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2006 National Taiwan UniversityInternational Conference in Finance

Michael T. ChngDept of Finance, University of Melbourne

Aihua XiaDept of Mathematics & Statistics, University of

Melbourne

The price formation of substitute markets

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Introduction• Price discovery: the process by which private information

implicit in investor trading is revealed in subsequent price formation.

• Price formation models:• Hasbrouck (1991a,b): Signed trade size• Madhavan, Richardson and Roomans (1997): trade

direction • Dufour and Engle (2000): time between trades• Al-Suhaibani and Kryzanowski (2000): order size• 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• J. Financial Markets dedicated a special issue [5(3), 2002]

to the two commonly used measures of cross market price discovery:

• Gonzalo & Granger (1995) common factor weights (JBES):• Computes the coefficient of error correction terms to infer

orthogonal weights on the efficient price contributed by various price sequences.

• Hasbrouck (1995) information share (JF):• 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• 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)

• 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:

• 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• Highlights the role of 1st order serial

correlation in trade direction Xt-1 • Xt assumed to follow a general Markov

process

• The model considers 3 states S: {+1, 0, -1}

• 3x3 transition matrix

• Transition of Xt illustrated in Figure 1

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The MRR (1997) model

1 1

1 1

( [ | ])

* [ | ] , where 2 (1 )

[ (1 ) (1 ) ]

t t t t t t

t t t t

t t t

t t t t t

u u X E X X

p u X

E X X X

r p L L X

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Our model• A bivariate system that highlights the joint

trade direction (Xt, Yt) in price formation.

• (Xt, Yt) assumed to follow a general Markov process

• We consider 4 states S:{(1,1), (1,-1), (-1,1), (-1,-1)}

• 4x4 transition matrix

• Transition of (Xt, Yt) illustrated in Figure 2

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Categorizing the 16 transitions

• Full continuation: Pr (Xt=Xt-1,Yt=Yt-1|Xt-1 ,Yt-1) =

• X-continuation: Pr (Xt=Xt-1,Yt=-Yt-1|Xt-1 ,Yt-1) = X

• Y-continuation: Pr (Xt=-Xt-1,Yt=Yt-1|Xt-1 ,Yt-1) = Y

• Full reversal: Pr (Xt=-Xt-1,Yt=-Yt-1|Xt-1 ,Yt-1) = (1--X-Y)

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The model’s focus• 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 system1 1 1

1 1 1 1

1 1

( [ | , ])

* [ | , ]) ,

where 2( ) 1 and 2( ) 1

2( )

( ) (1 ) (1 )

(

t t t t t t t t t

X X Xt t t t

Y Y Yt t t t

t t t t t t

X Y

X Y

X X Xt t t t t t

Yt

u u X Y E X Y X Y

p u X

p u Y

E X Y X Y X Y

r X Y X Y

r

1 1) (1 ) (1 )Y Yt t t t tY X X Y

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Twin-share Chinese firms• Why Chinese market?

• 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.

• Some institutional details• 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

• For all firms that are selected:• 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• A pair of A-B and A-H firms for each of 10 sectors

of the Chinese economy.

• Sample period: 4th Jan~30th Sep 05 ( 170 days).

• Each day has 100 min-by-min trade observations.• 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• Apply GMM procedure on the bivariate

system to estimate the 5 trading parameters.

• Specify 6 moment conditions

E

X X X

Y Y Y

X

Y

X

Y

t t t

t t t

tX

t

tXt

tY

t

tYt

F

H

GGGGGGGG

I

K

JJJJJJJJ

1 12

1 12

1

1

1

1

0

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Testing methodology• 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.

• 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• 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.

• 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.

• Unable pick up distinctions in trading since the boards themselves are no longer distinct.

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The informativeness ofcorporate bond trades

ByPeter 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

ByYong Chern Su & Han Ching Huang

Discussant’s report by Michael T. Chng

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Background 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 OINUM: number of trade OISHA: Number of shares OIDOL: Dollar terms

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Data

For each of 100 stocks: Sample period: Month of Dec 2003 Each trading day partition into 3 sub-

periods: 9:30-11:30 11:30-14:30 14:30-16:00

Sample frequency is 90-sec

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Comments I think the authors did well in handling such a

comprehensive database.

They trade off time-series robustness for cross-sectional robustness.

However, I am sure a potential referee would still question how representative are time-series results based solely on Dec data.

Hence authors should highlight details of previous slide.

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Comments

The 5-sec rule in Lee and Ready (1991) applies to NYSE and AMEX tick data. 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 Authors present two sets of GARCH (1,1)

results with slightly different specifications to both mean and variance equations.

Eq (1)~(2) versus Eq (5)~(6)

As OIit-1 can be negative, could there be problem applying Eq (2) out of sample?

I guess this makes Eq (5)~(6) appealing.

If this is the case, shouldn’t one GARCH specification suffice for empirical estimation.

Could vest excess effort to expand sample period.

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Comments Authors motivate their choice of 3 proxy

variable for information asymmetry across firms.

However, I think that the analysis itself is not well motivated. Why should the return-order imbalance

relation vary with the degree of information asymmetry?

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Suggestions I got confused reading from Eq (7) to Eq

(8) to Eq (9). From Eq (7) to Eq (8):

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): 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 This paper attempts to cover quite a

few issues. Maybe the authors could write an objective paragraph on page 1 listing their (4?) objectives. 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?

Footnote 5: “event day” ??

Abstract & title both quite lengthy

Chordia, Roll and Subrahmanyam (2005) in the JFE is a good ref to include.

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Life cycle of the weekend effect

ByNan 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

Michael T. ChngDept of Finance, University of Melbourne

Aihua XiaDept of Mathematics & Statistics, University of

Melbourne

The price formation of substitute markets