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2006 National Taiwan University
International Conference in Finance
The price formation of substitute markets
Michael T. Chng
Dept of Finance, University of Melbourne
Aihua Xia
Dept of Mathematics & Statistics, University of Melbourne
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Introduction
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Price discovery: the process by which private information implicit
in investor trading is revealed in subsequent price formation.
Price formation models:
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Hasbrouck (1991a,b): Signed trade size
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Madhavan, Richardson and Roomans (1997): trade direction
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Dufour and Engle (2000): time between trades
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Al-Suhaibani and Kryzanowski (2000): order size
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Chng (2005): trade and net order sizes.
All of the above are single market models, although some models
consider two or more trading parameters.
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Literature review
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J. Financial Markets dedicated a special issue [5(3), 2002] to the
two commonly used measures of cross market price discovery:
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Gonzalo & Granger (1995) common factor weights (JBES):
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Hasbrouck (1995) information share (JF):
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Computes the coefficient of error correction terms to infer orthogonal
weights on the efficient price contributed by various price sequences.
Computes contribution to the variance of the efficient price change by
various price sequences.
Both consider only price parameters of multiple markets.
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Main objectives
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Derive a joint trade direction model (JTDM) from the single
market MRR (1997) trade direction model.
Demonstrate the use of the JTDM and test it against the VECM
using a comprehensive sample of 20 Chinese twin-board firms
(A-B & A-H)
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Lee and Rui (2000), Sun and Tong (2000), Wang and Jiang (2004)
and Yeh, Lee and Pen (2004) use a sample period that is prior to
either or both:
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Feb 2001: Locals with forex accounts can trade B-shares
Dec 2002: QFII are allowed to trade A-shares
This becomes a test of the relevance of price versus non-price
parameter in cross market price formation.
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The MRR (1997) model
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Highlights the role of 1st order serial
correlation in trade direction Xt-1
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Xt assumed to follow a general Markov process
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The model considers 3 states S: {+1, 0, -1}
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3x3 transition matrix
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Transition of Xt illustrated in Figure 1
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The MRR (1997) model
ut  ut 1   ( X t  E[ X t | X t 1 ])   t
pt  ut   X t  t
*E[ X t | X t 1 ]   X t 1 , where   2  (1   )
rt  pt  [ (1   L )  (1  L ) ] X t   t   t
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Our model
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A bivariate system that highlights the joint trade
direction (Xt, Yt) in price formation.
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(Xt, Yt) assumed to follow a general Markov process
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We consider 4 states S:{(1,1), (1,-1), (-1,1), (-1,-1)}
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4x4 transition matrix
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Transition of (Xt, Yt) illustrated in Figure 2
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Categorizing the 16 transitions
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Full continuation: Pr (Xt=Xt-1,Yt=Yt-1|Xt-1 ,Yt-1) = 
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X-continuation: Pr (Xt=Xt-1,Yt=-Yt-1|Xt-1 ,Yt-1) = X
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Y-continuation: Pr (Xt=-Xt-1,Yt=Yt-1|Xt-1 ,Yt-1) = Y
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Full reversal: Pr (Xt=-Xt-1,Yt=-Yt-1|Xt-1 ,Yt-1) = (1--X-Y)
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The model’s focus
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To infer Pr (X-continuation) = X
Pr (Y-continuation) = Y
Conditional on opposite trade directions
observed at t-1, the JTDM measures which
market is more likely to persist in the same
direction i.e. continuity.
This has a natural interpretation as a
measure of price leadership/discovery.
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Bivariate structural system
ut  ut 1   ( X t  Yt  E[ X t  Yt | X t 1 , Yt 1 ])   t
ptX  ut   X X t  tX
ptY  ut   Y Yt  tY
*E[ X t  Yt | X t 1 , Yt 1 ])   X t 1   Yt 1 ,
where   2(   X )  1 and   2(   Y )  1
     2( X   Y )
rt X  (   X )X t  Yt   (1   ) X t 1   (1   )Yt 1  tX
rtY  (   Y )Yt  X t   (1   ) X t 1   (1   )Yt 1  tY
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Twin-share Chinese firms
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Why Chinese market?
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Some institutional details
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Chinese financial markets attracting increasing attention
Multiple exchanges (SHSE, SZSE HKEx) and multiple listing boards (A, B, H)
Similar institutional characteristics
Large number of twin-board firms; overlapping trading hours.
SHSE: A-shares in RMB; B-shares in USD
SZSE: A-shares in RMB; B-shares in HKD
HKEx: H-shares in HKD
A, B, H, A-B or A-H, but not B-H.
Either the B or H board provides access to a substantial foreign
investor clientele, although they are not foreign boards per se.
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Sampling methodology
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For all firms that are selected:
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Tradable share ≥ 30% of issued capital (2005
overall average)
Must have ≥ 10% of issued capital allocated to
each board.
Tradable capital on the smaller board is ≥ 1/5 that
which is issued on the larger board.
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Overall sample
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A pair of A-B and A-H firms for each of 10 sectors of
the Chinese economy.
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Sample period: 4th Jan~30th Sep 05 ( 170 days).
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Each day has 100 min-by-min trade observations.
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All 3 exchanges host a morning and afternoon session
Restrict to overlapping trading hours on both sessions
10:05-11:24; 14:35-14:54
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Testing methodology
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Apply GMM procedure on the bivariate system to
estimate the 5 trading parameters.
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Specify 6 moment conditions
FX X  X
G
Y Y  Y
G
G
 X
EG
 Y
G
G
 X
G
G
H Y
t
t
t 1
2
t 1
t 1
X
t
t 1
X
t
t 1
Y
t
t 1
Y
t
2
t 1
t 1
I
J
J
J
J
0
J
J
J
J
K
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Testing methodology
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Apply VECM & JTDM to rank twin boards for
each of 20 firms.
When models give conflicting rankings, apply
Wald test and J-test statistics to model
selection.
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Either or both tests favour one model over the
other
Both test statistics are conflicting or fail to reject
both models.
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Main results
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VECM and JTDM give consistent ranking in 6 firms; 3 firms
(Southern Airline, China Shipping and ZTE Corp) provide
strong evidence of H-board performing price discovery.
Wald and J tests indicate VECM (JTDM) as the preferred
model for 3 firms. In all 3, the B/H (A) board is ranked
above the A (B/H) board.
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JTDM ranks A above B/H for the 3 firms with the highest % of
no-trade in their B/H samples.
VECM and JTDM generate conflicting rankings in 8 out of
10 A-B firms. Subsequent Wald and J tests fail to reject
both models in 7 of those 8 firms.
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Unable pick up distinctions in trading since the boards
themselves are no longer distinct.
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The informativeness of
corporate bond trades
By
Peter Chen, Junbo Wang & Chunchi Wu
Discussant’s report by Michael T. Chng
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Background
• Empirical (daily & intraday) analysis of
the contribution of trades to price
discovery in the US corporate bond
market.
• Report six sets of results:
• OLS (1 & 2-step regression)
• VAR (bivariate and bivariate with duration)
• GARCH (univariate and bivariate)
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Motivation
• Lack of study on volume-volatility dynamics of corporate bond
market.
• Reliable transaction data not readily available until recent years.
• 3 measure of trading activity:
• daily volume
• trade size
• number of trades
• Contrary to equity studies, trading activity does not play a
significant role in volatility dynamics.
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Comments
• This is a detailed empirical analysis.
• The results are well presented & well discussed.
• Important as there are a lot of results to churn through
• I believe it is at least a 2nd draft, and may be in a
later stage of journal review.
• The main question I ponder on is the need to go
through six empirical analysis. I have 3 reasons for
making this comment.
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1st reason
• The bond market is a clear underdog.
• The authors report that daily bond trade averages 0.53% of
corresponding daily stock trades.
• For the market to learn from trading activity, there must be
enough generated parameters to begin with.
• The paper contributes by providing formal empirical
evidence.
• It is the value of their numerous robustness checks that I
query.
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2nd reason
• Second, even if I accept that 6 sets of results
are necessary, I would actually view them as
3 pairs of alternative empirical estimation.
• For each pair, surely one specification is more
appropriate than the other.
• E.g. If bivariate GARCH is appropriate, why
consider univariate GARCH at all?
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3rd reason
• There is a need to distinguish between the
informational efficiency of the US corporate bond
market & the informativeness of US corporate bond
trades.
• If bond trade parameters are found to be informative, this
suggest that the bond market is (more or less) performing
price discovery.
• But if bond trade parameters are not found to be
informative, this does not imply that that US corporate bond
market is NOT performing price discovery.
• Quotes could still adjust in the absence of trading, and in
response to non-trade parameters.
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Suggestions
• Rather than presenting 3 sets of ‘overlapping’ results,
maybe the authors could consider reducing the set of
results and instead:
• Providing more institutional details to further motivate a
study on bond markets and potential causes for trades to be
non-informative, and/or
• Consider other intraday measures of trade informativeness
often used in microstructure studies:
• Hasbrouck family of measures (1991a, 1991b, 1993): signed
trade size
• Madhavan, Richardson and Roomans (1997) : trade direction
• Theobald and Yallup (2004): speed of adjustment coefficients
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Questions
• Why is the stock-bond transmission effect examined in a
bivariate GARCH and not as a 4-equation VAR?
• Price discovery in equity markets is caused by interaction among
distinct investor clienteles (retail/institutional; local/foreign;
liquidity/informed). Do the sample clienteles readily apply to the
corporate bond market?
• Is it necessarily true that debt and equity securities similarly
reflect the value of a firms assets?
• Should the authors perform a nested test on Eq (2)~(4) since
(2) and (3) are nested in (4)? Similar for Eq (5)~(7).
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Editorial
• The paper is well-written, but maybe it has too many
equation numbers.
• Maybe Eq (2), (3) & (4) can be presented as one
equation since (2) and (3) are nested in (4)?
• Similar comment for Eq (5), (6) & (7)
• Eq (8) & (9) is a bivariate system and should be
labeled under as one equation number.
• Similar comment for Eq (13) & (14)
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Time varying GARCH and nested causality
relations between intraday return and order
imbalance in Nasdaq-100 component stocks
By
Yong Chern Su & Han Ching Huang
Discussant’s report by Michael T. Chng
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Background
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This paper analyze the role of order
imbalance (OI) on return and return volatility
dynamics in a GARCH framework for Nasdaq
100 component stocks.
OI is defined as buyer minus seller initiated
trades
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OINUM: number of trade
OISHA: Number of shares
OIDOL: Dollar terms
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Data
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For each of 100 stocks:
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Sample period: Month of Dec 2003
Each trading day partition into 3 subperiods:
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9:30-11:30
11:30-14:30
14:30-16:00
Sample frequency is 90-sec
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Comments
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I think the authors did well in handling such a
comprehensive database.
They trade off time-series robustness for crosssectional robustness.
However, I am sure a potential referee would still
question how representative are time-series results
based solely on Dec data.
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Hence authors should highlight details of previous slide.
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Comments
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The 5-sec rule in Lee and Ready (1991)
applies to NYSE and AMEX tick data.
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Not sure how relevant it is to Nasdaq data.
Is it possible to provide a reference that
applies the 5-sec rule on Nasdaq data?
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Comments
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Authors present two sets of GARCH (1,1) results with
slightly different specifications to both mean and
variance equations.
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Eq (1)~(2) versus Eq (5)~(6)
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As OIit-1 can be negative, could there be problem applying
Eq (2) out of sample?
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I guess this makes Eq (5)~(6) appealing.
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If this is the case, shouldn’t one GARCH specification suffice
for empirical estimation.
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Could vest excess effort to expand sample period.
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Comments
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Authors motivate their choice of 3 proxy
variable for information asymmetry across
firms.
However, I think that the analysis itself is not
well motivated.
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Why should the return-order imbalance relation
vary with the degree of information asymmetry?
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Suggestions
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I got confused reading from Eq (7) to Eq (8)
to Eq (9).
From Eq (7) to Eq (8):
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Shifting the dynamics back 1 period to focus on
out-of-sample predictive ability of OI on return
generating process.
From Eq (8) to Eq (9):
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Wouldn’t it be more interesting to investigate
cross-sectional discrepancies in the relevance of
OI in return based on varying degrees of
information asymmetry.
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Editorial
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This paper attempts to cover quite a few
issues. Maybe the authors could write an
objective paragraph on page 1 listing their
(4?) objectives.
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GARCH (1,1) estimation of return, volatility and OI
dynamics
Contrast OI & trading volume
How the return and OI interaction vary across
information asymmetry
Causality tests between return and OI in a VAR
framework.
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Editorial

Should the various  coefficients from Eq
(1)~(7) have a subscript i since it is written
against Rit?
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Footnote 5: “event day” ??
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Abstract & title both quite lengthy
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Chordia, Roll and Subrahmanyam (2005) in
the JFE is a good ref to include.
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Life cycle of the weekend effect
By
Nan Ting Chou
Charles Mossman &
Dennis Olson
Discussant’s report by Michael T. Chng
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Background
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14th Securities and Financial Markets (SFM)
conference, Kaohsiung
The price formation of substitute markets
Michael T. Chng
Dept of Finance, University of Melbourne
Aihua Xia
Dept of Mathematics & Statistics, University of Melbourne
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