Dynamics of information leadership in the volatility complex with trading time changes: Evidence from VIX futures and VIX ETPs

Abstract

We examine the effect of VIX futures’ new trading hours on price discovery as these causal relations have not been investigated before and are consequential for regulators and practitioners involved in the VIX futures market. Our data include VIX futures and VIX ETPs for four different periods in which trading hours were changed. Employing three different measures of information share, we find that VXX ETN leads VIX futures in 2009 and 2010, while in 2011 and 2013, the ETPs’ leadership varies depending on the exchange-traded product under consideration. Furthermore, in 2013 before the change of trading hours, the VIX futures contribute more to price discovery than they do after trading hours expansion. Less of the price discovery occurs from the exchange-traded products in the latter half of the trading period in 2010. OLS regression results of the determinants of price discovery as well as panel regression results show that the effect of volume and spread, which are the main determinants of price discovery in the prior literature, change significantly before and after futures trading hour expansions, for both VIX futures and ETPs.

Keywords

VIX futures VIX ETPs price discovery volatility information leadership information share G13 G14

1 Introduction

On March 24, 2004, the CBOE (Chicago Board Options Exchange) introduced VIX futures, the first securities on the so-called fear gauge, as practical tools to diversify or hedge. However, small retail investors could not trade in the futures market, and other institutions (e.g., pension funds, endowment funds, etc.) are by law not allowed to speculate in the futures and options markets. To attract such investors to trade volatility, Barclays Bank PLC in January 2009 introduced the first VIX ETNs (Exchange Traded Notes), thus facilitating the ability for small retail investors and other institutions to hedge volatility in the VIX futures market (see Bollen, O’Neill, and Whaley, 2017). There are by now more than twenty different VIX ETPs (Exchange Traded Products) trading. Therefore, the VIX futures market is a vital volatility venue directly or indirectly linked through arbitrage with the underlying index (the VIX), VIX ETPs, and the VIX Options market. To bring trade prices to a greater degree in line with real economic forces, in other words, the supply and demand for volatility trading, the CBOE extended the trading hours of the VIX futures market. With futures and notes pioneered in 2004 and 2009, respectively, CBOE’s motive for extended trading hours has been to broaden the accessibility of investors to hedge the risk of stock-market swings. The economic implications of extending trading hours are increased liquidity and volume of the futures market and encouraging investors to zig when markets zag (Bollen, O’Neill, and Whaley, 2017). Informed traders benefit from the increased trading opportunities as they may trade the volatility on their schedule. To give a few current examples, U.S. traders may trade in these extended hours minutes before an expected Federal Reserve announcement or a national presidential election and may pre-empt economic or world events like Brexit (British Exit). Thus, CBOE identified VIX and its products as a “major opportunity and priority.”

Our paper examines how information leadership changes as VIX futures trading hours expand for the VIX complex of futures and ETPs, which has not been addressed in other empirical studies. Our paper is particularly important for other asset classes as well. The introduction of bitcoin futures in December 2017 on regulated exchanges - the Chicago Mercantile Exchange (CME) and the Chicago Board Options Exchange (CBOE) has prompted academic research to investigate bitcoin markets’ price discovery 1 . Our key questions are, one, whether an expansion in VIX futures trading hours causes a higher or lower information contribution to pricing efficiency and, two, whether VIX futures or VIX ETPs lead the price discovery process 2 . We consider only VIX futures and ETPs for a couple of reasons. First, these instruments have similar trading hours, while the non-tradable underlying index, VIX, only reflects the trading hours for the underlying S&P 500 options of 8:30 a.m. to 3:15 p.m. Central Time. Second, it is historically interesting for researchers to look back at these innovations in the volatility investment territory because, although they were introduced to cater to different groups of investors, there is one common motive of hedging when trading these instruments.

Although theory predicts that these instruments should incorporate new information simultaneously, our results show instead that the price leadership information is not simultaneously impounded. We show that the time extension is associated with an increase in VIX futures contribution in 2010, but a decrease in 2013. In the bitcoin futures market Entrop, Frijns, and Seruset (2020) show that the price discovery measures (information share (IS) and component share (CS)) are subject to time variation 3 . While they find the bitcoin futures market leads the price formation process in nine contract months and the spot market is the leader in the remaining six months, we find that the VXX ETN leads VIX futures in 2009 and 2010, but the ETPs’ leadership varies depending on the exchange-traded product under consideration in 2011 and 2013.

We use the vector error correction model and intraday data sampled at a one-minute interval to investigate the information leadership role in the volatility complex and whether this leadership changes when the trading hours of VIX futures are extended. We employ the well-known metric of price discovery, the information share (IS) proposed by Hasbrouck (1995). We also use the price discovery share (PDS) metric proposed by Sultan and Zivot (2014), which decomposes the volatility of the efficient price innovation. Furthermore, to control different levels of noise, we adopt the information leadership share (ILS) metric developed by Yan and Zivot (2010) and Putnins (2013). The comparative assessment of price discovery for volatility products is a new application of the latest methodologies for examining information dissemination. We compare these three metrics to ascertain the role of each instrument in the process of price adjustment during periods of high and low volatility. Additionally, this comparison of information share measures serves as a robustness check to assess the sensitivity of our results to each measure and confirm how much each measure lends support to the other measures.

The findings of our study are of importance because studies on price discovery in the volatility complex are few. A study of price discovery on VIX ETPs is conducted by Bordonado, Molnar, and Samdal (2017), who arrange the most liquid six VIX ETPs into three groups, i.e., direct, leveraged, and inverse. In terms of VIX products and empirical evidence, the closest study to ours is by Bollen, O’Neill, and Whaley (2017), who use a methodological approach distinct from ours; they show that the VXX ETP and the S&P 500 VIX ST futures index are closely linked 4 . There are two other studies in the volatility market of Shu and Zhang (2012) and Karagiannis (2012), although they differ from our study. Shu and Zhang (2012) examine the lead-lag relationship between the spot VIX index and VIX futures using the linear Engle-Granger cointegration test with an error correction mechanism. Karagiannis (2012) investigate similar dynamics by employing the Johansen cointegration approach with a vector error correction model and Granger causality test. The majority of the above studies find that VIX futures lead the spot VIX index. This motivates our research question: Since futures trading assembles rich sources of private information, is there information content in the extended trading hours for the efficient price; if so, how do the VIX futures and VIX ETPs compare in terms of leadership?

In order to examine the effect of new trading hours on price discovery, we employ four matching sets of overlapping hours between VIX ETPs and VIX futures markets across all periods. After the implementation of new trading hours, the rise or the decline in VIX futures contribution is consistently gauged by Hasbrouck (IS), Sultan and Zivot (PDS), and Yan, Zivot, and Putnins (ILS) measures. We observe similar patterns during 2010, 2011, and 2013. All the same, our two-instrument analysis shows that the informativeness of VIX futures increases after the expansion of trading hours in 2010, whereas the exchange-traded products’ contribution to information increases in 2013. We follow the bootstrap method that has been applied by Grammig and Peter (2013) and Sultan and Zivot (2014) to confirm that VIX futures show a reduced contribution to the efficient price once the implementation of the expansion in trading hours is in effect, compared to their prior share.

The last noteworthy contribution of this paper is about the observable liquidity factors such as average bid-ask spread, daily volume per trade, and volatility, and their role in VIX futures and ETPs price discovery determination. Using ordinary least-squares regression, we estimate the information shares function of these classic determinants. The significance of the coefficients in the OLS regressions is the opposite after implementing the new trading hours from what it was before, which indicates an increase in liquidity and reduction in transaction cost after trading hour expansion. This helps in understanding the underlying factors that potentially change the information share. We also employ the random effects panel regression model, enhancing the model by including the interaction terms of the effect of the bid-ask spread and volume determinants of price discovery process changes before and after the new trading hours are in effect.

Our paper is organized as follows. Section 2 reviews the related literature and develops hypotheses. In section 3, we discuss our data set, and in section 4, we describe the measures of price discovery. Empirical results are reported and discussed in Section 5. Section 6 concludes our paper.

2 Literature review and hypotheses development

Price discovery studies are scarce in the volatility realm. Consequently, this section discusses two streams of the literature associated with volatility trading and price discovery after hours, namely studies related to the lead-lag relation of volatility in the volatility market and studies on price discovery during extended trading hours in other security markets.

The lead-lag relation between VIX index futures returns and the underlying index has received considerable interest. Shu and Zhang (2012) use the Baek and Brock nonlinear Granger test to find bi-directional causality between the VIX and the VIX futures market, proving that both instruments react simultaneously to new information. Karagiannis (2012), implementing the Granger VECM model, finds that VIX futures contain more important information than the spot; in other words, VIX futures lead in the price discovery process to the spot 5 .

Recently the comovement of the exchange-traded note VXX with the VIX index is investigated on timescales varying from days to months. Using wavelet analysis, Basta and Molnar (2019) observe no lead/lag relationship on short timescales of days. However, they show that the VIX index leads VXX ETN on long timescales of several months. Bollen, O’Neill, and Whaley (2017) investigate VIX ETPs and confirm that not only do VIX ETPs boost VIX futures trading volume, but these derivatives also offer great potential as hedges against stock market losses6, 7. Bollen, O’Neill, and Whaley (2014) regress the relative change in the level of the VIX futures indexes on the incremental dollar hedging demand across all VIX ETPs. Despite exchange-traded products’ daily trading volume and market capitalization growth, their results show that VIX ETPs have no role in the price discovery process. Our paper differs from Bollen, O’Neill, and Whaley (2014) since they focus on the benefits of introducing VIX ETPs into the VIX derivatives market. In contrast, we examine the information effect inferred from the extended VIX futures trading hours 8 .

The last stream of research that we discuss is the effect of the after-hours process on the price discovery of securities, including those closely linked, across markets 9 . Since no such study exists in the volatility trading universe, we examine a few conclusions drawn from other markets 10 . The first after-hours studies are supplied by Barclay and Hendershott (2003) and McInish, Van Ness, and Van Ness (2002). The former study investigates after-hours trading (AHT) periods before the NASDAQ market opens (BMO) and after the market closes (AMC), and McInish, Van Ness, and Van Ness (2002) focus on after-hours trading of NYSE stocks. Barclay and Hendershott (2003) find that the price discovery process is significant, although less efficient, after hours, due to the noise in the stock prices 11 . McInish, Van Ness, and Van Ness (2002) detect very little price discovery during after-hours trading, with most trades taking place at the NYSE closing trade, bid, or ask price 12 . Cheng, Jiang, and Ng (2004), Covrig, Ding, and Low (2004), and Sohn and Zhang (2017) investigate extended trading hours for futures and the underlying index. Liu, Hsieh, and Tu (2017) examine index option contracts traded on the Taiwan Futures Exchange 15 min earlier than the underlying index. Cheng, Jiang, and Ng (2004) employ a weighted price contribution methodology on Hang Seng Index futures and the spot index, whereas Covrig, Ding, and Low (2004) and Sohn and Zhang (2017) employ Gonzalo and Granger (1995) common factor components and the Hasbrouck (1995) information share methods 13 . Over a relatively long period (2010– 2014), the extended trading hours of the CSI 300 index futures facilitate price discovery more during early synchronous hours (Sohn and Zhang 2017).

In this study, we consider closed-linked securities in the two informationally affiliated markets— i.e., VIX futures and VIX ETPs— as this presents a more comparable scenario in terms of the common motive of hedging and similar trading times. The results are more consequential, as it is crucial to know whether VIX ETPs, which were created as an alternative instrument for investors who do not have ample access to VIX futures, can provide the fair alternative for which they are intended.

Our paper is different in several ways. For instance, we quantify the contribution of ETPs and not the underlying VIX index, examine the new extended trading hours of VIX futures, and use recent measures of information share. Finally, we examine whether the traditional determinants of price discovery play a role in the price discovery mechanism of the volatility instruments.

We expect the empirics to support, most of the time, the assertion that the VIX exchange-traded products have a leading role in the price discovery process (Alexander and Korovilas, 2012 and Bollen, O’Neill, and Whaley, 2017). Indeed, Bollen, O’Neill, and Whaley (2017) demonstrate that from January 29, 2009, to February 29, 2012, ETPs strategically lead VIX futures 36% of the time, VIX futures lead ETPs 6% of the time, and 52% of the time remains inconclusive. Furthermore, from February 29, 2012, to April 30, 2013, 15% of the price discovery occurs in the futures market, 23% in the ETPs market, and 60% of the time statistically we do not know. We are willing to consider that where price discovery takes place first may be a developing process.

Our testable hypothesis is as follows:

H₀: There is no influence of VIX futures trading hours’ expansion on the price discovery process. The contribution of the VIX futures and ETPs’ to the efficient price in the period before as well as in the period after the expansion stays the same.∥H_a: The expansion in VIX futures trading hours is conducive to an increase in VIX futures price discovery.

Bollen, O’Neill, and Whaley (2017) report that between 2004 and 2005, when only VIX futures were available, their average daily trading volume was low at about 500 contracts per day. When VIX options were introduced in 2006, VIX futures’ daily trading volume increased considerably, by 568% from the original level. After VIX ETPs were launched in 2009, the average daily volume increased even more dramatically, with a 645% increase from the level of 2006. Our analysis does not encompass S&P 500 or VIX options because between 2009 and 2013, options on U.S. options volatility (VIX) and options on the S&P 500 Index futures monthly (SPX) and weekly (SPXW) contracts were not traded during the extended hours. Based solely on the VIX futures extended trading hours and the introduction of additional VIX ETPs, we expect a priori that VIX futures will increase in terms of trading volume whenever new trading hours are in effect. This is usually confirmed by CBOE ex-post. However, the effect of the VIX futures extended trading hours on the price discovery process is not as easily predictable “before” and “after” within the period. We expect rejection of the null hypothesis that there is no effect. In other words, we anticipate an effect once the VIX futures trade over longer hours (extended hours), which is based on the idea that the new trading hours of VIX futures represent a bonanza for proponents that desire a deep, liquid futures market. However, the magnitude and the direction of change, i.e., whether there is greater conduciveness to price discovery dominance, may or may not ratify the alternative hypothesis.

3 Data

In this section, we focus on each instrument (i.e., VIX futures and VIX ETPs) to determine which instrument leads in terms of information to the price discovery of volatility. This study is not subject to sample selection bias because of the exclusion of VIX options from the sample. We exclude the S&P 500 index and VIX options because they were traded during regular trading hours (from 8:30 a.m. to 3:15 p.m. Central Time) from 2009 to 2013. Our interest is to test whether the extended trading hours have incremental information for the price formation. Later on March 2, 2015, the CBOE extended the trading hours of the S&P 500 index and VIX options from 2 a.m. to 8:15 a.m. Central Time; however, this change occurred after our sample period ended in December of 2013. Therefore, our study is not subject to sample selection bias. Additionally, we try to include E-mini S&P 500 futures in our model and provide additional details later since VIX is their volatility estimator (see Bollen and Whaley, 2014). Although not linked by arbitrage, VIX futures and E-minis are closely linked by profitable hedging strategies (Simon and Campasano, 2013).

VIX futures possess expirations corresponding to SPX options expirations 30 days after VIX futures settlement; they are thereby consistent with the VIX 30-day implied volatility foundation. Over recent years, VIX futures trading hours have expanded considerably. In 2009 and most of 2010, regular trading hours for VIX futures were from 8:30 a.m. to 3:15 p.m. Central Time in the United States. On December 10, 2010, the opening time for VIX futures changed from 8:30 a.m. to 7:20 a.m., and then to 7:00 a.m. on September 26, 2011. In 2013, a 45-minute post-settlement trading period was added to the end of the trading day on Monday through Thursday 14 . The second adjustment for the year occurred a week later on October 28, 2013, when the exchange opened at 2 a.m. Monday through Friday. In addition, starting in 2009, a series of ETPs began to trade, allowing non-futures investors and hedgers to take positions in the volatility complex. For a detailed discussion on VIX ETPs, their attributes, and their investors, refer to the study of Bollen, O’Neill, and Whaley (2017). Our data are obtained from multiple sources. We acquire VIX futures data (prices, quotes, and trading volume) and E-mini S&P 500 futures(ES) from SIRCA and CQG 15 . Exchange-traded products data are taken from the TAQ Trade and Quotes databases.

We determine our four periods of analysis by cross-referencing the VIX ETP inception dates with the VIX futures trading time changes (see Table 1 and 2) 16 . On January 29, 2009, the very first two VIX ETPs were launched— VXX and VXZ ETNs. VXX and VXZ ETNs provide exposure to the S&P 500 VIX short-term and S&P 500 VIX mid-term futures total return, respectively 17 . Therefore, we include VXX together with VX in the first period of our analysis from January 30 to March 27, 2009. The first period encompasses 40 days, and we treat it as a benchmark period. Conversely, the remaining periods incorporate a 40-day window before and after the futures trading time changed. Our second period is from October 14, 2010, to February 7, 2011, with the futures change in trading hours midway on December 10, 2010.

Table 1
Characteristics of the VIX ETPs under consideration

Ticker Index Full Name Inception Date

VXX SPVXSTR iPath S&P 500 VIX Short-Term Futures ETN 1/29/2009

VXZ SPVXMTR iPath S&P 500 VIX Mid-Term Futures ETN 1/29/2009

TVIX SPVXSP VelocityShares Daily 2x VIX Short-Term ETN 11/29/2010

XIV SPVXSP VelocityShares Daily Inverse VIX Short-Term ETN 11/29/2010

UVXY SPVXSP ProShares Ultra VIX Short-Term Futures ETF 10/3/2011

SVXY SPVXSP ProShares Short VIX Short-Term Futures ETF 10/3/2011

Ticker	Index	Full Name	Inception Date
VXX	SPVXSTR	iPath S&P 500 VIX Short-Term Futures ETN	1/29/2009
VXZ	SPVXMTR	iPath S&P 500 VIX Mid-Term Futures ETN	1/29/2009
TVIX	SPVXSP	VelocityShares Daily 2x VIX Short-Term ETN	11/29/2010
XIV	SPVXSP	VelocityShares Daily Inverse VIX Short-Term ETN	11/29/2010
UVXY	SPVXSP	ProShares Ultra VIX Short-Term Futures ETF	10/3/2011
SVXY	SPVXSP	ProShares Short VIX Short-Term Futures ETF	10/3/2011

The website employed is http://etfdb.com/etfdb-category/volatility/. We made our selection based on inception date along with average volume and total asset value. First ETN launched on January 29, 2009 is tracking S&P 500 VIX Short-Term Futures Index Total Return and is known as VXX. Secondly, TVIX ETN commenced on November 29, 2010 and is linked to twice the daily performance, before fees, of the S&P 500 VIX Short-Term Futures Index ER. Last group of exchange traded products were inaugurated on October 3, 2011. Among them, UVXY is associated with twice the performance, before fees and expenses, of the S&P 500 VIX Short-Term Futures Index TM.

The second pair of ETPs, TVIX, and XIV (TVIX and XIV are both ETNs), was launched on November 29, 2010. TVIX and XIV are Velocity Shares senior, unsecured obligations linked to twice (2x) and inverse (-1x), respectively, of the daily performance of the S&P 500 VIX Short-Term Futures. TVIX was considered for the Period 3 investigation based on its inception date. Almost a year later, the third ETP pair was introduced on October 3, 2011 (UVXY and SVXY). Both ProShares ETFs seek a return that is twice (2x), respectively, (-1x) the return of the S&P 500 VIX Short-Term Futures index for a single day. Only UVXY was considered for Period 4 analysis, as VXZ, XIV, and SVXY are excluded because of thin trading 18 .

Summary statistics for all four periods are provided in Table 3. We employ the most active nearby expiration for the VIX futures. We roll over to the nearest maturity contract the Friday before the VIX expiration date. As shown in Table 3, kurtosis varies widely, and the Jarque-Bera statistic rejects normality for each of the four periods. Further, we check that our price series satisfies the stationarity requirement by conducting the Augmented Dickey-Fuller (ADF), the Phillips-Perron (PP), and the Kwiatkowski-Schmidt-Shin (KPSS) tests (see Table 4). The ADF and PP tests— the most general model of a constant (single mean) and trend or the most specific (zero mean and no trend)— display in a statistically significant fashion that one cannot reject the null of a unit root for our data. To conserve space, the results summarized in Table 4 show only constant and trend; they skip the returns’ results that are not tabulated, but they are available upon request. KPSS complements the other two unit root tests reinforcing the conclusion that all return series are stationary.

Table 2

Sample descriptions

Period	Futures Change Date	Observation Period		Number of Days	Hours (CST)	Instruments Available
First Period		January 30, 2009	March 27, 2009	40	8:30am– 3.15pm	VXX, VX
Second Period	December 10, 2010	October 14, 2010	December 9, 2010	40	8:30am– 3.15pm	VXX, VX
		December 10, 2010	February 7, 2011	40	7:20am– 3:15pm	VXX, VX
Third Period	September 26, 2011	July 29, 2011	September 23, 2011	40	7:20am– 3:15pm	VXX, TVIX, VX
		September 26, 2011	November 18, 2011	40	7:00 am– 3:15pm	VXX, TVIX, VX
Fourth Period	October 21, 2013	August 23, 2013	October 18, 2013	40	7:00 am– 3:15pm	VXX, TVIX, UVXY, VX
	October 28, 2013	October 28, 2013	December 23, 2013	40	2:00am– 3:15pm,	VXX, TVIX, UVXY, VX
					3:30pm– 4:15pm
					(Mon-Thursday)

The period in 2009 labeled first period when no futures trading hours adjustment occurred, yet the first VIX ETN was introduced incorporates 40 days. The last three periods labeled second, third and fourth comprise 80 days, 40 days before the futures trading hours change and 40 days after the change.

Table 3

Summary Statistics

	N	Mean	Median	Min	Max	STD	Skewness	Kurtosis	Jarque-Bera
Period 1: January 30, 2009-March 27, 2009
VXX	16200	4.5	0	– 0.042	0.045	0.002	1.67	140.91	0.13
VX	16200	– 0.83	0	– 0.037	0.05	0.002	1.18	71.45	0.03
Period 2: October 14, 2010-December 9, 2010
VXX	16200	60.89	0	– 0.052	1.369	0.011	121.93	15293.41	1580
VX	16200	– 8.42	0	– 0.053	0.138	0.002	12.66	739.37	3.65
Period 2: December 10, 2010-February 7, 2010
VXX	19000	– 15.23	0	– 0.036	0.037	0.001	– 0.29	96.66	0.07
VX	19000	– 3.16	0	– 0.02	0.127	0.002	25.37	1587.21	20
Period 3: July 29, 2011-September 23, 2011
VXX	19000	38.76	0	– 0.052	0.06	0.003	1.77	68.25	0.04
TVIX	19000	66.99	0	– 0.106	0.127	0.006	1.66	69.2	0.04
VX	19000	31.25	0	– 0.245	0.074	0.004	– 14.48	1055.87	8.83
Period 3: September 26, 2011-November 18, 2011
VXX	19800	– 2.32	0	– 0.072	0.071	0.002	171.55	0.5	0.24
TVIX	19800	– 13.54	0	– 0.155	0.137	0.005	– 0.42	167.05	0.23
VX	19800	– 9.5	0	– 0.073	0.091	0.003	0.76	191.65	0.3
Period 4: August 23, 2013-October 18, 2013
VXX	19800	– 8.37	0	– 0.039	0.044	0.002	– 0.19	156.01	0.2
TVIX	19800	97.09	0	– 0.082	2.315	0.017	133.56	18467.33	2810
UVXY	19800	– 20.44	0	– 0.081	0.084	0.003	– 0.42	142.93	0.17
VX	19800	– 3.7	0	– 0.069	0.074	0.002	– 1.78	548.54	2.44
Period 4: October 28, 2013-December 23, 2013
VXX	33272	36.24	0	– 0.032	1.383	0.008	178.45	32294.42	14400
TVIX	33272	– 11.69	0	– 0.038	0.037	0.002	– 0.22	69.26	0.07
UVXY	33272	– 11.58	0	– 0.036	0.035	0.002	– 0.66	42.65	0.03
VX	33272	– 0.87	0	– 0.048	0.103	0.001	17.11	1787.49	44.3

Exchange traded products tickers were defined previously (see table 1). VIX futures have as symbol the VX ticker, one contract size is $1000 times VIX, and 0.01 is the minimum tick size (each tick is worth $10 per contract). For each specific period the trading hours data is sampled at one-minute intervals to generate the returns series r_t = log(P_t/P_t - 1) where P_t is the price of each security. The table reports the mean, median, minimum, maximum, standard deviation, skewness, kurtosis and Jarque-Bera statistics. Mean and Jarque-Bera statistics are multiplied by 10⁶ and 10^–7 respectively.

Table 4

ADF test results

	τ Dickey-Fuller		τ Phillips-Perron		η KPSS
	Constant	Trend	Constant	Trend	Constant	Trend
Period 1: January 30, 2009-March 27, 2009
VXX	– 2.736^*	– 2.755	– 2.752^*	– 2.777	21.64^***	11.37^***
VX	– 3.243^**	– 3.457^**	– 3.233^**	– 3.437^**	14.66^***	7.94^***
Period 2: October 14, 2010-December 9, 2010
VXX	– 1.275	– 1.580	– 1.272	– 1.574	77.72^***	10.42^***
VX	– 1.602	– 2.372	– 1.619	– 2.442	29.18^***	5.9^***
Period 2: December 10, 2010-February 7, 2011
VXX	– 0.026	– 2.588	– 0.103	– 2.605	112.81^***	9.72^***
VX	– 2.105	– 2.760	– 2.116	– 2.770	34.76^***	8.39^***
Period 3: July 29, 2011-September 23, 2011
VXX	– 1.148	– 2.162	– 1.227	– 2.248	95.76^***	13.05^***
TVIX	– 0.976	– 2.356	– 1.050	– 2.457	92.7^***	7.93^***
VX	– 1.936	– 2.348	– 2.034	– 2.434	59.27^***	7.95^***
Period 3: September 26, 2011- November 18, 2011
VXX	– 1.805	– 1.763	– 1.851	– 1.826	44.32^***	15.39^***
TVIX	– 1.602	– 1.768	– 1.633	– 1.821	71.32^***	14.48^***
VX	– 1.700	– 1.886	– 1.873	– 1.978	63.93^***	14.95^***
Period 4: August 23, 2013-October 18,2013
VXX	– 0.757	– 1.342	– 0.759	– 1.349	28.7^***	12.09^***
TVIX	– 2.642^*	– 2.304	– 2.641^*	– 2.304	22.03^***	9.65^***
UVXY	– 0.702	– 1.452	– 0.703	– 1.445	37.18^***	11.41^***
VX	– 1.661	– 1.489	– 1.669	– 1.495	17.67^***	11.32^***
Period 4: October 28, 2013-December 23, 2013
VXX	– 1.941	– 1.755	– 1.941	– 1.758	105.76^***	30.54^***
TVIX	– 1.067	– 2.107	– 1.099	– 2.171	143.2^***	29.34^***
UVXY	– 1.172	– 2.111	– 1.197	– 2.158	135.75^***	29.79^***
VX	– 2.281	– 2.510	– 2.282	– 2.510	41.47^***	22.31^***

4 Methodology

4.1 Information share, information leadership share, price discovery share

The price discovery process in multiple markets previously is utilized by assuming one single implicit efficient security price. We adopt this dynamic process and efficient price concept from the perspective that divergences are caused by trading activities and order flows in multiple markets. Once again, our instruments trade in two different markets: VIX futures and stock exchange based ETPs.

We follow Hasbrouck’s Information Share metho-dology such that the focal point is the variance of the efficient price innovation. Sultan and Zivot (2014) provide an extension of Hasbrouck by introducing a price discovery beta that represents the (normalized) covariance contributions of an asset’s or market’s innovation to the variance of the efficient price innovation.

Hasbrouck’s work is founded on the VECM concept: $Δ y_{t} = α β^{'} y_{t - 1} + \sum_{i = 1}^{p - 1} Γ_{i} Δ y_{t - i} + ɛ_{t}$ (1)

where y is a (Kx1) vector of I(1) securities prices, α and β are (Kxr) parameter matrices with rank r < K, α is the adjustment matrix, and β matrix describes the cointegrating vectors. Γ ₁, ... Γ _p-1 are (KxK) matrices of parameters, and ɛ _t is a (Kx1) vector of normally distributed errors that is serially uncorrelated but has contemporaneous covariance matrix Ω. We use the Akaike information criterion (AIC) to select the optimal lag length p, which is set such that VAR residuals are free of autocorrelation.

The proportion of each instrument relative to the total variance of the efficient price is defined as that instrument’s information share (e.g., instrument j): $I S_{j} = \frac{ψ_{j}^{2} Ω_{jj}}{ψ^{'} Ω ψ}$ (2)

where Ω is the covariance matrix and ψ′Ωψ is the total variance of the efficient price innovations. Alternatively, $I S_{j} = \frac{{(ψ_{j} σ_{j})}^{2}}{ψ^{'} Ω ψ}$ as a special case when Ω is diagonal.

A difference exists between the lower and upper bound information shares when the covariance matrix is not diagonal; that is, when the Cholesky decomposition is utilized; hence we employ a second price discovery metric. The PDS measure proposed by Sultan and Zivot (2014) does not require price permutations, is order invariant, and as such is unique. Sultan and Zivot (2014) apply this new price discovery share metric to two tradable S&P 500 ETFs, namely the SPY and the IVV, both in normal and extremely volatile situations.

For two instruments, price discovery share measurement (PDS) distributes the covariance contributions of each one to the permanent shock variance. $PD S_{1} = \frac{ψ_{1}^{2} σ_{1}^{2} + ψ_{1} ψ_{2} σ_{12}}{ψ_{1}^{2} σ_{1}^{2} + ψ_{2}^{2} σ_{2}^{2} + 2 ψ_{1} ψ_{2} σ_{12}}$ (3) $PD S_{2} = \frac{ψ_{2}^{2} σ_{2}^{2} + ψ_{1} ψ_{2} σ_{12}}{ψ_{1}^{2} σ_{1}^{2} + ψ_{2}^{2} σ_{2}^{2} + 2 ψ_{1} ψ_{2} σ_{12}}$ (4)

Although this procedure possesses the same denominator as the Hasbrouck information share metric and similarly sums to 1, this PDS measurement can be less than 0.

In most price discovery studies, the Hasbrouck (1995) metric is accompanied by the component share (CS) measure, as based on the Gonzalo and Granger (1995) permanent-transitory decomposition technique. Only Yan and Zivot (2010) combine the component share (CS) and the information share (IS) metrics and so extricate the relative impacts of the permanent and transitory shocks. Putnins (2013) formulates this new metric as the Information Leadership Share (ILS) metric. As described, ILS identifies the price series that is both first to lead and less susceptible to noise (the relative noise in one price series compared to the other cancels out). We use the ILS metric, which is especially relevant for our third period, which is less robust due to differences in noise levels 19 .

Based on estimated coefficients of VECM, the component share is: $C S_{1} = \frac{α_{2}}{α_{2} - α_{1}}, C S_{2} = \frac{α_{1}}{α_{1} - α_{2}}$ (5)

Since CS measures the relative level of noise in one price series versus the other, and IS measures the former as well as the relative leadership of one price series versus the other, Yan and Zivot (2010) propose dividing them.

When CS and IS are divided, the relative level of noise is eliminated and the price leadership is clearly exposed. The downside of the Yan– Zivot information leadership (IL) metric— which is calculated as $I L_{1} = | \frac{I S_{1}}{I S_{2}} \frac{C S_{2}}{C S_{1}} |, I L_{2} = | \frac{I S_{2}}{I S_{2}} \frac{C S_{1}}{C S_{2}} |$ (6)

— is that it takes values from 0 to infinity and may be a challenge to interpret, since it does not sum to 1.

Therefore, Putnins proposes an information leadership share (ILS) metric computed as $IL S_{1} = \frac{I L_{1}}{I L_{1} + I L_{2}}, IL S_{2} = \frac{I L_{2}}{I L_{1} + I L_{2}}$ (7)

This addresses the issue of information share metrics being between 0 and 1 and summing up to 1.

4.2 The determinants of price discovery in the volatility market

We use ordinary least-square (OLS) regressions to estimate the determinants of the VIX futures and ETPs information shares. We also estimate panel regressions using VIX futures and VIX ETPs random-effects model to deal with any possible dependence of errors within the securities series as well as to explicitly allow both within- and between-instrument variation in the determinants of the bid-ask spread, volume, and realized volatility. Both regression models are specified to explain the information share behavior of our VIX instruments in terms of volume, volatility, and spread. Spread is the difference between the ask and the bid, average daily trading volume is the number of shares traded, and volatility is the square root of the returns’ variance calculated as the sum of the squared one-minute returns 20 .

Models for all periods and in particular for Period 1:

Model 1: $M 1 : I S_{it} = α_{j}^{1} + β_{j}^{1} Spread + ɛ_{t}$ (8)

Model 2: $M 2 : I S_{it} = α_{j}^{2} + β_{j}^{2} Volatility + ɛ_{t}$ (9)

Model 3: $M 3 : I S_{it} = α_{j}^{3} + β_{j}^{3} Volume + ɛ_{t}$ (10)

Model 4: $\begin{matrix} M 4 : I S_{it} & = α_{j}^{4} + β_{j}^{4} Spread + β_{j}^{5} Volatility + \\ β_{j}^{6} Volume + ɛ_{t} \end{matrix}$ (11)

Where i and t subscripts denote the instrument (VXX or VX) and date. In case of period 1, j = 1.

We create a dummy variable ch (Change), which takes on the value 0 for the first half of the time change interval and 1 during the second half of the time interval. The dummy variable is added to the panel regression either alone or as part of an interaction term 21 .

Models for Periods 2, 3 and 4:

Model 5: $\begin{matrix} M 5 : I S_{it} & = α + β_{j}^{5} + γ_{j}^{1} Spread + γ_{j}^{2} ch + \\ γ_{j}^{3} Spread * ch + ɛ_{t} \end{matrix}$ (12)

Model 6: $\begin{matrix} M 6 : I S_{it} & = α + β_{j}^{6} + γ_{j}^{4} Volatility + γ_{j}^{5} ch + \\ γ_{j}^{6} Volatility * ch + ɛ_{t} \end{matrix}$ (13)

Model 7: $\begin{matrix} M 7 : I S_{it} & = α + β_{j}^{7} + γ_{j}^{7} Volume + γ_{j}^{8} ch + \\ γ_{j}^{9} Volume * ch + ɛ_{t} \end{matrix}$ (14)

Model 8: $\begin{matrix} M 8 : I S_{it} & = α + β_{j}^{8} + γ_{j}^{10} ch + γ_{j}^{11} Spread + \\ γ_{j}^{12} Spread * ch + γ_{j}^{13} Volatility + \\ γ_{j}^{14} Volatility * ch + γ_{j}^{15} Volume + \\ γ_{j}^{16} Volume * ch + ɛ_{t} \end{matrix}$ (15)

As before we differentiate the volatility instruments through the subscript i and for the date through the subscript t. The number of combinations (ETPs, futures) that we consider are indicated by the subscript j.

5 Empirical results

Since the price discovery results are structured by the cointegrated vector autoregression tests, we determine the order of integration and optimal lag length. We carry out the Johansen cointegration test between VIX futures and ETPs prices sampled at one-minute intervals and report the results in Table 5. The results suggest that we can reject the null hypothesis of no cointegration and accept the alternative hypothesis of one cointegrating vector. In general, with n = 2 instruments, only one (n-1) cointegrating relation exists at most, so we confirm one cointegration for the nonstationary price series of VIX futures and VIX ETPs over each period.

Table 5
Johansen Cointegration

Instruments Number of lags in VAR H₀ = r Eigenvalue Statistics Maximum Eigenvalue Pr > Maximum Trace Statistics Pr > Trace

Period 1: January 30, 2009-March 27, 2009

VXX, VX 20 0 0.0002 4.02 0.62 4.03 0.71

1 0.0000 0.01 0.99 0.01 0.99

Period 2: October 14, 2010-December 9, 2010

VXX, VX 3 0 0.0001 2.07 0.92 2.10 0.94

1 0.0000 0.03 0.90 0.03 0.90

Period 2: December 10, 2010-February 7, 2010

VXX, VX 8 0 0.0005 9.50 0.25 9.50 0.32

1 0.0000 0.03 0.96 0.03 0.96

Period 3: July 29, 2011-September 23, 2011

VXX, VX 5 0 0.0003 6.42 0.56 6.91 0.58

1 0.0000 0.48 0.48 0.48 0.48

TVIX, VX 11 0 0.0001 2.78 0.82 2.84 0.87

1 0.0000 0.06 0.84 0.06 0.84

Period 3: September 26, 2011-November 18, 2011

VXX, VX 16 0 0.0002 4.39 0.82 4.65 0.84

1 0.0000 0.27 0.61 0.27 0.61

TVIX, VX 11 0 0.0001 2.91 0.80 2.93 0.86

1 0.0000 0.01 0.93 0.01 0.93

Period 4: August 23, 2013-October 18,2013

VXX, VX 2 0 0.0013 24.72 0.01 25.20 0.01

1 0.0000 0.48 0.55 0.48 0.55

TVIX, VX 2 0 0.0005 8.86 0.13 8.98 0.17

1 0.0000 0.12 0.77 0.12 0.77

UVXY, VX 2 0 0.0008 15.67 0.01 16.39 0.01

1 0.0000 0.73 0.45 0.73 0.45

Period 4: October 28, 2013-December 23, 2013

VXX, VX 3 0 0.0001 4.86 0.50 4.88 0.58

1 0.0000 0.01 0.92 0.01 0.92

TVIX, VX 9 0 0.0001 2.91 0.80 4.37 0.66

1 0.0000 1.22 0.27 1.22 0.27

UVXY, VX 12 0 0.0001 2.80 0.82 4.32 0.66

1 0.0000 1.47 0.25 1.47 0.25

Instruments	Number of lags in VAR	H₀ = r	Eigenvalue Statistics	Maximum Eigenvalue	Pr > Maximum	Trace Statistics	Pr > Trace
Period 1: January 30, 2009-March 27, 2009
VXX, VX	20	0	0.0002	4.02	0.62	4.03	0.71
		1	0.0000	0.01	0.99	0.01	0.99
Period 2: October 14, 2010-December 9, 2010
VXX, VX	3	0	0.0001	2.07	0.92	2.10	0.94
		1	0.0000	0.03	0.90	0.03	0.90
Period 2: December 10, 2010-February 7, 2010
VXX, VX	8	0	0.0005	9.50	0.25	9.50	0.32
		1	0.0000	0.03	0.96	0.03	0.96
Period 3: July 29, 2011-September 23, 2011
VXX, VX	5	0	0.0003	6.42	0.56	6.91	0.58
		1	0.0000	0.48	0.48	0.48	0.48
TVIX, VX	11	0	0.0001	2.78	0.82	2.84	0.87
		1	0.0000	0.06	0.84	0.06	0.84
Period 3: September 26, 2011-November 18, 2011
VXX, VX	16	0	0.0002	4.39	0.82	4.65	0.84
		1	0.0000	0.27	0.61	0.27	0.61
TVIX, VX	11	0	0.0001	2.91	0.80	2.93	0.86
		1	0.0000	0.01	0.93	0.01	0.93
Period 4: August 23, 2013-October 18,2013
VXX, VX	2	0	0.0013	24.72	0.01	25.20	0.01
		1	0.0000	0.48	0.55	0.48	0.55
TVIX, VX	2	0	0.0005	8.86	0.13	8.98	0.17
		1	0.0000	0.12	0.77	0.12	0.77
UVXY, VX	2	0	0.0008	15.67	0.01	16.39	0.01
		1	0.0000	0.73	0.45	0.73	0.45
Period 4: October 28, 2013-December 23, 2013
VXX, VX	3	0	0.0001	4.86	0.50	4.88	0.58
		1	0.0000	0.01	0.92	0.01	0.92
TVIX, VX	9	0	0.0001	2.91	0.80	4.37	0.66
		1	0.0000	1.22	0.27	1.22	0.27
UVXY, VX	12	0	0.0001	2.80	0.82	4.32	0.66
		1	0.0000	1.47	0.25	1.47	0.25

This table presents the results of the Johansen cointegration test (trace and maximal eigenvalue) on the VIX futures and VIX ETPs. The minute-by-minute price series were employed for each instrument in each period. Lag length is selected based on the Akaike Information Criterion (AIC). We consider the number of unique cointegrating relations where r represents the number of cointegrating vectors. In the majority of cases the results show that the null hypothesis that there is at most one cointegrated process cannot be rejected.

The Hasbrouck information share is by nature between 0 and 1; in Tables 6A -D, the information shares of all instruments add up to approximately 1. Table 6A shows that the price discovery is dominated by the VXX ETN, accounting for about 65% of the information share (average of all three metrics). This result is not surprising and, in fact, somehow identical to Bollen, O’Neill, and Whaley (2017), who document that VXX leads VIX futures on three out of four days during Phase 3, from January 29, 2009, to February 29, 2012. Thus, Table 6A shows that we find the informativeness degree of the leader; however, we are much more interested in the contribution of VIX futures to price discovery after the expansion of trading hours. Here, VXX incorporates new information faster; however, we are more interested in the price discovery of the volatility instruments in Periods 2 to 4 by examining the effect of the extended trading hours (Tables 6B-D) on the price discovery process. The results in Table 6B show an excellent agreement (in Period 2) across the three measures that the VIX futures contribution to price discovery increases after the trading hours expansion.

Table 6A

Information Shares, Price Discovery Shares, Information Leadership Shares Period 1 – VIX futures and VIX ETPs (one minute sampling)

IS		PDS		ILS
First Period:
January 30, 2009 - March 27, 2009
VXX	VX	VXX	VX	VXX	VX
0.698	0.302	0.741	0.259	0.505	0.495
(0.018)	(0.018)	(0.026)	(0.026)	(0.032)	(0.032)

The table reports the information share (IS), price discovery share (PDS), and information leadership share (ILS) averages for Period 1 comprising 40 days. We use a one minute timing frequency and determine the model daily. Thus, all metrics are estimated for each day separately and the values reported represent the average over the entire period. In particular, for Hasbrouck information share (IS) the average of the upper and lower bounds in accordance with Baillie is reported. We report in parentheses bootstrapped standard errors.

Table 6B

Information Shares, Price Discovery Shares, Information Leadership Shares Period 2 – VIX futures and VIX ETPs (one minute sampling)

IS		PDS		ILS
Second Period Before:
October 14, 2010 - December 9, 2010
VXX	VX	VXX	VX	VXX	VX
0.844	0.156	0.887	0.113	0.686	0.314
(0.029)	(0.029)	(0.055)	(0.055)	(0.021)	(0.021)
Second Period After:
December 10, 2010 - February 7, 2011
VXX	VX	VXX	VX	VXX	VX
0.835	0.165	0.862	0.138	0.676	0.324
(0.022)	(0.022)	(0.036)	(0.036)	(0.031)	(0.031)

The metrics are estimated for each day separately and the values reported represent the average over the entire period. The table reports the information share (IS), price discovery share (PDS), and information leadership share (ILS) averages for Period 2 comprising 40 days before and 40 days after the change in futures trading hours. We use a one minute timing frequency and determine the model daily. Thus, all metrics are estimated for each day separately and the values reported represent the average over the entire period. In particular, for Hasbrouck information share (IS) the average of the upper and lower bounds in accordance with Baillie is reported. We report in parentheses bootstrapped standard errors.

Table 6C

Information Share, Price Discovery Share, Information Leadership Share Period 3 – VIX futures and VIX ETPs (one minute sampling)

IS		PDS		ILS
Third Period Before:
July 29, 2011 - September 23, 2011
VXX	VX	VXX	VX	VXX	VX
0.735	0.265	0.758	0.242	0.831	0.169
(0.035)	(0.035)	(0.075)	(0.075)	(0.035)	(0.035)
TVIX	VX	TVIX	VX	TVIX	VX
0.416	0.584	0.405	0.595	0.753	0.247
(0.019)	(0.019)	(0.046)	(0.046)	(0.029)	(0.029)
Third Period After:
September 26, 2010 - November 18, 2011
VXX	VX	VXX	VX	VXX	VX
0.722	0.278	0.743	0.257	0.797	0.203
(0.032)	(0.032)	(0.072)	(0.072)	(0.038)	(0.038)
TVIX	VX	TVIX	VX	TVIX	VX
0.491	0.509	0.491	0.509	0.816	0.184
(0.023)	(0.023)	(0.048)	(0.048)	(0.039)	(0.039)

The table reports the information share (IS), price discovery share (PDS), and information leadership share (ILS) averages for Period 3 comprising 40 days before and 40 days after the change in futures trading hours. We use a one minute timing frequency and determine the model daily. Thus, all metrics are estimated for each day separately and the values reported represent the average over the entire period. In particular, for Hasbrouck information share (IS) the average of the upper and lower bounds in accordance with Baillie is reported. We report in parentheses bootstrapped standard errors.

Table 6D

Information Share, Price Discovery Share, Information Leadership Share Period 4 – VIX futures and VIX ETPs (one minute sampling)

IS		PDS		ILS
Fourth Period Before:
August 23, 2013 - October 18, 2013
VXX	VX	VXX	VX	VXX	VX
0.549	0.451	0.549	0.451	0.506	0.494
(0.024)	(0.024)	(0.034)	(0.034)	(0.023)	(0.023)
TVIX	VX	TVIX	VX	TVIX	VX
0.432	0.568	0.431	0.569	0.496	0.504
(0.025)	(0.025)	(0.025)	(0.025)	(0.029)	(0.029)
UVXY	VX	UVXY	VX	UVXY	VX
0.476	0.524	0.476	0.524	0.538	0.462
(0.031)	(0.031)	(0.038)	(0.038)	(0.031)	(0.031)
Fourth Period After:
October 28, 2013 - December 23, 2013
VXX	VX	VXX	VX	VXX	VX
0.664	0.336	0.664	0.336	0.587	0.413
(0.016)	(0.016)	(0.017)	(0.017)	(0.022)	(0.022)
TVIX	VX	TVIX	VX	TVIX	VX
0.504	0.496	0.504	0.496	0.611	0.389
(0.017)	(0.017)	(0.017)	(0.017)	(0.025)	(0.025)
UVXY	VX	UVXY	VX	UVXY	VX
0.525	0.475	0.525	0.475	0.593	0.407
(0.022)	(0.022)	(0.022)	(0.022)	(0.025)	(0.025)

The table reports the information share (IS), price discovery share (PDS), and information leadership share (ILS) averages for Period 4 comprising 40 days before and 40 days after the change in futures trading hours. We use a one minute timing frequency and determine the model daily. Thus, all metrics are estimated for each day separately and the values reported represent the average over the entire period. In particular, for Hasbrouck information share (IS) the average of the upper and lower bounds in accordance with Baillie is reported. We report in parentheses bootstrapped standard errors.

Our findings also support the assertion of Alexander and Korovilas (2012) and Bollen, O’Neill, and Whaley (2017) that exchange-traded products should lead the VIX futures market. Indeed, Tables 6B-D clearly show that VIX ETPs lead the VIX futures on most occasions when in fact, VIX ETPs should track VIX futures since their returns are linked to VIX futures performance. This is, however, in contrast to the study of Schlusche (2009), who see clear price leadership of the futures over the ETFs in the derivative markets for the German blue-chip DAX index.

However, VIX futures lead in Period 3 versus TVIX ETN, and in Period 4 before the introduction of extended hours versus TVIX ETN and UVXY ETF with the same IS and PDS measures. In Period 3, the information share and the price discovery metric fluctuate based on the exchange-traded product under consideration. This disagreement could be described better in connection with the recent work by Fernandez-Perez et al. (2018). They show substantial time variation in the price leadership between the VXX and XIV, arguing that informed investors switch trading strategies between the VXX and XIV according to changing market conditions. We ascribe to that explanation for Period 3’s VIX ETPs because Period 3 is highly volatile (see footnote 16). Nonetheless, the information leadership share metric shows a non-contested leadership for all ETPs, both before and after the change in trading hours. In Period 4 (Table 6D), the newly introduced UVXY ETF behaves in a similar fashion to the VXX and TVIX ETNs with regard to price leadership. Period 4 distinctly reveals that, within a period, the stretch in trading hours makes the VIX futures contribution less than before.

Our explanation for the results is that there are indirect effects. For example, the VXX ETP is based on the S&P 500 short-term futures index returns (SPVIXSTR Index). The S&P 500 short-term futures index exposes investors to returns from a rolling long position in the first- and second-month VIX futures contracts. While we assert that VIX futures are directly affected by the trading hours expansions, exchange-traded products are indirectly affected based on their construction. The effect is heavier on VIX exchange-traded products since they have migrated away from being tax- or cost-efficient plain-vanilla alternatives to open-ended funds. Although the absence of short-sales restrictions works in favor of both instruments, we associate the ETPs leadership by tick size. While VIX futures are quoted in 0.01 of a point— which means that each futures tick value is $10— the smaller tick size of exchange-traded funds adjusts more frequently.

Data limitations preclude any resolution regarding the extended time periods Period 2 (7:20 a.m. to 8:30 a.m.), Period 3 (7 a.m. to 7:20 a.m.), and Period 4 (2 a.m. to 7 a.m. and 3:30 p.m. to 4:15 p.m. (Monday through Thursday)). VIX futures contribution to price discovery during these extended periods (i.e., 7:20 a.m. to 8:30 a.m.) is unknown to us, and it is equally likely that it might be higher or lower since we cannot calculate the information share. We re-run the IS, PDS, and ILS tests for the overlapping periods (i.e., 8:30 a.m. to 3:15 p.m.) and the evidence provided in Appendix Table 10B-D (not included) is that both Tables 6B-D and 10B-D match perfectly. In Table 10B, where the computation of the information share is restricted to common intervals in the time sequences (i.e., 8:30 a.m. to 3:15 p.m.), we see the same increase in VIX futures contribution in 2010, as known from Table 6B. Similarly, we observe the same decrease in VIX futures leadership after the new trading hours are in effect in Periods 3 and 4, as in Table 6C-D.

To check the robustness of our results, we bootstrap all three measures of information share in all four periods using 1,000 bootstrap replications. We report the corresponding p-values, which are all significant at a 0.05 percent level, underneath the information share estimates. Therefore, we confirm that price discovery improvement after trading hours change is not confined to futures, but in fact, sometimes is in the exchange-traded products’ direction.

Next, we delve into the determinants of price discovery by examining Table 7, which provides a brief summary of our explanatory variables spread, volatility, and volume. Spread and volume, respectively, are also the determinants considered by Fernandez-Perez et al. (2018) and Chen and Tsai (2017). The last entrant ETP, TVIX in period 3 and UVXY in period 4, has larger bid– ask spreads and volatility, but not necessarily a lower trading volume. VXX ETN trading volume double from Period 1 to Period 4, while VX futures soar to as high as four times their Period 1 level. This result is documented by Bollen, O’Neill, and Whaley (2017) whose phase 3 starts on the same day as our Period 1, which is the launch day of the first VIX ETP.

Table 7

Summary Statistics for the bid-ask spread and trade volume

	Period 1		Period 2		Period 3			Period 4
	VXX	VX	VXX	VX	VXX	TVIX	VX	VXX	TVIX	UVXY	VX
Panel A: Spread Summary Statistics
Mean	0.46	0.19	0.06	0.06	0.06	0.19	0.07	0.07	0.05	0.11	0.05
Min	0.32	0.13	0.01	0.05	0.03	0.07	0.06	0.01	0.01	0.06	0.05
Max	0.67	0.26	0.19	0.07	0.1	0.32	0.09	0.41	0.14	0.34	0.07
Median	0.45	0.18	0.04	0.06	0.05	0.18	0.07	0.02	0.04	0.09	0.05
Std Dev	0.09	0.03	0.05	0.003	0.01	0.05	0.01	0.08	0.03	0.05	0.01
Comparing ETPs spread means					TVIX vs. VXX			UVXY vs. VXX
T-test					18.22^***			3.4^***
Panel B: Volatility Summary Statistics
Mean	0.0012	0.0019	0.0248	0.0022	0.0031	0.0137	0.0049	0.0009	0.082	0.003	0.0015
Min	0.0003	0.0008	0.0001	0.0003	0.0007	0.003	0.001	0.0002	0.023	0.0005	0.0003
Max	0.0033	0.0049	1.8738	0.0197	0.0144	0.058	0.0615	0.0037	2.316	0.012	0.011
Median	0.0009	0.0015	0.0009	0.0014	0.0024	0.0098	0.0029	0.0006	0.046	0.002	0.0009
Std Dev	0.0007	0.0011	0.2107	0.0033	0.0025	0.0113	0.0075	0.0007	0.264	0.003	0.002
Comparing ETPs volatility means					TVIX vs. VXX			UVXY vs. VXX
T-test					6.88^***			6.24^***
Panel C: Volume Summary Statistics
Mean	256.62	1.71	362.67	4.32	228.7	289.34	2.92	518.63	500.28	290.17	7.51
Min	108.15	1.27	198.44	2.62	181.77	178.65	2.04	214.84	248.43	201.91	3.93
Max	1152.69	2.75	2090.23	12.78	322.11	3305.13	4.43	1502.83	2133.12	548.1	12.44
Median	195.30	1.59	283.41	4.05	220.04	235.21	2.81	553.07	420.26	277.71	7.47
Std Dev	197.49	0.37	278.77	1.35	29.23	411.93	0.53	206.7	350.65	65.11	1.49
Comparing ETPs volume means					TVIX vs. VXX			UVXY vs. VXX
T-test					1.10			– 8.95^***

This table presents the summary statistics of bid– ask spread, volatility and trading volume for each period and its affiliated trading hours. For exchange traded products as well as futures, to calculate the spread, we employ the best bid and ask prices observed every second and calculate the spread as the ask minus the bid. Volume is the number of shares traded, and volatility is the square root of the returns variance calculated as the sum of the squared one-minute returns.

The panel regressions in Tables 8A and 8B present the liquidity position of our volatility instruments for each period. We cannot assign a dummy variable to differentiate pre and post because there is no change in futures’ trading hours during period 1. Nevertheless, we find the dummy variable ch representing the change in trading hours statistically significant in period 2 and period 3 at the 5% level. The third period is highly volatile because VIX took multiple excursions into the 40s in August and September of 2011, while in the preceding months, it was trading in the 20s. On August 6th, 2011, Standard and Poor’s downgraded US Treasury bonds from AAA to AA+ status; on August 8th the S&P 500 dropped 6.7%, with all 500 stocks falling sharply. This unusual spike in volatility halted only after our period 3 ended in December of 2011. The interaction estimates between spread and change as well as volume and change are typically significant (Table 8 A-B) 22 . This indicates that the trading volume and bid-ask spread alter the price discovery contribution of both instruments after trading hours adjustments. The regression coefficients on the realized volatility variable do not turn out to be significant; in this case, we believe the cause could be the correlation between determinants and suppress M6 models from the display.

Table 8A

Determinants of the Information Share

	Dependent Variable: Information Share
	Period 1 (VXX, VX)		Period 2 (VXX, VX)
	M1	M4	M5	M7	M8
intercept	0.76^*** (3.42)	0.81^*** (2.77)	0.48 (1.59)	0.50 (1.55)	0.46 (1.88)
ch	N/A	N/A	0.28^** (2.04)	– 0.07 (– 1.58)	0.12 (0.68)
volume		– 0.0001 (– 0.41)		0.00 (0.26)	0.00005 (0.5)
volume^*ch				0.0004^*** (2.65)	0.0004^** (1.86)
spread	– 0.8^* (– 1.82)	– 1.07^** (– 2.19)	0.24 (0.43)		0.43 (0.73)
spread^*ch			– 5.43^** (– 2.13)		– 3.10 (– 1.09)
volatility		29.66 (0.83)			0.02 (0.16)
volatility^*ch					– 4.95 (– 0.49)
R²	0.04	0.07	0.03	0.05	0.06

This table reports random effects regressions that test the impact of the new trading hours and liquidity factors effects on information share. All regression models are described in the paper in Section 4-2. The dependent variable is the midpoint Hasbrouck’s information share and the independent variables are the change, labeled “ch”, a dummy variable that takes the values of one and zero (zero before the trading time change and one after the time change), the bid-ask spread, realized volatility, and daily trading volume. Spread is the difference between the ask and the bid, average daily trading volume is the number of shares traded, and volatility is the square root of the returns variance calculated as the sum of the squared one-minute returns. Standard errors are given in parenthesis under the coefficients. ^*, ^** and ^*** represents significance at the 10%, 5% and 1% levels.

Table 8B

Determinants of Information Share

Dependent Variable: Information Share
	Period 3 (TVIX, VX)			Period 4 (TVIX, VX)			Period 4 (VXX, VX)
	M5	M7	M8	M5	M7	M8	M5	M7	M8
intercept	0.65^* (– 1.74)	0.52 (– 1.31)	0.72^* (1.74)	0.19 (1.09)	0.49 (1.3)	0.18 (0.42)	0.33 (1.43)	0.70^** (2.21)	– 0.02 (– 0.02)
ch	– 0.34^** (– 2.44)	– 0.15^* (– 1.66)	– 0.35^** (– 2.27)	0.24 (1.07)	– 0.12 (– 1.34)	0.25 (0.51)	0.03 (0.22)	– 0.13 (– 1.66)	0.45 (0.53)
volume		– 0.0001 (– 0.8)	– 0.0001 (– 1.12)		0.00003 (0.27)	0.0001 (0.51)		– 0.0007^*** (– 2.76)	0.0005 (0.46)
volume^*ch		0.001^** (2.29)	0.00 (0.04)		0.0005^* (1.93)	0.00 (0.55)		0.0004^** (2.00)	0.00 (– 0.55)
spread	– 1.21 (– 1.18)		– 1.54 (– 1.24)	7.39^* (1.79)		6.81 (0.73)	5.04 (1.53)		13.97 (0.84)
spread^*ch	2.62^*** (2.76)		2.60 (1.64)	– 6.39 (– 1.36)		– 5.64 (– 0.59)			– 12.57 (– 0.75)
volatility			– 1.11 (– 0.31)			0.08 (– 1.1)			– 51.82^* (– 1.85)
volatility^*ch			1.20 (0.11)			– 52.59^* (– 1.72)			16.18 (0.39)
R²	0.07	0.05	0.08	0.02	0.03	0.05	0.08	0.05	0.11

This table reports random effects regressions that test the impact of the new trading hours and liquidity factors effects on information share. All regression models are described in the paper in Section 4-2. The dependent variable is the midpoint Hasbrouck’s information share and the independent variables are the change, ch, a dummy variable that takes the values of one and zero (zero before time change and one during the after time change period), the bid-ask spread, realized volatility, and daily trading volume. Spread is the difference between the ask and the bid, average daily trading volume is the number of shares traded, and volatility is the square root of the returns variance calculated as the sum of the squared one-minute returns. Standard errors are given in parenthesis under the coefficients. ^*, ^** and ^*** represents significance at the 10%, 5% and 1% levels.

For each period, we run ordinary least-squared (OLS) regressions with the same dependent and independent variables as in Models M1 through M4. For brevity, we do not report the results, but there are differences in statistical significance for the independent variables during each period. Indeed, when spread, volatility, or volume are significant in one half-period, they lose their significance in the other half and vice versa. Whenever that happens, we see a big increase or decrease in R². The presence versus absence of statistical significance back up the price discovery results, and most importantly the panel regression results; in the latter, we discover the alteration of roles. As just stated, we confirm that the influence of spread, volatility, and volume on price discovery is dynamic after trading hours change. Finally, in Table 9 we look at the effects of changes in spread, volatility, and volume on the difference in leadership between ETPs and futures. The results for Period 2 qualitatively support the earlier unreported results, such that the difference in the spread is an unambiguous and significant influence of Hasbrouck information share change. Indeed, bid-ask spreads for the (VXX, VX) combination are negative and significant in period 2, but positive and significant in period 4, which indicates that large spreads are an inconvenience for price discovery.

Table 9

Ordinary-least squares (OLS) regressions that show how the change in the spread, volatility and volume determinants affects the leadership remaking between VIX ETPs and futures for each information share measure

	ΔIS	ΔPDS	ΔILS
Period 2 (VXX, VX)
Δspread	– 163.17^*** (– 2.8)	– 211.94^*** (– 3.56)	– 116.37^* (– 1.88)
Δvolatility	– 5.05 (– 1.52)	– 11.51^** (– 2.61)	2.83 (– 0.58)
Δvolume	0.001^*** (2.81)	0.001^*** (2.77)	0.0004^** (2.11)
Period 3 (VXX, VX)
Δspread	4.09 (0.03)	127.31 (0.85)	– 78.39 (– 0.47)
Δvolatility	8.03^*** (3.44)	– 1.28 (– 0.52)	3.39 (1.41)
Δvolume	0.003^*** (5.29)	0.003^*** (4.09)	0.003^*** (3.46)
Period 3 (TVIX, VX)
Δspread	194.04^*** (2.89)	74.78 (0.84)	324.30^*** (3.52)
Δvolatility	– 8.21^*** (– 4.04)	– 4.63 (– 1.61)	0.37 (0.17)
Δvolume	– 0.0001 (– 1.44)	0.0003^** (2.19)	– 0.00005 (– 0.23)
Period 4 (VXX, VX)
Δspread	2.41^*** (4.34)	0.22 (0.37)	1.98^*** (3.09)
Δvolatility	– 7.21^*** (– 2.74)	3.03 (0.8)	– 0.59 (– 0.15)
Δvolume	– 0.00003 (– 0.21)	0.0005^*** (3.29)	– 0.0001 (– 0.7)
Period 4 (TVIX, VX)
Δspread	– 0.19 (– 0.08)	– 0.48 (– 0.2)	0.45 (0.19)
Δvolatility	1.02 (0.34)	– 5.99^** (– 2.28)	4.36 (1.55)
Δvolume	– 0.0001 (– 0.32)	0.0003^** (2.19)	0.00005 (0.23)
Period 4 (UVXY, VX)
Δspread	– 0.04 (– 0.02)	2.83 (1.13)	0.14 (0.09)
Δvolatility	3.24 (1.15)	– 4.24 (– 1.64)	5.51^** (2.32)
Δvolume	– 0.0002 (– 0.24)	– 0.001 (– 0.73)	– 0.00002 (– 0.03)

The table compares the changes caused by the classic determinants (spread volatility, and volume) in the difference of price discovery metrics between VIX ETPs and VIX futures. For Period 2– 4, ΔIS, ΔPDS, ΔILS represent the difference in information share, price discovery share and information leadership share between VIX ETPS and futures. Δspread, Δvolatility and Δvolume is the difference in spreads, volatility and volume between futures and exchange-traded products. ^*, ^**, ^*** represent the statistical significance at the 10%, 5% and 1% level, respectively.

On the contrary, a substantial increase in trading activity followed by a reduction in spreads is a salutary contribution to price discovery. Further, the results for trading volume are not striking between Period 2 and Period 4 for the price discovery share (PDS) measurement, both being positive and significant. In fact, Bollen, Smith, and Whaley (2004) develop a model showing that the inverse of trading volume is an important determinant of the market maker’s bid– ask spread. For Period 3, we see that the volatility determinant changes from positive to negative maintaining significance for VXX versus TVIX ETN, a fact that perfectly supports the results in Table 6C. Thus, Table 9 Period 3 further supports our contention that ETPs’ leadership varies depending on the exchange-traded product under consideration. Finally, we want to mention that all results in Table 9 are robust to alternative measures of spread and volatility.

6 Conclusions

We examine the importance of VIX futures’ new trading hours on their’s and their associated VIX ETPs’ price leadership. Our approach contributes to the ‘who is the leader’ debate in terms of variation in influence associated with changes in VIX futures trading hours. Our study rejects the null hypothesis and supports the premise that VIX futures play a significant but not dominant role in the price discovery process.

Since variance is additive in contrast with standard deviation when we average all periods in our study before and after the expanded hours, the average information share of all periods is 0.598 for VIX ETPs and 0.402 for VIX futures. Averaging all “after” periods generates, in comparison, an information share equivalent to 0.621 and 0.414 for VIX ETPs and VIX futures, respectively. A few comments are in order to explain the increase in the information share of the VIX futures as a result of averaging. The “after” periods average does not add up to exactly one, and is roughly one, as averaging is done across all periods, all metrics, and all ETPs. Second, after the expansion of the trading hours, the leadership still rests more on the side of VIX ETPs, while VIX futures still attain second place.

Our empirical results show that when information share (IS) and price discovery share (PDS) metrics are used, the ultimate leader of the price discovery process varies with the VIX ETP under consideration. However, when the information leadership share (ILS) metric is used, the specific ETP selection is irrelevant, and the results depend only on the period at hand. One possibility could be that the ILS metric does not assent so well with the IS and PDS metrics. The other explanation could be that although trading in both VIX futures and VIX ETPs have set records, investors who do not have to register to trade ETPs quickly detect different market conditions. Such findings are important for investors, policymakers as well as exchanges whenever deciding on risk management, portfolio diversification, and/or on other asset classes 23 . Overall, the VIX exchange-traded products are investments in their own right attracting better-informed traders who understand their risk and return characteristics and their diversification benefits.

Another important finding of our study is that the effect of bid-ask spreads, volatility, and trading volume on price discovery differs after the change in trading hours for both VIX futures and ETPs from what it was before the change. Although the purely extended periods (i.e., 7:20 a.m. to 8:30 a.m.) cannot divulge price informativeness due to data limitations, the supplemental analysis in the appendix (available upon request) supports our conclusion that the extended trading hours affect price discovery in both ETPs and futures markets. As estimated by Bollen, O’Neill, and Whaley (2017), the long-term informational role of VIX futures has increased. In this sense, CBOE made the right decision in June 2014 to expand the trading hours to almost 24 hours a day, meeting the expectations and needs of various traders.

Footnotes

Bitcoin futures (BTC) trading does not occur 24/7; trading takes place Sunday to Friday, 6 p.m. to 5 p.m. Eastern time, so maybe these contracts could be made more accessible to investors.

There are important differences between ETFs and ETNs: with an ETF, the investor holds VIX futures, while ETNs are debt securities issued by a major bank (and so do not hold any securities). Moreover, there are differences in tracking errors (ETNs should not have any tracking errors) and tax treatment.

analyze the information flow between the BitMEX perpetual swap and three major bitcoin spot exchanges and find that the strength of the price discovery of BitMEX fluctuates over time.

The working paper by Bollen, O’Neill and Whaley (2014) uses the lead-lag ratio, which is based on simple R-squared values and shows that VIX ETPs are partly contemporaneous with VIX futures.

When considering VIX futures’ statistical properties, Konstantinidi and Skiadopolous (2011) report weak evidence of statistically predictable patterns in the evolution of prices. Aragon, Mehra, and Wahal (2018) embrace this idea— i.e., prior returns in VIX futures do not predict future price changes. Besides extending results for VIX futures, they look at predictability in volatility and deny that predictability in the VIX carries over to the futures. The VIX nearest contract futures prices are less volatile than the VIX index, according to Zhang, Shu, and Brenner (2010), though the instruments are highly correlated.

The VIX ETP was launched on January 29, 2009, the TVIX ETP on November 29, 2010, and the UVXY ETP on October 3, 2011.

Alternatively, Alexander and Korovilas (2012) point out diversification benefits by including VIX futures in a portfolio. They summarize three previous studies of Szado (2009), Warren (2012), and Chen, Chung, and Ho (2010) that examine the benefits of VIX futures allocation.

VIX futures prices are informationally efficient (); however, the trading volume of VIX futures is dominated by VIX ETPs (Alexander 2012) because exchange-traded products signify a volatility trade for short-term turns and a term structure trade for long-term horizons.

Closely linked securities are defined as in and include securities that may be technically different but are linked by arbitrage or meet short-term equilibrium requirements.

VIX futures trade longer hours than the underlying VIX index to give investors more time to align their positions with the market. The exchanges reason that such a strategy attracts the business of informed investors.

More information is disclosed per hour during the regular trading period. However, the pre-open is packed with more information per trade in the after-hours market due to the high frequency of informed trades.

He et al. (2009) expose overnight trading activity as a substantial piece of the puzzle in the round-the-clock U.S. Treasury market. Jiang, Likitapiwat, and Mcinish (2012) study price discovery following quarterly earnings announcements released outside normal trading hours. They find that the highest amount of information incorporated into the efficient price occurs for after-hours trading following announcements.

Covrig, Ding, and Low (2004) examine overlapping and non-overlapping trading periods and three informationally linked markets: the domestic spot market of the Tokyo Stock Exchange (TSE), and two futures markets, the Osaka Securities Exchange (OSE) and the Singapore Exchange (SGX).

This change took place on October 21, 2013, when after a break from 4:15 p.m. to 4:30 p.m., the market reopened, and trading in VIX futures resumed from 4:30 p.m. to 5:15 p.m.

VIX futures trade on the CBOE Futures Exchange (CFE), and ETPs trade on the NYSE exchange.

Step 1: most traded VIX products are selected. Step 2: each ETP pair with the same inception date is looked at individually, and the most frequently traded product is retained.

We construct our price series at one-minute intervals such that we have 16,200 observations for period one and the first half of period two; 19,000 observations for the second half of period two and the first half of period three; 19,800 observations for the second half of period three and the first half of period 4; and finally, 33,272 observations during the last 40 days of period four.

Credit Suisse’s Velocity Shares Daily Inverse VIX Short Term ETN, XIV, was liquidated in February 2018 because investors suffered heavy losses on bets against the index. This period is called “Volmageddon” because, over just a few trading days, the XIV fund went “poof” (Wall Street Journal, September 4, 2017). ProShares Short VIX Short-Term Futures ETF, SVXY, continued operating, but its price fell more than 90%.

Period 3 is highly volatile. For example, on August 8, 2011, three major U.S. stock indexes, the S&P 500, Dow Jones Industrial Average, and the NASDAQ composite fell 6.7%, 5.6%, and 6.9%, respectively.

We eliminate negative spreads and spreads higher than 5 dollars.

We also run the regression involving the product of volatility with the dummy variable.

As a robustness check, we also performed our panel regressions using the quoted spread QS=(Ask-Bid)/[(Ask + Bid)/2], with similar results.

Talking about leveraged and inverse ETFs, Gary Gensler – the Securities and Exchange Commission chair – said, “I believe that potential rulemaking could strengthen the investor protections around these products. [Leveraged and inverse ETPs] can pose risks even to sophisticated investors and can potentially create system-wide risks by operating in unanticipated ways when markets experience volatility or stress conditions.”

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