A Factor Analytical Approach to Price Discovery
| Author | Joakim Westerlund,Paresh Narayan,Simon Reese |
| DOI | http://doi.org/10.1111/obes.12167 |
| Published date | 01 June 2017 |
| Date | 01 June 2017 |
366
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 79, 3 (2017) 0305–9049
doi: 10.1111/obes.12167
A FactorAnalytical Approach to Price Discovery*
Joakim Westerlund,†,‡Simon Reese,†Paresh Narayan‡
†Department of Economics, Lund University, P. O. Box 7082 S–220 07, Lund, Sweden
(e-mail: joakim.westerlund@nek.lu.se)
‡Centre for Financial Econometrics, Deakin University
Abstract
Existing econometric approaches for studying price discovery presume that the number of
markets are small, and their properties become suspect when this restriction is not met.
They also require making identifying restrictions and are in many cases not suitable for
statistical inference. The current paper takes these shortcomings as a starting point to
develop a factor analytical approach that makes use of the cross-sectional variation of the
data, yet is very user-friendly in that it does not involve any identifying restrictions or
obstacles to inference.
I. Introduction
Financial markets incorporate new information into asset prices by matching buyers and
sellers. They thereby facilitate the discovery of what the price of an asset should be. This
price discovery role of financial markets can take place across separate exchanges and
instruments, as many securities and derivatives based on the same underlying asset may
trade on multiple venues. In the case of such a multiplicity, there may be variation in the
share with which each market’s trades contribute to discovering the one true price of the
underlying asset. The present paper is about the modelling and measuring of these so-
called ‘information shares’ (ISs), which are important for both investors concerned with
priceormativeness and adverse selection risk, as well as policy makers investigating the
determinants of price efficiency.
The measurement of price discovery requires isolating informative price movements
from noise. Observed price changes constitute the most obvious indicator of price dis-
covery. However, they form an imperfect measure, as observed prices are susceptible to
transitory mispricing, caused by noise trading or temporary order imbalances, for example.
JEL Classification numbers: C12; C13; C33
*Earlier versions of this paper were presented at the 1st Conference on Recent Developmentsin Financial Econo-
metrics and Applications in Geelong and at the 8th International Conference on Computational and Financial Econo-
metrics in Pisa. The authors wouldlike to thank conference participants, and in par ticular Morten Ørregaard Nielsen,
Debopam Bhattacharya (Editor) and two anonymousreferees for many useful comments and suggestions. Westerlund
thanks the Knut and Alice Wallenberg Foundation for financial support through a Wallenberg Academy Fellowship.
Thank you also to the Jan Wallanderand Tom Hedelius Foundationfor financial support under research grant number
P2014–0112:1.
A factor analytical approach 367
In contrast, when security prices absorb new information due to informed trading, these
price changes last permanently. To formalize these ideas, let us denote by Pi,tthe price
of a particular asset on market i=1,…, Nat time period t=1,…, T, and let P*
tbe the
fundamental value of the same asset at the same time period. The structural model we
have in mind is taken from the market microstructure literature (see Madhavan,2000, for a
survey), as is standard in studies of price discovery (see Hasbrouck, 1993; De Jong, 2002;
de Harris, McInish and Wood, 2002; Lehmann, 2002; De Jong and Schotman, 2010, to
mention a few). It is given by
Pi,t=P*
t+Ei,t,(1)
where Ei,tis an idiosyncratic (or market-specific) term capturing microstructure effects.
While P*
tis assumed to follow a random walk, Ei,tis stationary. Hence, while shocks to
the fundamental value have a permanent effect on prices, the effectof idiosyncratic shocks
is transitory. The transitory nature of Ei,timplies that Pi,twill adjust to the fundamental
value over time. In fact, as Hasbrouck (1995) points out, under said assumptions, Pi,tand
Pj,tare cointegrated with cointegrating vector (1, −1).
A market is relatively efficient in the price discovery process if it incorporates a larger
amount of fundamental shocks than other markets. Hasbrouck (1995) defines the IS of a
particular market as the variance share of that market that is attributable to the fundamental
value. Unfortunately, as equation (1) makes clear, the fundamental value is not directly
observed, but is instead contaminated by additivemarket-specific pricing er rors.Therefore,
legitimate inference on the price discovery process cannot be made until the confounding
effects of these errors have been appropriately accounted for. The most common approach
by far is the one of Hasbrouck (1995), in which the effects of the shocks are retrievedfrom
an estimated reduced form vector error correction model (VECM). This VECM route to
the IS has in recent years become very popular, and is by nowthe workhorse of the industry
with a huge number of applications (see e.g. Brenner and Kroner, 1995, for a survey).
But while popular, the VECM approach also has its fair share of drawbacks.First, since
theVECM is just a reduced form model, the fundamental shocks cannot be retrieved without
suitable identifying restrictions. Hasbrouck (1995) uses Cholesky factorization, which
makes the IS dependent on the ordering of the series. WithNmarkets, there are no less than
N! such orderings, suggesting that without prior knowledge about the appropriate order,
the IS is likely to be an uninformative measure. As a remedy, Hasbrouck (1995) suggests
reporting upper and lower bounds, as obtained by considering all possible orderings.The
resulting largest and smallest ISs for each market constitute the upper and lower bounds,
respectively. These bounds can, however, be quite far apart (see e.g. Hasbrouck, 2002;
Huang, 2002). This is true when Nis relatively small, and the bounds become wider when
Nincreases. Specifically, the width depends critically on the covariances of the shocks,
whose number increases at the rate N2. The number of degrees of freedom will therefore
decrease very rapidly with N, leading to increased estimation uncertainty, and hence wider
bounds. For example, Booth et al. (2002) use trading intervals averaging about 30 minutes
for only two markets, namely, the upstairs and downstairs markets on the Helsinki stock
exchange. According to their results, the average IS interval for the downstairs market is
[13%, 99.2%], which is clearly too wide for any interesting conclusions (see, for example,
Martens, 1998; Tse, 1999; Baillie et al., 2002, for similar findings).
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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