frijns et al. (2013) suggested that certain types of investors with a demand for volatility trading prefer to trade in the VIX futures markets, rather than constructing volatility trading strategies in the S&P 500 index options. Following the findings in the extant literature, we posit that trading activity in VIX derivatives may exhibit a lead-lag relationship with the changes in the VIX index. We therefore propose one additional hypothesis: Hypothesis 3: (The causality hypothesis) a lead-lag relationship will be found to exist between trading activity in VIX derivatives and the changes in the VIX index. 3. DATA AND METHODOLOGY 3.1 Data The primary data adopted for this study are the intraday VIX levels and VIX futures and options tick information, with the sample period, which runs from 2 January 2008 to 31 March 2010, providing a total of 566 trading days VIX Levels and Changes The daily VIX levels for our sample period are illustrated in Figure 1, where the mean 10

11 level of the VIX index for the full sample period is found to be about 30.8 per cent; however, when ignoring the recent financial crisis period, which encompasses the collapse of Lehman Brothers, the mean level of the VIX index is found to be about 20 per cent. <Figure 1 is inserted about here> As the figure shows, following the filing for bankruptcy protection by Lehman Brothers on 15 September 2008, by end-october/early-november, the VIX had jumped to an all-time high of over 80 per cent; however, by March 2009, the level had slowly declined to 40 per cent, and by October 2009, the VIX index had finally returned to its pre-financial crisis level. 12 <Table 1 is inserted about here> The summary statistics of the VIX levels and changes in the VIX are reported in Table 1, which shows that although the mean (S.D.) of the changes in the VIX is only 0.20 per cent (2.42 per cent), significantly negative skewness and high kurtosis are discernible; however, the two effects are clearly attributable to the significant changes that occurred during the financial crisis period. Since this high-volatility period reveals crucial information on the extreme behavior of volatility, it is clearly important and relevant to investigate the information hypothesis over this period. 12 We follow Bartram and Bodnar (2009) to define the crisis period as 15 September 2008 to 27 February

12 3.1.2 Measures on the Trading Activity of VIX Derivatives Trading activity can be measured under three different types of VIX derivatives trading, total number of transactions, trading volume and dollar volume. For each time interval, we calculate the trading volume by summing the total number of contracts traded across all VIX futures and options. The dollar volume is approximated by multiplying the transaction price by the number of contracts traded in each VIX contract (futures or options) and then aggregating this total across all VIX contracts. The total number of transactions is computed by counting all transactions across all VIX futures or options during a time interval. For each type of trading activity, the variable is compiled from the aggregation of: (i) the entire VIX futures market (Fall); (ii) VIX options (All); (iii) VIX calls (Call); (iv) VIX puts (Put); and quite importantly (v) signed trading activities, which have been shown within the related literature to contain even greater information. 13 With regard to the signed trading variables, we determine whether a transaction in the VIX futures or option markets involves buyer- or seller-initiated trading, since each transaction in our dataset includes a buyer and a seller who possess contrary perspectives on the changes in the underlying asset price. 13 See, for example, Amin and Lee (1997), Easley, O Hara and Srinivas (1998), Lee and Yi (2001), Chan et al. (2002), Cao et al. (2005), Schlag and Stoll (2005) and Pan and Poteshman (2006). 12

13 Similar to the prior related studies, we adopt the Lee and Ready (1991) algorithm implemented under the following two steps: (i) those transactions occurring below (above) the midpoint of the bid and ask prices are classified as seller- (buyer-) initiated transactions; and (ii) those transactions occurring at the midpoint of the bid and ask prices are first classified using a tick test which compares the trade price to the price of the previous transaction. In specific terms, if the current transaction occurs at a higher (lower) price than the previous transaction, it is classified as a seller- (buyer-) initiated transaction. If, on the basis of the previous trade, the transactions are still unclassifiable, we use a zero-uptick or a zero-downtick test, depending on the direction of the last non-zero price change. 14 The three signed variables in the VIX futures market are FBuy, FSell and FNet. FBuy (FSell) is generated by combining the trading activities of buyer-initiated futures (seller-initiated futures); FNet is generated by calculating buyer-initiated volume minus seller-initiated volume in VIX futures. Four signed variables are used For VIX options, Positive, Negative, CallNet and PutNet. Positive (Negative) is generated by combining the trading activities of buyer-initiated calls and seller-initiated puts (seller-initiated calls and buyer-initiated puts); and CallNet (PutNet) is generated by calculating buyer-initiated calls (puts) minus seller-initiated calls (puts). 14 The unclassified transactions in our sample account for less than 1 per cent of the total. 13

14 The tick data on VIX futures (VIX options) are obtained from the CFE (CBOE), with the VIX derivatives dataset providing comprehensive information on each quote and transaction. Taking VIX options as an example, the columns in the dataset include the formation date, formation time (in seconds), expiration date, strike price, option type (call or put), bid and ask prices for a quote/trading price for a transaction, order or transaction size, and the closest VIX level. There are two implementation issues which must be taken into consideration. The first of these issue considered in this study is the choice of time frequency, essentially because having sufficient transactions during a time interval is extremely important. Although many of the prior empirical studies examining the linkage between the stock and options markets use five-minute intervals, this interval may not be appropriate for VIX options, largely because investors in the VIX options market do not trade as aggressively as investors in the other options markets, such as the S&P 500 index options market. We therefore use fifteen-minute time intervals in the present study, which is essentially a trade-off between selecting a short time interval and having sufficient transactions during the interval to ensure that the analysis is meaningful. The trading hours for VIX futures (VIX options) in the CFE (CBOE) start at 8:30am and end at 3:15pm; thus, each trading day contains 27 intraday intervals. 14

15 The second implementation issue to be considered is trade aggregation. As in trading in all other options markets, VIX options can be simultaneously traded at different strike prices and maturity dates, whilst VIX futures can be traded at different maturity dates. Therefore, when generating the trading activity measures, we do not need to focus on any of the particular properties of VIX options, but instead, we can follow the approach of Easley et al. (1998) to aggregate the transactions across all strike prices and maturities, unless otherwise stated, with the transactions of VIX futures being similarly aggregated across all maturity periods. In addition to excluding those transactions and quotes that violate any no-arbitrage condition, we also filter out all VIX derivatives with a time-to-maturity period of less than one week, or greater than one year, in order to avoid the issue of liquidity. The daily averages of the three types of trading activity in VIX futures are reported in Table 2, along with the averages of all call and put options for the full period and the financial crisis period. <Table 2 is inserted about here> For each type of trading activity, we report the total number of transactions and also distinguish between buyer-and seller-initiated transactions using the Lee-Ready (1991) algorithm; these are then referred to as signed trading activities (the figures in parentheses are the percentages of the corresponding averages of the signed trading 15

16 activities). For the full sample, it is clear that call options are traded much more actively than put options; indeed, with the exception of the dollar volume measure on VIX futures, more than half of all of the transactions are found to be buyer-initiated. We do, however, find some notable differences with regard to the results obtained during the financial crisis period. Firstly, transactions in both futures and call options become far less active (in terms of both the number of transactions and the trading volume), whereas the dollar volume during this period is found to be higher than that during the overall sample period. We surmise that investors may have become much more conservative during the financial crisis period, turning more towards trading in in-the-money calls, essentially as a result of risk concerns. Secondly, as shown in Table 2, the daily averages of the total number of transactions in put options during the financial crisis period is higher than that during the overall sample period. Thirdly, the difference between buyer- and seller-initiated transactions is reduced during the financial crisis period; indeed, sellers are found to have initiated most of the transactions, in terms of the dollar volume for call options and both the total number of transactions and trading volume for put options. The second and third findings jointly suggest that investors regarded volatility as being too high during the crisis period, and that when it eventually reverted to the long-term level, they were more willing to stand on the bearish side 16

17 of volatility. 3.2 Empirical Methodology We refer to several prior related works to specify the following empirical model: 15, (1) where r t VIX is the change in the VIX; X t is the trading activity measure of interest in the VIX futures and VIX options markets; and ε t is the turbulence term at time t. Since highly developed computer techniques have provided an enormous boost to the speed of information transfer, only four periods of lagged information are included within the model, with all of the intraday time series being normalized by subtracting the daily mean value and dividing by the standard deviation of the series. As documented in a number of related studies, net signed volume has been found to be a useful trading activity variable for extracting information on future price movements in the underlying asset. 16 As such, we hypothesize that the net signed volume may capture the trading activity of certain types of traders who are able to react much more rapidly (and indeed, more effectively than the non-signed variables) to publicly available information on VIX derivatives. If the information hypothesis holds, then we would expect to find a positive contemporaneous relationship between the movement of the VIX index and FBuy, 15 See Hasbrouck (1991), Stoll (2000), Schlag and Stoll (2005) and Chang et al. (2013). 16 Examples include Easley et al. (1998), Cao et al. (2005) and Schlag and Stoll (2005). 17

18 FNet, Positive and CallNet, and a negative contemporaneous relationship between the movement of the VIX index and FSell, Negative and PutNet (i.e., β 0 ), but no significant relationship between the movement of the VIX index and the lagged net signed variables (i.e. β 1 ). 17 As noted earlier, liquidity shocks in VIX derivative trading may also bring about a temporarily significant relationship with the change in the underlying asset. In order to distinguish between the information hypothesis and the liquidity hypothesis, we can focus on the sign of the lagged net signed variables. Under the liquidity hypothesis, we expect to find the price impact being temporary in nature, thereby implying significant, contrary signed coefficients on β 0 and β 1. In order to examine the lead-lag relationships between trading activity in VIX derivatives and movements in the VIX index, we further specify the following bivariate regression for all possible pairs of changes in the VIX, the trading activity variables on VIX futures and the same trading activity variables on VIX options, in order to run the Granger causality test:. (2) If a lead-lag relationship is indeed found to exist between the X and Y variables, that is to say, variable X Granger-causes variable Y, then the Wald test (F-statistics) 17 Intuitively, the coefficient on β 0 in our empirical model, which measures the impact on the changes in the underlying asset, is similar to the coefficient on λ 0 in Kyle (1985). 18

19 should reject the null hypothesis β 1 = β 2 = β 3 = β 4 = 0. In the following analyses (Table 5 and 7), VIX daily returns is denoted as r t VIX, trading activity of VIX futures including FBuy, FSell, FNet, and that of VIX options including Positive, Negative, CallNet, and PutNet are used to proxy the X and Y in the Equation (2), respectively. 4. EMPIRICAL RESULTS We begin in Section 4.1 by running the regression model with the contemporaneous relationship between the trading activity of VIX derivatives and the changes in the VIX index. In Section 4.2, we drop the simultaneous term and go on to investigate the predictive ability of trading activity in VIX derivatives on changes in the VIX index. Section 4.3 examines the bi-directional relationships between the signed trading variables of the VIX derivatives and changes in the VIX index using Granger causality tests, the use of which can help to identify the information flows between the VIX index and the VIX futures and VIX options markets. 4.1 Relationship between Trading Activity and VIX Index Changes In order to gain a clear understanding of the association between trading activity in VIX derivatives and movements in the VIX index, we run regression model (1) to determine whether a contemporaneous relationship does indeed exist between trading activity in VIX derivatives and changes in the VIX index. In this regression model, the two most important and meaningful coefficients are β 0 and β 1, which respectively 19

20 denote the effects of contemporaneous and one-period lagged trading activity. Since the VIX derivatives markets have very satisfactory liquidity levels, it would make very little sense for us to jump to any conclusions if we find significant β 2, β 3 or β 4 but insignificant β 0 or β 1, essentially because it is quite difficult for us to accept that the market should take such a long time to digest the information; thus, our regression results report only the estimates of β 0 and β 1, with the two-, three- and four-period lagged information serving to control for the greater autocorrelation usually found in high-frequency time series. Panel A of Table 3 reports the regression results on trading activity measured by the total number of transactions, with none of the contemporaneous coefficients (β 0 ) on the non-signed variables (Fall, All, Call and Put) revealing any level of significance. By contrast, clear contemporaneous relationships are found to exist between changes in the VIX and the signed variables of both VIX futures (FBuy, FSell, and FNet) and VIX options (Positive, Negative, CallNet and PutNet). The coefficients are not only significant at the 1 per cent level, but also consistent with our expected signs; for example, the β 0 coefficient on FBuy, FNet or CallNet (FSell, CallNet or PutNet) is found to be consistently positive (negative) at the 1 per cent significance level, which suggests that the net signed variables on VIX futures and options have significant correlations on contemporaneous changes in the VIX. 20

21 The results on trading volume (dollar volume), reported in Panel B (Panel C) of Table 3, are largely consistent with those on the total number of transactions, albeit with some variables (such as FSell and Negative) having less significance. <Table 3 is inserted about here> A point worth noting is that the sign of the lagged coefficients (β 1 ) on the signed variables of VIX options runs in the opposite direction to the sign of their own contemporaneous coefficients (β 0 ), regardless of which measure of trading activity is used. According to the liquidity hypothesis of Schlag and Stoll (2005), this sign reversal implies that the impact of VIX options trading volume on changes in the VIX index is a temporary liquidity effect. However, since the sign reversal is not observed in the VIX futures market, our results tend to imply that trading activity in the VIX futures market provides more information on changes in the VIX index, which is consistent with the information hypothesis, whereas the VIX options volume provides support for the liquidity hypothesis of Schlag and Stoll (2005). 4.2 Lead-Lag Relationship between Trading Activity and VIX Index Changes In this subsection, we go on to further investigate whether trading activity in VIX derivatives predicts the changes in the VIX index by re-running the regressions without the contemporaneous volume variables. As shown in Panels A to C of Table 4, the coefficients on FNet, β 1, are all found to be positively significant, regardless of 21

22 which measure of trading activity is used. By contrast, only one of the signed variables on option trading activities, Negative, is found to be significantly negative with regard to dollar volume. These results clearly provide support for the predictive ability of the volume imbalance in VIX futures with regard to changes in the VIX; however, the trading activity in VIX options has no clearly discernible predictive ability on changes in the VIX. <Table 4 is inserted about here> 4.3 Granger Causality Tests for Trading Activity and VIX Index Changes As our earlier findings have shown that the informational effect on the future movement of the VIX index is more pronounced for VIX futures trading than VIX options trading, we carry out Granger causality tests to analyze the information flows between the VIX index and the VIX futures and VIX options markets, with the results being reported in Table 5. Since only the signed variables of trading activities are found to be informative, the non-signed variables are excluded from this analysis. The results on the trading activity variables, measured by the total number of transactions, are reported in Panel A of Table 5, where changes in the VIX index are found to Granger-cause all of the signed variables on VIX futures (FBuy, FSell and FNet) and VIX options (Positive, Negative, CallNet and PutNet). We further observe that the signed variables on VIX futures (FBuy, FSell and FNet) also Granger-cause 22

23 the movements in the VIX index. Thus, the information content in VIX futures trading, in terms of changes in the VIX, is greater than that provided by VIX options trading, which implies that investors prefer to act on their volatility information in the VIX futures market, as opposed to the VIX options market. Furthermore, referring specifically to VIX options, none of the trading activity variables is found to Granger-cause changes in the VIX at the 5 per cent significance level; thus, it is evident that changes in the VIX Granger-cause the signed variables of VIX options trading, as opposed to the reverse. Hence, it is likely that investors trade in the VIX options market for hedging purposes in response to changes in the VIX. As shown in Panel B of Table 5, when the information source is measured by trading volume, changes in the VIX index are found to Granger-cause the changes in the two bearish signed variables on VIX options (Negative and PutNet). Panel C of Table 5 further shows that in terms of dollar trading volume, changes in the VIX index will also Granger-cause the PutNet variable on VIX options. Once again, it seems likely that these phenomena reflect the hedging needs of investors in the VIX options market in response to a rise in the VIX index. <Table 5 is inserted about here> Furthermore, the bearish signed variables of VIX futures (FSell) and the changes in the VIX index are found to have the strongest bi-directional Granger- 23

24 causality relationship, regardless of the measures of trading activity being used. We therefore conclude that informed traders are willing to use their volatility information to trade in VIX futures, as opposed to VIX options, particularly those investors who are bearish in the VIX index. Our empirical evidence thus far indicates that: (i) the trading activity in VIX futures and options has information content on changes in the VIX index, with the information content from VIX futures trading being greater than that of VIX options trading; and (ii) the net signed variable (FNet) on VIX futures can predict changes in the VIX index, although the signed variables on VIX options appear to have no predictive ability on changes in the VIX index. 5. TESTS FOR ROBUSTNESS We undertake two robustness analyses to verify the effects of trading activity in VIX futures and options on changes in the VIX index. First of all, we rerun the regressions using data on the financial crisis period to examine whether our findings hold during that turbulent period; we then rerun the regressions with consideration of intraday periodic patterns in trading activities to examine whether our empirical findings are robust to these intraday patterns. Since the most significant results in our main empirical analysis are found when using the total number of transactions as the proxy for trading 24

25 activity, the focus of our robustness analyses is placed on this proxy only Impacts of the Financial Crisis In this sub-section, we examine the impacts of the financial crisis on the degree of informativeness of trading activity, in terms of changes in the VIX, by using only the financial crisis period dataset. The results of the Equation (1) regression model on the financial crisis period are reported in Panel A of Table 6, from which we can see that almost all of the contemporaneous coefficients on the signed variables on the VIX derivatives are not only significantly correlated to the changes in the VIX index, but also consistent with the sign predictions on the information effects of these significant contemporaneous coefficients in the VIX derivatives markets. <Table 6 is inserted about here> We find that the signs of the lagged coefficients on the signed variables on VIX options still run in the opposite direction to the signs of their own contemporaneous coefficients, whereas no similar sign reversal is observed for VIX futures. 19 Furthermore, we also note that the R 2 value of the regression using FNet (0.1121) is slightly higher than the R 2 values of the regressions using the option-related signed variables (where the highest R 2 is about ). Overall, our results would seem to 18 Although not reported here, the empirical results using trading volume and dollar volume as the information source are available from the authors upon request. 19 For example, the contemporaneous coefficient on Positive is , whilst the lead-lag coefficient on Positive is , both at the 1 per cent significance level. This suggests that trading activity in VIX options is largely consistent with the liquidity hypothesis of Schlag and Stoll (2005). 25

26 imply that during the financial crisis period, informed investors chose to initially trade in VIX futures as opposed to VIX options. We subsequently carried out a further empirical test on the predictive ability of trading activity in the VIX derivatives markets during the financial crisis period, with Panel B of Table 6 clearly showing that the one-lag coefficients on FNet (β 1 ) are found to be significantly positive, at least at the 1 per cent level, whereas the signed variables on VIX options seem to provide no information on future changes in the VIX during the financial crisis period. These results verify that the predictive ability of VIX futures trading activity on changes in the VIX is stronger than that of VIX options trading. Table 7 shows that the signed variables on VIX futures (FNet and FSell) are Granger-caused by the VIX return series (p-values <1 per cent), whilst none of the bullish signed variables on VIX futures (FBuy) or VIX options (Positive and CallNet) either Granger-cause (or are Granger-caused by) changes in the VIX index. This highlights the difficulty in determining the effects of the information content of VIX bullish signed variables on changes in the VIX index during the financial crisis period. Changes in the VIX index Granger-cause the bearish signed variables of VIX futures (FSell) but the reverse is not true, which suggests that investors expecting a drop in the VIX were likely to trade in VIX futures during the financial crisis. <Table 7 is inserted about here> 26

27 5.2 Impacts of Intraday Patterns Figure 2 reveals obvious intraday periodical patterns in trading activity in VIX futures and VIX options, with the intraday patterns of these two time series being quite similar; that is, they are roughly U-shaped with higher levels for those intervals close to the open and close periods. <Figure 2 is inserted about here> To determine whether these intraday patterns affect our empirical results, we include an additional dummy variable in our original regression model, with the new model then being specified as: δ, (3) where D t(l) is a dummy variable taking into consideration the effect of the intraday periodical pattern of the total number of transactions, which is equal to 1 if t is one of the intraday intervals in which the value of the total number of transactions is higher than the mean plus one standard deviation, otherwise 0. Table 8 reports the regression results on Model (3) during the full sample period, with more than half of the δ coefficients being found to be significant at the 1 per cent level. Nevertheless, the general patterns of the coefficients on β 0 and β 1 in Panel A are found to be exactly the same as those previously reported in Table 3. In particular, when dropping the contemporaneous impact, similar to Table 4, the predictive ability 27

28 of the two signed variables on VIX futures (FBuy and FNet) are both significantly positive, whereas none of the VIX option-related signed variables is found to be informative. Thus, the conclusions derived from our empirical results remain unchanged when intraday patterns are also taken into consideration. <Table 8 is inserted about here> 6. CONCLUSIONS We investigate information transmission between derivatives and the underlying asset markets by examining the intraday relationship between changes in the VIX index and trading activity in VIX futures and options. To the best of our knowledge, our study is the first of its kind to provide a comprehensive analysis of price discovery in VIX derivatives trading relative to changes in the VIX index. Focusing on an intraday dimension with fifteen-minute time intervals, we consistently find significant associations between contemporaneous changes in the VIX and the net signed trade variables of both VIX futures and VIX options. We also find that only the signed variables of VIX futures are able to predict the changes in the VIX index, particularly when using the net signed trades of VIX futures. The Granger causality tests subsequently carried out provided strong evidence of bi-directional Granger causality between the net signed trading variable on VIX futures and changes in the VIX index. Of considerable interest is our finding that 28

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