Has the introduction of S&P 500 ETF options LED to improvements in price discovery of SPDRs?

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mous referee for their helpful comments and suggestions. The ﬁnancial supports provided by the National Science Council of Taiwan and the MoE ATU plan of National Chiao Tung University are also gratefully acknowledged. Any errors are the sole responsibility of the authors.

*Correspondence author, Department of Finance, Shih Hsin University, No. 111 Mu-Cha Road, Section 1, Taipei 11645, Taiwan. Tel: 886-2-2236-8225, Ext. 63443, Fax: 886-2-2236-2265, e-mail: [email protected]. edu.tw.

Received April 2011; Accepted May 2011

■ Wei-Peng Chen is an Assistant Professor in the Department of Finance at the Shih Hsin University, Taipei, Taiwan.

■ Huimin Chung is a Professor in the Graduate Institute of Finance at the National Chiao Tung University, Hsinchu, Taiwan.

S&P 500 ETF O

PTIONS

L

ED

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I

MPROVEMENTS IN

P

RICE

D

ISCOVERY OF

SPDR

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WEI-PENG CHEN* HUIMIN CHUNG

This study sets out to investigate trading in Standard and Poor’s Depository Receipt Trust Series I (SPDR) options and the impact on the price-discovery process of SPDRs. The empirical results reveal a signiﬁcant rise in liquidity with-in the SPDR market followwith-ing the with-introduction of SPDR options. Furthermore, the results also show that the introduction of SPDR options has led to a signiﬁ-cant improvement in the information share of SPDRs, and that the contribution of SPDRs to price discovery has become very close to that of E-mini index futures. These findings imply that developments in the derivatives market can lead to improvements in market quality, including the level of liquidity and price discovery of the underlying securities. © 2011 Wiley Periodicals, Inc. Jrl Fut

Published online July 5, 2011 in Wiley Online Library (wileyonlinelibrary.com) The Journal of Futures Markets, Vol. 32, No. 7, 683–711 (2012)

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The authors thank Robert Webb (the Editor), Wen-Liang Hsieh, Tsung-Wu Ho, and especially an

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2 Chen and Chung

Journal of Futures Markets DOI: 10.1002/fut

1. INTRODUCTION

Standard and Poor’s Depository Receipts Trust Series I (SPDRs) were ﬁrst list-ed on the American Stock Exchange (AMEX) on January 29, 1993, and have since become the most active ‘exchange traded funds’ (ETFs). On January10, 2005, trading in SPDR options began on the Chicago Board Options Exchange (CBOE) hybrid trading system. Both efﬁciency and quality in the SPDR market would be enhanced by the introduction of this new derivative, essentially because market participants could actually replicate certain trading strategies

using these tradable instruments.1

In the current study, we analyze the impact of the introduction of SPDR options on the contribution to the price-discovery process of SPDRs. Although many studies have been undertaken on derivatives trading, and the resultant inﬂuence on the market quality of the underlying assets, very few have exam-ined the impact of derivatives trading on price discovery of the underlying assets. This is, nevertheless, an important topic, since the introduction of derivatives trading may have significant impacts on the market quality of the underlying security, which ultimately affects the contribution made by the underlying security to the overall process of price discovery.

A variety of authors have investigated the price-discovery process for S&P 500 index derivatives. Chu, Hsieh, and Tse (1999) and Hasbrouck (2003), ana-lyzing the issue of price discovery for S&P 500 index derivatives, indicate that most of the price discovery is contributed by S&P 500 index futures, with SPDRs playing an insignificant role on the price-discovery process within the S&P 500 index market. Tse, Bandyopadhyay, and Shen (2006) subsequently argue that the primary explanatory reason for the prior findings, that SPDRs provided no significant contribution to price information, was the ‘electronic

communications network’ (ECN) platform examined in the prior studies.2

Although Tse et al. (2006) demonstrate that E-mini futures contribute the most to price discovery, the contribution to price discovery by electronically-traded ETFs on the Archipelago (ArcaEx) ECN was found to be higher than in

1_{The Chicago Mercantile Exchange (CME) also announced the launch of futures contracts on June 20, 2005} on three of the largest and most actively traded ETFs in the United States, with trading in the new CME ETF futures contracts on SPDRs subsequently taking place on the exchange’s CME Globex electronic trading platform. One of the advantages of ETF futures, like all futures, is that they allow investors to take a short position without borrowing shares from a broker, which is necessary to short sell securities or ETFs. Furthermore, the initial margin with ETF futures will generally be lower than the Regulation T margins asso-ciated with the underlying ETF.

2_{ECNs are electronic trading systems that automatically match buy and sell orders at speciﬁed prices} with-out having to go through any intermediaries. They feature fast and efﬁcient trade execution, lower transac-tion costs and trader anonymity.

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the prior studies, indicating that ETFs play a signiﬁcant role in the

price-dis-covery process.3

According to the results of the aforementioned studies, S&P 500 index E-mini futures still dominate SPDRs, although a gradual rise has become dis-cernible in the contribution to price discovery made by SPDRs traded on ECNs. Tse et al. (2006) suggest that ECNs offer the advantages of both anonymity and speed of execution, both of which can attract informed investors to trade in SPDRs. Since the introduction of derivatives trading also affects the trading of informed investors on the underlying securities, this rais-es the main qurais-estion as to whether S&P 500 ETFs have provided a greater con-tribution to price discovery from the introduction of S&P 500 ETF options onwards.

Further, considerable concern has arisen within the prior literature over the past few decades with regard to the impact of derivatives trading on the market quality of the underlying securities. These works can essentially be clas-siﬁed under two distinct themes: whether trading in derivatives has a beneﬁcial

or harmful effect on the market of the underlying securities.4

For example, some studies argue that due to the higher degree of leverage, derivatives markets tend to attract uninformed speculative investors, and thus, destabilize the underlying asset markets through the increase in volatility; these studies contend that derivatives encourage speculation, thereby causing desta-bilization of the spot markets (see, for example, Conrad, 1989; Cox, 1976; Figlewski, 1981; Harris, Sofianos & Shapiro, 1994; Rahman, 2001). Conversely, other studies argue that since the derivatives markets increase the overall market quality and informativeness, this may well reduce the overall volatility of the underlying securities through the transfer of risk (see, for exam-ple, Danthine, 1978; Powers, 1970; Schwartz & Laatsch, 1991).

From their examination of the impact of stock options listings on various aspects of the market quality of the underlying stock, Kumar, Sarin, and Shastri (1998) found discernible reductions in the spread along with increases in quoted depth, trading volume, trading frequency and transaction size after options list-ings. Their empirical ﬁndings suggest that options listings improve the market quality of the underlying stocks. Further, de Jong, Koedijk, and Schnitzlein (2006) suggest that the presence of listed options is associated with the high quality of the underlying asset market, since they argue that if market makers

3_{Tse et al. (2006) argue that the prior research result, i.e., ETFs play an insignificant role in the} price-discovery process, is surprising because ETFs are traded actively and have low transaction costs. Therefore, they suggest that this possible anomaly is due to informed traders’ preference for electronic trading markets over ﬂoor trading markets.

4_{Danielsen, Van Ness, and Warr (2007) provide another viewpoint, which is that the options do not} system-atically improve the market quality of the underlying security, but rather that the market quality of the under-lying security is improved prior to the listing decision.

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4 Chen and Chung

in the stock learn from transactions in the option, they can ultimately set a more accurate price.

According to the extant literature, there are three possible explanations as to why the introduction of derivatives may improve the contribution to price discovery by the underlying securities (see Chakravarty, Gulen, & Mayhew, 2004; de Jong et al., 2006; Fleming, Ostdiek, & Whaley, 1996; Kumar et al., 1998). First, derivatives markets can improve the efﬁciency of incomplete asset markets by expanding the opportunity set that market participants are faced with (Hakansson, 1982; Ross, 1976). Arbitrageurs can easily replicate arbitrage trading strategies by simultaneously using both the derivatives and the

underly-ing securities.5_{Second, derivatives trading may improve the efﬁciency of the}

underlying market by increasing the level of public information within the mar-ket (Kumar et al., 1998). As such, informed traders usually trade simultane-ously in both the underlying security and derivatives markets in order to exer-cise certain trading strategies (Chakravarty et al., 2004). Thirdly, if the market makers in the underlying security learn from the transactions that transpire in derivatives markets, they can ultimately set a more accurate price in the market of the underlying asset (de Jong et al., 2006).

The process of price discovery is influenced by many factors, including market depth, trading volume, bid-ask spread and market volatility. Several the-oretical hypotheses indicate that markets with greater liquidity, lower transac-tion costs and fewer restrictransac-tions are likely to play more important roles in terms

of price discovery.6 _{The prior studies demonstrate that the introduction of}

derivatives trading has signiﬁcantly improved the market liquidity of the

under-lying securities;7 _{however, such improvement in the market liquidity would}

have simultaneously led to an increase in the contribution to price discovery made by the underlying securities. It is therefore surmised that as a result of the introduction of SPDR options, SPDRs now make a greater contribution to the share of information.

Several studies have investigated the impact of options trading on the mar-ket quality of the underlying securities (Danielsen et al., 2007; de Jong et al., 2006; Kumar et al., 1998); however, the current study differs from the extant literature in several ways. Firstly, Chakravarty et al. (2004) investigate the con-tribution of options markets to price discovery using the ‘information share’

5_{Richie, Daigler and Gleason (2008) demonstrate that the limited volume size is the key arbitrage limitation} for SPDRs; as such, arbitrage between SPDRs and SPDR options cannot be replaced by arbitrage between the S&P 500 index futures and SPDR options.

6_{Chu et al. (1999) summarize the four main hypotheses (leverage, trading cost, uptick rule and market-wide} information hypotheses) to explain the preferences of informed traders according to different market struc-tures and security designs.

7_{Kumar et al. (1998) note that the bid-ask spread, quoted depth and information efﬁciency all improved for} the underlying securities as a result of the introduction of options trading; however, they do not discuss the issue of the contribution to price discovery by the underlying securities.

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approach. Although they argue that stock options trading directly contributes to price discovery in the underlying stock market, there is no empirical evi-dence in the change of price discovery for the underlying stocks in their study.

Second, as compared with the prior studies (Chu et al., 1999; Hasbrouck, 2003; Tse et al., 2006), this study focuses on the four venues–AMEX, Island ECN, ArcaEx ECN and NASDAQ—which account for over 95% of all transac-tions in the SPDR market. The analysis of the four venues explains how SPDR options affect the improvement in the contribution to price discovery, whether it is due to the market competition (the AcaEx ECN) or the product competi-tion (the overall SPDR market).

Third, the present study differs from de Jong et al. (2006), in which an experimental approach was used to compare a market with a traded option with a market operating in isolation. In comparison, the ‘permanent-transitory’ ‘information share’ and ‘modified information share’ MIS (Lien & Shrestha, 2009) approaches are used in this study to measure the level of price discovery across the SPDR market. The MIS approach provides a unique measure of price discovery, which is independent of the ordering of variables in the Cholesky factorization of the innovation covariance matrix.

The empirical results reveal that the introduction of SPDR options has led to an increase in both market liquidity and price discovery of SPDRs. According to the ‘transaction cost’ hypothesis, those securities with lower trad-ing costs contribute a higher level of price discovery; it is therefore argued that as a result of the introduction of derivatives, the beneﬁts obtained by market participants, essentially as a result of improved liquidity, have led to a reduction in implicit trading costs. This is attributable to either a reduction in the bid-ask spread or an increase in quoted depth, ultimately leading to SPDRs contribut-ing a greater information share to price discovery.

This analysis further reveals that SPDRs traded electronically on the ArcaEx ECN dominate the price discovery process for SPDR shares, with the contribution to price-discovery being very close to E-mini futures, thereby indicating that SPDRs and E-mini futures possess equal importance in the price-discovery process of the S&P 500 index market. The empirical results also show that the leverage effect is signiﬁcant during high-volatility periods. The main implication of these ﬁndings is that developments in the derivatives markets provide valuable improvements in market quality for the underlying securities, both in terms of liquidity and price discovery.

The remainder of this study is organized as follows. A description of the data is provided in Section 2, followed in Section 3 by a discussion of the research methodology. Section 4 presents the empirical results pertaining to the change in the contribution to price discovery made by SPDRs. Finally, con-clusions drawn from this study are presented in Section 5.

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6 Chen and Chung

2. DATA DESCRIPTION

The sample for this study is comprised of SPDRs, S&P 500 index regular futures and E-mini futures. The SPDR prices are usually scaled down in order to make them comparable to stock prices; thus, the SPDR prices are set at one-tenth of the S&P 500 index level. The sample covers the period from February 25, 2004 to November 23, 2005, a 22-month period that begins approximately 11 months prior to the date of the introduction of SPDR options (January 10, 2005) and ends approximately 11 months after their introduction.

The tick-by-tick data on the S&P 500 index are obtained from the Tick Data database, whereas the SPDRs data, which includes the tick-by-tick quote as well as the trade prices, trading volume, quoted depth and bid-ask spread, are obtained from the NYSE Trade and Quote (TAQ) database. This study retains only those trades and quotes that occurred during regular trading hours between 9:30 a.m. and 4:00 p.m., EST. The corresponding data on regular and E-mini index futures, which include the trade prices and number of trades, are obtained from the Tick Data intraday database, while the data on futures are obtained from the Chicago Mercantile Exchange (CME), and cover the trading hours from 8:30 a.m. to 3:00 p.m., CST.

A comprehensive introduction to the market structures of index futures

and ETFs has already been provided in many prior studies.8_{Brieﬂy, S&P 500}

index regular futures are traded on the open-outcry ﬂoor of the CME, whereas S&P 500 index E-mini futures are traded on the CME’s electronic platform. The regular futures and E-mini futures are similar in many ways. For example, both contracts have the same underlying cash index, the same expiration date and time and the same settlement price, among other similarities. The main differences between the E-mini and regular futures contracts are the contract size and trading hours. The E-mini futures contract multiplier is one ﬁfth of the regular futures contract multiplier. In addition, E-mini futures contracts are traded electronically and are available nearly 24 hours per day. As such, E-mini futures are designed for individual or small investors.

ETFs are listed on the AMEX; however, trading in ETFs takes place in multiple venues. On July 31, 2001, the NYSE began trading the three most active ETFs, the NASDAQ-100 Trust Series I, the Standard and Poor’s Depository Receipt Trust Series I and the Dow Jones Industrial Average Trust

Series I, all listed on the AMEX on an ‘unlisted trading privilege’ (UTP) basis.9

8_{See for example Tse and Erenburg (2003), Tse and Hackard (2004), Hendershott and Jones (2005a,} 2005b), Ates and Wang (2005), Tse et al. (2006), Nguyen, Van Ness, and Van Ness (2007) and Bandyopadhyay, Martinez, and Tse (2009).

9_{An UTP is a right provided by the Securities Exchange Act of 1934 which permits securities listed on any} national securities exchange to be traded by other such exchanges.

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Under the UTP framework, a stock listed on the AMEX can also trade on other exchanges without a dual listing. Various studies subsequently provide evi-dence of the impact of the UTP system on market quality. For example, Boehmer and Boehmer (2003) and Tse and Erenburg (2003) investigate the entry of the NYSE on the ETF market. They show a dramatic improvement in liquidity due to the elimination of market maker rents, and that the competi-tion within multi-market trading improves market quality with regard to reduced spreads and greater price discovery.

Although the primary listing exchange for SPDRs is the AMEX, the major-ity of the trading volume and transactions come from ECNs such as ArcaEx and Island. Huang (2002) and Barclay, Hendershott, and McCormick (2003) focus on the role and impact of ECNs on NASDAQ trading. They suggest that the main advantages of trading in ECNs are the rapid and efﬁcient execution of trades and the anonymity of traders, which together attract more informed traders to trade on ECNs resulting in better price discovery. The property of trader anonymity is not available for NASDAQ traders. The dominant trading platform for the major ETFs was the Island ECN up until September 2002, when it stopped displaying its limit order book; this lack of information display led to reduced volumes and higher transaction costs (Hendershott & Jones, 2005a). In turn, a considerable proportion of the market share of the Island ECN subsequently migrated to the ArcaEx ECN, such that their market share more than doubled (Tse & Hackard, 2004). When the Island ECN later chose to redisplay its orders, it was no longer a dominant player in this market. Tse et al. (2006) summarize the two previous studies to show that the ETFs traded on the ArcaEx ECN relatively dominated the price-discovery process for ETF shares in 2004.

Comprehensive details on the number of trades, trade size and transac-tions by trade size within different trading centers are reported in Table I. This table depicts the number of transactions and trading volumes of SPDRs on nine trading venues including: the AMEX (A, the exchange code in TAQ data), the Boston Stock Exchange (B), the Cincinnati Stock Exchange (C), the Chicago Stock Exchange (M) the NYSE (N), the Paciﬁc Stock Exchange (P), the NASDAQ (T), the Chicago Board of Options Exchange (W), and the Philadelphia Stock Exchange (X). In 2005, over half of the SPDR volume was traded on ECNs.

Table I also shows that in the second sample period, the growth in total transactions and trading volume was close to 65% and 40%, respectively. This result indicates that trading activities have increased signiﬁcantly in the SPDR markets following the introduction of SPDR options trading. In addition, Table I shows that over 95% of all transactions are concentrated on four exchanges in the first and second periods: the AMEX (A), Cincinnati (C), Pacific (P) and

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T ABLE I Number of T ransactions and T rading V o

lume for SPDRs in Different T

rading Centers T rading V olume T ransactions by T

rade Size (No. of Shares)

T rading T rades Total No. Small Size Medium Size Large Size Centers Total No. % ( 100 Shares) % ( 1,000) % (1,001–9,999) % ( 10,000) % P anel A: F irst period (F ebruary 25, 2004–J

anuary 7, 2005, 220 trading days)

A (AMEX) 449,526 3.73 11,079,178 12.24 283,735 2.60 141,314 13.42 24,477 29.69 B (Boston) 124,926 1.04 10,69,220 1.18 106,050 0.97 18,095 1.72 781 0.95 C (Cincinnati) 3,890,510 32.25 29,393,969 32.48 3,341,028 30.57 536,587 50.97 12,895 15.64 M (Chicago) 73,183 0.61 631,553 0.70 63,976 0.59 8,649 0.82 558 0.68 N (NYSE) 190,966 1.58 4,000,786 4.42 153,561 1.41 29,777 2.83 7,628 9.25 P (Paciﬁc) 6,859,987 56.87 20,861,891 23.05 6,589,482 60.30 260,036 24.70 10,469 12.70 T (NASDAQ) 443,032 3.67 22,830,184 25.22 366,053 3.35 52,417 4.98 24,562 29.79 W (CBOE) 5,769 0.05 439,091 0.49 2,453 0.02 2,399 0.23 917 1.1 1 X 24,764 0.21 200,968 0.22 21,166 0.19 3,447 0.33 151 0.18 (Philadelphia) Total 12,062,663 100.00 90,506,840 100.00 10,927,504 100.00 1,052,721 100.00 82,438 100.00

Panel B: Second period (January 10, 2005

–

November 23, 2005, 220 trading days)

A (AMEX) 506,656 2.55 9,885,202 7.82 366,647 1.99 121,1 17 8.47 18,892 21.26 B (Boston) 106,232 0.53 937,372 0.74 89,163 0.49 16,364 1.14 705 0.79 C (Cincinnati) 6,959,797 34.97 37,083,839 29.33 6,314,937 34.35 630,372 44.06 14,488 16.30 M (Chicago) 128,146 0.64 884,854 0.70 121,358 0.66 6,174 0.43 614 0.69 N (NYSE) 168,650 0.85 325,71 16 2.58 130,590 0.71 30,916 2.16 7,144 8.04 P (Paciﬁc) 9,349,067 46.98 32,474,709 25.68 8,916,748 48.51 416,464 29.1 1 15,855 17.84 T (NASDAQ) 2,674,821 13.44 41,149,130 32.54 2,439,085 13.27 206,467 14.43 29,269 32.93 W (CBOE) 7,760 0.04 781,585 0.62 2,967 0.02 2,884 0.20 1,909 2.15 Total 19,901,129 100.00 126,453,807 100.00 18,381,495 100.00 1,430,758 100.00 88,876 100.00 Note.

This table presents the transactions and trading volumes of SPDRs on nine trading venues including the

AMEX (A, the exchange co

de in

T

AQ data), the Boston Stock Exchange

(B), the Cincinnati Stock Exchange (C), the Chicago Stock Exchange (M), the NYSE (N), the Paciﬁc Stock Exchange (P), the NASDAQ

(T), the Chicago Board Options Exchange (W) and

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NASDAQ (T). In particular, 56% (46%) of all transactions in the first (second) period are attributable to the Pacific Exchange. Clearly, therefore, the Pacific Exchange may be responsible for most of the information on SPDR prices.

Consistent with prior studies ( Hendershott & Jones, 2005a, 2005b; Tse & Erenburg, 2003), this study deﬁnes small-sizes trades as those consisting of 1–1,000 shares, medium-sized trades as 1,001–9,999 shares, and large-sized (block) trades as 10,000 shares or greater. From observations of the size distri-bution of transactions during the first period, we find that the Pacific Exchange accounts for 68% of small trades, the Cincinnati Exchange accounts for 55% of medium-sized trades and the NASDAQ accounts for 28% of block trades. Following the introduction of options trading, these three exchanges remain the most active in terms of small, medium and block trades. This result is also consistent with the finding of Nguyen et al. (2007), who found that the ECN mean trade size within the ETF market is small, and that large trades usually occur in traditional markets such as the NASDAQ, AMEX and NYSE.

The Paciﬁc Exchange created a coalition with the ArcaEx ECN in 2003 to provide the exchange with the ability to electronically trade listed securi-ties; the Island ECN also started to report its trades through the Cincinnati Stock Exchange in the same year. Therefore, this study adopts the Pacific Exchange data for the ArcaEx ECN and the Cincinnati Exchange data for the Island ECN. Although the current study covers all of the exchanges in the TAQ database, the examination of price discovery for SPDR trades and quotes focuses on a sample of SPDRs traded on the AMEX, Island ECN, ArcaEx ECN and NASDAQ. As shown in Table I, these four exchanges accounted for approximately 93% of the total trading volume in the ﬁrst peri-od and 95% of the total trading volume in the second periperi-od. Therefore, this investigation of the four venues also provides insights into whether the improvement in the contribution to price-discovery stems from the ArcaEx ECN or the overall SPDR market.

In order to ensure the accuracy of the sample data, all trades and quotes that are out of time sequence are deleted, while quotes meeting any of the following three conditions are also discarded: (i) either the bid or the ask price is equal to or less than zero; (ii) either the bid or the ask size is equal to or less than zero and (iii) either the price or the volume is equal to or less than zero. Data errors are further minimized by eliminating trades and quotes meeting the criteria outlined in Hasbrouck (2003). All quotes are screened to remove zero and negative spreads, and spreads greater than one dollar. In addition, the trades are screened for outliers using a filter that removes prices that differed by more than 10% from the last prices, i.e.,

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10 Chen and Chung

3. RESEARCH METHODOLOGY 3.1. Measurement of Price Discovery

For those securities trading in multiple venues, price discovery plays an impor-tant role in determining the dominant market by identifying new equilibrium prices. Within the prior literature on common factor models, two popular approaches have emerged within the investigation of the mechanics of price discovery: the PT model discussed by Gonzalo and Granger (1995), and the ‘information shares’ (IS) model developed by Hasbrouck (1995). Although both models are based on the ‘vector error correction model’ (VECM), different def-initions of price discovery are adopted in each model.

The PT and IS models have attracted considerable attention within the lit-erature, where the relationships and differences between the two models have been discussed at length. The Gonzalo and Granger (1995) model focuses on the common factor components and the process of error correction, whereas the Hasbrouck (1995) model considers the contribution of each market to the variance in the innovations to the common factor. For an overview of the vari-ous price-discovery issues, refer to Baillie, Booth, Tse, and Zabotina (2002), Hasbrouck (2002), de Jong (2002), Lehmann (2002) and Harris, McInish and Wood (2002a, 2002b).

These two models are directly related and provide similar results if the residuals are uncorrelated between markets; however, they typically provide quite diverse results in those cases where there is substantive correlation. Numerous studies have adopted the two models as the means of examining the price-discovery contribution from closely related markets (see Booth, So, & Tse, 1999; Chu et al., 1999; Hasbrouck, 2003; So & Tse, 2004). The analysis is based on the information share approach which requires the estimation of the VECM. According to Engle and Granger (1987), the representation of the VECM can be shown as follows:

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where ; Yt is an n 1 vector of cointegrated prices;

Ai represent n n matrices of autoregressive coefﬁcients; k is the number of

lags; zt1  bYt1is an (n – 1) 1 vector of error correction terms; a is an n

(n – 1) matrix of adjustment coefficients; and t is an n 1 vector of price

innovations.

The coefﬁcient a’s of the error correction term measure the price reaction to the deviation from the long-run equilibrium relationship. The current study

Yt1 abYt1 azt1 ¢Yt m Yt1 a k i1 A_i¢Y_t_i e_t 692

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follows Hasbrouck (1995, 2003) for the deﬁnition of zt; if there are n

securi-ties, then there are n – 1 linearly independent differences, and thus, zt can be

deﬁned as:

(2) 3.1.1 Measurement of permanent-transitory (PT)

decomposition

The Gonzalo and Granger (1995) study focuses on the error correction process, which involves only permanent (as opposed to transitory) shocks resulting in disequilibrium. The measure is based on the PT decomposition, where the permanent component is assumed to be a linear function of the orig-inal series. The PT model measures the contribution to the common factor for each market, where the contribution is deﬁned as a function of the error cor-rection coefficients of the markets. Stock and Watson (1988) demonstrated that the price vector can be decomposed into permanent and transitory compo-nents. Accordingly, the common trend of the price series is as follows:

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where ft is the common factor, and Gt is the transitory component that has

no permanent impact on Yt. Gonzalo and Granger (1995) decompose the

common factor ft into a linear combination of the prices, in which

, where is the common factor coefﬁcient vector,

are normalized so that their sum is equal to 1, and the coefﬁcients of ican be

interpreted as portfolio weights (de Jong, 2002). In this study, we follow the

approach proposed by Gonzalo and Ng (2001) for the estimation of a⬜and b⬜.10

Brieﬂy, the common factor framework provides an opportunity to examine the extent to which each market is involved in the price-discovery process, with the advantage of the Gonzalo and Granger (1995) model being that the common factor estimates are identiﬁed exactly, since they are not dependent on the ordering of the variables. However, the common factor weights may be negative for each estimated VECM.

3.1.2. Measurement of information share (IS)

The IS model measures the relative contribution of each market to this vari-ance; this contribution is then referred to as the information share of that par-ticular market. The process of price discovery is analyzed using the Hasbrouck

ft Yt (a⬜b⬜)1a⬜Yt

Yt ft Gt

zt [(Y1t Y2t) (Y1t Y3t)] . . . (Y1t Ynt)]

10_{Gonzalo and Ng (2001) provide three methods for the calculation of a}

⬜. The method used in the current study is to calculate the eigenvector associated with the smallest eigenvalues of the matrix aa; this eigenvec-tor is the estimaeigenvec-tor of a_⬜. Furthermore, from the deﬁnition of z_t, b_⬜ I , where I is an n 1 vector of ones.

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12 Chen and Chung

(1995) model, which calculates ‘information shares’ as the relative contribu-tions of the variance of a security to the overall variance in the innovacontribu-tions of the unobservable efﬁcient price. According to Hasbrouck (1995), the efﬁcient

price, vt, follows a random walk: vt  vt1 ut. The observed prices of several

cointegrated markets contain the same random walk component, as well as components incorporating the effects of market friction.

In contrast to the PT model, Hasbrouck (1995) transforms the VECM into a vector moving average (VMA) model, which is represented as follows:

(4) along with its integrated form:

(5)

where Yt is the vector of the price series; t is a zero-mean vector of serially

uncorrelated innovations with covariance matrix , such that is the

vari-ance in it, and rijis the correlation between itand jt. Furthermore, t is a column

vector of ones, c is a row vector, and c(L) and c*(L) are matrix polynomials in the lag operator L.

Hasbrouck (1995) notes that the common factor innovation in Equation

(5) is the increment, c t, with the price change component permanently

impounded into the price. He demonstrates that Equation (5) is closely related to Equation (3). In addition, he further decomposes the variance in the

inno-vations in the common factor, Var(c t) c c, and deﬁnes the information

share of a trading center as the proportion of Var(c t) attributable to the

inno-vations in that market.

Hasbrouck (1995) uses the Cholesky factorization of FF to eliminate the contemporaneous relationship, where F is a lower triangular matrix. The information shares are then given as:

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where [cF]_jis the jth _{element of the row of matrix cF.}11 _{The contribution to}

price discovery by a particular market is measured as its relative contribution to the variance of the innovation in the common trend.

ISj ([cF]j)2 c c , j 1, 2, . . . , n s2_i Yt Y0 c(1) a t i1 e_i c*(L)e_t ¢Yt  c(L)et

11_{It should be further noted that Baillie et al. (2002) present evidence of the existence of an important} rela-tionship between c(c1, c₂, . . . , c_n) and (g1, g₂, . . . , g_n), i.e., c_i/c_j, gi/gj. This relationship is

sub-stituted into Equation (6) to calculate the information share. 694

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Baillie et al. (2002) demonstrate a simpler method of calculating informa-tion shares directly from the VECM results without obtaining the VMA repre-sentation, with the calculations of information share based on the VECM method. The upper and lower bounds of the information share of a market will, however, become apparent when the variables are given different orderings, with the largest (smallest) information share value occurring when the variable is ﬁrst (last) in a sequence, assuming that the cross-correlation, r, is positive. This relationship also indicates that the higher the correlation, the greater (smaller) the upper (lower) bound. Baillie et al. (2002) therefore propose the use of the mean of the bounds to resolve such interpretational ambiguity. 3.1.3 Measurement of Modiﬁed Information

Share (MIS)

The results of the information shares are typically dependent on the ordering of the variables in the Cholesky factorization of the innovation covariance matrix. The ﬁrst (last) variable in the ordering tends to have a higher (lower) information share, with this discrepancy potentially being substantial if the innovations of the series are highly and contemporaneously correlated.

Lien and Shrestha (2009) propose a MIS approach that leads to a unique measure of price discovery, as opposed to upper and lower IS bounds. When adopting the MIS model, it is suggested that the factorization matrix (based on the correlation matrix) be used. Lien and Shrestha (2009) further deﬁne as representing the innovation correlation matrix and as representing the diag-onal matrix, with the diagdiag-onal elements being the eigenvalues of the correla-tion matrix , where the corresponding eigenvectors are given by the columns of matrix G. In addition, V is a diagonal matrix containing the innovation

stan-dard deviations on the diagonal—that is, V diag( ). Lien

and Shrestha (2009) subsequently transform F* [G1/2 GV1]1 from

 F*(F*). Under this factor structure, the MIS is given by:

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where c* cF*. Under this new factor structure, Lien and Shrestha (2009)

show that the resultant IS are independent of ordering, which leads to a meas-ure of price discovery that is order invariant, but not unique. Based on their use of the square-root matrix, they indicate that this solves the problem of the lack of uniqueness. In addition, they also show that the MIS measure outper-forms both the IS measure and the PT measure.

IS*j

c*j2

c c

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14 Chen and Chung

3.2. Regression Model

The empirical methodologies have thus far tended to focus on the contribution of SPDRs to price discovery; however, the change in price discovery for SPDRs may have been affected by changes in market factors beyond the introduction of SPDR options. Thus, we follow Chakravaty et al. (2004) and Ates and Wang (2005) to control for other factors, by ﬁrst of all examining the change in the market liquidity of SPDRs. This study also adopts the market quality index (MQI), which, according to Bollen and Whaley (1998), is deﬁned as the ratio of the average share depth at the prevailing bid and ask price quotes to the per-centage quoted spread:

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where Paskis the ask price, Pbidis the bid price, Qaskis the depth at ask, and Qbid

is the depth at bid.

Bollen and Whaley (1998) use this measure to consider changes in the trade-off between the quoted spread and market depth; as such, the MQI rep-resents a measure of market liquidity. Following the introduction of SPDR options, any inferences to improvements in the contribution made to price dis-covery by SPDRs may well be affected by changes in market liquidity over the sample period. Therefore, this study follows Bollen and Whaley (1998) by adopting a dummy variable, along with trading volume and market volatility, all of which are employed as control variables in order to determine the improve-ments in the market liquidity of SPDRs as a direct result of the introduction of SPDR options. We investigate the change in the MQI following the introduc-tion of SPDR opintroduc-tions using a regression model as defined in the following equation:

(9)

where t denotes the daily time interval; MQIt is the market quality index of

SPDRs during trading day t; is a dummy variable that is equal to 0 for

those options in the pre-listing period, and 1 thereafter; Voltis the trading

vol-ume of SPDRs during trading day t and st is the Parkinson (1980) extreme

value estimator that proxies for the volatility of the S&P 500 index market. According to the arguments of Stoll (1978) and Bollen and Whaley (1998), a higher daily trading volume will lead to a lower margin requirement by market makers to cover the ﬁxed costs of their operations due to the faster transaction time rates. Furthermore, greater volatility will lead to a greater like-lihood of an adverse price move during the time that the stock is in the market maker’s inventory, resulting in a greater spread. Therefore, it is expected that in

DOpt

t

log(MQIt) a0 a1DOptt a2log(Volt) a3st et

MQI (Qbid Qask)兾2

(Pask Pbid)兾[(Pask Pbid)兾2]

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Equation (9), the coefﬁcients on both the dummy variable and trading volume will be positive, whereas the coefﬁcient on volatility will be negative.

This study also investigates the change in price discovery for SPDRs. Chakravaty et al. (2004) argue that price discovery is related to trading volume, spread and volatility. We can consider the change in the level of price discovery after the introduction of derivatives by using a regression model, as deﬁned in the following equation:

(10)

where t denotes the daily time interval; PDtdenotes the daily share of

informa-tion for the SPDRs measured by the PT, IS and MIS models for SPDR trades

on an venue and compared with E-mini futures prices, is a dummy

variable that is equal to 0 for those options in the pre-listing period, and

1 thereafter; log(Volt兾Volt1) is the rate of change in the trading volume of

SPDRs during trading day t; and stis the Parkinson (1980) extreme value

esti-mator that proxies for the volatility of the S&P 500 index market.

In order to provide additional support for the argument that the improve-ment in the contribution of SPDRs to price discovery is caused by enhance-ments to market liquidity, the MQI is added into Equation (10) and deﬁned as follows:

(11)

where MQIt is the market quality index for SPDRs during trading day t. The

dummy variable is also included in the regression to test for the structural

shift in the level of price discovery following the introduction of SPDR options. Since both market liquidity and price discovery may be determined

simultane-ously following the introduction of SPDR options,12_{Equation (11) is estimated}

using the two-stage least-squares (2SLS) approach, which employs the lagged MQI, lagged market volatility, and previous day’s trading volume as the instru-ment variables for the MQI.

A significantly positive coefficient on the dummy variable is expected prior to considering the MQI variable. If market liquidity improves as a result of the intro-duction of SPDR options, then this indicates a reintro-duction in market impact costs; as such, any significantly positive coefficient on the dummy variable will be dilut-ed due to the rising liquidity after considering the MQI variable. A significantly positive coefficient on the rate of change in trading volume is also expected.

DOpt

t

PDt b0 b1DOptt b2log(Volt兾Volt1) b3st b4log(MQIt) et

DOpt

t

PDt b0 b1DOptt b2log(Volt兾Volt1) b3st et

12_{Bloomﬁeld, O’Hara, and Saar (2005) explain why electronic markets can endogenously create liquidity} even in the presence of information asymmetry. They show that informed traders take liquidity when the value of their information is high and provide liquidity when the value of their information is low. As such, the improvement in liquidity also implies the possibility that more informed traders are participating in the SPDR market since the introduction of SPDR options.

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16 Chen and Chung

Regarding the impact of market volatility on price discovery, it is argued in some prior studies (see Capelle-Blancard, 2001; Chakravaty et al., 2004; Chen & Gau, 2009) that in those cases where there is a higher level of uncertainty in the underlying market, a greater (lesser) share of information will be found in the underlying market (derivatives market). Ates and Wang (2005) further argue that E-mini index futures make a larger contribution to price discovery during periods of high volatility than during periods of low volatility. Nevertheless, Kawaller, Koch, and Koch (1987) suggest that one of the primary reasons for the existence of informed traders is the leverage effect, whilst trad-ing hours of E-mini futures contracts are virtually 24 hours per day. This study argues that the leverage effect will be signiﬁcantly higher for informed traders during high-volatility periods. Therefore, a signiﬁcantly negative relationship between the information share of SPDRs and market volatility is expected

4. EMPIRICAL RESULTS 4.1. Summary Statistics

The changes in the liquidity of SPDRs surrounding the introduction of SPDR options are reported in Table II, which shows that not all of the trading centers experience improvements in terms of the liquidity measures (spread and depth). In the second period, the MQI measure, calculated as the ratio between half quoted depth and percentage quoted spread, is enhanced in all four exchanges, which is consistent with Kumar et al. (1998) and de Jong et al. (2006), in that the introduction of options improves the market quality of the underlying securities.

As argued above, higher liquidity indicates a lower market impact cost within the transaction costs as a whole. Accordingly, the study infers that improvements in market liquidity will lead to an increase in the contribution of SPDRs to the overall process of price discovery in the S&P 500 index market.

4.2. Price Discovery Analyses in the SPDR and Futures Markets

4.2.1. Price discovery in the SPDR market

According to the trading cost hypothesis, an asset with lower trading costs will tend to lead in the price-discovery process; this hypothesis implies that a reduc-tion in transacreduc-tion costs will improve the contribureduc-tion to price discovery. Based on the literature review provided above, it is evident that following the intro-duction of SPDR options, there has been an increase in the MQI of SPDRs. Therefore, this section examines which trading center plays the most important

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T

ABLE II

Summary Statistics of SPDRs

Relative

Market

National Best Bid and

Quoted Difference Quality Offer (NBBO) Quoted Depth Difference Quoted Spread (t-statistic) Index No. of Quotes % ( 100 Shares) (t-statistic) Spread (%) (%) (MQI) A: F irst period (F ebruary 25, 2004–J

anuary 7, 2005, 220 trading days)

(AMEX) 1,478,061 3.03 57.75 – 0.0391 0.0346 – 11.51 123,738 0.25 13.90 – 0.2663 0.2356 – 0 .47 7,673,102 15.74 373.45 – 0.0238 0.0210 – 133.12 298,037 0.61 9.99 – 0.2199 0.1960 – 0 .40 2,174,01 1 4 .46 1038.89 – 0.0365 0.0322 – 168.61 (Paciﬁc) 20,828,224 42.74 386.70 – 0.0149 0.0131 – 139.26 (NASDAQ) 15,923,861 32.67 214.97 – 0.0360 0.0318 – 34.72 226,422 0.46 495.44 – 0.0590 0.0522 – 61.31 11,539 0.02 22.02 – 0.3286 0.2916 – 0 .79 48,736,995 100.00 344.79 – 0.0270 0.0239 – 99.98

anuary 10, 2005–November 23, 2005, 220 trading days)

(AMEX) 1,805,107 2.50 78.65 20.86*** 0.0361 0.0301 0.0045*** 15.69 117,624 0.16 12.37 1.53*** 0.2755 0.2302 0.0054*** 0.46 9,053,010 12.55 478.52 105.06*** 0.0198 0.0165 0.0045*** 180.92 1,047,664 1.45 56.15 46.17*** 0.1015 0.0841 0.1 119*** 6.76 2,289,504 3.17 383.48 655.40*** 0.0414 0.0345 0.0023*** 56.88 –1 (Paciﬁc) 21,319,619 29.56 628.68 241.96*** 0.0173 0.0145 0.0014*** 206.02 (NASDAQ) 36,255,265 50.27 166.49 48.47*** 0.0238 0.0198 0.01 19*** 41.69 234,942 0.33 597.12 101.60*** 0.0561 0.0470 0.0052*** 81.64 72,122,735 100.00 346.52 1.73*** 0.0239 0.0199 0.0040*** 107.13

The quoted depth (QD) is calculated as (

Qbid

Qask

) and the quoted spread is calculated as (

Pask

Pbid

), where

Qask

is the depth at ask,

Qbid

is the depth at bid,

Pbid

is the bid price.

The relative quoted spread (PQS) is calculated as [(

Pask – Pbid )/ M ], and the MQI is calculated as [QD/2/100]/[PQS 100], where M

is the midpoint of the bid and ask

ference refers to the dif

ference in quoted depth, relative quoted spread and

MQI

between the second and ﬁrst periods for each SPDR trading center

ference for the traditional

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18 Chen and Chung

role in the SPDR price-discovery process both before and after the introduc-tion of SPDR opintroduc-tions. Price discovery is modeled in this study using one-sec-ond resolution, with lagged terms of up to five minutes, as in Hasbrouck (2003). The trade (quote) price is set as the last sale price (prevailing quote midpoint) at the end of the second period. We also follow the suggestion of Hasbrouck (2003) for the computation of the daily common factor weight, information share and MIS measures.

In order to analyze the change in the contribution of SPDRs to price dis-covery after the introduction of SPDR options, we ﬁrst examine price disdis-covery of the S&P 500 ETF market on the four venues—AMEX, Island ECN, ArcaEx ECN and NASDAQ. As shown in Table I, these four venues account for 96.52% (97.94%) of all transactions and 92.99% (95.37%) of the total volume in the ﬁrst (second) period. Therefore, the analysis of the price discovery for SPDRs focuses on these four venues; the remaining exchanges, which account for less than 5% of all transactions, are excluded from the analysis. Although Tse et al. (2006) indicate that ArcaEx accounts for most of the price discovery for SPDRs, duplicating the analysis based on the inclusion of the periods before and after the introduction of SPDR options assists in ensuring the com-pleteness and robustness of this study.

The results of the examination of price discovery in SPDR trades for these four venues are reported in Table III, with Panel A1 showing that the correla-tion coefficients between the different trading venues are very low, with the exception of the Island and ArcaEx ECNs, where the coefﬁcient is 0.290.

The price-discovery results using the PT, IS and MIS models are reported in Panel A2 of Table III, from which we can see that in the ﬁrst period, ArcaEx accounts for 56.6% of the price discovery in the PT model, 58.9% in the IS model, and 59.4% in the MIS model, contributions that are much higher than those of any of the other venues. A similar result is also shown in Panel B2 of Table III, again indicating that ArcaEx accounts for most of the price discovery for SPDRs in the second period. These results are consistent with the ﬁndings of Tse et al. (2006), that in the price discovery of SPDRs, the ArcaEx ECN

dominates all of the other venues.13 _{This result also implies that informed}

traders still favor the ETF electronic trading platform following the introduc-tion of SPDR opintroduc-tions trading.

13_{In September 2002, the Island ECN stopped displaying its limit order book in the three most active ETFs} where it was the dominant venue. When Island chose to redisplay its quotes about a year later, it was no longer a dominant player. Hendershott and Jones (2005a) indicate that at the same time ArcaEx reduced its fees, improved its technology and discontinued the practice of ‘sub-penny’ trading, all of which led to improvements in its market share in ETFs, which ultimately resulted in ArcaEx becoming a formidable com-petitor in the subsequent period. Hendershott and Jones (2005a) and Tse et al. (2006) also show that ArcaEx has proven to be a signiﬁcant contributor within the overall the process of price discovery.

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4.2.2. Price discovery for SPDRs versus futures

The price-discovery results for the SPDR and futures markets using the PT, IS and MIS models are reported in Table IV. We use the SPDR trade prices from the AMEX, Island ECN, ArcaEx ECN and NASDAQ for our analysis of the SPDR market.

The results of the PT model indicate that relative to the other markets, ArcaEx is quite dominant, with a significant contribution to the price-discovery process of 36.5% (37.2%) in the first (second) period. In contrast, the results of the IS and MIS models indicate that E-mini futures are more dominant, con-tributing approximately 43% (40%) to the price-discovery process in the first (second) period.

Although there are obvious differences in the results obtained from the various models, when comparing the results for the first period with those

TABLE III

Analysis of Price Discovery in the SPDR Markets

AMEX Island ArcaEx NASDAQ

Panel A: First period (February 25, 2004–January 7, 2005, 220 trading days) Panel A1: Disturbance correlation matrix

AMEX 1.000 0.007 0.008 0.003

Island 0.007 1.000 0.290 0.034

ArcaEx 0.008 0.290 1.000 0.045

NASDAQ 0.003 0.034 0.045 1.000

Panel A2: Price-discovery measures

PT model 0.062 0.322 0.566 0.050

IS model 0.022 0.363 0.589 0.026

MIS model 0.022 0.359 0.594 0.025

Panel B: Second period (January 10, 2005–November 23, 2005, 220 trading days) Panel B1: Disturbance correlation matrix

AMEX 1.000 0.014 0.013 0.004

Island 0.014 1.000 0.276 0.086

ArcaEx 0.013 0.276 1.000 0.157

NASDAQ 0.004 0.086 0.157 1.000

Panel B2: Price-discovery measures

PT model 0.075 0.298 0.548 0.079

IS model 0.023 0.293 0.607 0.076

MIS model 0.023 0.289 0.615 0.073

Note. The results for trade price discovery using the common factor (PT), information share (IS) and modiﬁed information share (MIS) models are reported for the AMEX, Island, ArcaEx and NASDAQ. The statistics are based on a VECM of prices for S&P 500 index securities that are estimated as one-second resolution data. The models are estimated for each day during our sample period (from February 25, 2004 to November 23, 2005, for a total of 440 trading days). The ﬁgures throughout the table are the means of the daily estimates. Panels A1 and B1 show the residual correlation matrices of the VECM, whereas Panels A2 and B2 present the daily measures of price discovery.

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20 Chen and Chung

for the second period, the contribution made by SPDRs to price discovery within the S&P 500 index market is clearly enhanced by those SPDRs traded on the ArcaEx ECN. This result provides support for the argument that the introduc-tion of SPDR opintroduc-tions has helped to improve the contribuintroduc-tion made by SPDRs to price discovery as a whole within the S&P 500 index market.

The price-discovery results on the SPDR trade and quote prices in the ArcaEx ECN, the regular futures market and the E-mini futures market are depicted in Table V; these results are provided in order to check the robustness

TABLE IV

Analysis of Price Discovery in the SPDR and Futures Markets Based on a Comparison Between SPDR and Futures Trades

AMEX Island ArcaEx NASDAQ Regular Futures E-mini Futures

AMEX 1.000 0.005 0.004 0.003 0.003 0.002 Island 0.005 1.000 0.263 0.032 0.011 0.099 ArcaEx 0.004 0.263 1.000 0.042 0.014 0.122 NASDAQ 0.003 0.032 0.042 1.000 0.002 0.012 Regular futures 0.003 0.011 0.014 0.002 1.000 0.027 E-mini futures 0.002 0.099 0.122 0.012 0.027 1.000

PT model 0.060 0.219 0.365 0.048 0.114 0.193

IS model 0.018 0.195 0.293 0.021 0.041 0.432

MIS model 0.018 0.193 0.293 0.021 0.041 0.434

AMEX 1.000 0.010 0.008 0.002 0.007 0.006 Island 0.010 1.000 0.249 0.076 0.014 0.092 ArcaEx 0.008 0.249 1.000 0.144 0.014 0.136 NASDAQ 0.002 0.076 0.144 1.000 0.004 0.053 Regular futures 0.007 0.014 0.014 0.004 1.000 0.024 E-mini futures 0.006 0.092 0.136 0.053 0.024 1.000

PT model 0.071 0.204 0.372 0.061 0.115 0.178

IS model 0.023 0.160 0.332 0.048 0.038 0.400

MIS model 0.023 0.157 0.335 0.046 0.038 0.402

Note. The results of trade price discovery using the common factor (PT), information share (IS) and modiﬁed information share (MIS) models are reported for the AMEX, Island, ArcaEx and NASDAQ. The statistics are based on a VECM of prices for S&P 500 index securities that are estimated as one-second resolution data. The models are estimated for each day during our sample period (from February 25, 2004 to November 23, 2005, for a total of 440 trading days). The ﬁgures throughout the table are the means of the daily estimates. Panels A1 and B1 show the residual correlation matrices of the VECM, whereas Panels A2 and B2 present the daily measures of price discovery.

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of the empirical results and to facilitate a comparative analysis with that of the

results obtained by the prior studies (Hasbrouck, 2003; Tse et al., 2006).14

First of all, Table V shows that the contribution to price discovery by SPDR trade prices improves signiﬁcantly in the ArcaEx ECN. This result also provides support for the argument of an increase in the contribution of SPDRs

14_{This study also examines the price-discovery results on the SPDR trade and quote prices in the other three} venues (AMEX, Island ECN, and NASDAQ), and find that they are similar to those from the ArcaEx ECN. In addition, the distribution of the contribution to price discovery in the AMEX is also found to be very sim-ilar to that reported by Hasbrouck (2003) and Tse et al. (2006). Therefore, these results reemphasize the sig-nificant contribution made by SPDRs to price discovery within the S&P 500 index market after the intro-duction of SPDR options. Consistent with the findings of Huang (2002), the Island and ArcaEx quotes also play an important role in the price-discovery process for SPDRs. In the interests of space, this paper only reports the results pertaining to the ArcaEx ECN.

TABLE V

Analysis of Price Discovery in the SPDR Markets Based on a Comparison Between ArcaEx SPDR Trades and Quotes and Regular and E-mini Futures Prices

ArcaEx Quote ArcaEx Trade Regular Futures E-mini Futures

Midpoint Price Prices Prices

ArcaEx quote midpoint 1.000 0.322 0.014 0.155

ArcaEx trade price 0.322 1.000 0.008 0.101

Regular futures price 0.014 0.008 1.000 0.023

E-mini futures price 0.155 0.101 0.023 1.000

PT model 0.560 0.198 0.095 0.147

IS model 0.450 0.170 0.035 0.345

MIS model 0.457 0.161 0.035 0.346

ArcaEx quote midpoint 1.000 0.264 0.018 0.127

ArcaEx trade price 0.264 1.000 0.011 0.128

Regular futures price 0.018 0.011 1.000 0.022

E-mini futures price 0.127 0.128 0.022 1.000

PT model 0.481 0.272 0.097 0.150

IS model 0.333 0.266 0.035 0.366

MIS model 0.335 0.263 0.035 0.368

Note. The results of trade price discovery using the common factor (PT), information share (IS) and modiﬁed information share (MIS) models are reported for SPDR trades and quotes on the ArcaEx and compared with regular and E-mini futures prices. The sta-tistics are based on a VECM of prices for S&P 500 index securities that are estimated as one-second resolution data. The models are estimated for each day during our sample period (from February 25, 2004 to November 23, 2005, for a total of 440 trading days). The ﬁgures throughout the table are the means of the daily estimates. Panels A1 and B1 show the residual correlation matrices of the VECM, whereas Panels A2 and B2 present the daily measures of price discovery.

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22 Chen and Chung

to price discovery following the introduction of SPDR options. Furthermore, the results in Panel A of Table V are similar with the results reported in Tse et al. (2006), where an investigation was undertaken into the price discovery in the ArcaEx ECN between May and July 2004.

According to the prior studies (Chu et al., 1999; Hasbrouck, 2003; Tse et al, 2006), S&P 500 index E-mini futures dominate the price-discovery process within the S&P 500 index market. In order to demonstrate the enhanced con-tribution to price discovery made by SPDRs relative to E-mini futures following the introduction of SPDR options, this study further compares the SPDR trades for each venue (AMEX, Island, ArcaEx and NASDAQ) with the prices of E-mini futures. The results for the PT, IS and MIS models are reported in Table VI.

Firstly, the contribution made to price discovery by SPDRs is found to have improved in all four venues following the introduction of SPDR options. Second, the results on the Island and ArcaEx ECNs from the PT model reveal that the weights of the common factor coefﬁcients are greater than 50%, there-by indicating that as compared with E-mini futures prices, SPDR trades may have become dominant in the overall process of price discovery, particularly with regard to the ArcaEx ECN in the second period. These results reveal that the introduction of SPDR options has enhanced the contribution made by SPDRs to the overall process of price discovery.

TABLE VI

Analysis of Price Discovery Based on a Comparison Between AMEX, Island, ArcaEx and NASDAQ SPDR Trades and E-mini Futures Prices

AMEX vs. E-mini Island vs. E-mini ArcaEx vs. E-mini NASDAQ vs. E-mini

Futures Futures Futures Futures

Panel A: First period (February 25, 2004–January 7, 2005, 220 trading days)

PT model 0.236 0.590 0.689 0.197

IS model 0.047 0.379 0.458 0.048

MIS model 0.047 0.378 0.457 0.048

Panel B: Second period (January 10, 2005–November 23, 2005, 220 trading days)

PT model 0.282 0.615 0.703 0.321

IS model 0.075 0.386 0.499 0.152

MIS model 0.074 0.386 0.499 0.151

Note. The results of trade price discovery using the common factor (PT), information share (IS) and modiﬁed information share (MIS) models are reported for SPDR trades on the AMEX, Island, ArcaEx and NASDAQ and compared with E-mini futures prices. The trade prices are collected at one-second intervals, with the models estimated for each day during our sample period (from February 25, 2004 to November 23, 2005, for a total of 440 trading days). The ﬁgures throughout the table are the means of the daily estimates.

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4.3. Regression Analyses of Market Liquidity and Price Discovery

Following the introduction of SPDR options, any inferences on improvements in the contribution made to price discovery by SPDRs may well be affected by changes in market liquidity over the sample period. Therefore, we follow Bollen and Whaley (1998) to adopt a dummy variable, along with trading volume and market volatility, all of which are employed as control variables in order to determine the improvements in the market liquidity of SPDRs as a direct result of the introduction of SPDR options.

The regression results are shown in Table VII, which depicts that all of the coefficients on the dummy variable are significantly positive, indicating that the market liquidity of SPDRs is significantly enhanced in all the four venues as a result of the introduction of SPDR options. Furthermore, the impacts on the market liquidity of SPDRs from both trading volume and mar-ket volatility are found to be consistent with the arguments of Bollen and Whaley (1998), in that greater price variability or a lower trading volume results in a lower MQI.

This study infers that improvements in the contribution made by SPDRs to price discovery are caused by the increase in market liquidity as a direct result of the introduction of SPDR options. Details on the relationship that

TABLE VII

Regression Analyses of Market Liquidity for SPDRs

Variables AMEX Island ArcaEx NASDAQ

DOpt _0.317*** _0.299*** _0.332*** _0.203*** (4.724) (7.376) (7.555) (2.817) Log (Vol) 0.094 0.099* 0.144*** 0.093* (1.296) (1.820) (2.781) (1.868) Volatility 2.692*** 1.990*** 1.829*** 0.923 (3.815) (4.890) (4.252) (1.185) Constant 1.569** 3.875*** 3.432*** 2.448*** (2.073) (6.129) (6.071) (4.518) Adjusted R2 _0.187 _0.400 _0.556 _0.118

Note. Following the introduction of SPDR options, the changes in the MQI are tested based on the following regression model:

where t denotes the daily time interval, MQItrefers to the SPDR market quality index during trading day t, is a dummy variable

that is equal to 0 for options in the pre-listing period, otherwise 1, Voltis the SPDR trading volume during trading day t and stis the

Parkinson (1980) extreme value estimator that proxies for the volatility of the S&P 500 index market. The Newey and West (1987) procedure is used to calculate the consistent standard errors of the regression parameter estimates under a serially correlated and heteroskedastic error process. Figures in parentheses are t-statistics. ***indicates the significance of the traditional t-test at the 1% level; **indicates significance at the 5% level and *indicates significance at the 10% level.

DOpt

t

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24 Chen and Chung

exists between price discovery and the MQI based on the regression analysis are presented in Table VIII. The results of Model (1) in Table VIII-based

upon Equation (10)–reveal that the coefficients on are all positive,

thereby indicating a clear increase in the contribution made to price discov-ery by SPDRs as a result of the introduction of SPDR options.

Relative to all the other trading venues, the ArcaEx ECN is found to be dominant in the price-discovery process, since the results show that the coefﬁ-cient on the dummy variable is signiﬁcantly positive for ArcaEx, thereby imply-ing that the contribution made by SPDRs to price discovery increases as a result of the introduction of SPDR options.

In order to provide support for the argument that this improvement in the contribution of the SPDRs to price discovery is caused by enhancements to market liquidity, the MQI is inserted into Equation (10) to obtain Equation (11). Model (2) in Table VIII shows that the coefﬁcients on the MQI variable reveal signiﬁcant explanatory power offsetting the effect of the dummy variable on the price discovery measures, especially for the ArcaEx ECN. In addition, the new regression models, with the addition of the MQI variable, almost

always present insigniﬁcant constant terms and higher adjusted R2_{values than}

the original regression models. The results listed in Tables VII and VIII clearly demonstrate that the introduction of SPDR options results in improved liquid-ity within the SPDR market, which in turn leads to a substantial rise in the contribution made by SPDRs to the overall process of price discovery. As Bloomﬁeld et al. (2005) point out, results such as these also raise the possibil-ity that informed traders provide more liquidpossibil-ity after the introduction of SPDR options.

The coefficients on the volatility variable are found to be negative, and nearly attain signiﬁcance in Table VIII, a ﬁnding which indicates that informed traders have a preference for trading on the E-mini futures market during peri-ods of high volatility. These results can be seen as providing support for the leverage hypothesis proposed by Kawaller et al. (1987) where during periods of high volatility, informed traders have a preference for using high leverage instruments.

An additional advantage of E-mini futures—the fact that these instru-ments can be traded on an almost 24-hour basis—may also represent a strong attraction for informed traders to trade in the E-mini futures market during periods of high volatility, since this feature offers them the ability to adjust their position at any time. In contrast with Chakravarty et al. (2004), this ﬁnding stresses the importance of the leverage hypothesis on the analysis of price dis-covery in high-volatility periods.

DOpt

t

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T

ABLE VIII

Regression

Analyses of Price Discovery for SPDRs

AMEX Island ArcaEx NASD A Q Model (1) Model (2) Model (1) Model (2) Model (1) Model (2) Model (1)

A: Common factor (PT) model

0.042** 0.029 0.017 0.014 0.009 0.046* 0.1 16*** (2.306) (1.360) (0.958) ( 0.571) (0.638) ( 1.736) (6.304) Vo lt /Vo lt1 ) 0.076** 0.064** 0.046** 0.040** 0.058*** 0.041** 0.018 0.017 (2.478) (2.058) (2.544) (2.334) (3.196) (2.036) (1.092) 0.525** 0.383 1.438*** 1.270*** 0.951*** 0.731*** 1.368*** ( 2.022) ( 1.391) ( 5.463) ( 4.747) ( 3.959) ( 2.784) ( 6.376) MQI ) – 0.044 – 0.095* – 0.140** – – (1.295) – (1.928) – (2.286) – 0.283*** 0.167* 0.717*** 0.239 0.773*** 0.066 0.318*** (10.531) (1.810) (28.876) (0.975) (35.222) (0.212) (13.236) R 2 0.033 0.037 0.082 0.1 10 0.042 0.075 0.196 0.026*** 0.022** 0.001 0.024 0.036* 0.035 0.101*** (2.639) (2.148) (0.034) ( 0.753) (1.696) ( 0.888) (7.975) Vo lt /Vo lt1 ) 0.047** 0.044** 0.068*** 0.063*** 0.101*** 0.079** 0.019 (2.407) (2.174) (2.772) (2.668) (3.174) (2.309) (1.442) 0.242** 0.201* 1.059*** 0.924*** 0.917*** 0.632* 0.465*** ( 2.178) ( 1.814) ( 3.467) ( 2.877) ( 2.621) ( 1.692) ( 3.120) MQI ) – 0.013 – 0.076 – 0.181** – – (0.794) – (1.239) – (2.078) – 0.069*** 0.035 0.473*** 0.090 0.539*** 0.376 0.089*** (5.814) (0.825) (14.947) (0.291) (15.681) ( 0.854) (5.932) R 2 0.036 0.036 0.028 0.042 0.027 0.047 0.194 (Continued

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T ABLE VIII (Continued ) AMEX Island ArcaEx NASD A Q P

anel C: Modiﬁed information share (MIS) model

D Opt 0.026*** 0.022** 0.001 0.024 0.036* 0.035 0.100*** 0.099*** (2.633) (2.143) (0.039) ( 0.751) (1.697) ( 0.885) (7.931) (7.397) Log ( Vo lt /Vo lt 1 ) 0.047** 0.044** 0.068*** 0.063*** 0.102*** 0.080** 0.019 0.019 (2.407) (2.174) (2.762) (2.657) (3.176) (2.313) (1.438) (1.407) V olatility 0.242** 0.200* 1.067*** 0.931*** 0.929*** 0.642* 0.464*** 0.462*** ( 2.177) ( 1.813) ( 3.473) ( 2.882) ( 2.629) ( 1.702) ( 3.1 15) ( 3.063) Log ( MQI ) – 0.013 – 0.077 – 0.182** – 0.006 – (0.793) – (1.241) – (2.075) – (0.393) Constant 0.069*** 0.035 0.473*** 0.087 0.540*** 0.382 0.089*** 0.070 (5.810) (0.825) (14.856) (0.280) (15.553) ( 0.860) (5.922) (1.281) Adjusted R 2 0.036 0.036 0.028 0.042 0.027 0.047 0.192 0.191 Note:

Following the introduction of SPDR options, the changes in the contribution of SPDRs to price discovery are tested based on the

following regression model (Equation 10):

where

t

indicates the daily time interval,

PD

t

refers to the daily share of information for SPDRs measured by the common factor (PT), information share (IS) and modiﬁed infor

mation share

(MIS) models for SPDR trades on an venue and compared with E-mini futures prices,

is a dummy variable that is equal to 0 for op

tions in the pre-listing period, otherwise 1;

Log( Vo lt /Vo lt 1

) is the rate of change in trading volume for SPDRs during trading day

t

and

st

is the Parkinson (1980) extreme value estimator that proxies for the volatility of the S&P

500

index market. In order to provide support for our argument that the improvement in the contribution of SPDRs to price discovery

is caused by enhancements to market quality

, the MQI is

added into the above equation and deﬁned as follows (Equation 1

1):

where

MQI

t

refers to the SPDR market quality index during trading day

t. Model (2) is estimated by using the two-stage least-squares (2SLS) approach, which uses the lagged

MQI

, lagged

market volatility and the previous day’

s trading volume as the instrument variables for the

MQI

.

The Newey and W

est (1987) procedure is used to calculate the consistent standard errors

of the regression parameter estimates under a serially correlated and heteroskedastic error process. Figures in parentheses are

t

-statistics. ***indicates the signiﬁcance of the traditional

t-test at the 1% level; **indicates signiﬁcance at the 5% level and *indicates signiﬁcance at the 10% level.

PD t b0 b1 D Opt t b2 log (Vol t yV olt 1 ) b3 st b4 log (MQI t ) et D Opt t PD t b0 b1 D Opt t b2 log (Vol t y Vol t 1 ) b3 st et