information asymmetry in warrants and their underlying stocks on the stock exchange of thailand

Journal of Empirical Finance 18 (2011) 474–487

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Journal of Empirical Finance

j ourna l homepage: www.e lsev ie r.com/ locate / jempf in

Information asymmetry in warrants and their underlying stocks on the stockexchange of Thailand☆

Nuttawat Visaltanachoti a, Charlie Charoenwong b, David K. Ding a,c,⁎a School of Economics and Finance, College of Business, Massey University, Auckland, New Zealandb Division of Banking and Finance, Nanyang Business School, Nanyang Technological University, Singapore 639798, Singaporec Department of Finance, Lee Kong Chian School of Business, Singapore Management University, Singapore 178899, Singapore

a r t i c l e i n f o

☆ The authors thank Kee H. Chung, Quentin C. Chu,University, Mahidol University, Massey University, Naneditor) and an anonymous referee were particularly h⁎ Corresponding author at: School of Economics an

fax: +64 9 441 8177.E-mail address: [email protected] (D.K. Ding).

1 Chan et al. (2002) find that informed investors ini(2002) document the impact of market architecture onhavemoved fromNASDAQ to the NYSE or AMEX becaudifferentiating informed traders from liquidity traders

0927-5398/$ – see front matter © 2011 Elsevier B.V.doi:10.1016/j.jempfin.2011.02.001

a b s t r a c t

Article history:Received 26 January 2011Available online 11 March 2011

This paper examines the informational role of warrants based on the unique order data fromthe Stock Exchange of Thailand, where both warrants and stocks are traded under the samemarket structure and where warrants are as liquid as stocks. The estimated probability ofinformed trading (PIN) in warrants is found to be statistically higher than their underlyingstocks regardless of order submission type and order size. The PIN explains a substantialportion of the cross-sectional variation in the opening spread beyond trading volume andminimum tick size. We find evidence that a signed warrant trade contains information aboutthe future stock price and that warrants with a higher PIN have greater predictive powers.

© 2011 Elsevier B.V. All rights reserved.

JEL classification:G14G15

Keywords:Probability of informed trading (PIN)WarrantsInformation asymmetryPrice discoveryThailand

1. Introduction

Onwhichmarketdoes an informed trader exercisehis private information? Inaperfect andcompletemarket,warrantpricing requiresinformationonanunderlying stock's price and its volatility. Theend result is that stock tradesunilaterally drivewarrant trading.However,the reverse does not necessarily hold because a stock's pricing should rightly be driven by its systematic risk independent fromwarranttrading. In an incompletemarketwith frictions, the asset price reflects information that stems from its trading,which canbe influencedbymany factors.Warrants,with their inherentfinancial leverage, are especially attractive to informed traderswhenborrowingopportunitiesare limited. Warrants also allow traders to capitalize on volatility information. On the other hand, uninformed traders are indifferent totrading in warrants or their underlying stocks because their trades are primarily driven by their liquidity imbalance. While leveragedinformedtradersgenerallyprefer trading inwarrantsover stocks, theempirical evidence regarding the informational roleofwarrants thusfar has been inconclusive because other factors such as liquidity and market structure also affect traders' decisions.1

Nattawut Jenwittayaroje, Chandrasekhar Krishnamurti and the seminar participants at the Chulalongkornyang Technological University and Waikato University. The constructive suggestions by Franz C. Palm (theelpful. Any remaining errors are the responsibility of the authors.d Finance, College of Business, Massey University, Auckland, New Zealand. Tel.: +64 9 414 0800x9465

tiate trades on the stock market but not on the options market due to liquidity concerns. Heidle and Huangwhere informed investors trade. They show that the probability of informed trading is lower for stocks thase competing dealers on NASDAQwho could observe only part of the total order flow havemore difficulty inthan specialists on the NYSE.

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475N. Visaltanachoti et al. / Journal of Empirical Finance 18 (2011) 474–487

In this study, we do not encounter the problems faced by past researchers2 who compare stock trading in one market toderivatives trading in another because both stocks and warrants trade under the same market architecture and similar tradingrules on the Stock Exchange of Thailand (SET). The existence of such a market provides an ideal platform for testing the choice ofsecurity and order type and is an important contribution of this paper. Additionally, on the SET, warrants are as liquid as stocks.Thus, security preference is effectively disentangled from liquidity and market architecture preferences. The existence of such amarket provides an ideal platform for testing the informed trader's choice of security.

Weestimate theprobability of informed trading (PIN)basedonfirm-specific private information inwarrants and stocks by extendingthe sequential trading model of Easley et al. (1996), which allows investors to trade both warrants and underlying assets. Similar toAlbuquerque et al. (2008), we distinguish across-firms private information from firm-specific private information so that the cross-sectional order flow dependence among different securities is reflected in the across-firms private information.3 We examine whetherour PIN results are sensitive to the order submission type and order size. In an asymmetric informationmarket, informed traders such ascorporate insiders and thosewith superior informationwouldwant to execute their orders in a timely fashiondue to the short shelf life oftheir information quality. As such, they prefer to submit market orders for their trades. However, limit order traders receive a morefavorable price compared to market order traders. The tradeoff between adverse selection risk, execution probability of the limit order,and the cost of liquidity determines the choice between amarket and limit order. Bloomfield et al. (2005) examine the strategy of tradersbased on experimental asset markets. They show that informed and liquidity traders use both limit and market orders. However, overtime, informed traders change their order submission strategy preferences frommarket orders to limit orders to optimally capitalize ontheir informational advantage by earning profits that result from differences in the true value of the asset and the bid-ask spread. Inaddition, informed traders are likely to maximize their informational benefits by hiding their identity and engaging in medium-sizedtrades (Chakravarty, 2001). Easley et al. (1997b) find that large and small trades contain different information that varies across stocks.Our unique order data allow us to address questions relating to the informational content of order type (market and limit orders) andorder size (large, medium, and small orders).

The goodness of fit of the model indicates that not all orders occur for liquidity reasons and rejects the cross-sectional order flowindependence hypothesis confirming the importance of across-firms order flow impact.4 Our results show that, for a given order, theprobability of informed trader participation in warrants is higher than that in stocks. We show that the PIN is 22% for warrant ordersand 17% for stock orders. In addition, inwarrant trading, informed traders aremore likely to usemarket orders (26%) than limit orders(21%).5 We find evidence that is consistent with the stealth trading proposition, where informed traders hide their identity throughorder splitting. We find that the PIN of a large-sized order is significantly lower than the PIN of a medium-sized order.

We show that the PIN explains a significant amount of the cross-sectional variation in the opening spread — beyond tradingvolume and minimum tick size. This result provides the economic merit of the estimation. When considering stocks and warrantscollectively, the PIN alone significantly explains 43% of the cross-sectional variation in the opening spread while trading volumealone explains only 8%. Taken together, trading volume, PIN, and theminimum tick size explain 62% of the variation in the openingspread. Further investigation reveals that a signed warrant trade carries predictive information about future stock price changes,and that the predictability is stronger for warrants with higher PINs.

This study contributes to both the theoretical and empirical literature. In terms of theoretical contributions, we extend theexisting model developed by Easley et al. (1996) and Albuquerque et al. (2008) and incorporate traders' choices of order types(market or limit order) and security types (underlying stock or warrant) when estimating the probability of informed trading. Theuniqueness of the Stock Exchange of Thailand, where stocks and warrants trade under the same market architecture and rules,provides an excellent opportunity for testing how informed traders choose their order and security types. Our results differ fromthose of Chan et al. (2002) who found that options' net trade volume have no incremental information due to the low liquidity inthe optionsmarket. Our findings complement those of Pan and Poteshman (2006) and support the pooling equilibrium hypothesisof Easley et al. (1998) that warrant trades contain useful information about future stock prices.

The remainder of the paper is organized as follows. Section 2 presents our model and estimation process. Section 3 describesthe institutional background of the SET and our sample selection process. Section 4 presents the empirical estimates and economicvalidation of the estimates. Section 5 summarizes and concludes.

2. Model construction

2.1. Model description

We extend the sequential trade model developed by Easley et al. (1996) to include choices between trading in stocks orwarrants. We take into account the cross-sectional dependence of order flows by distinguishing between firm-specific and across-firms private information. Albuquerque et al. (2008) suggest that across-firms private information induces the abnormal tradingthat occurs consistently across firms in a day, while firm-specific private information is idiosyncratic and leads to trading in that

2 Most of past studies consider the CBOE options and NYSE listed stocks. For instance, see Chan et al. (2002), Pun and Poteshman (2006), and Stephan andWhaley(1990).

3 Theacross-firmsprivate information is similar to the ‘market-wideprivate information’which is extensivelydiscussed inAlbuquerqueetal. (2008). Anearlierversionof this paper does not distinguish between across-firms private information and firm-specific private information. Nevertheless, we find qualitatively similar results.

4 We thank the referee for pointing out the importance of cross-sectional order flow dependence.5 We do not differentiate between near-the-best-quote limit orders and deep-in-the-book limit orders. Bias et al. (1995) discuss the impact of order flow

concentrated near and far away from the quote.

476 N. Visaltanachoti et al. / Journal of Empirical Finance 18 (2011) 474–487

firm alone. The model assumes that all agents are risk neutral and that the arrival of informed and uninformed traders during afinite number of days follow an independent Poisson process. All across-firms and firm-specific private information events areassumed to be independently distributed across various trading periods.6

At the beginning of any trading day, nature determines across-firms and firm-specific events. Informed investors with across-firms private information participate on one side across all stocks and warrants while firm-specific private informed traders takepart on one side in a single stock or warrant. Investors submit their orders over t=1,…,T trading periods, where a trading period isassumed to last for one trading day. A trader has a prior belief regarding the probability of an event, and the learning occurs fromobserving the event. The conditional probability of the observed event incorporates the new information, becomes a new beliefabout the future, and is computed according to Bayes' rule. An event provides a signal regarding the asset's value.When there is nonews, the asset value simply remains at its unconditional level. At the end of a trading period, the asset value fully reflects the newinformation. A similar process applies to the subsequent trading period.

Fig. 1 depicts our model. At the beginning of each period, an across-firms information event occurs with a probability of θand a probability of 1−θ that no across-firms information event occurs. Conditional on an across-firms information arrival,an across-firms low signal occurs with probability ρ while 1−ρ is the probability that an across-firms high signal occurs.Both θ and ρ are constant across different pairs of assets. A firm-specific trading process follows across-firms information. Theprobability of firm i's private information event occurring is αi, and 1−αi is the probability that no private information eventtakes place. Conditional on firm-specific information occurring, δi is the probability of bad news occurring at firm i, and 1−δiis the probability that good news occurs. Unlike the across-firms information parameters (θ and ρ), αi and δi vary acrossdifferent pairs of securities.

At the end of the tree diagram in Fig. 1, we depict the case when traders decide whether to buy or sell warrants and theirunderlying stocks based on the information they possess. Let εi,b and εi,s be the arrival rates of firm i's uninformed buyers andsellers while μi,f and μi,a represent the arrival rates of firm-specific and across-firms (or aggregate) informed traders. Thesuperscripts ‘w’ and ‘c’ denote order submission in warrants and common stocks, respectively. We assume that uninformedtraders may or may not respond to an information event, but informed traders always react only to an information event. Whenacross-firms and firm-specific information events do not occur (box 9 in Fig. 1), all orders come solely from uninformed investors.For example, εi,bw and εi,bc are the arrival rates of an uninformed buyer of warrants and stocks, and similarly, εi,sw and εi,sc are the arrivalrates of uninformed sellers of warrants and stocks.

When there is only a firm-specific information event with no across-firms information event (boxes 7 and 8), informed investorstrade according to the firm-specific signal while uninformed traders always trade regardless of the signal. For instance, informedinvestors (μi,fw and μi,fc ) sell warrants and stocks when the firm-specific signal is low (lines 3 and 4 of box 7). Likewise, when the firm-specific signal is high, informed traders buy warrants and stocks (lines 1 and 2 of box 8). When there is only an across-firmsinformation eventwith nofirm-specific event (boxes 3 and 6), informed traders (μi,aw and μi,ac ) tradewarrants and stocks based on theiracross-firms information. If an across-firms signal is high, informed investors buy the assets (lines 1 and 2 in box 6); following a lowacross-firms signal, informed traders sell warrants and stocks (lines 3 and 4 in box 3).When an across-firms signal is consistentwith afirm-specific-wide signal (boxes 1 and 5), the arrival rates of informed traders inwarrants (μi,fw+μi,aw) and stocks (μi,fc +μi,ac ) comprise ofinformed traders who exploit across-firms and firm-specific private information.

If an across-firms signal is inconsistent with a firm-specific signal (boxes 2 and 4), we assume that informed traders rely on thefirm-specific signal only. This assumption is consistent with the evidence documented by Albuquerque et al. (2008) and Vega(2006) that firm-specific information is likely to be more accurate than across-firms information. In other words, if the firm-specific signal is high when the across-firms signal is low (lines 1 and 2 in box 2), informed traders (μi,fw and μi,fc ) buy warrants andstocks based on the firm-specific signal. In contrast, if the firm-specific signal is low when the across-firms signal is high (lines 3and 4 in box 4), informed traders (μi,fw and μi,fc ) sell warrants and stocks based on the firm-specific signal. To simplify the notation,we leave out the subscript i for all firm-specific probabilities in the remaining sections.

2.2. Model estimation

We use the maximum likelihood technique to estimate the parameters in the model based on observing buy-and-sell orders ofwarrants and stocks per day across I firms during N trading days. We assume that orders arrive continuously and independentlyaccording to known Poisson processes and that the unknown underlying parameters capture constant arrival rates of different tradertypes. The Poisson distribution also assumes that the current event is independent of the prior event. The choice of the Poisson processfollows the suggestions of Albuquerque et al. (2008), and Easley et al. (1996,1997a,b). Let P[q, λ] be a Poisson probability distributionfunction of the orders' arrival. Specifically,

where

6 BecNeverthevent ddifferen

P q;λ½ � = e−λλq= q! ð1Þ

q is the number of observed orders, and λ is a parameter of the trader's arrival rate.

ause assetvolatility exhibits time-dependence, the independencehypothesis of information events across tradingdaysmayappear tobea restrictedassumptioneless, Easley et al. (1997b) examine the independence of information across days. After classifying days based on posterior beliefs at the end of the day into no-ays, good-event days, and bad-event days, they find that private information events are independent across days, as runs in an event day are not statisticallyt from each other by chance. We therefore maintain the assumption of an independent private information event across trading days.

.

Fig. 1. The information structure and trading process for stocks and warrants.


In this study we consider observed orders in two ways: order submission type and order size. With order submission type, aninvestor independently submits either amarketor limit order so the joint probabilityorder arrival is aprobabilityofmarket order arrivalsmultiplied by a probability of limit order arrivals. Similarly, an order size is classified into small, medium and large orders and the jointprobability order arrival is a probability of larger order arrivals multiplied by a probability of medium order arrivals andmultiplied by aprobability of small order arrivals. We consider informed trading by order submission type in Table 3 and by order size in Table 4.

Let P1, P2, …, P9 be the joint probability of observing the buy-and-sell orders of warrants and stocks according to box1,box2, …, box9 in Fig. 1.7 At any day n, the low signal of an across-firms private information event occurs with probability θρ,and its conditional probability of observing the buy-and-sell orders of warrants and stocks with a low across firms signal,LLow, is ∏i=1,..,I [αiδiΡ1+αi(1−δi)Ρ2+(1−αi)P3]. Similarly, a high across-firms signal of a private information event occurswith probability θ(1−ρ), and its conditional probability of observing buy-and-sell orders of warrants and stocks with a highacross-firms signal, LHigh, is ∏i=1,..,I [αiδiΡ4+αi(1−δi)Ρ5+(1−αi)P6]. Also, a day without any across-firms privateinformation event occurs with probability (1−θ), and the conditional probability of observing the buy-and-sell orders ofwarrants and stocks with no across-firms signal, LNo, is ∏i=1,..,I [αiδiΡ7+αi(1−δi)Ρ8+(1−αi)P9].

On any day n, the unconditional likelihood of observing buy-and-sell orders of warrants and stocks is the weighted average ofthe three conditional probabilities abovewith theweights given by the probability of each type of across-firms private informationevent. The likelihood of observing I×N buy-and-sell orders of warrants and stocks is:

7 LetP[Siw,εi,sw

P[Siw,εi,sw

P[Bic,εi,bc

L = ∏n=1;::; N θρLLow + θ 1−ρð ÞLHigh + 1−θð ÞLNoh i

: ð2Þ

Wemaximize the likelihood function in Eq. (2) by imposing independence conditions across trading days to solve for {θ, ρ, αi,δi, εi,bw , εi,bc , εi,sw, εi,sc , μ i,f

w , μi,fc , μ i,aw , μi,ac }i=1,…,I. Easley et al. (1997b) conduct a run test to examine the independence assumption by

classifying days into good-event days, bad-event days, and no-event days based on the implied posterior beliefs at the end of the

Biw, Bic, Siw and Sic be the number of observed buy and sell orders of warrants and stocks in day n. Given independent order submission, P1=Ρ[Biw,εi,bw ]P[Bic,εi,bc ]×+μi,fw+μi,aw]P[Sic,εi,sc +μi,fc +μi,ac ]; P2=Ρ[Biw,εi,bw +μi,fw]P[Bic,εi,bc +μi,fc ]P[Siw,εi,sw]P[Sic,εi,sc ]; P3=Ρ[Biw,εi,bw ]P[Bic,εi,bc ]P[Siw,εi,sw+μi,aw]P[Sic,εi,sc +μi,ac ]; P4=Ρ[Bi

w,εi,bw ] P[Bic,εi,bc ]×

+μi,fw]P[Sic,εi,sc +μi,fc ]; P5=Ρ[Biw,εi,bw +μi,fw+μi,aw ]P[Bi

s,εi,bc +μi,fc +μi,ac ]P[Siw,εi,sw ]P[Sic,εi,sc ]; P6=Ρ[Biw,εi,bw +μi,aw ]P[Bi

c,εi,bc +μi,ac ]P[Snw,εi,sw ]P[Sic,εi,sc ]; P7=Ρ[Biw,εi,bw ]×

]P[Siw,εi,sw +μi,fw]P[Sic,εi,sc +μi,fc ]; P8=Ρ[Biw,εi,bw +μi,fw]P[Bi

c,εi,bc +μi,fc ]P[Siw,εi,sw]P[Sic,εi,sc ]; P9=Ρ[Biw,εi,bw ]P[Bi

c, εi,bc ]P[Siw, εi,sw ]P[Sic,εi,sc ].


day after observing all trades, and they cannot reject the null hypothesis of independent information events of trading days. Allparameters except θ and ρ vary by the firm. The parameters εi,bw , εi,bc , εi,sw, and εi,sc measure the average number of buy-and-sellorders of warrants and stocks for firm i when there is no across-firms and firm-specific private event. This means μi,fw, μi,fc , μi,aw , andμi,ac measure the abnormal number of buy-and-sell orders for warrants and stocks that are driven by firm-specific and across-firms private information.

The likelihood function uses information from I firms and N trading days of warrants and stocks so that there are I×N×2observations for estimating (I×10)+2 parameters. Therefore, there are (2N−10)×I−2 degrees of freedom, and the quality ofthe estimation increases as the number of firms and the number of trading days increase.8 The estimation of firm i's parametersdepend on the estimation of the other parameters as they are linked by the arrival of across-firms information.

It is important to note that the assumption of independence of buy and sell orders across firms does not imply the absence ofconditioning variables that affect eachpair of assets i.9 In fact, eachpair of assets i is cross-sectionally dependent on each other throughthe impact of across-firms factors. Albuquerqueet al. (2008, Page2,297) argue that across-firmsorderflows contain informationaboutco-movement of future firm cash flows and industry or economy-wide business conditions, or aggregate risk premium.

The structural model in Fig. 1 includes conditioning variables through across-firms private information. Without informedtrading, the parameters εi,bw , εi,bc , εi,sw, εi,sc capture the average daily number of buy and sell orders in firm i.With informed trading, theparameters εi,bw , εi,bc , εi,sw, εi,sc still capture the average daily trading. In addition, the parameters μi,fw, and μi,fc measure the abnormalfirm-specific buy or sell orders and μi,aw , and μi,ac allow themodel to capture abnormal trading that occurs consistently across firms ina day. Albuquerque et al. (2008) explain that the across-firms private information model uses the time-series fluctuation in thecross-sectional average across firms' order flow to identify the common parameters such as the probability of an aggregateinformation event arrival, θ, and the probability that the aggregate signal is low, ρ. As a result, order arrivals to each firm are notindependent, and informed investors can use across-firms news that are useful to trading across all firms. The estimation of firm i'sparametersαi, δi, εi,bw , εi,bc , εi,sw, εi,sc , μi,fw, μi,fc , μi,aw , and μi,ac depends on the estimation of the other firms' parameters as they are connectedthrough the arrival of across-firms news.

In this article, we assume independence of information events across trading days. This assumption is widely used in theliterature including Albuquerque et al. (2008) and Easley et al. (1996). In addition, Easley et al. (1997b) show that theindependence hypothesis is a reasonable assumption (see their Table 7, Page 181). Following Easley et al. (1996), we define theprobability of firm-specific information-based trading by the ratio of the arrival rate of informed traders to the arrival rate of alltraders. Hence, firm i's probability of firm-specific informed-based order submission is:

8 Theat least

9 In Emedian

PINi = αiμ i;f = αiμ i;f + εi;b + εi;s� �

ð3Þ

αi is the probability of firm i's specific information event occurring; μi,f is firm i's arrival rate of informed traders for warrants
whereand stocks; and εi,b and εi,s are the arrival rates of uninformed buyers and sellers of firm i.
We estimate {θ, ρ, αi, δi, εi,bw , εi,bc , εi,sw, εi,sc , μi,fw, μi,fc , μi,aw, μi,ac }i=1,…,I jointly across all warrants and stocks of all firms using a constrainedmaximum likelihood shown in Eq. (2). To simplify the optimization process, we transform the probability parameters {θ, ρ, αi, and δi}which are constrained to [0,1] into unconstrained parameters using a logistic function, ψ=1/(1+e−z), where ψ is the originalconstrained parameter and z represents the transformed unconstrained parameters.We transform the constrained arrival rates {εi,bw , εi,bc ,εi,sw, εi,sc , μi,fw, μi,fc , μi,aw, and μi,ac } from non-negative parameters [0, and ∞] to unconstrained parameters using a squared function, ψ=z2.

As a result of a complex, highly non-linear and non-concave likelihood function, a gradient-based optimization technique canyield a local instead of a global solution. To alleviate a local solution problem, we employ the Nelder–Mead simplex direct searchand genetic algorithm combinedwith a random grid search on 10,000 different starting values of parameters {μi,fw, μi,f, μci,av, and μi,ac }.Specifically, the initial values of informed trader arrival rates are random values between 0.1 and 1 multiplied by the differencebetween the maximum daily number of sell orders and the mean number of sell orders. Similar to Albuquerque et al. (2008) andVega (2006), we set the initial values of the arrival of uninformed traders to the mean daily value of buy-and-sell orders and theinitial values of the remaining probability parameters {θ, ρ,αi, and δi} to 0.50 because these probabilities have no priors. We reportthe set of estimated parameters that have the highest likelihood function.

We examine the overall fit of the model by testing the hypothesis that all order submissions occur for liquidity reasons andorders flow independently across-firms. The null hypothesis H0: θ=ρ=αi=δi=μi fw =μi fc =μi aw =μi ac =0, for all firm i, will betested using a likelihood ratio test which has an asymptotic chi-square distribution with 6I+2 degrees of freedom in this case.

3. Data

3.1. Institutional background

The Stock Exchange of Thailand (SET) operates under an automated limit-order trading system called the Automated Systemfor the SET (ASSET). The SET has two trading sessions separated by a two-hour lunch break starting from 10:00 am to 12:30 pm

re are I×N×2observations for estimating (I×10)+2parameters. Our sample consists of 38pairs (I) and at least 60 tradingdays (N) results in (2N−10)I−2 or4178 degrees of freedom.q. (2), the likelihood function implies independence of buy and sell orders across firms. This independence is observed in our sample. The range of theregression R-squares between firm i's and other firms' order flow is relatively low (from 3.6% to 13.7%).

,


and 14:30 pm to 16:30 pm, local time (GMT+07:00). Orders are executed according to price-time priority. The ASSET determinesthe opening price in the morning and afternoon sessions of each security from among all valid orders in the system by a batchsystem. Warrants and stocks are traded in the main board using the same trading rules.10

On the SET, there are three types of traders. Retail traders account for the largest group of traders, 71% when measured by thenumber of shares and 47% by trading value. Foreign traders account for around 23% of the trades by volume and 43% by value. Theremaining trades are represented by local institutional investors. Contrary to those in well-established capital markets, institutionalinvestors account for a very small portion of the total trade volume. Even though foreigners are prohibited from owning the majorityshare in Thai firms, Thai citizens face even greater restrictions in foreign currency and security transactions, including foreign-currencydenominated derivatives. Foreign ownership in Thai firms is restricted to a maximum of 49% of a company, except for banking andinsurance companies where the restriction is capped at 25% but can increase to 49% subject to approval by the Bank of Thailand.11

Foreigners can hold either foreign shares or a Non-Voting Depository Receipt (NVDR). Foreigners who hold NVDRs are eligible fordividends, rights issues, andwarrants only; in the caseof foreign sharesholding, the foreignerswill be entitled todividends, right issues,warrants, andvoting rights. In addition,when the foreignownership limit hasbeen reached, sharesboughton themainboard cannotbesold on the foreign board, but shares bought on the foreign board can be sold on the main board. Hence, most trades involve retailinvestors trading within their group or trading against the foreign institutional investor.

3.2. Sample selection

Easley and O'Hara (1987) report that the occurrence of an event triggers informed trading. Our choice of the SET affords us anideal setting for a natural experiment to take place because warrants are subject to the same trading rules as stocks. Moreover, in1997, warrants are actively traded on the SET, where 940,930 units trade on an average day compared to 823,280 shares of theunderlying stocks. Warrants compared to common stocks were more liquid in 1997 than in other years; five warrants are amongthe top 20 most traded securities in 1997. The extended bearish market from 1998 to 2001 resulted in the negative gearing effectamong warrants and their liquidity relative to liquidity of common stocks fall sharply. In 2010, even though warrants had asubstantial positive gearing when the SET index increased more than 70%, there was no warrant listed in the top 70 most tradedsecurities and only 2 warrants listed in the top 150 most traded securities. Furthermore, the average ratio of total value tradedbetween warrants and common stocks is 46% in 1997 compared to 30% in 2010.

In1997,47warrantswere listedon theSET. Toobtainmeaningful estimatesof theconditional probabilities inour tradingmodel, it isimportant to select only the stocks and warrants that are most actively traded. Each of the identified warrants and their underlyingstocksmust have traded for at least 60 days during the year.12 Information-based tradingwill bemeasuredmore precisely whenmoretrading days are used (Easley et al., 1997a). The final sample consists of 38 warrants and their underlying stocks.

The data set provided by the SET contains all trades and orders of equity securities, including warrants from January 2, 1997 toDecember 31, 1997. From the order file, we obtain the time-stamped order price, order size, and the buy/sell indicator. From thetrade and order files, we can distinguishmarketable limit orders from other limit orders. On the SET, only limit orders are accepted.Hence, effective market orders are limit orders (or marketable limit orders) that, when submitted, can be immediately executedagainst the existing quotes.13 By matching with the order files, we can accurately classify a trade as buyer- (seller-)initiated if thebuy (sell) order is executed against the prevailing offer (bid) quote.14

The profiles of all 38warrants and their underlying stocks traded on the SET are presented in Table 1. Themajority of the stocks andwarrants are from thefinance, banking, andproperty industries.Most of thewarrants havematurities longer thanone year and are out-of-the money as the exercise price is much higher than the underlying stock price. On average, eachwarrant can be exercised for 1.41shares of stock.15 On an average trading day, more units of warrants change hands than shares of the underlying stock (940,930warrants versus 823,280 shares) on the SET. The average stock and warrant prices are 43.28 and 18.26 Baht, respectively.

The cross-sectional statistics of order arrivals for various order types during each trading day are presented in Table 2. Thedaily average number of market (limit) orders is 127.45 (364.39) for stocks, while that for warrants is 143.63 (403.98). As aproportion, limit orders of both stocks and warrants represent about 74% of their respective total orders. In the stock market,there is no statistical difference between buy-and-sell order arrivals of both market and limit orders. Among market ordersof warrants, the number of buy order arrivals is not significantly higher than the number of sell order arrivals; and for limitorders, sell order arrivals are not significantly higher than buy order arrivals. This suggests that there is no imbalance

10 On December 1, 1997, the SET widened a floor and ceiling stock price limit from a range of ±10% to a range of ±30% from the previous day's closing price onthe main board. For warrants, the floor and ceiling price limits are derived from the absolute price limits (in Baht) of the underlying stocks. Our results are robustto the exclusion of the period after December 1, 1997.11 Thailand changed the rules regarding foreign ownership of banks and insurance companies. Under the Financial Institutions Business Act (2008), which cameinto force on August 3, 2008, a foreign bank may now own up to 25% of a Thai bank without approval by the Bank of Thailand, and up to 49% of a Thai banksubject to approval by the Bank of Thailand. Source: Bangkok International Associates website (http://www.bia.co.th/legalupdates/). Nevertheless, currentlythere are a few banks and finance companies with majority foreign ownership because in an attempt to solve a 1997 financial crisis, Bank of Thailand temporarilyallowed Thai banks and finance businesses to be majority foreign owned for a period of up to ten years. After that foreign ownership will be gradually diluted.12 Easley et al. (1996) use 60 trading days to estimate PIN.13 This method of limit order book construction is similar to that used by Kavajecz (1999) for NYSE stocks. Unlike the NYSE, the SET clears all remaining ordersin the system after the market close. Hence, there is no need to estimate the initial balance of the order book at the beginning of each trading day.14 Hence, our estimation of the probability of informed trading does not suffer from trade misclassification bias as documented in Boehmer et al. (2007).15 Since the average exercise ratio is greater than one, the price of a warrant may be greater than that of a stock. Nevertheless, in our sample all warrant pricesare lower than their corresponding stock prices.

http://www.bia.co.th/legalupdates/

Table 1Details of warrants traded on the stock exchange of Thailand.

Industry Company name Exerciseprice (Baht)

Exerciseratio (W:S)

Days tomaturity

Units ofwarrants(millions)

Activetradingdays

Warrantprice (Baht)

Dailywarrantvolume

Stockprice(Baht)

Daily stockvolume

Banking Industrial Fin. Corp. 57.00 1:1.18846 310 59.900 180 8.93 8315.79 38.98 942.33Nakornthon Bank 46.74 1:1.06978 334 21.500 108 10.07 776.20 42.43 74.56Siam City Bank 52.00 1:0.50000 1017 120.000 243 3.56 2818.08 15.17 2622.73Thai Farmer Bank 181.69 1:1.00000 1002 75.000 246 16.69 3908.42 98.95 1957.97

Building Thai German Ceramic 85.00 1:1.00000 827 22.500 246 18.40 88.53 98.95 25.76Thai Gypsum Product 32.00 1:1.00000 1002 13.500 16 2.55 90.66 20.27 67.22Tipco Asphalt 72.00 1:3.62883 729 4.000 24 197.11 6.22 113.80 259.82

Comm. United Communication 391.41 1:1.00406 1225 11.070 224 16.73 657.28 40.17 375.99Energy Banpu 288.00 1:1.00000 683 6.000 68 80.02 14.43 324.05 38.88Finance CMIC Fin. And Sec. 90.00 1:1.00000 1565 31.503 118 11.38 1457.82 20.95 9,35.06

Dhana Siam Fin. 89.87 1:3.62000 665 12.000 246 34.10 1384.09 32.82 2378.35Ekachart Fin. and Sec. 98.74 1:1.60018 867 15.750 173 9.39 1207.25 18.52 121.52Finance One 133.11 1:2.80976 803 24.000 61 18.89 3515.69 23.23 11,087.93General Fin. and Sec. 96.05 1:2.34261 727 5.000 111 21.87 121.07 22.96 1474.66Kiatnakin Fin. and Sec. 102.00 1:1.00000 1184 7.513 104 12.58 153.20 20.91 267.70National Finance 100.00 1:1.03522 1048 62.659 246 12.88 4913.19 29.37 2889.60Nithipat Finance 129.79 1:1.00159 1078 18.000 69 7.64 244.27 20.97 133.39Prime Fin. and Sec. 156.33 1:1.00000 395 10.000 77 6.25 111.53 12.74 127.33

Finance Securities One 284.09 1:1.07359 1354 15.000 240 20.06 728.31 38.77 838.02Siam General Factoring 30.00 1:1.00000 1506 5.478 119 7.73 98.18 16.05 153.73Siam Panich Leasing 45.00 1:1.00000 1171 22.427 204 4.23 708.04 7.70 448.51Sri Dhana Finance 52.49 1:1.14319 1337 8.875 56 5.79 126.01 11.59 183.75United Finance and Sec 88.00 1:1.00000 1048 9.100 231 17.10 45.03 119.80 25.84Wall Street 144.10 1:1.15891 730 4.792 43 1.97 216.75 3.89 269.13

Food Pizza 90.00 1:1.00000 981 7.500 6 58.98 8.51 143.82 15.58Others One Holding 31.27 1:1.40726 1734 32.000 122 2.79 1316.85 4.92 2195.16Packaging Thai Modern Plastic 41.44 1:2.60627 971 4.480 2 1.43 0.70 12.16 21.84Property Christiani and Nielsen 61.66 1:2.60000 637 13.500 38 2.58 142.51 4.05 159.16

Italian Thai Development 314.00 1:1.00000 1379 17.500 197 10.37 891.33 75.16 160.76Land and House 175.00 1:1.64195 406 10.000 191 8.88 589.30 57.58 348.77M.K. Real Estate 102.00 1:1.03522 728 12.000 21 12.56 12.21 22.27 21.25Property Perfect 268.00 1:1.43445 917 8.000 34 10.70 35.47 17.46 70.64Quality House 41.00 1:1.19063 1029 13.600 158 8.28 259.88 14.08 272.51Supalai Property 152.71 1:1.08048 1091 5.125 54 7.50 64.84 16.90 65.61Univest Land 61.43 1:1.28608 1436 45.000 17 4.45 490.66 12.03 284.68

Publishing Nation Publishing 73.00 1:1.00000 1019 12.000 24 11.87 53.03 43.93 21.06Transport Thoresen Agency 30.00 1:1.00000 1337 7.500 11 1.42 175.70 6.01 39.49Vehicles Sweden Motor 125.00 1:1.93480 557 3.600 3 6.26 8.38 21.30 20.24Average 116.10 1:1.40509 969 20.46 114 18.26 940.93 43.28 823.28

This table presents the profiles of all 38 warrants and their underlying stocks listed on the Stock Exchange of Thailand from January 2 to December 31, 1997. TheExercise ratio refers to the number of shares of stock received per unit of warrant exercised. The Days to maturity are from January 1, 1997. Active trading days arethose with at least 20 trades in a day. Warrant and stock trading volume are given in thousands of units.


between buy-and-sell orders in both the market and limit orders of warrants. On average, the order arrival characteristics ofstocks and warrants are similar in all aspects. For example, the total number of daily order arrivals for stocks (491.84) is notsignificantly different from that of the warrants (547.60). Similarly, there is no significant difference in the total number ofmarket orders, total number of limit orders, or the number of buy-and-sell orders for stocks and warrants.

4. Empirical results

4.1. Estimation results

Table 3 shows the summary statistics for the parameter estimates based on the sequential trade model when order submissionis classified as a market or limit order. Panel A shows the goodness of fit of the model based on the likelihood ratio statistics. Wereject the hypothesis that all orders are submitted because of liquidity reasons at the 1% significance level (p-valueb0.0001). PanelB presents the maximum likelihood parameter estimates. We report the mean, median, and standard deviation of each estimatedparameter across all firms. The probability of an across-firms private information event occurring (θ) is 0.12 and the conditionalprobability of a low across-firms signal is 0.97. These indicate that an across-firms private information event, if it occurs, ismost likely a bad news event. This finding corresponds with the observation that the Thai market index fell 55.2% in 1997from 831.57 at the end of 1996 to 372.69 at the end of 1997. Nonetheless, this does not suggest that the data isuninformative in the case of a high across-firms signal because the structural model in Fig. 1 includes both across-firms andfirm-specific private information. In the case of more than one piece of news affecting trading, we assume that firm-specific

Table 2Order submission statistics.

Warrants Stocks Warrants–stocks (t-stat.)

Total orders 547.60 491.84 55.76 (0.31)Market orders Total 143.63 127.45 16.18 (0.36)

Buys 74.39 66.08 8.31 (0.35)Sells 69.23 61.37 7.87 (0.36)Buys–sells (t-stat.) 5.16 (0.21) 4.71 (0.21)

Limit orders Total 403.98 364.39 39.58 (0.30)Buys 186.02 181.97 4.05 (0.51)Sells 217.96 182.43 35.53 (0.52)Buys–sells (t-stat.) −31.94 (−0.41) −0.46 (−0.01)

This table presents the cross-sectional descriptive statistics of the number of order arrivals across order types for stocks and warrants over a trading day. A markeorder is defined as a limit order that, when submitted, is executed immediately against the existing quote.

Table 3Average estimators across individual securities.

Panel A: goodness of fit of the model

Log-likelihood (×106) LR test statistic (×106) p-Value

Unrestricted log-likelihood −1.57 1.60 b0.0001Restricted log-likelihood −2.37 – –

Panel B: estimators across individual securities

Mean Median SD

Across-firms information event occurs (θ) 0.12 – –

Across-firms signal low (ρ) 0.97 – –

Firm-specific information event occurs (αi) 0.31 0.30 0.13Firm-specific signal low (δi) 0.74 0.93 0.33Uninformed warrant buyer arrival rate (εi,bw ) 224.28 85.97 329.19Uninformed stock buyer arrival rate (εi,bc ) 215.13 76.41 301.91Uninformed warrant seller arrival rate (εi,sw) 139.88 50.19 243.66Uninformed stock seller arrival rate (εi,sc ) 178.13 68.43 302.22Across-firms informed warrant trader arrival rate (μi,aw) 439.14 52.85 830.93Across-firms informed stock trader arrival rate (μi,ac ) 381.62 28.59 1943.23Firm-specific informed warrant trader arrival rate (μi,fw) 265.89 138.79 310.64Firm-specific informed stock trader arrival rate (μi,fc ) 233.55 93.95 318.04

Panel C: probability of informed trading

Order type Warrant Stock Warrant–stock (t-stats)

All 0.22 0.17 0.05 ⁎⁎ (2.18)Market order 0.26 0.18 0.07 ⁎⁎⁎ (3.24)Limit order 0.21 0.17 0.04 ⁎ (1.95)Market–limit (t-stats) 0.04 ⁎⁎⁎ (3.02) 0.01 (1.53)

This table contains the parameter estimates across individual securities of the model. Panel A shows the likelihood ratio which indicates the goodness of fit ofthe model and its p-value. Critical value based on the p-value of 0.01 with 230 degrees of freedom (6 38+2) is 283. Panel B shows the summary of parametersestimated by the maximum likelihood technique. We report the mean, median, and standard deviation of each estimated parameter across all firms. Panel Cshows the estimated probability of firm-specific private information for both stocks and warrants.

⁎⁎⁎ Denotes statistical significance at 99%.⁎⁎ Denotes statistical significance at 95%.⁎ Denotes statistical significance at 90%.


t

news dominates investors' behavior. As discussed in Section 2.1, boxes 2 and 4 of Fig. 1 imply that informed traders rely onthe firm-specific signal only. This assumption is consistent with the evidence documented by Albuquerque et al. (2008) andVega (2006) that firm-specific information is likely to be more accurate than across-firms information. If the firm-specificsignal is high when the across-firms signal is low (lines 1 and 2 in box 2), informed traders (μi,fw and μi,fc ) buy warrants andstocks based on the firm-specific signal. In contrast, if the firm-specific signal is low when the across-firms signal is high(lines 3 and 4 in box 4), informed traders (μi,fw and μi,fc ) sell warrants and stocks based on the firm-specific signal.

The average probability of a firm-specific event occurring across individual securities, α, is 31%. If such an event occurs,the probability of it being a low signal for the security is 74%, reflecting the impact of a negative market sentiment during theAsian financial crisis on firm-specific private signals. Taken together, the probability of firm-specific bad news, αδ, is 23%; theprobability of firm-specific good news, α(1−δ), is 8%; and the probability of no firm-specific news, 1−α, is 69%. There are266 (234) firm-specific informed warrant (stock) order arrivals daily compared to 224 (215) arrivals of uninformed warrant(stock) buyers and 140 (178) uninformed warrant (stock) sellers. For across-firms informed order arrivals, the arrival rates(439 for warrants and 382 for stocks) are higher than the arrival rates of firm-specific informed traders. Panel B does not


indicate anything regarding the likelihood of informed or uninformed traders' arrival because the estimates of μ, εb, and εsare related to trading frequency.

Panel C presents the probability of informed trading computed from the estimates of α, μ, εb, and εs in panel B based onEq. (3). The average firm-specific probability of informed trading across the 38 warrants and stocks are 0.22 and 0.17,respectively. Easley et al. (2002) show that the time-series averages, across the years 1983 through 1998, of the cross-sectionalmeans of the PIN for the monthly sample between 997 and 1316 stocks is 0.19. In our sample, the cross-sectional mean of thePIN forwarrants is 0.22, which is slightly higher than the PINs observed in the sample of Easley et al. (2002). However, themeanof the PIN for stocks is slightly lower at 0.17. The result comes with no surprise since Thai firms that issue warrants are mostlylarge ones with lower levels of information asymmetry.

We find that the average PIN of 0.17 for stocks is significantly lower than the PIN of 0.22 for warrants (t=2.18). In otherwords, for a given warrant order, there is a probability of 22% that an informed trader submitted the order while such aprobability is only 17% for a stock order. The result suggests an important informational role of warrants. Extensive evidenceindicates that informed investors trade in the options market. The prominent ones are those cases where individuals havebeen prosecuted and convicted of illegal insider trading in the options market by the U.S. Securities and ExchangeCommission (SEC).16 In addition, Cao et al. (2005) test the hypothesis that in the presence of extreme informational eventssuch as takeover announcements, the options market supersedes the stock market as the principal informed trading location.They find that prior to takeover announcements, call options volume imbalances are highly predictive of a pending takeover,whereas stock volume imbalances are informative of future stock returns during a normal period but not during a takeoverannouncement. Cao et al. (2005) conclude that the options market is informative ahead of material events while the stockmarket distributes normal information flow.

Our structural model allows for the exploration of the PIN, conditional on both security and order type. The literaturesuggests that an order submission strategy could reflect a trader's firm-specific private information. We compare submissionsthat are market orders with those that are limit orders. We find that for warrants, the likelihood of informed traderssubmitting a limit order (0.21) is significantly lower than the probability of them submitting a market order (0.26, t=3.02).The results are consistent with the notion that informed traders demand a fast execution of their orders by using moremarket orders. This finding is consistent with the prior literature that informed traders consume liquidity (e.g., Biais et al.,1995; Handa and Schwartz, 1996). Harris (1998) suggests that informed traders are more likely to use market orders if thecurrent asset value is farther away from its fundamental value, which is when the information is more valuable. He predictsthat liquidity traders act strategically to complete their objective using limit orders and only switch to market orders towardthe end of the trading day. However, for stocks we do not find any significant statistical difference between the PIN of marketorders and limit orders. Interestingly, the experimental study by Bloomfield et al. (2005) suggests that large liquidity tradersprefer limit orders early in the trading period and shift their preferences to market orders over time, which is contrary toinformed traders who employ market orders at the start of market trading and shift to limit orders over time to optimallycapitalize on the true value of an asset and its bid-ask spread. Their study explains why an electronic limit order-drivenmarket can create liquidity in the presence of information asymmetry.

We consider the probability of firm-specific informed trading under various order sizes in Table 4. Following Chakravarty(2001), we define any order of more than 10,000 shares to be a large order size; a medium order size is an order of more than 500shares but nomore than 10,000 shares; and a small order size is an order with less than 500 shares. Panel A presents the number oflarge, medium, and small order arrivals. The number of medium-sized order arrivals is higher than the number of large- or small-sized order arrivals. Warrants have 400 medium-sized orders a day compared to the 353 medium-sized stock orders. For large-sized orders, we observe 63 warrant orders compared to 48 stock orders. Nevertheless, we do not find any statistically significantdifference that large- and medium-sized order arrivals of warrants are higher than those of stocks. We find however that stockshave a significantly higher number of small-sized order arrivals (87 orders) compared to 30 small-sized orders of warrants.

Panel B of Table 4 presents the probability of informed trading of small, medium, and large order sizes. We find that, regardlessof order size and consistent with the evidence based onmarket and limit orders shown in panel C of Table 3, warrants have higherPINs than stocks. Also, consistent with the stealth trading hypothesis, we find that for both warrants and stocks, the PINs ofmedium-sized orders are higher than those of large-sized orders. Our results so far suggest that informed traders consider thesecurity type before deciding on their order type or order size for submission.

Duarte and Young (2009) introduce an adjusted PIN, which allows for a positive correlation between buys and sells andthey compute the probability of symmetric order flow shock (PSOS) as a proxy for illiquidity. Although we recognize that the PINcan be decomposed into two components — information and liquidity but unlike Duarte and Young (2009) we do not estimateeach component of the PIN in our study. Our model reflects a certain portion of the cross-sectional dependence of order flowwiththe across-firms informed trader arrival. Furthermore, warrant trading in our sample is generally as active as trading in theunderlying stock. Asmentioned earlier, thewarrants in our sample have a daily average trading volume of 940,930 units comparedto 823,280 shares of the underlying stocks. For the number of trades, the average daily number of market (limit) orders for stocksis 127.45 (364.39), while that for warrants is 146.63 (403.98). The results imply that the illiquidity component of warrants should

16 For example, Charles Brumfield purchased call options to benefit from AT&T's plans to acquire four companies between 1988 and 1991 (SEC litigation releases16507); Alan Stricoff purchased call options of Caesars World, Inc. prior to its tender offer (SEC litigation releases 16890); and Stephen Cowley purchased commonstocks and call options prior to the acquisition announcement of 4Front Technology, Inc. (SEC litigation releases 17331).

whereclosin

17 The tick-size rule was changed on November 5, 2001. Under the current rule, there are 10 tick sizes starting from a tick size of 0.10 Baht for securities with aprice below 2 Baht to a tick size of 6 Baht for securities with a price above 800 Baht.

Table 4Order size and informed trading.

Panel A: order size statistics

Warrants Stocks Warrants–stocks (t-statistic)

Large size Total 63.22 48.22 15.00 (0.62)Buys 31.23 24.36 6.87 (0.57)Sells 31.99 23.86 8.13 (0.67)Buys–sells (t-stat) −0.76 (−0.06) 0.50 (0.04)

Medium size Total 400.12 353.25 46.87 (0.39)Buys 189.86 177.12 12.74 (0.21)Sells 210.26 176.13 34.13 (0.57)Buys–sells (t-stat) −20.40 (−0.34) 0.99 (0.02)

Small size Total 30.39 86.83 −56.44 ⁎⁎ (−2.17)Buys 13.29 44.66 −31.37 ⁎⁎ (−2.26)Sells 17.09 42.16 −25.07 ⁎⁎ (−2.05)Buys–Sells (t-stat) −3.80 (−0.53) 2.50 (0.15)

Panel B: probability of informed trading by order size

Type Warrant Stock Warrant–stock

Large 0.17 0.12 0.05 ⁎ (1.72)Medium 0.22 0.15 0.07 ⁎⁎⁎ (3.09)Small 0.21 0.17 0.04 (1.49)Medium–large 0.06 ⁎⁎⁎ (3.29) 0.03 ⁎⁎⁎ (2.82)Medium–small 0.02 (0.88) −0.02 (−1.28)Large–small −0.04 (1.40) −0.05 ⁎⁎⁎ (−2.45)

This table shows the effect of order size on informed trading. Any order of more than 10,000 shares, more than 500 shares but no more than 10,000 shares, andno more than 500 shares are considered large, medium, and small order sizes, respectively. We use the paired t-test for the mean difference between buy andsell of warrants and stocks. Panel A presents the cross-sectional descriptive statistics of the number of order arrivals across three order sizes for stocks and warrantsrespectively, over each day. Panel B presents the PIN and the paired t-test of the mean difference between the PINs conditioned on large, medium, and small order sizes

⁎⁎⁎ Denotes statistical significance at 99%.⁎⁎ Denote statistical significance at 95%.⁎ Denotes statistical significance at 90%.


,.

be at a similar level of the underlying stock. Since our evidence shows that the PIN for warrants is higher than the PIN for theunderlying stocks, there seems to be a disparity between the information-related components of the two asset classes.

4.2. Economic implication of estimates

As suggested by Easley et al. (1996), a de facto test on the economic validity of their sequential trade model is to examinehow well information-based estimates determine bid-ask spread behavior. We employ a regression analysis to investigatehow the probabilities of informed trading in warrants and stocks perform in explaining bid-ask spread behavior. Easley et al.(1996) show that the opening bid-ask spread is a product of the price range of the asset and the probability that the openingtrade comes from an informed trader. Given the assumption that the price range of the asset is a linear function of the stockprice, the opening spread is:

OpeningSpread = β1·Price × PIN ð4Þ

β1 is a constant multiplier in the linear relation. Another important factor that determines the bid-ask spread is the
whereinventory cost. We expect trading volume to have a negative impact on inventory cost because higher trading levels allowliquidity providers to move their inventory to a desired level more quickly, thereby reducing inventory cost and,consequently, the bid-ask spread. The minimum price variation (minimum tick size) is another factor that affects thevariation of the opening spread. The SET sets the tick size according to the stock's closing price in the previous trading day. In1997, there were six different tick sizes.17 The smallest tick size was 0.10 Baht for securities with a price below 10 Baht, andthe largest tick size was 6 Baht for securities with a price above 1000 Baht. We use the following regression to examine theeconomic content of the PIN estimates:
OpeningSpread = β0 + β1·Price × PIN + β2·Volume + β3·MinTickSize + ε ð5Þ

OpeningSpread is the average opening spread as defined by Eq. (5) over the period of study. Price is the averageg price over the same period. Volume is the average of the natural logarithm of trading volume in baht. PIN is the

probathe laprice.provid

18 A frminimu19 Res20 Res21 Res22 Eas23 MA


bility of informed trading in stocks for the first 38 observations and the probability of informed trading in warrants forst 38 observations. MinTickSize is the average minimum price variation or tick size based on the previous day's closingPositive β1 is an indication that the model accurately estimates the PIN. In addition, positive β0 reflects any fixed cost ofing liquidity. On the other hand, β2 is expected to be negative as a result of the inventory effect. We expect theient of the minimum tick size, β3, to be positive due to a mechanical relation between minimum tick size and spread.
coeffic
We estimate the regression using the Two Stage Least Squares (2SLS) method with White heteroskedasticity-consistent co-variances. All variables except PIN can be directly observed. Since PIN is the only estimated variable, we address the error-in-variable problem by regressing the PIN with instrumental variables in the first stage regression. We then compute the fitted valueof PIN, and in Eq. (5) we replace the estimated PIN with the fitted PIN from the first stage regression. The selected instrumentalvariables include firm size, average trade size, and volatility.

Table 5 reports the estimation results of the economic content of the PIN. The results in the first column are consistent with ourpredictions. The coefficient of the PIN is statistically significant and positive; indicating that the opening spread is wider forsecurities with higher asymmetric information. Consistent with the inventory effect, the coefficient of trading volume is negativelyassociated with the opening bid-ask spread. The regression model can explain a substantial portion of the variation in the openingbid-ask spread. The adjusted R-square is 62.10% with an F-value of 62.45. Comparatively, Easley, et al. (1996) show that the PINand trading volume in their sample can explain the opening bid-ask spread quite well with their adjusted R-square of 52.16%. Wealso examine the explanatory power of trading volume alone by restricting β1=0 and β3=0. As expected, trading volume alonehas a negative coefficient. However, the explanatory power of the regression falls sharply from an adjusted R-square of 62.10% to7.79%with an F-value of 7.34. This suggests that the average trading volume alone has little explanatory power on determining theopening bid-ask spread. We then consider the importance of the PIN alone by setting β2=0 and β3=0 as a direct test of Eq. (5).Table 5 shows that the PIN has a positive and strongly significant coefficient at the 99% confidence level. Themodel has an adjustedR-square of 43.26% and an F-value of 58.76. We explore further by controlling for the impact of the tick-size rule by incorporatingthe average minimum price variation. It turns out that, although the minimum tick size has a negative coefficient contrary toexpectation, the coefficient is not statistically significant. On the other hand, the negative relation betweenminimum tick size andspread may reflect the front-running effect among very small tick size securities because the minimum tick size is a direct cost of afront-runner.18 The presence of a front-runner or a parasite trader discourages other traders, resulting in a decrease in liquidityand high spread. Moreover, the minimum tick-size factor does not add to the explanatory value beyond the PIN and tradingvolume factors as its adjusted R-square of 61.67% is below the adjusted R-square of the regression without the minimum tick-sizefactor. Overall, these results indicate that the estimated PIN is a better predictor of the opening spread than trading volume orminimum tick size.

4.3. Future stock prices and warrant net trade volume

This section examines the separating and pooling equilibrium proposition by investigating how future stock price changes andwarrant volume are related. Easley et al. (1998) consider information asymmetry in options and stocks. They address the twoequilibriums from a model of multi-market trading, where traders choose to trade options or stocks with risk-neutral andcompetitive market makers. A separating equilibrium occurs when the informed trader only trades on the stock market and theliquidity trader only trades on the options market. A pooling equilibrium occurs when informed traders choose to trade in allsecurities. While Pan and Poteshman (2006) present strong evidence that options trading volume contains predictive power aboutfuture stock prices, Chan et al. (2002) find that options net trade volume has no incremental information due to the low liquidity inthe options market.

Using a unique setting wheremarket architecture and liquidity of warrants and stocks are similar, we examine the informationrole of the net trading volume of warrants using the regression of future stock price changes and net trading volume of warrants.We compute the change in trade price19 and use the signed warrants trading volume, which is the ratio of the number of buyer-initiated warrant trades to the total number of warrant trades.20 Each variable of interest is constructed over 5-minute intervalsand is normalized by subtracting its mean and dividing by its standard deviation. The normalization procedure controls for thelevel effect and removes any cross-sectional variations, thereby allowing for the aggregation of variables across all firms in thesample. The fine interval period (5-minutes) can result in many zero activity intervals, creating a negative first-orderautocorrelation in stock price changes and net trading volume.21 Panel A of Table 6 reveals a serial correlation in standardizedstock price changes. The strongest correlation occurs at lag one with a substantially less correlation thereafter. The presence ofserial correlation contaminates any conclusions about the relation between stock price changes and net warrant trading volume.Following the approach taken in the literature,22 we model stock price changes as an MA(1) process.23 The residuals from themodel are serially uncorrelated. We use the residuals or the stock price innovations instead of the changes in stock price toexamine the lead–lag relation. As shown in panel A, the serial correlation in the residual series is not significant.

ont runner is a trader who observes other traders' orders and front-runs other traders by using an order submission with a slightly better price. Largem tick size is costly for front-running strategy.ults based on change in quote midpoint to control for the bid-ask bounce effect are qualitatively similar.ults are robust to other net trade volume measurements (i.e., the number of trades or the trade value in Thai Baht).ults do not change when we select trading days that both warrants and their underlying stocks have at least 10 trades a day.ley et al. (1998) and Stephan and Whaley (1990).(1) process: ΔSt=c+ut and ut=εt+ςεt−1, where ΔSt is the standardized change in the stock price.

Table 5Informativeness of the probability of informed trading.

EKOP (1996) Trading volume alone PIN alone EKOP (1996) with tick size

Intercept 7.13 ⁎⁎ (2.61) 5.97 ⁎ (1.93) 0.03 (0.11) 7.14 ⁎⁎ (2.59)Price PIN 0.22 ⁎⁎⁎ (3.80) 0.20 ⁎⁎⁎ (3.30) 0.24 ⁎⁎ (2.49)Log(BathVol) −0.49 ⁎⁎⁎ (−2.66) −0.33 ⁎ (−1.68) −0.49 ⁎⁎⁎ (−2.67)MinTickSize −0.38 (0.31)Adjusted R2 62.10% 7.79% 43.26% 61.67%F-stat. 62.45 ⁎⁎⁎ 7.34 ⁎⁎⁎ 58.76 ⁎⁎⁎ 41.22 ⁎⁎⁎

This table examines the informativeness of the estimated PIN following the asymmetric information model of Easley et al. (1996). As PIN is unobservable andneeds to be estimated, we implement a 2SLSmodel to address the error-in-variable problem. Our instrumental variables include firm size, trade size, and volatility.The specification of the 2SLS model is:

1st stage regression: PIN=γ0+γ1·FirmSize+γ2·TradeSize+γ3·Volatility+ς,

2nd stage regression: OpeningSpread=β0+β1·Price×PINF+β2·Volume+β3·MinTickSize+ε

where OpeningSpread is the average opening spread over the period of study. Price is the average closing price for the same period. Volume is the natural logarithm ofaverage volume in baht. PIN is the probability of informed trading in stocks for the first 38 observations and the probability of informed trading inwarrants for the next38 observations. Price is the average stock's closing price. MinTickSize is the average minimum price variation or tick size based on closing price. PINF in the 2nd stageregression is the fitted value of the PIN from the 1st stage regression. White heteroskedasticity consistent t-statistics are reported in parentheses.

⁎⁎⁎ Denotes statistical significance at 99%.⁎⁎ Denotes statistical significance at 95%.⁎ Denotes statistical significance at 90%.


We examine the informational role ofwarrants by testingwhether a signedwarrant trade can predict future stock prices. A signedwarrant trade is the ratio of the number of buyer-initiated warrant trades to the total number of warrant trades. We assign missingvalues to any interval with no trades. We then run a regression between stock price innovation as the dependent variable and thecontemporaneous and six lagged 5-minute signed warrant trades as explanatory variables. The second column in panel B of Table 6shows that the contemporaneous and the first 5-minutes' warrant net trades contain a significant predictive power of stock priceinnovation. The positive coefficients indicate that stock price innovation is positive with an increase in the contemporaneous and thepast 5-minute buyer-initiated warrant trades.24 Consistent with Easley et al. (1998) and Pan and Poteshman (2006), this findingsupports the pooling equilibrium hypothesis that warrant trades contain useful information about future stock prices.

Our findings so far indicate that informed traders participate in the warrants market. It would be interesting to investigatewhether the predictive power of signed warrant trades is driven by the participation of informed traders. To address thishypothesis, we add interaction variables to the regression. The interaction variables are the product of the signed warrant tradeand the PIN. The statistical significance of interaction variables suggests that the economic source of the prediction is in theparticipation of informed traders in the warrants market. The third column of panel B in Table 6 presents coefficient estimates ofthe signed warrant trade and its interaction with the PIN. As expected, we find that the contemporaneous and first lag ofinteraction variables are statistically different from zero, suggesting that the participation of informed traders is the likelyeconomic source of the signed warrant trade's predictive power on stock price innovation. Nevertheless, we find a negativecoefficient for the contemporaneous interaction between the signed warrant trade and the PIN while the first lag interaction has apositive coefficient, which is consistent with what we expected. The contemporaneous negative interaction coefficient isconsistent with delta-neutral hedging, where a warrant buyer simultaneously offsets her warrant trade through selling stock. Theresult is also consistent with the contemporaneous substitution effect between warrants and stocks. Traders sell stocks and buywarrants to enjoy the benefits of higher leverage and volatility information. This can be viewed as a hedging effect.

Lastly, as the PIN andfirm size have a negative correlation of−23%, onemayquestionwhether the PIN is simply a restatement of thesize. We control for size when evaluating the independence effect of the PIN on the prediction by adding both interaction terms in theregression as seen in the fourth columnof panel B in Table 6.Wefind that the PIN still has a strong impact on the predictive power of thesigned warrant trades. Taken together, our results highlight the importance of non-public information contained in warrant trades.

5. Conclusions

This paper investigates buy/sell orders ofwarrants and their underlying stocks of 38firms tradedon theStockExchangeof Thailand(SET), where both types of securities trade under the same rules and market structure. The choice of the SET allows us to avoid theproblems faced by past researchers when stocks and derivatives trade under different market architectures. We measure theprobabilities of the trading process based on the sequential trade model of Albuquerque et al. (2008) and Easley et al. (1996). Ourresults show that there is a significantdifferencebetween theprobability of informed trading in stocks andwarrants. Theprobability ofmarket orders being used by informed traders is higher than the probability of limit orders being used by informed traders.

We show that informed tradersmay use an order splitting strategy to hide their identity as the probability of a large-sized orderused by informed traders is lower than that of a small- or medium-sized order. We find that the estimated PIN has superior power

24 The interpretation of coefficient magnitude is difficult to make due to the normalization and pre-whitening process.

Table 6Stock price change and signed warrant trade.

Panel A: serial correlation

Lag 1 2 3 4 5 6

Stock price change series −0.064 −0.041 −0.032 −0.021 −0.016 −0.011Pre-whitening series 0.003 −0.043 −0.036 −0.025 −0.019 −0.013

Panel B: future stock price and signed warrant trade

Coefficients Signed warrant trade Signed warrant trade and PIN Signed warrant trade, PIN, and firm size

Intercept 0.002 (0.39) 0.002 (0.39) 0.002 (0.43)Vtwarrant

0.179 ⁎⁎⁎ (18.41) 0.227 ⁎⁎⁎ (11.94) 0.275 ⁎⁎⁎ (4.93)Vt−1warrant

0.030 ⁎⁎⁎ (3.43) −0.009 (−0.48) −0.099 ⁎ (−1.92)Vt−2warrant

−0.004 (−0.67) −0.023 (−1.51) −0.050 (−1.05)Vt−3warrant

−0.002 (−0.37) 0.015 ⁎ (1.73) −0.003 (−0.11)Vt−4warrant

−0.006 (−1.02) 0.004 (0.21) 0.022 (0.57)Vt−5warrant

−0.017 ⁎⁎⁎ (−2.99) −0.040 ⁎⁎⁎ (−2.34) −0.098 ⁎ (−1.79)Vt−6warrant

0.013 ⁎⁎⁎ (2.91) 0.039 ⁎⁎⁎ (3.58) 0.019 (0.69)Vtwarrant

×PIN −0.217 ⁎⁎⁎ (−3.19) −0.236 ⁎⁎⁎ (−2.75)Vt−1warrant

×PIN 0.174 ⁎⁎⁎ (2.37) 0.211 ⁎⁎⁎ (4.87)Vt−2warrant

×PIN 0.081 (1.36) 0.093 ⁎ (1.67)Vt−3warrant

×PIN −0.076 ⁎⁎ (−2.02) −0.069 ⁎ (−1.68)Vt−4warrant

×PIN −0.047 (−0.75) −0.054 (−1.07)Vt−5warrant

×PIN 0.103 (1.54) 0.126 (1.55)Vt−6warrant

×PIN −0.112 ⁎⁎⁎ (−3.05) −0.102 ⁎⁎⁎ (−2.71)Vtwarrant

×Size −0.005 (−0.90)Vt−1warrant

×Size 0.009 ⁎ (1.70)Vt−2warrant

×Size 0.003 (0.56)Vt−3warrant


×Size −0.002 (−0.38)Vt−5warrant


×Size 0.002 (0.77)Adj. R2 3.45% 3.50% 3.51%F-stat. 143.32 ⁎⁎⁎ 129.50 ⁎⁎⁎ 867.64 ⁎⁎⁎

This table shows the relation of stock price changes and signed warrant trades during a lag interval of 5 min. Panel A shows the impact of the pre-whitened stockprice change series using an MA(1) process. Panel B presents the estimated coefficient of the pre-whitened stock price change series from the MA(1) process andsigned warrants, which is the ratio of the number of buyer-initiated warrant trades (measured in the number of underlying shares) divided by the total numberof warrant trades. Firm size is the natural logarithm of firm's market capitalization. t-statistics in parentheses are computed from the panel regression adjustedfor the impact of firm clustering as discussed in Peterson (2009).

⁎⁎⁎ Denotes statistical significance at the 99% level.⁎⁎ Denotes statistical significance at the 95% level.⁎ Denotes statistical significance at the 90% level.


in explaining the cross-sectional variation of the opening bid-ask spread compared to trading volume and minimum tick size. ThePIN is indeed reflected in the bid-ask spread, and the market appears to be aware of the adverse selection problem faced byuninformed traders. Lastly, we find that a signed warrant trade predicts future stock price innovation and that a concentration ofinformed trading in warrants increases the predictability.

From our results, we conclude that on the SET, the warrant market plays a significant role in impounding the privateinformation released through trading by informed traders. The results also suggest that informed traders, who wish to capitalizeon their private information, prefer faster execution through the use of market orders and trade using warrants and avoid using alarge order to conceal their identity. The evidence provided is consistent with the assumptions commonly used in the existinginformation models.

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information asymmetry in warrants and their underlying stocks on the stock exchange of thailand

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