Trading Imbalances and the
Relative Prices of Stock Pairs
April 2011
Mark S. Seasholes
HKUST
AH Xsec
Clark Liu
HKUST
© MSS 2011
Page 1
AH Premium Index
• Clark and I recently had a short paper accepted at Economics Letters
– There are 42 companies in the AH Index as of April 2009
– Pa is a share price in China (mainland) converted to US$
– Ph is a share price in Hong Kong converted to US$
WgtAvg  Pt a 
100
h
– Shares have same dividend and voting rights
WgtAvg  Pt 
250
200
150
100
50
AH Xsec
AH Premium
Index
© MSS
2011
Parity
Apr-2009
Jan-2009
Oct-2008
Jul-2008
Apr-2008
Jan-2008
Oct-2007
Jul-2007
Apr-2007
Jan-2007
Oct-2006
Jul-2006
Apr-2006
Jan-2006
0
Page 2
Jiangxi Copper
• Below is a graph of the ratio of Jiangxi Copper’s relative stock prices
– Shares have same dividend and voting rights
• Two interesting points:
a) High level of difference
Pt a
100
b) High level of volatility
Pt h
400
350
300
250
200
150
100
50
AH Xsec
© MSS 2011
Apr-2009
Jan-2009
Oct-2008
Jul-2008
Apr-2008
Jan-2008
Oct-2007
Jul-2007
Apr-2007
Jan-2007
Oct-2006
Jul-2006
Apr-2006
Jan-2006
0
Page 3
Economic Questions
AH Xsec
© MSS 2011
Page 4
Economic Questions
• Main questions:
– Why do a given company’s shares, trading at two different locations,
have different prices?
– Can we changes explain changes in relative prices?
– Can we link trading imbalances to these changes?
– Can we estimate economic magnitudes that tell us about the amount of
noise in a developed stock market (Hong Kong)?
– Ultimately (not today) I hope to learn something about the relative
importance of studying sentiment vs. frictions in markets?
• Frictions:
– This paper continues my work on market frictions, investor trading
behavior, and asset prices.
– In this paper, we study a short-sale constraint in one market combined
with limited risk-bearing capacity in two different markets.
AH Xsec
© MSS 2011
Page 5
Institutional Background
AH Xsec
© MSS 2011
Page 6
China (Mainland) Companies
• Chinese companies can have different share classes
– “a” shares trade in China (mainland) and are originally for domestic
shareholders
• Listed on Shanghai or Shenzhen stock exchanges
– “h” shares trade in Hong Kong
• There are additional share classes:
– “b” shares trade in the PRC and are originally for foreigners
– ADRs trade in the USA
– “n” shares trade on the NYSE or Nasdaq
– “s” shares trade in Singapore
• While the shares are technically different classes, many have the same
dividend and voting rights.
AH Xsec
© MSS 2011
Page 7
Why Study a- and h-shares?
• Nice institutional setting
– Two classes of shares from the same company with same dividend and
voting rights.
– Shares are not fungible.
– Relative share prices are tracked by investors and the financial media
on a daily basis (Hang Seng publishes the “AH Premium Index”)
– Shanghai and Hong Kong are in the same time zone.
– No off-exchange trading on either exchange.
– Investors read/write using Chinese characters (simple and traditional).
– Many investors can trade on both exchanges.
– Both a-shares and h-shares have high turnover. There are few worries
about liquidity and illiquidity in this study.
AH Xsec
© MSS 2011
Page 8
Theoretical Framework
AH Xsec
© MSS 2011
Page 9
Theoretical Model
• We model an economy with a single firm that has two claims to its
dividends (i.e., two share classes).
– The shares are equal in all respects except they trade on two separate
markets and are not fungible.
• There are four dates t = { 0, 1, 2, 3 }
• There are two markets { a , h } generally shown as super-scripts
• Risky assets pay the same dividend (i.e. for each share class):
t  N 0, t 
D3  D  1   2  3
•
We denote the prices of the risky assets at date t as:
P , P 
a
t
AH Xsec
P3a  P3h  D3
h
t
© MSS 2011
Page 10
Theoretical Model (2)
We use “X” to denote the holdings of a group on a given date t:
• Market a has two groups of investors that trade only in that market:
– { Xti(a) , Xth(a) }
i(a) = informed; h(a) = noise traders
•
Market h has two groups of investors that trade only in that market:
– {Xti(h) , Xth(h) }
i(h) = informed; h(h) = noise traders
•
Final group consists of arbitrageurs who may hold shares in both markets
– {Xta(a) , Xta(h) }
•
Short-sale constraint
– The arbitrageurs holdings in market a are constrained to be nonnegative on all dates: Xta(a) ≥ 0
– Assumption captures: one of the markets has a short sale constraint
AH Xsec
© MSS 2011
Page 11
Theoretical Model (3)
•
Part of the dividend (t) is revealed to all investors at each date t
•
Agent’s maximize expected CARA utility: U[ W(3) ] = – elW(3)
– To simplify expressions, we need to make an assumption about risk
aversion coefficients: l = lia = 0.5lih = 0.5la
•
We can solve for prices and holdings of each group at each date using
backwards induction
– At each date, we need to consider whether or not the short-sale
constraint is binding
– We then need to consider the possibility that the short-sale constraint
might bind in the future
•
Key point: Arbitrageurs drive prices so that expected returns (not prices)
are equal across markets
AH Xsec
© MSS 2011
Page 12
Theoretical Model (4)
•
We can solve for prices and holdings of each group at t={0, 1, 2, 3}
– Therefore, we solve for changes in prices (returns)
– We also solve for changes in holdings (“order imbalances” or “OIB”)
•
The AH Premium at date t is defined as: AH Premt = Pta – Pth
•
Date
AH Premium in
Non-Binding Case
t=1
l 12  32  X1h ( a )  X1h ( h) 
l 32
 a2

2  a2  h2

 h.o.t.
AH Premium in
Binding Case
l  22  12  32  X1h ( a )  X1h ( h) 
l 32
 a2

2  a2  h2

 h.o.t.
Arbitrageurs care about the possibility that the short-sale constraint might
bind in the coming periods
AH Xsec
© MSS 2011
Page 13
Theoretical Model (5)
•
A disclaimer…
•
This is a CARA-normal model and we define returns and the AH Premium
using price differences. Market conventions define both using ratios and
we will too in our empirical analysis
AH Premt = Pta – Pth
AH Xsec
© MSS 2011
Pi ,at
AH Premi ,t  h 100
Pi ,t
Page 14
Numerical Analysis
AH Xsec
© MSS 2011
Page 15
Numerical Analysis
•
•
•
•
•
We draw one set of random numbers and then calculate prices and holdings
at each date: t = { 0, 1, 2, 3 }
Calc. returns, OIBs, and auto-corr. over intervals t = 0→1 and t = 1→2
We repeat the exercise 170 times to simulate having 170 weeks of data
Numerical parameters are chosen to match empirical moments
For example: DXh(a) ~N[0,0.0050] and
DXh(h) ~N[0,0.0020]
•
Same assumption about risk tolerance: l = lia = 0.5lih = 0.5la
•
Holdings chosen to match steady-state equilibrium values:
Group
Stock a
Stock h
Noise Traders
50%
50%
Informed Investors
50%
25%
Arbitrageurs
0%
25%
100%
100%
Total
AH Xsec
© MSS 2011
Page 16
Numerical Analysis (2)
The model generates a number of predictions:
#1
#2
#3
#4
#5
#6
#7
AH Xsec
Mean Reversion: The AH Premium is mean reverting
Skewness: The AH Premium is positively skewed
Binding of Short Sale Constraint:
- This implication is not testable (quantities are not observable)
Volume and Order Imbalances
- Volume in mkt a is more than double that of mkt h
Cross-Market Return Correlations
- Correlation of ra and rh is 0.64
Return-OIB Correlations
- Correlation is stronger in mkt a than in mkt h
Company-Level AH Premiums
- Average level is proportional to fundamental volatility
© MSS 2011
Page 17
Empirical Data
AH Xsec
© MSS 2011
Page 18
Sample Selection & Table I, Panel A
• We choose the 43 companies that have been included in the AH Premium
Index between Jan-2006 and Apr-2009
• Average market capitalization is USD 12.6 billion (median USD3.6 bn)
Name
Air China
Anhui Conch
Anhui Expressway
Bank of China
Bankcomm
Beijing N Star
CCB
CHALCO
China Coal
China COSCO
Average
Median
AH Xsec
A Ticker H Ticker
601111
0753
600585
0914
600012
0995
601988
3988
601328
3328
601588
0588
601939
0939
601600
2600
601898
1898
601919
1919
Mkt Cap
(US$ mil)
3,611
8,784
549
31,116
34,094
1,147
133,111
8,833
5,781
5,954
12,639
3,611
© MSS 2011
# of Wks
Indus (GICS Codes)
of Data
Airlines
140
Construction Materials
173
Transp. Infrastructure
165
Commercial Banks
147
Commercial Banks
102
Real Estate Mgmt
132
Commercial Banks
82
Metals & Mining
104
Oil, Gas & Fuels
60
Marine
96
118
122
Page 19
Empirical Data
• Paper shows weekly results (defined Wednesday-to-Wednesday)
– 03-Jan-2006 to 30-Apr-2009
• Price and return data
– Prices and returns from Datastream
– All values (prices) are converted to USD
• FX rates from Datastream
Pi ,at
AH Premi ,t  h 100
Pi ,t
• Volume and turnover data
– Number of tradeable shares (free floats) are from Hang Seng
– Volume data from Datastream
AH Xsec
© MSS 2011
Page 20
Figure 1: Cross-Section of AH Premiums
• Below is a graph of the 25th, 50th, and 75th highest AH Premiums
Pt a
100
Pt h
400
350
300
250
200
150
100
50
25th
AH Xsec
50th
© MSS 2011
75th
Apr-2009
Jan-2009
Oct-2008
Jul-2008
Apr-2008
Jan-2008
Oct-2007
Jul-2007
Apr-2007
Jan-2007
Oct-2006
Jul-2006
Apr-2006
Jan-2006
0
Parity
Page 21
Figure 2: AH Premiums of Three Companies
• Below is a graph of the AH Premium for three companies
Pt a
100
Pt h
400
350
300
250
200
150
100
50
China Ship
Jiangxi Copper
AH Xsec
Apr-2009
Jan-2009
Oct-2008
Jul-2008
Apr-2008
Jan-2008
Oct-2007
Jul-2007
Apr-2007
Jan-2007
Oct-2006
Jul-2006
Apr-2006
Jan-2006
0
Shenzhen Expressway
Parity
© MSS 2011
Page 22
Table I, Panel B
• Overview stats of price related variables
Name
Air China
Anhui Conch
Anhui Expressway
Bank of China
Bankcomm
Beijing N Star
CCB
CHALCO
China Coal
China COSCO
Average
Median
AH Xsec
Avg
AH Premi,t
206.6
104.9
126.0
142.6
125.0
291.0
124.3
219.0
146.7
184.0
Stdev
AH Premi,t
65.1
16.8
26.3
28.3
22.5
70.5
19.8
45.1
29.1
46.2
AR(1)
Coef
0.94
0.87
0.93
0.94
0.92
0.89
0.91
0.86
0.78
0.84
Frac w/
Pa ≤ Ph
4%
43%
24%
15%
24%
0%
9%
0%
2%
0%
Corr
(ra, rh)
0.56
0.60
0.15
0.43
0.57
0.54
0.61
0.51
0.52
0.50
182.1
153.6
39.5
36.6
0.84
0.88
8%
2%
0.47
0.50
© MSS 2011
Page 23
Empirical Data: OIB
Order imbalance data
• From Thomson Reuters Tick History (TRTH) database
• 563 million plus 61 million trades
Step 1: For each stock “i” and each day
“k” and each market {a or h}, we
calculate order imbalances.
Winsorized at the 0.5% and 99.5%
levels
OIB 
a*
i ,k
Step 2: Standardize daily, order
imbalances.
Step 4: Calculate a weekly, companylevel measure
AH Xsec
Buyia,k  Sellia,k
OIB 
Shrsia,k
a
i ,k
© MSS 2011
OIBia,t 
OIBia,k  mean OIBia,k 11:k 70 
stdev OIBia,k 11:k 70 

kweek "t "
OIBia,k*
Page 24
Table I, Panel C
• Overview stats of trading related variables
Name
Air China
Anhui Conch
Anhui Expressway
Bank of China
Bankcomm
Beijing N Star
CCB
CHALCO
China Coal
China COSCO
Average
Median
AH Xsec
Free Float
Mkt a
0.16
0.26
0.33
0.03
0.25
0.43
0.92
0.21
0.18
0.20
Free Float
Mkt h
0.54
1.00
1.00
0.39
0.62
1.00
0.20
1.00
0.98
0.96
Avg
Turn(a)
0.17
0.07
0.10
0.11
0.10
0.24
0.07
0.11
0.13
0.15
Avg
Turn(h)
0.07
0.04
0.02
0.07
0.03
0.05
0.04
0.07
0.05
0.10
Corr
(OIBa, OIBh)
0.20
0.12
0.09
0.07
-0.09
0.11
-0.25
0.12
-0.11
0.09
0.24
0.22
0.89
1.00
0.13
0.12
0.05
0.05
0.01
0.04
© MSS 2011
Page 25
State Space (Statistical) Model
AH Xsec
© MSS 2011
Page 26
State Space Model with Trading Variables
•
Assume observable prices are composed of two unobservable components
– Component #1: “Efficient price” ( mi,t ) follows a process of
uncorrelated increments with a non-zero drift ( di,t )
– Component #2: “Transitory price pressure” ( si,t ) assumed stationary
•
In this paper, a given company has two observable stock prices and one
efficient (fundament) price. Think about Hong Kong prices only
pia,t  mi ,t  sia,t  c
pih,t  mi ,t  sih,t
mi ,t  mi ,t 1  d i ,t  wi ,t
wi ,t   aOIBia,t   hOIBih,t  ui ,t
sia,t   a sia,t 1   aOIBia,t   ia,t
sih,t   h sih,t 1   hOIBih,t   ih,t
AH Xsec
© MSS 2011
Page 27
State Space Model (2)
•
Estimated on a stock-by-stock basis
– We don’t estimate coefs for two companies due to lack of data
– Price of stock i is in logs
– The “c” is used to estimate the average amount that Pa is above Ph
– The ( di,t ) is the required return on the stock
– Assume ( ui,t ) and ( i,t ) are normally distributed and independent
•
We use Kalman filter to get estimates of mi,t and si,t :
– Estimation is implemented in Ox ; Kalman filter w/ ssfpack add-on
AH Xsec
© MSS 2011
Page 28
Parameter Estimates
•
•
Results related to the efficient price equation
a
h
u
Param
0.0012
-0.0001
0.0288
Stderr
(0.0005)
(0.0004)
(0.0021)
Fundamental information appears to be incorporated into prices via trading
in the a-share market
AH Xsec
© MSS 2011
Page 29
Parameter Estimates (2)
•
•
•
Results related to the transitory price equations
a
h
a
h
(a)
(h)
Param
0.8561
0.8469
0.0056
0.0040
0.0580
0.0584
Stderr
(0.0055)
(0.0116)
(0.0006)
(0.0006)
(0.0023)
(0.0023)
A first-order auto-correlation coefficient of 0.85 implies shocks have halflives of 4.27 weeks.
The -coefficients indicate that order imbalances affect transitory prices in
both the a- and h-markets.
AH Xsec
© MSS 2011
Page 30
Economic Magnitudes
•
•
We multiply coefficients by the standard deviations of our trading variables
to better understand economic magnitudes
Effic. Eq
b.p.
a (OIBa)
h (OIBh)
(w)
34
-4
203
Trading explains only a small about of efficient price changes
AH Xsec
© MSS 2011
Page 31
Economic Magnitudes (2)
•
We multiply coefficients by the standard deviations of our trading variables
to better understand economic magnitudes
Trans Eq
b.p.
Trans Eq
b.p.
a (OIBa)
(Dsa)
166
h (OIBh)
(Dsh)
122
797
576
•
A one standard deviation shock to OIBa is associated to a 166 bp move in
transitory a-share prices at a weekly frequency
•
A one standard deviation shock to OIBh is associated to a 122 bp move in
transitory h-share prices at a weekly frequency
AH Xsec
© MSS 2011
Page 32
Variance Decomposition
•
We decompose total variance to get more economic results
pih,t  mi ,t  sih,t
pih,t 1  mi ,t 1  sih,t 1
Dpih,t  Dmi ,t  Dsih,t
 2  ri h,t    2  mi ,t    2  Dsih,t   2Cov  mi ,t , Dsih,t 
2(rh)
2(Dm)
2(Dsh)
2Cov(m,Ds)
Average
100%
39.6%
45.6%
14.8%
Stderr
n.a.
(6.2%)
(7.1%)
(2.3%)
AH Xsec
© MSS 2011
Page 33
Cross-Sectional Analysis
• We test Implication #7, by regressing a company’s avg(AH Premi,t) over the
sample period on the standard deviation of efficient price changes which
we can calculate as (wi,t)
– This makes use of the Kalman filter as we extract the time series of mi,t
and use it to calculate (wi,t)
Avg  AH Premi,t   b0  b1  (wi,t )  ei,t
• The coefficient b1 is estimated to be 0.26 with a 4.92 t-statistic.
AH Xsec
© MSS 2011
Page 34
Conclusions
AH Xsec
© MSS 2011
Page 35
Our Conclusions
• Trading imbalances are associated with cross-border price deviations.
• A one standard deviation shock to trading imbalances in mainland China
(or Hong Kong) is associated with 166 bp (or 122 bp) movement in
transitory prices at a weekly frequency.
• We estimate 45.6% of a Hong Kong stock’s total variance is due to
transitory price movements.
• The half-live of these movements is around 4.2 weeks.
• This research helps focus future efforts on understanding where the trading
imbalances are coming from.
AH Xsec
© MSS 2011
Page 36
Comments on Investor Sentiment
AH Xsec
© MSS 2011
Page 37
Investor Sentiment
• Currently, a “hot” topic or theme in financial economics
– What is an exact definition of investor sentiment?
• Scenario #1: Investors in both markets have relatively homogeneous beliefs
about a company’s prospects. Good news is released.
– Stock prices in both markets rise
– AH Premium is constant
– Trading volume is low (everyone wants to buy at old prices)
• Scenario #2: Investors in both markets have relatively homogeneous beliefs
about a company’s prospects. A “wave of positive sentiment” hits investors
in Shanghai.
– Prices in Shanghai rise
– AH Premium increases
– Trading volume in Shanghai is low (everyone wants to buy)
AH Xsec
© MSS 2011
Page 38
Investor Sentiment (2)
• Scenario #3: Investors in both markets have similar dispersion in beliefs
about a company’s prospects. Good news is released.
– Prices in both Shanghai and Hong Kong rise
– AH Premium is constant to a first order
– Trading volume in Shanghai and Hong Kong can be large as investors
rebalance portfolios based on the new information.
• Scenario #4: A “wave of positive sentiment” hits a subset of investors in
Shanghai
– Prices in Shanghai can rise
– AH Premium can go up
– Trading volume in Shanghai can be large as the sentiment prone
investors buy shares from the other investors in Shanghai
– Trading volume in Shanghai and Hong Kong should be uncorrelated
AH Xsec
© MSS 2011
Page 39
Extra Slides
AH Xsec
© MSS 2011
Page 40
AH Xsec
AH Premium Index
© MSS 2011
Jan-2011
Sep-2010
May-2010
Jan-2010
Sep-2009
May-2009
Jan-2009
Sep-2008
May-2008
Jan-2008
Sep-2007
May-2007
Jan-2007
Sep-2006
May-2006
Jan-2006
AH Premium Index
• Updated graph through last week
250
200
150
100
50
0
Parity
Page 41