Quantile information share

• Author: Donald Lien,Zijun Wang
• DOI: http://doi.org/10.1002/fut.21940
• Published date: 01 January 2019
• Date: 01 January 2019

Received: 12 September 2017

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Revised: 25 May 2018

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Accepted: 1 June 2018

DOI: 10.1002/fut.21940

RESEARCH ARTICLE

Quantile information share

Donald Lien

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Zijun Wang

Department of Economics and

Department of Finance, College of

Business, University of Texas, San

Antonio, Texas

Correspondence

Donald Lien, Department of Economics

and Department of Finance, College of

Business, University of Texas, One UTSA

Circle, San Antonio, TX 78249.

Email: don.lien@utsa.edu

This paper presents a new method to estimate Hasbrouck‐type market information

share in price discovery. The prevailing market information share is calculated

on the basis of conditional mean. We propose a conditional quantile regression

approach to obtain a new market information share measure, quantile information

share, which varies across the combinations of different price quantiles. The method

is illustrated with two data sets, one on the spot and futures markets in pricing S&P

500 equity index, and the other on price discovery for a cross‐listed stock.

KEYWORDS

bivariate quantile regression, market information share, price discovery

JEL CLASSIFICATION

G14

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INTRODUCTION

Price discovery, referred to the process by which new information is impounded into prices, is probably the most important

function of financial markets. As it is often the case that there are more than one market or trading venue where the same

security or very similar securities can trade, or when both a security and its derivatives are traded, one of the long‐standing key

issues is how to estimate the contribution of each market to the price discovery process. The empirical finance literature has

proposed and used a variety of methods for estimating price discovery. The Hasbrouck’s (1995) measure, commonly known as

Hasbrouck information share (HIS), has received the most attention and has been applied in many empirical studies. In

essence, the information share is the fraction of the variance of the random walk component of the market efficient price that

can be attributed to a particular market, trading venue, or a dealer.

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Another popular definition of the contribution to price

discovery is the component share (CS) measure proposed by Gonzalo and Granger (1995) and Harris et al. (2002).

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Regardless of which measure is adopted, often the information share is assumed to be constant across all the

samples. That is, given the observations are all generated from the same underlying distribution function, the

information share is the same regardless of the values of the prices. We believe the market prices themselves provide

signals and affect information share accordingly. Specifically, the information share varies with the historical ranks of

market prices and thus displays a quantile variation pattern. It is possible that the time‐varying behavior of information

share discovered in the literature may be captured instead by the quantile‐dependent information share.

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A bivariate

J Futures Markets. 2019;39:38–55.wileyonlinelibrary.com/journal/fut38

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© 2018 Wiley Periodicals, Inc.

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Some relevant and important papers are Harris, McInish, and Wood (2002) and Hupperets and Menkveld (2002) on US equities and European equitiescross ‐listedin the US market, De Jong, Mahieu,

and Schotman (1998) and Covrig and Melvin (2002) on the foreign exchange market, Mizrach and Neely (2008) on the US Treasury market, and Dittmar, and Yuan (2008) forcorporate and sovereign

bonds in emerging markets.

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There are many other important recent advances in the area. For example, rather than defining information share within a reduced form time series model as the Hasbrouck and the CS measures, De

Jong and Schotman’s (2010) suggest a new measure which is defined directly within a structural time series model. This new measure has been applied and extended by Westerlund, Reese, and

Narayan (2015) and Ozturk, van der Wel, and van Dijk (2017). On the other hand, while IS focuses on innovation variance allocation, Sultan and Zivot (2014) propose the price discovery share based

upon volatility decomposition which is order‐invariant and unique.

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Suppose that each observation corresponds to a different information share. When time is applied to mark the observation, we have time‐varying information share. If quantile is the marker, then we

have quantile‐dependent information share. The quantile marker is appropriate only if all observations are generated by the same distribution. On the other hand, time‐varying information share is

mostly due to different underlying distributions.

quantile regression would help in validating this conjecture. Consequently, we adopt the method of Chakraborty (2003)

to construct “quantile information share”analytically.

In the empirical section, we first present an application of the new method of quantile‐based information shares to

the price discovery of the most‐traded S&P 500 index by the spot and the futures markets. We find that the spot market

contributes much less information than the futures, which is consistent with the literature. The result is true before the

2008 financial crisis, during the crisis, and after the crisis. More interestingly, we document evidence of significant

quantile variation in the market information shares in both the precrisis and the crisis periods, although with different

patterns. In a second application, we study the informational role played by the Toronto and New York stock exchanges

in pricing Teck Resources, a Canadian firm cross‐listed in the two exchanges. Here, we also find significant quantile

variation in the market information share for a single stock.

The plan of this paper is as follows: Section 2 provides evidence of time‐varying information share from the

literature. Section 3 presents a brief current literature on the relationships between quantiles and market information

discovery. In Section 4, we first introduce the vector error correction model and the measures of the market information

share. We then set forth the univariate and bivariate quantile regression framework. Section 5 summarizes the

application results of the proposed method. And finally, a short summary of our findings concludes the paper.

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EVIDENCE OF TIME‐VARYING INFORMATION SHARE

Existing studies on price discovery often implicitly assumes that relative contributions of different markets or trading

venues to the efficient price innovations to be constant over the sample period. As Ozturk et al. (2017) point out, this may

not always hold true in empirical data with large samples due to changes in the characteristics of underlying exchanges

and securities—such as increases in trade volume and electronization of trading mechanisms. Over the past decade, there

have been empirical interests in studying time variation in measured shares of price discovery for individual markets. For

example, using trades for Dow Jones stocks from three different years (1988, 1992, and 1995), Harris et al. (2002)

document strong evidence of time‐varying CS in price discovery among the New York, Chicago, and Pacific exchanges

likely as the result of competition for informed and uninformed order flow being an ebb‐and‐flow dynamic process. In

examining intradaily DM‐$US quotes, Sapp (2002) find that while Chemical Bank’s quotes, in general, are the first to

contain new information, in the periods of uncertainty around central bank interventions, Deutsche Bank is the price

leader and its quotes are influenced by information and inventory considerations. Time variation can also be caused by

trade volume change in the markets. For example, Eun and Sabherwal (2003) find,among Canadian stocks cross‐listed in

the US market, that the home market share of total adjustment in prices is directly related to the US shareof total trading

in a stock and to theratio of proportions of informative trades on the US and the home exchanges, and inversely related to

the ratio of bid‐ask spreads on both the domestic and the overseas markets.

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More recently, Frijns, Indriawan, and Tourani‐Rad (2015) use macroeconomic news announcements as a proxy for

new information arrivals in comparing the price discovery of Canadian companies listed in the Toronto Stock Exchange

(TSE) and the New York Stock Exchange (NYSE). They observed that price discovery shifts significantly during

macroeconomic news announcement days and the NYSE becomes more important in terms of price discovery,

regardless of the origin of the news. The reason is, they argue, that there is a difference in information‐processing

capability of the two markets with the US market being better at processing information than the Canadian market is

during the macroeconomic news announcement days.

Generally, time variation in Hasbrouck‐type information shares could come from either of its two components: Time

variation in model parameters and time variation in residuals variances (market volatility). In their study on whether thinly

traded futures markets efficiently fulfill their price discovery function, Adämmer, Bohl, and Gross (2016) account for time

variation in the parameters by applying the Kalman filter. Observing that important public news and market responses mostly

happen in a matter of seconds or minutes and market volatility show significant intraday time variation, Ozturk et al. (2017)

argue that current information share methodologies which typically consider daily measurements of information shares are not

able to answer questions about differences in price discovery across different parts of the day. By allowing for time‐varying

volatilities of the efficient price innovations and idiosyncratic noises in their state‐space representation of the unobserved

components model for Expedia data, the authors demonstrate intraday time variation in the measures of information share and

conclude that the overall dominant trading venue does not lead the entire day.

LIEN AND WANG

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See Lei and Wu (2005) for empirical perspectives on the time‐varying trading behavior of informed and uninformed traders.