Estimation of Market Information Shares: A Comparison

• Published date: 01 November 2016
• Author: Zijun Wang,Donald Lien
• Date: 01 November 2016
• DOI: http://doi.org/10.1002/fut.21781

Estimation of Market Information Shares:

A Comparison

Donald Lien* and Zijun Wang

This note investigates via Monte Carlo simulation the finite-sample performance of two

identification schemes that provide unique measures of Hasbrouck-type information share in

price discovery. The Lien and Shrestha (2009) method is based on factorization of the full

correlation matrix and the Grammig and Peter (2013) method is based on different correlations

of price innovations in the tails and in the center of the distributions. We find that the GP

method performs poorly under the chosen data generation processes. The LS method provides

at most marginal improvement over the method based upon the upper/lower bound midpoint of

the Hasbrouck measure. The results, therefore, support the common practice of the midpoint

approach. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 36:1108–1124, 2016

1. INTRODUCTION

Price discovery is probably the most important function of financial markets and is one of the

long-standing issues pursued by financial economists. The issue becomes more interesting

and has been proven to be more complicated when there are more than one market/trading

venue where the same security or very similar securities trade, or when both a security and its

derivatives are traded. The question in this situation 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.

1

Among them, Hasbrouck’s (1995)

measure, commonly known as information share (IS), has received the most attention and

has been applied in many empirical studies.

2

In essence, the information share is the fraction

Donald Lien is the Richard S. Liu Distinguished Chair in Business and Professor of Economics at University

of Texas—San Antonio and Zijun Wang is an Associate Professor of Finance at University of Texas—San

Antonio. The authors are grateful to the editor and an anonymous referee for helpful comments and

suggestions.

JEL Classification: G14

*Correspondence author, Department of Economics, College of Business, University of Texas at San Antonio, San

Antonio, TX 78249, United States. Tel: 210-458-8070, Fax: 210-4585837, e-mail: don.lien@utsa.edu

Received August 2015; Accepted January 2016

1

Another popular definition of the contribution to price discovery is the component share measure of Gonzalo and

Granger (1995). This measure is closely related to Hasbrouck’s (1995) information measure on which we focus.

However, as pointed out by De Jong (2002), the component share measure does not take into account the variability

of the innovations in each market’s price. Yan and Zivot (2010) also show that both measures account for the relative

avoidance of noise trading and liquidity shocks, but that only the latter can provide information on the relative

informativeness of individual markets.

2

A partial list includes: Harris, McInish, and Wood (2002), and Hupperets and Menkveld (2002) for U.S. equities

and European equities cross-listed in the U.S. market, De Jong, Mahieu, and Schotman (1998) and Covrig and

Melvin (2002) for the foreign exchange market, Mizrach and Neely (2008) for the U.S. Treasury market, and

Dittmar and Yuan (2008) for corporate and sovereign bonds in emerging markets.

The Journal of Futures Markets, Vol. 36, No. 11, 1108–1124 (2016)

© 2016 Wiley Periodicals, Inc.

Published online 2 March 2016 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21781

of the variance of the random walk component of the efficient price that can be attributed to a

particular market, trading venue, or a dealer.

Whereas this methodology is intuitive and easy to compute, it is based on reduced form

vector error correction models and suffers an identification issue that is common to all

applications of this type of multivariate time series models. Put in another way, the IS

measure depends on the ordering of price series in the model. To empirical researchers, the

indeterminacy is certainly an undesirable property of a measure of information share. As an

attempt to resolve the issue of ordering dependence, Lien and Shrestha (2009) suggest

deriving factorization from the full matrix of correlation, rather than from the triangular

decomposition of reduced form innovations matrix (the Choleski decomposition). More

recently, Grammig and Peter (2013) propose to achieve identification by exploiting

distributional features of multivariate price processes, namely, correlations of price changes

being different in their tails and in the center of the distribution.

3

Like any other empirical method, both Lien and Shrestha’s (2009) measure of

information share (LSIS) and that of Grammig and Peter’s (2013) (GPIS) have their pros and

cons. Lien and Shrestha’s (2009) approach is easy to implement and can be computed along

with Hasbrouck’s (1995) measure from a simple OLS regression. However, as a data-driven

method, it is subject to the common critique of lacking economic rationale (Grammig &

Peter, 2013, p. 464).

4

The motivation of GPIS, on the other hand, is appealing. Nevertheless,

its application is limited in the sense that not all market price dynamics can be characterized

with a pattern of tail-dependence.

Practically, due to the different assumption than other IS measures about the constancy

of the innovation’s variance-covariance matrix, GPIS measure may be higher than the upper

bound or/and lower than the lower bound of Hasbrouck’s (1995) measure.

5

It is not clear

whether this feature is desirable for a measure of market information share.

The intent of this note is to examine the finite sample performance of the two new

modifications on the IS measure through Monte Carlo simulation. As a result, practitioners

and policy researchers could have some guidance on which method is likely to work better in

which market structure. This is especially relevant to the GPIS measure because to

implement the method empirical researchers first need to select an “appropriate”significance

level to determine if the approach is applicable. Like many other two-step probability-based

procedures, the first-step testing and the second-step estimation are separate and it is often

difficult to comment, a priori, on the underlying probability distribution of the final results.

Based upon the chosen data generation process, we find that the GP method performs

poorly whereas the LS method provides mostly similar performance to the average of the

upper and lower bounds of the Hasbrouck measure. Consequently, the latter common

practice is supported.

3

We concentrate on these two developments. Of course, there are many other important advances in the area. For

example, rather than defining information share within a reduced form time series model, De Jong and Schotman’s

(2010) new measure is defined directly within a structural time series model. Ozturk, van der Wel, and van Dijk

(2014) take one step further and estimate a structural model with time-varying parameters in state space to study

intraday variation in the contribution to price discovery. Westerlund, Reese, and Narayan (2015) incorporate this

new measure with a factor analytical approach. On the other hand, while IS focuses on innovation variance

allocation, Sultan and Zivot (2014) propose price discovery share (PDS) based upon volatility decomposition which

is order invariant and unique.

4

Figuerola-Ferretti, Gilbert, and Yan (2013) point out that LSIS is a rotation of the principal component analysis

(PCA) factors that weights each PCA factor in the proportion that it contributes to each market price.

5

For example, among their estimates of credit risk market IS for 26 entities, 9 are higher than and 4 are equal to the

Hasbrouck IS upper bounds whereas another estimate is equal to Hasbrouck IS lower bound (Grammig & Peter,

2013, Table II).

Market Information Share 1109