Directory UMM :Data Elmu:jurnal:J-a:Journal Of Banking And Finance:Vol25.Issue2.2001:
Journal of Banking & Finance 25 (2001) 355±375
www.elsevier.com/locate/econbase
Relative informational eciency of cash,
futures, and options markets: The case of an
emerging market
Raymond Chiang a, Wai-Ming Fong
a
b,*
Department of Accountancy, Hong Kong Ploytechnic University, Kowloon, Hong Kong
Department of Finance, Chinese University of Hong Kong, Shatin, N.T., Hong Kong
b
Received 12 July 1999; accepted 7 October 1999
Abstract
We study the lead±lag relationships among the spot, futures, and options markets on
Hong KongÕs Hang Seng Index (HSI). The young options market experiences thin
trading, and the option returns lag the cash index returns. The more mature futures
market experiences active trading. Yet its lead over the cash index appears to be less than
the counterparts in other countries. A possible reason is the dominance of a few major
stocks in the index; and these stocks have symmetric lead±lag relations with the futures.
Furthermore, the informativeness of the non-lasting futures and options quotations
seems to depend on the market maturity. Ó 2001 Elsevier Science B.V. All rights reserved.
JEL classi®cation: G10; G12; G13
Keywords: Hang Seng Index; Futures; Options; Lead±lag relationships
1. Introduction
Citing the leverage eects and lower trading costs in index derivatives, ®nancial economists often argue that returns on index futures or options lead
*
Corresponding author. Tel.: +852-2609-7903; fax: +852-2603-6586.
E-mail address: wmfong@baf.msmail.cuhk.edu.hk (W.-M. Fong).
0378-4266/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 6 6 ( 9 9 ) 0 0 1 2 7 - 2
356
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
the cash index returns more than the feedback. Empirical evidence has been
widely documented for mature ®nancial markets such as the United States
(e.g., Finnerty and Park, 1987; Kawaller et al., 1987; Stoll and Whaley, 1990;
Chan, 1992; Fleming et al., 1996). These studies suggest that index derivative
markets are more ecient in incorporating new information, particularly
market-wide information. 1 In mature ®nancial markets, market participants
are well acquainted with derivative securities, which are therefore common
investment and ®nancial management tools. On the other hand, derivative
securities are novel in emerging ®nancial markets. In these markets, derivatives
may encounter low liquidity because they are unfamiliar to investors. It is then
possible that they are not more informationally ecient than the underlying
spot index.
In this paper, we study the lead±lag relation of two derivative markets with
the underlying cash market of an emerging ®nancial center in the Asia±Paci®c
Rim. The derivatives studied are the Hang Seng Index (HSI) futures and options traded on the Hong Kong Futures Exchange (HKFE). HSI is a valueweighted index composed of 33 blue-chip stocks in Hong Kong. We study the
lead±lag relation between the intraday HSI futures (options) returns and spot
HSI returns to shed light on the relative informational eciency across the
futures (options) market and the spot market. Because the HSI futures market
(completely revamped after the 1987 market crash) is more mature than the
HSI options market (commenced in 1993), our analysis could also provide
insights on the relative informational eciency across emerging derivative
markets at dierent stages of development. 2 In Finland, Puttonen (1993) ®nds
that the Finnish Options Index (FOX) futures and options markets, which
both commenced on 2 May 1988, have similar informational eciency.
Using intraday data from January to September 1994, we ®nd that HSI
option returns lag more than lead HSI returns. This contrasts sharply with
options markets in other countries where cash index returns lag more than lead
option returns, e.g., the United States (Finucane, 1991; Fleming et al., 1996),
Finland (Puttonen, 1993), and Switzerland (Stucki and Wasserfallen, 1994). To
investigate why HSI options lag the spot index, we compare their liquidity with
the index component stocks. We observe that the option contracts are thinly
traded. In fact, even the relatively popular contracts are less actively traded
than most of the component stocks. These suggest that the staleness of option
prices causes the spot indexÕs lead. Furthermore, the option quotations do not
1
See Chan (1990) and Subrahmanyam (1991). Chan (1992) argues and provides evidence that
index futures market can process market-wide information better than cash market. His argument
should also apply to index options market.
2
Related studies include Fung et al. (1997) and Bae et al. (1998), which examine the arbitrage
opportunities between the HSI futures and options markets.
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
357
seem to be as informative as good-till-revision quotations on other markets.
The option returns computed with bid±ask midpoints still lag the HSI returns.
This contrasts with the ®nding of Chan et al. (1993) that the stockÕs lead over
the option documented in Stephan and Whaley (1990) disappears when goodtill-revision quotes replace trade prices in calculating option returns. 3 A likely
explanation for our results is that the HSI option quotes may sometimes be
stale. In the open outcry trading system of the HKFE, the quotes are only good
for immediate trade and non-lasting, so they need to re¯ect market conditions
solely at the time of posting. These quotes can be stale if they are not updated
to re¯ect change in market conditions, yet unlike the case of good-till-revision
quotes, traders cannot take advantage of the stale non-lasting quotes. Consistent with this explanation, we observe that the HSI option quotes are updated infrequently.
The options marketÕs relative informational ineciency could be attributed
to the fact that it is much less mature than the futures market, such that traders
prefer to trade futures rather than options and the market makers focus on
their futures quotes. Consistent with this, we observe that on the futures
market, there are transactions and quotes in almost every minute. The futures
are even more actively traded than all the HSI component stocks. Not surprisingly, they are found to lead more than lag the cash index. One possible
reason for the futuresÕ lead is the non-synchronous trading among component
stocks in the index. Indeed, we ®nd ®rst-order autocorrelation exists in the HSI
returns. Following Stoll and Whaley (1990), the autocorrelation in the HSI
returns is purged to mitigate the eects of non-synchronous trading. The lead±
lag relation between the futures and cash then becomes symmetric. This contrasts with the results from other countries which show that cash index lags
more than leads index futures even after non-synchronous trading among
component stocks is considered (e.g., for the United States, see Stoll and
Whaley (1990) and Chan (1992); for the Finnish markets, see Puttonen (1993)).
Since the HSI futures are very actively traded, it is puzzling that their lead over
the cash appears to be less than the counterparts in other countries. One likely
explanation is that the HSI is value-weighted and aected substantially by a
few major stocks, which are nearly as actively traded as the futures and are in
dominant economic sectors. Consistent with this explanation, we ®nd that four
of the biggest component stocks, which account for nearly 35% of index
capitalization, have more or less symmetric lead±lag relations with the futures.
3
When Stephan and Whaley (1990) ®nd that stocks lead stock options using trade prices to
calculate returns, Chan et al. (1993) suspect that it is probably caused by stale option prices. They
proceed to resolve the puzzle using good-till-revision quotes to calculate option returns. They then
®nd that stocks no more lead the options. Unlike trade price, good-till-revision quote has to
account for market conditions until the next quote. It cannot be stale, otherwise the market maker
may incur loss.
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R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
This ®nding contrasts sharply with the results for other countries such as Chan
(1992) who ®nds that each MMI component stock lags the MMI futures.
The rest of the paper is organized as follows. In Section 2, we describe our
data. Our methodology is explained in Section 3. We present our ®ndings in
Section 4. The paper is concluded in Section 5.
2. Data
The HSI, a value-weighted index, is the most commonly used benchmark for
Hong KongÕs stock market. Its 33 component stocks account for more than
70% of the total market capitalization. All of the component stocks are traded
on the Stock Exchange of Hong Kong (SEHK), which is open from Monday to
Friday, from 10:00 to 12:30 and from 14:30 to 15:45 (15:30 before July 1994).
Trading on the market is conducted by an order-driven system, the Automatic
Order Matching and Execution System (AMS), without the services of specialists or designated market makers.
The HSI futures contracts were introduced on 6 May 1986 by the HKFE
and completely revamped after the 1987 market crash. As the stock market
began to rise in 1992, futures trading became active again. In 1994, the average
daily volume was about 17,000 contracts. The contract size is the HSI futures
price times HK $50. The last trading day is the second last business day of the
maturity month. The delivery (expiration) months include the spot month, the
next calendar month, and the next two calendar quarter months. The market
opens from Monday to Friday, from 10:00 to 12:30 and from 14:30 to 16:00
(15:45 before July 1994), so the afternoon market close is 15 minutes later than
the stock market. Trading on the futures market is conducted by the open
outcry system.
The HSI option contracts were launched on 5 March 1993 by the HKFE.
The contracts are European in nature. At expiration, the contracts are cash
settled if they are in-the-money. The contract cycle and trading hours are the
same as the HSI futures contracts. The trading was thin in 1993, with a daily
average of only several hundred lots. The contracts gained more popularity in
1994, and the average daily volume was about 2500 contracts. Similar to the
futures, trading on the options market is conducted by the open outcry
system.
Our data on the HSI are provided by HSI Services. The data set consists of
minute-by-minute data on the index from January to September 1994. Each
trading day is divided into 5-minute trading intervals. Consequently, the ®rst
(last) trading interval in the morning ends at 10:05 (12:30) and the ®rst (last)
trading interval in the afternoon ends at 14:35 (15:30 before July 1994 and
15:45 otherwise). Because we exclude overnight return (over-the-lunch-break
return), the ®rst 5-minute return of every morning (afternoon) is computed as
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
359
the logarithmic ratio between the HSI at 10:10 (14:40) and the HSI at 10:05
(14:35).
The data on the HSI futures and options trades and quotations are provided
by the HKFE. The data set consists of all time-stamped records of trades, bids,
and asks, and all records of opening prices and closing prices of all HSI futures
and options contracts for each trading day during January±September 1994.
There are many dierent contracts of futures and options available for trading
each day. To mitigate thin trading problem, we focus on more frequently
traded futures and options contracts. Since trading occurs mainly in the nearby
contracts, the data from the spot-month contracts are used; ®ve trading days
before expiration, the contracts are rolled over to the next-month to mitigate
the expiration eects documented elsewhere. For futures, there is only one
spot-month contract each day. For calls and puts, there are many strike prices
per delivery month; each day we use the data from the most frequently traded
call and the most frequently traded put (by number of trades during the day).
Thus, for each of the 185 sample trading days, we focus on one futures contract, one call contract, and one put contract.
The data are then divided into 1-minute trading intervals such that the ®rst
(last) trading interval in the morning ends at 10:01 (12:30) and the ®rst (last)
trading interval in the afternoon ends at 14:31 (15:45 before July 1994 and
16:00 otherwise). For each of the futures, call, and put contracts, we keep the
data on the last price, bid, and ask for each trading interval. If there is no trade
(bid quotation or ask quotation) in the interval, the last price (bid or ask) is
regarded as missing.
Using the above minute-by-minute data set, 5-minute returns for every
contract are computed as follows. First, each trading day is divided into 5minute trading intervals. We then keep the data on the last available price, bid,
and ask for each trading interval. If there is missing price (bid or ask) in the
interval, the price (bid or ask) of the previous interval is used. Finally, we
compute the 5-minute trade return in every interval as the logarithmic ratio
between the price of the interval and that of the previous interval. Quotation
returns are computed with the bid±ask midpoints of the intervals. We exclude
overnight returns and over-lunch-break returns.
In the absence of accurate data on intraday transaction volume from the
HKFE, we report trading (quotation) frequency in terms of the frequency of
intervals having trades (quotes) in Table 1. 4 In our sample, there are 185 fu-
4
In Hong Kong Futures Exchange (1995, p. 4), the HKFE ocials wrote: ``The price reporting
system is designed to report prices on a real time basis, but not volume. Under the open outcry
system, the price reporting sta members can report the volume only after a trade is concluded.
Hence, they will input the estimated volume based on initial observation and then update it from
time to time during the day in accordance with the actual volume entered into the clearing system''.
360
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Table 1
HSI futures and options: Trading and quotation frequencies, January±September 1994a
I. Futures days
1. Percentage of 5-min intervals
having trades/bids/asks
2. Average time of the last trade/
bid/ask in a 5-min interval
II. Option mornings
A. The most active call
1. Percentage of 5-min intervals
having trades/bids/asks
2. Average time of the last trade/
bid/ask in a 5-min interval
B. The most active put
1. Percentage of 5-min intervals
having trades/bids/asks
2. Average time of the last trade/
bid/ask in a 5-min interval
Trade
Bid
Ask
99.99
99.96
99.94
4.93
4.92
4.91
28.28
36.88
37.06
3.24
3.3
3.3
23.84
31.85
30.84
3.19
3.19
3.21
a
Reported are trading and quotation frequencies of the spot-month futures each day, of the most
active call and the most active put each morning. Trading and quotation frequencies are expressed
in terms of the percentage of 5-minute intervals having trades/bids/asks and the average time of the
last trade/bid/ask in a 5-minute interval (if the last trade/bid/ask is observed in the 4th (5th) minute,
the time is recorded as 4 (5)).
tures days; and as illustrated in Panel I, practically all the intervals have trades
and quotes. For every interval having trades (or quotes), we take the time when
the last trade (or quote) is observed as the time of observation. For example, if
the last trade is observed in the 4th minute, the time of observation is 4. The
average observation time for intervals with trades (bids and asks) displayed in
Panel I is 4.93 (4.92 and 4.91). In other words, the last trade and the last quotes
for the futures are observed mainly during the 5th minute of each interval.
Given the timing of the last trade and quotes are almost identical, any dierence in ®ndings between futures trade returns and quote returns should arise
from bid±ask bounce in trade prices.
The trading and quotation frequencies during morning for the calls and the
puts are displayed in Panel II. 5 Many of the 185 call mornings and 185 put
mornings in our sample actually experience thin trading. For the calls, only
28.28% of the intervals have trades. We fare better with quotes: there are
observations about 37% of the time. The puts are even less active than the calls;
5
Afternoon trading sessions are too short and produce too few observations to be usable for the
later tests.
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
361
the frequency is 23.84%, 31.85%, and 30.84%, respectively, for trades, bids, and
asks. Furthermore, the time of observing the trade and quotes for the calls
(3.24, 3.30, and 3.30) is also closer to the 5-minute mark than that for the puts
(3.19, 3.19, and 3.21). Thus, it seems that the market makers pay less attention
to the put quotes and update them less frequently. One likely reason is that the
put contracts are less actively traded than the calls, such that the market
makers have less incentive to update put quotes. Overall, the trading and
quotation frequencies and the average timing of the last trade/quotes for these
calls and puts are nowhere near those for futures contracts. As a result, we
expect information to be re¯ected in the futures prices and quotes better than
the options.
One key factor of the lead±lag relation between the spot market and the
futures (options) market is the trading frequency of the index component
stocks. We thus examine the trading frequency of the component stocks. Our
data for the component stocks are from the trade record ®le provided by the
SEHK. 6 The ®le contains the time stamp, price, and volume for each trade.
Ordering by market capitalization, Table 2 shows the stocksÕ trading frequencies in terms of percentage of 5-minute intervals having trades and average
time of the last trade in a 5-minute interval. The average 5-minute volume is
also reported. Note that the HSI is aected heavily by the stocks of big ®rms.
These big ®rms are in the infrastructure, property development, and banking
sectors, which dominate the Hong Kong economy. Also note that trading
frequency tends to increase with the stockÕs capitalization. Smaller stocks are
not actively traded, yet only one of them (Miramar Hotel, which accounts for
less than 0.7% of the index capitalization) is less actively traded than the 185
call mornings and the 185 put mornings. On the other hand, all the component
stocks are less actively traded than the 185 futures days.
As the smaller stocks are less liquid, the non-synchronous trading among the
component stocks may lead to autocorrelation in index returns. We thus estimate the return autocorrelation in each trading session (morning and afternoon separately) and present the summary statistics in Table 3. The
autocorrelation is signi®cant in the ®rst order (see Panel I): both the means of
the coecients (0.367 in the mornings and 0.253 in the afternoons) and the
numbers of coecients that are signi®cantly positive (96 out of the 185
mornings and 13 out of the 184 afternoons) are sizable. Higher orders of
autocorrelation, however, are not detected. Panel II displays the autocorrelation of the cash index return innovations generated by an AR (1) model ®tted
to the return series. As depicted in the panel, the means of the coecients
become close to zero and the numbers of coecients that are signi®cantly
dierent from zero become trivial.
6
Bid and ask records before May 1996 are not available.
362
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Table 2
The component stocks of HSI: market value weight and trading frequency, January±September
1994a
a
Firms' names
Market
value
weight in
HSI (%)
5-minute
intervals
having
trades (%)
Average time
of the last
trade in a
5-minute
interval
Average volume in a
5-minute
interval (in
$1000)
Hong Kong Telecommunications
HSBC Holdings plc
Sun Hung Kai Properties
Hutchison Whampoa
Hang Seng Bank
Cheung Kong (Holdings)
China Light & Power
Henderson Land Development
Wharf (Holdings)
Swire Paci®c A
Hong Kong Land Holdings
Hong Kong Electric Holdings
CITIC Paci®c
Jardine Matheson Holdings
New World Development
Cathay Paci®c Airways
Wheelock
Hopewell Holdings
Hong Kong & China Gas
Jardine Strategic Holdings
Bank of East Asia
Hysan Development
Dairy Farm International Holdings
Hang Lung Development Co
Television Broadcasts
Hong Kong and Shanghai Hotels
Miramar Hotel & Investment
Great Eagle Holdings
Shun Tak Holdings
Mandarin Oriental International
Hong Kong Aircraft Engineering
Lai Sun Garment (International)
Winsor Industrial Corporation
10.65
90.70
4.05
3326.3
9.33
8.26
8.16
6.48
5.11
4.84
4.74
4.16
3.63
3.18
3.17
2.95
2.94
2.63
2.17
2.12
1.94
1.86
1.83
1.49
1.35
1.13
94.56
90.38
91.39
89.82
93.48
90.50
79.88
87.62
82.23
90.53
88.06
90.52
75.70
90.32
71.11
85.37
90.92
89.44
67.11
89.03
82.23
70.94
4.37
3.98
4.08
4.02
4.23
4.00
3.57
3.85
3.65
4.05
3.92
4.00
3.48
4.00
3.33
3.73
4.07
3.98
3.27
3.98
3.58
3.35
9009.7
4404.6
4443.3
2567.7
5302.4
2574.5
1588.8
2362.7
2943.7
2713.4
1491.6
2089.3
2093.0
2230.7
578.2
1041.3
2010.4
1245.0
856.3
1464.0
919.0
616.1
1.08
0.93
0.76
85.80
32.12
52.41
3.78
2.90
3.08
1062.3
337.0
271.6
0.68
0.61
0.59
0.44
0.41
23.06
79.47
55.44
47.55
45.02
2.90
3.45
3.10
3.02
3.02
163.1
574.8
306.6
169.5
239.4
0.24
0.17
40.92
42.46
2.87
2.88
118.1
136.5
Reported are the market value weights as on 30 September 1994 and trading frequencies of HSI
component stocks sorted by descending market capitalization. Trading frequency is expressed in
terms of the percentage of 5-minute intervals having trades, the average time of the last trade in a 5minute interval (if the last trade is observed in the 4th (5th) minute, the time is recorded as 4 (5)),
and the average 5-minute volume.
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
363
Table 3
Autocorrelation of cash HSI returns, January±September 1994a
Lag
Mean of
coecients
Median of
coecients
No. of signi®cant coecients
+
)
I. Cash HSI returns
A. Mornings (n 185)
1
0.367
2
0.131
3
)0.04
4
)0.124
5
)0.141
6
)0.101
0.382
0.14
)0.038
)0.125
)0.14
)0.111
96
4
0
0
0
0
0
0
1
1
0
1
B. Afternoons (n 184)
1
0.253
2
)0.003
0.284
0.007
13
0
0
0
II. HSI return innovations generated by an AR (1) model
A. Mornings
1
0.031
0.081
2
0.004
0.014
3
)0.073
)0.066
4
)0.087
)0.094
5
)0.087
)0.085
6
)0.04
)0.036
0
3
0
0
0
0
0
0
4
4
4
1
B. Afternoons
1
2
0
0
0
0
0.04
)0.072
0.022
)0.086
a
We estimate the autocorrelation of HSI returns and innovations of HSI returns ®tted to an AR (1)
model in each trading session (morning and afternoon separately). We allow the coecient of the
AR (1) model to vary across dierent trading sessions. Reported are the means and medians of
autocorrelation coecients. The number of coecients being signi®cantly dierent from zero at 2
standard deviations or higher is also reported. There are 184, not 185, afternoons because trading
was closed for the afternoon just prior to the Chinese New Year Eve.
3. Methodology
3.1. Between spot and futures
Following Stoll and Whaley (1990) and Chan (1992), the lead±lag relationship between the spot market and the futures market is investigated with
the following model: 7
7
We ®nd that the coecients of longer lags/leads (4th or beyond) are small and insigni®cant.
Furthermore, the ®rst three lag/lead coecients are found to be robust whether the longer lags/
leads are included or not. Thus for model parsimony, we use three lags/leads in model (1).
364
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Rs;t a
3
X
bk Rf ;tk et ;
1
kÿ3
where Rs;t is the 5-min cash index return and Rf ;t is the 5-minute futures
trade return at time t. For every morning, the ®rst three and the last three
Rs;t s are dropped because there are no corresponding lag or lead Rf ;t s. For
every afternoon, the ®rst three Rs;t s are dropped because there are no corresponding lag Rf ;t s. This means that we examine the lead±lag relation based
on the middle parts of morning and afternoon only, and the results may not
apply to the market open or close. The coecients bk with negative (positive) subscripts are lag (lead) coecients. If the lag (lead) coecients are
signi®cantly dierent from zero, the cash index lags (leads) the futures. 8 All
the t-statistics for the coecients are estimated with the generalized method
of moments (Hansen, 1982; Chan, 1992, p. 133). 9
Because the HSI may suer from non-synchronous trading among component stocks, model (1) is repeated with serially uncorrelated cash index return innovations to analyze the lead±lag behavior after the non-synchronous
trading bias is mitigated (Chan, 1992, p. 134). The return innovations are
generated by an autoregressive model ®tted to the series of cash index returns. 10 Unlike trade returns, quotation returns are not aected by bid±ask
bounce. Given the non-lasting nature of futures quotes and that the time of
observation is virtually the same for trade prices and quotes, repeating model
(1) with futures quotation returns allows us to investigate the eect of bid±ask
bounce.
8
Previous studies such as Stoll and Whaley (1990) usually emphasize whether the lag/lead
coecients are signi®cantly positive to infer the lead±lag relation between the futures and the spot
markets. Yet a signi®cantly negative lag or lead coecient could also have implications for the
lead±lag relation (we thank an anonymous referee for suggesting this). For example, if the spot
return series on average exhibit negative autocorrelation in the third lag (this is the case for HSI as
shown by Table 3), the third lead coecient in model (1) might also be negative. The reason is that
usually the contemporaneous coecient in the model would be large suggesting substantive
comovement between futures returns and spot returns, thus any reversal in the spot returns would
likely be associated with an analogous reversal in the futures returns.
9
The t-statistics are calculated with standard error using GMM estimation in PROC MODEL of
SAS, v. 6.09.
10
We will report the results using the return innovations generated by a parsimonious AR (1)
model. The results are robust even if we have used the return innovations generated by an AR (2)
model. We allow the coecients of the autoregressive models to vary across dierent trading
sessions.
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
365
3.2. Between spot and options
Unlike the futures, a factor of the relation between option returns and spot
returns is the optionÕs delta. OptionÕs delta usually diers from one and it also
diers across various option contracts. Based on Chan et al. (1993, pp. 1957±
1958, 1960±1961), the lead±lag relationship between the spot market and the
call market is investigated with the following non-linear system equation
model: 11; 12
Rs;t ac
4
X
bk hc Rc;tk tc;t ;
c 1; . . . ; M;
t 1; ; T ;
2
kÿ4
where Rc;t is the 5-minute trade return for a call contract c at time t, bk s the lag/
lead coecients, hc the delta value of the contract c and is assumed to be
constant throughout the morning, M the number of call mornings (i.e., 185), T
the number of Rs;t s during the morning )8 (the ®rst 4 and the last 4 Rs;t s are
dropped because there are no corresponding lag or lead Rc;t s). We study
mornings only because T for afternoons is too small for model (2) to be estimated. This means that we examine the lead±lag relation based on the middle
part of morning only, and the results may not apply to afternoon, or morningÕs
open or close. Since the lag/lead coecients are always multiplied P
by hc , there is
an indeterminacy that we resolve by normalizing the bk s so that 4kÿ4 bk 1.
As a result, only 8 bk s are independent from one another. In model (1), we can
estimate the actual value of every coecient. Now because of the normalization, we cannot estimate the actual value of each lag/lead coecient, but we
can still estimate the relative values across the coecients (the sum of the
relative values is one). By studying the relative values of the lag coecient
estimates versus the relative values of the lead coecient estimates, we can infer
whether the spot returns lag the option returns more than they lead. With a
similar reasoning, Chan et al. (1993) infer whether the stock option returns lag
the stock returns more than they lead from the relative values of the normalized lag/lead coecient estimates. Model (2) can be thought of as single time
11
This non-linear multivariate regression model is ®rst used in ®nance by Gibbons (1982). This
approach is simple and requires little information to be implemented (e.g., it can be used without
knowing the dividend ex-date). Yet Chan et al. (1993) show that this simple approach can replicate
the results generated using more complicated approaches (e.g., the approach of computing implied
stock prices through inverting the Black and Scholes or another option-pricing equation (Stephan
and Whaley, 1990)). For more details on this approach, see Gibbons (1982) and Chan et al. (1993).
12
We ®nd that the coecients of longer lags/leads (5th or beyond) are small and insigni®cant.
Furthermore, the ®rst 4 lag/lead coecients are found to be robust whether the longer lags/leads are
included or not. Thus, for model parsimony, we use 4 lags/leads in model (2).
366
bÿ4
a
bÿ3
bÿ2
2
bÿ1
b0
b1
b2
b3
b4
n
R
A.I. With call trade returns
0.006
0.022
0.073
(2.77)
(8.96)
0.156
(18.46)
0.227
(23.14)
0.225
(22.98)
0.161
(18.08)
0.094
(10.46)
0.036
(3.85)
3885
0.132
A.II. With call quotation returns
0.000
0.019
0.079
(2.91)
(12.41)
0.183
(26.14)
0.259
(31.39)
0.234
(30.41)
0.130
(18.75)
0.065
(8.78)
0.031
(4.10)
3885
0.256
B.I. With put trade returns
)0.013
0.019
0.046
(2.67)
(5.27)
0.152
(17.29)
0.224
(22.79)
0.228
(23.13)
0.184
(19.52)
0.107
(11.31)
0.053
(5.35)
3885
0.126
B.II. With put quotation returns
0.001
0.014
0.080
(1.77)
(10.80)
0.143
(18.97)
0.242
(27.40)
0.248
(26.84)
0.170
(21.01)
0.078
(9.70)
0.024
(2.74)
3885
0.206
We run the following regression:
Rs;t ao
4
X
kÿ4
bk ho Ro;tk vo;t ;
o 1; . . . ; 185;
t 1; . . . ; T ;
4
X
bk 1;
kÿ4
where Ro ,t is the 5-minute return at time t for a call or put contract o with delta ho (we use the most active call and the most active put each morning, so
we have 185 call mornings and 185 put mornings), and T is the number of 5-min spot HSI return, Rs ,t , during the morning )8. Reported are the
coecient estimates with t-statistics in parentheses (* means signi®cance at 0.1% level), the number of observations (n), and the average adjusted R2
over the 185 call mornings or the 185 put mornings. Only the t-statistics of eight bk s are reported, since the nine bk s are normalized such that their sum
is one and only eight bk s are independent from one another.
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Table 4
The results of regressing HSI returns on leads and lags of HSI option returns, January±September 1994a
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
367
series regressions with T observations in a pooled system of M equations. It is
estimated with iterated ordinary least-squares method. 13
Model (2) is then repeated with serially uncorrelated cash index return innovations to analyze the lead±lag behavior in the absence of the non-synchronous trading bias. In addition, we repeat model (2) with call quotation
returns to investigate the informativeness of the quotes. Given the non-lasting
nature of these open outcry quotes and that the time of observation (3.30, see
Panel II, Table 1) is substantially dierent from 5, this will provide an interesting contrast to the ®ndings for markets with good-till-revision quotes. To
investigate the lead±lag relationship between the spot market and the put
market and to study the informativeness of the put quotes, the whole procedure is repeated with the 185 put mornings.
4. Results
4.1. Between spot and options
The results on the lead±lag relation between cash HSI returns and call trade
and quotation returns are displayed in Panels A.I and A.II, Table 4. 14 Panel
A.I shows that cash returns lead call trade returns up to 15±20 minutes (b1
through b3 are signi®cantly positive while b4 is marginally so), and lag only
by 10 minutes (bÿ1 and bÿ2 are signi®cantly positive). 15 When we look at the
results using call quotation returns in Panel A.II, the lead±lag pattern seems to
be more or less the same as Panel A.I.
The relationship between the cash and puts is presented in Panels B.I and
B.II. The put returns based on trade prices lag the cash by 20 minutes and lead
only by 10 minutes. When we look at the put quotation returns, the puts appear to lag the cash slightly less than when we use the put trade returns: the 2nd
and the 3rd lead coecients become smaller and the 4th one even becomes
insigni®cant, whereas the feedback of the puts on the cash re¯ected by bÿ2 is
larger.
13
Our procedure is similar to that of Chan et al. (1993), but we replace the outdated PROC
SYSNLIN with PROC MODEL in SAS, v. 6.09.
14
As explained in Section 3.2, only eight normalized bk s are independent from one another.
Thus, we only report the t-statistics of eight, not nine, bk s. With the same reasoning, Chan et al.
(1993) only present six of the seven normalized coecients in their model. Although the coecient
bÿ4 is presented in Table 4 without the t-statistic, this should not cause major problems as we can
see that it is the smallest (in magnitude) among all the normalized coecients and our conclusion
that the option returns lag the spot returns more than they lead is robust.
15
We have nearly 4000 intraday observations. As Lindley (1957) points out, lower signi®cance
should be required for large samples. All the tests in this table use the 0.1% signi®cance level as the
rejection criterion, instead of conventional levels of signi®cance.
368
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
To summarize, cash index returns lead more than lag option trade returns
even before the non-synchronous trading bias in the cash returns is purged. 16
It seems that the HSI options market is much less informationally ecient than
the counterparts in other countries where cash index returns lag more than lead
option returns. For example, Fleming et al. (1996) ®nd that due to the dierence in trading costs, S&P 500 futures lead S&P 100 options, which in turn lead
the spot index. It is nevertheless not too surprising that the HSI options lag the
spot index. We have observed that the option contracts are inactive; even the
relatively popular contracts (Panel II, Table 1) are less actively traded than 32
of the 33 HSI component stocks, which account for 99.3% of the index capitalization. Thus, their prices could be stale as compared to the HSI component
stocks, leading to the result that option trade returns lag the spot index returns.
Further, the results using option quotation returns suggest that the relative
informational ineciency of the option bid±ask quotes is quite similar to the
possibly stale prices. This contrasts with other markets where quotes are goodtill-revision. For example, when Stephan and Whaley (1990) ®nd that stocks
lead stock options using trade prices to calculate returns, Chan et al. (1993)
suspect that it is probably caused by stale option prices. They proceed to resolve the puzzle using good-till-revision quotes to calculate option returns.
They then ®nd that stocks no more lead the options. Unlike trade price, goodtill-revision quote has to re¯ect market conditions until the next quote. It
cannot be stale, otherwise the market maker may incur loss. On the other hand,
we observe that the HSI option quotes from the open outcry system are updated infrequently, so they could be stale (Panel II, Table 1). A likely reason is
that even though the market makers update infrequently their quotes, unlike
the case of good-till-revision quotes, traders cannot take advantage of these
stale non-lasting quotes.
4.2. Between spot and futures
In Table 5, we examine the lead±lag relation between cash HSI returns and
futures returns. Panel A.I (A.II) shows the results when we use futures trade
16
To mitigate the thin trading problem in options, we repeat our tests using 40 call mornings and
23 put mornings, each of which has at least 40% of its 5-minute intervals with trades. The results,
not reported here, show that the calls and puts still lag more than lead the spot index. Alternatively,
if we lengthen the intraday time interval to 10 or more minutes, there will be less intervals with no
trade for the option mornings. However, the number of intervals per morning will also decrease,
causing problems in estimating model (2). Furthermore, when we repeat the analysis with serially
uncorrelated HSI return innovations from an AR (1) model to mitigate the non-synchronous
trading bias in the spot index, the results, not reported here, show as expected that the calls and
puts only lag the cash more.
369
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Table 5
The results of regressing HSI returns (or innovations of HSI returns ®tted to an AR (1) model) on
leads and lags of HSI futures returns, January±September 1994a
bÿ3
bÿ2
bÿ1
b0
b1
b2
2
b3
n
R
A.I. With futures trade returns & HSI returns
0.026
0.140
0.298
0.314
0.153
(2.66)
(16.26) (36.61) (11.00) (10.54)
0.016
(0.68)
)0.019
()1.45)
5917
0.565
A.II. With futures quotation returns & HSI returns
0.031
0.137
0.299
0.349
0.153
(3.51) (15.74) (36.14) (37.51) (16.23)
)0.016
()1.93)
)0.032
()3.93)
5917
0.588
B.I. With futures trade returns & HSI return innovations generated by an AR (1) model
)0.071
)0.018
0.120
0.235
0.120
0.002
)0.028
5862
0.297
()7.48) ()1.95)
(12.80) (11.25)
(8.47)
(0.10)
()1.84)
B.II. With futures quotation returns & HSI return innovations generated by an AR (1) model
)0.065
)0.022
0.122
0.257
0.130
)0.028
)0.044
5862
0.318
()7.41) ()2.32)
(12.77) (25.72) (11.94) ()2.99)
()5.06)
a
We run the following regression:
Rs;t a
3
X
bk Rf ;tk et ;
kÿ3
where Rs ,t is the 5-minutes cash HSI return or innovation of HSI return ®tted to an AR (1) model,
and Rf ,t is the 5-minutes futures trade return or quotation return calculated using the spot-month
futures each day. Reported are the coecient estimates with t-statistics in parentheses (* means
signi®cance at 0.1% level), the number of observations (n), and the adjusted R2 . Some mornings and
afternoons with problem in AR (1) estimation for cash HSI returns are deleted. Thus, n is smaller
with HSI return innovations.
(quotation) returns. The results in Panel A.I suggest that the futures lead the
cash by up to 10 minutes (bÿ1 and bÿ2 are signi®cantly positive), and the cash
only leads the futures by 5 minutes (b1 is signi®cantly positive). These suggest
that the futures lead more than lag the spot index. The results in Panel A.II
show that bÿ1 , bÿ2 , and bÿ3 are all signi®cantly positive while b1 is signi®cantly positive and b3 is signi®cantly negative. 17 The magnitudes of the ®rst 2
17
The negative signi®cance of the 3rd lead coecient is consistent with the negative
autocorrelation in the 3rd lag of HSI as shown by Table 3. The substantive co-movement between
futures returns and spot returns means that any reversal in the spot returns would likely be
associated with an analogous reversal in the futures returns. On the other hand, the magnitude of
this negative coecient estimate appears to be small relative to the magnitudes of the other positive
coecient estimates. This is consistent with the supposition that any tendency for the (spot and)
futures to reverse after 15 or so minutes, following a change in Rs;t , is dominated by the tendency
for spot and futures returns to move in the same direction, contemporaneously and across other
lags. (We thank an anonymous referee for suggesting this.)
370
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Table 6
The results of regressing HSI component stocksÕ returns on leads and lags of HSI futures returns,
January±September 1994a
Firms' names
bÿ3
bÿ2
Hong Kong Telecommunications
HSBC Holdings
)0.019
()0.63)
0.063
(1.01)
)0.061
()1.25)
)0.003
()0.08)
)0.021
()0.43)
0.002
(0.08)
)0.039
()0.82)
0.074
(2.02)
0.029
(0.77)
0.027
(0.74)
0.059
(1.56)
)0.007
Sun Hung Kai
Properties
Hutchison
Whampoa
Hang Seng Bank
Cheung Kong
(Holdings)
China Light &
Power
Henderson Land
Development
Wharf (Holdings)
Swire Paci®c A
Hong Kong Land
Holdings
Hong Kong
Electric
Holdings
CITIC Paci®c
Jardine Matheson
Holdings
New World
Development
Cathay Paci®c
Airways
Wheelock
Hopewell
Holdings
Hong Kong &
China Gas
Jardine Strategic
Holdings
Bank of East Asia
Hysan
Development
()0.23)
0.013
(0.46)
0.042
(0.70)
0.052
(1.27)
0.099
(2.75)
0.016
(0.56)
0.041
(1.16)
0.100
(2.51)
0.082
(1.70)
)0.011
()0.21)
0.068
(2.49)
bÿ1
b0
2
b1
b2
b3
R
0.111
0.214
0.330
(2.90)
(6.16) (9.58)
0.024
0.130
0.391
(0.36)
(1.84)
(5.49)
0.142
0.388
0.435
(2.92)
(7.30) (7.75)
0.182
0.310
0.531
(5.28) (7.39) (12.71)
0.101
0.258
0.327
(1.76)
(4.48) (5.62)
0.121
0.321
0.501
(4.26) (10.82) (16.40)
0.146
0.320
0.274
(2.59)
(6.19) (5.89)
0.155
0.425
0.429
(4.25) (10.36) (9.91)
0.173
0.385
0.347
(3.73) (9.60) (8.29)
0.162
0.377
0.365
(3.49) (8.18) (8.55)
0.174
(4.74)
0.154
(2.16)
0.263
(5.21)
0.262
(7.18)
0.196
(3.69)
0.215
(5.98)
0.075
(1.21)
0.158
(3.62)
0.187
(4.31)
0.168
(3.92)
)0.046
()1.25)
)0.179
()2.56)
0.007
(0.15)
0.015
(0.46)
)0.021
()0.43)
)0.017
()0.48)
)0.035
()0.61)
0.007
(0.15)
0.033
(0.74)
0.007
(0.14)
)0.049
()1.40)
0.051
(0.77)
)0.032
()0.57)
)0.048
()1.47)
)0.102
()1.89)
)0.007
()0.27)
0.050
(1.04)
)0.057
()1.46)
)0.032
()0.77)
)0.062
()1.39)
0.036
0.085
0.357
0.445
(2.26) (10.04) (11.29)
0.164
0.237
0.293
0.067
(1.43)
0.120
(4.16) (6.71)
0.192
0.247
(5.68) (5.94)
0.031
0.396
(0.49)
(5.79)
0.198
0.373
(5.31) (10.07)
0.125
0.267
(3.24) (6.72)
0.162
0.369
(5.46) (11.76)
0.132
0.316
(3.12)
(6.13)
0.170
0.256
(4.13) (5.53)
0.054
0.191
(1.02)
(3.80)
0.228
0.351
(3.63) (6.14)
0.165
0.379
(5.01) (15.10)
(3.91)
0.022
(0.66)
0.033
(0.51)
0.129
(3.26)
0.009
(0.21)
0.057
(1.92)
0.108
(3.11)
0.160
(3.81)
0.182
(3.07)
0.044
(0.73)
0.122
(3.28)
(8.72)
0.274
(8.05)
0.370
(5.42)
0.460
(9.60)
0.222
(4.95)
0.286
(9.67)
0.334
(9.68)
0.151
(3.38)
0.174
(3.32)
0.276
(4.74)
0.258
(8.31)
0.011
0.037
0.099
0.016
0.122
0.023
0.082
0.055
0.049
0.026 )0.026 0.076
(0.82) ()0.54)
)0.045 )0.063 0.049
()1.38)
0.041
(1.05)
0.075
(1.14)
0.033
(0.53)
)0.016
()0.37)
0.004
(0.12)
0.056
(1.67)
)0.048
()1.16)
)0.069
()1.34)
0.052
(0.94)
)0.040
()1.42)
()2.12)
)0.075
()2.16)
)0.090
()1.57)
0.032
(0.83)
)0.016
()0.45)
0.030
(0.86)
)0.024
()0.61)
)0.004
()0.09)
)0.117
()1.99)
)0.045
()0.79)
)0.004
()0.14)
0.058
0.013
0.044
0.037
0.082
0.059
0.019
0.010
0.015
0.103
371
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Table 6 (Contined)
Firms' names
bÿ3
Dairy Farm International Holdings
Hang Lung Development
Television Broadcasts
Hong Kong and
Shanghai Hotels
Miramar Hotel &
Investment
Great Eagle Holdings
Shun Tak Holdings
Mandarin Oriental
International
Hong Kong Aircraft Engineering
Lai Sun Garment
(International)
Winsor Industrial
Corporation
a
bÿ2
bÿ1
b0
b1
b2
b3
2
R
0.138 )0.040
0.209
0.198
0.042 )0.092 )0.004 0.004
(2.20) ()0.62)
(3.02)
(2.57)
(0.66) ()1.72) ()0.06)
0.049
0.243
0.346
0.331
0.074 )0.032
0.007 0.096
(1.80)
(8.50) (11.05) (11.87) (2.45) ()0.89)
(0.21)
0.062
0.102
0.075
0.014
0.034
0.010
0.028 0.007
(1.68)
(3.28) (2.46)
(0.38)
(0.75)
(0.29)
(0.94)
0.042
0.193
0.282
0.176 )0.024 )0.027
0.008 0.026
(0.92)
(4.37) (5.18) (4.42) ()0.50) ()0.63)
(0.21)
0.062
0.063
0.106
0.022
0.014
0.007 )0.014 0.007
(2.40)
(2.17)
(4.04) (0.87)
(0.53)
(0.29) ()0.55)
0.144
0.174
0.461
0.303
0.059
0.058 )0.012 0.055
(3.22) (3.99) (11.36) (7.71) (1.34)
(1.34) ()0.29)
0.077
0.127
0.127
0.033
0.072
0.030 )0.005 0.007
(2.29)
(3.11)
(3.31) (0.91)
(1.92)
(0.78) ()0.15)
0.069
0.106
0.309
0.006
0.097
0.020 )0.042 0.005
(1.17)
(1.66)
(4.58) (0.10)
(1.56)
(0.28) ()0.60)
0.048
0.121
0.135
0.027
0.012
0.014 )0.062 0.014
(1.65)
(3.34) (4.18) (0.89)
(0.44)
(0.44) ()1.60)
0.041
0.159
0.140
0.047 )0.069 )0.034
0.032 0.011
(1.02)
(3.77) (3.67) (1.19) ()1.80) ()0.97)
(0.87)
0.154
0.159 )0.081
0.316
0.063 )0.018 )0.182 )0.001
(1.70)
(2.85) ()0.36)
(1.36)
(1.00) ()0.25) ()1.43)
We run the following regression:
Rs;t a
3
X
bk Rf ;tk et ;
kÿ3
where Rs ,t is the 5-minute trade return on stock s, and Rf ,t is the 5-minute futures quotation return
calculated using the spot-month futures each day. Reported are the coecient estimates with tstatistics in parentheses (* means signi®cance at 0.1% level), and the adjusted R2 . The stocks are
sorted by descending market capitalization.
lag coecients are larger than the ®rst 2 lead coecients and the magnitude of
the 3rd lag coecient is similar to the 3rd lead coecient. Again, these results
suggest that the spot index lags more than leads the futures.
Comparing the above results with Table 4, the options trade prices (quotes)
seem to be less informationally ecient than the futures trade prices
(quotes). 18 In Finland, Puttonen (1993) ®nds that the FOX futures and options markets, which both commenced on 2 May 1988, have similar informational eciency. Thus, one likely explanation for our results is that the options
18
The lead±lag relationship between the HSI futures and options has been analyzed with model
(2) using both trade and quotation returns. The results, not reported here, show as expected the
futuresÕ lead over the options.
372
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
market is much less mature than the futures market, such that traders prefer to
trade futures rather than options and market makers focus on their futures
quotes. As shown in Table 1, the options are much less actively traded than the
futures, so their prices could be stale as compared to futures prices. It also
seems that the non-lasting futures quotes are updated together with the intense
trading activities to re¯ect market conditions. On the other hand, for the much
less active options market, it seems that the market makers simply do not
bother to update their non-lasting quotes.
Non-synchronous trading among the index component stocks might have
caused part of the HSI futuresÕ lead over the cash index. Thus, in Panels B.I
and B.II of Table 5, we repeat the analysis with serially uncorrelated cash index
return innovations. There is one marked dierence between the results in
Panels B.I and B.II and those in Panels A.I and A.II: the lead±lag relationship
between the cash and futures markets now becomes more or less symmetric.
Thus, it seems that after the non-synchronous trading bias in the cash index
returns is purged, the futures no longer lead more than lag the index. 19
4.3. Between HSI component stocks and futures
To summarize, the futures lead the spot index only before the cash return
non-synchronous trading bias is considered. This contrasts sharply with previous studies for other countries. For example, Chan (1992) shows that index
futures lead more than lag the cash index even after the non-synchronous
trading bias in the cash index returns is considered. While the staleness of
option prices and quotes may explain the cash lead over the options, the HSI
futures are very active. They are even more actively traded than all the HSI
component stocks. Then why does their lead over the cash market appear to be
less than the counterparts in other countries? One likely explanation is that the
HSI is value-weighted and aected heavily by a few major stocks. These major
stocks are nearly as actively traded as the futures, and are in the infrastructure,
property development, and banking sectors, which dominate the Hong Kong
economy. If the HSI futures only have little lead over these stocks, their lead
over the cash index would be dampened and less than the counterparts in other
countries. To investigate this, we examine the lead±lag relationship between the
futures and each of the component stocks.
19
To investigate the possibility that the futures lead more when the market is bearish than when
the market is bullish because of short-sale restrictions in the spot market, we have repeated the
analysis in Table 5 with trading sessions sorted into 4 quartiles by the sign and size of HSI returns.
The results, not reported here, suggest that the lead±lag relation between the futures and cash is not
aected by whether the market is bullish or bearish. These results are similar to those of Chan
(1992), and suggest that marginal traders have long positions in the stocks and are not constrained
by the short-sale restrictions.
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
373
Model (1) is repeated with returns of individual component stock replacing
HSI returns. For each stock, we generate 5-minute returns from trade prices,
which are also used by HSI Services in computing the HSI. The results, sorted
by individual stockÕs market
www.elsevier.com/locate/econbase
Relative informational eciency of cash,
futures, and options markets: The case of an
emerging market
Raymond Chiang a, Wai-Ming Fong
a
b,*
Department of Accountancy, Hong Kong Ploytechnic University, Kowloon, Hong Kong
Department of Finance, Chinese University of Hong Kong, Shatin, N.T., Hong Kong
b
Received 12 July 1999; accepted 7 October 1999
Abstract
We study the lead±lag relationships among the spot, futures, and options markets on
Hong KongÕs Hang Seng Index (HSI). The young options market experiences thin
trading, and the option returns lag the cash index returns. The more mature futures
market experiences active trading. Yet its lead over the cash index appears to be less than
the counterparts in other countries. A possible reason is the dominance of a few major
stocks in the index; and these stocks have symmetric lead±lag relations with the futures.
Furthermore, the informativeness of the non-lasting futures and options quotations
seems to depend on the market maturity. Ó 2001 Elsevier Science B.V. All rights reserved.
JEL classi®cation: G10; G12; G13
Keywords: Hang Seng Index; Futures; Options; Lead±lag relationships
1. Introduction
Citing the leverage eects and lower trading costs in index derivatives, ®nancial economists often argue that returns on index futures or options lead
*
Corresponding author. Tel.: +852-2609-7903; fax: +852-2603-6586.
E-mail address: wmfong@baf.msmail.cuhk.edu.hk (W.-M. Fong).
0378-4266/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 6 6 ( 9 9 ) 0 0 1 2 7 - 2
356
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
the cash index returns more than the feedback. Empirical evidence has been
widely documented for mature ®nancial markets such as the United States
(e.g., Finnerty and Park, 1987; Kawaller et al., 1987; Stoll and Whaley, 1990;
Chan, 1992; Fleming et al., 1996). These studies suggest that index derivative
markets are more ecient in incorporating new information, particularly
market-wide information. 1 In mature ®nancial markets, market participants
are well acquainted with derivative securities, which are therefore common
investment and ®nancial management tools. On the other hand, derivative
securities are novel in emerging ®nancial markets. In these markets, derivatives
may encounter low liquidity because they are unfamiliar to investors. It is then
possible that they are not more informationally ecient than the underlying
spot index.
In this paper, we study the lead±lag relation of two derivative markets with
the underlying cash market of an emerging ®nancial center in the Asia±Paci®c
Rim. The derivatives studied are the Hang Seng Index (HSI) futures and options traded on the Hong Kong Futures Exchange (HKFE). HSI is a valueweighted index composed of 33 blue-chip stocks in Hong Kong. We study the
lead±lag relation between the intraday HSI futures (options) returns and spot
HSI returns to shed light on the relative informational eciency across the
futures (options) market and the spot market. Because the HSI futures market
(completely revamped after the 1987 market crash) is more mature than the
HSI options market (commenced in 1993), our analysis could also provide
insights on the relative informational eciency across emerging derivative
markets at dierent stages of development. 2 In Finland, Puttonen (1993) ®nds
that the Finnish Options Index (FOX) futures and options markets, which
both commenced on 2 May 1988, have similar informational eciency.
Using intraday data from January to September 1994, we ®nd that HSI
option returns lag more than lead HSI returns. This contrasts sharply with
options markets in other countries where cash index returns lag more than lead
option returns, e.g., the United States (Finucane, 1991; Fleming et al., 1996),
Finland (Puttonen, 1993), and Switzerland (Stucki and Wasserfallen, 1994). To
investigate why HSI options lag the spot index, we compare their liquidity with
the index component stocks. We observe that the option contracts are thinly
traded. In fact, even the relatively popular contracts are less actively traded
than most of the component stocks. These suggest that the staleness of option
prices causes the spot indexÕs lead. Furthermore, the option quotations do not
1
See Chan (1990) and Subrahmanyam (1991). Chan (1992) argues and provides evidence that
index futures market can process market-wide information better than cash market. His argument
should also apply to index options market.
2
Related studies include Fung et al. (1997) and Bae et al. (1998), which examine the arbitrage
opportunities between the HSI futures and options markets.
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
357
seem to be as informative as good-till-revision quotations on other markets.
The option returns computed with bid±ask midpoints still lag the HSI returns.
This contrasts with the ®nding of Chan et al. (1993) that the stockÕs lead over
the option documented in Stephan and Whaley (1990) disappears when goodtill-revision quotes replace trade prices in calculating option returns. 3 A likely
explanation for our results is that the HSI option quotes may sometimes be
stale. In the open outcry trading system of the HKFE, the quotes are only good
for immediate trade and non-lasting, so they need to re¯ect market conditions
solely at the time of posting. These quotes can be stale if they are not updated
to re¯ect change in market conditions, yet unlike the case of good-till-revision
quotes, traders cannot take advantage of the stale non-lasting quotes. Consistent with this explanation, we observe that the HSI option quotes are updated infrequently.
The options marketÕs relative informational ineciency could be attributed
to the fact that it is much less mature than the futures market, such that traders
prefer to trade futures rather than options and the market makers focus on
their futures quotes. Consistent with this, we observe that on the futures
market, there are transactions and quotes in almost every minute. The futures
are even more actively traded than all the HSI component stocks. Not surprisingly, they are found to lead more than lag the cash index. One possible
reason for the futuresÕ lead is the non-synchronous trading among component
stocks in the index. Indeed, we ®nd ®rst-order autocorrelation exists in the HSI
returns. Following Stoll and Whaley (1990), the autocorrelation in the HSI
returns is purged to mitigate the eects of non-synchronous trading. The lead±
lag relation between the futures and cash then becomes symmetric. This contrasts with the results from other countries which show that cash index lags
more than leads index futures even after non-synchronous trading among
component stocks is considered (e.g., for the United States, see Stoll and
Whaley (1990) and Chan (1992); for the Finnish markets, see Puttonen (1993)).
Since the HSI futures are very actively traded, it is puzzling that their lead over
the cash appears to be less than the counterparts in other countries. One likely
explanation is that the HSI is value-weighted and aected substantially by a
few major stocks, which are nearly as actively traded as the futures and are in
dominant economic sectors. Consistent with this explanation, we ®nd that four
of the biggest component stocks, which account for nearly 35% of index
capitalization, have more or less symmetric lead±lag relations with the futures.
3
When Stephan and Whaley (1990) ®nd that stocks lead stock options using trade prices to
calculate returns, Chan et al. (1993) suspect that it is probably caused by stale option prices. They
proceed to resolve the puzzle using good-till-revision quotes to calculate option returns. They then
®nd that stocks no more lead the options. Unlike trade price, good-till-revision quote has to
account for market conditions until the next quote. It cannot be stale, otherwise the market maker
may incur loss.
358
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
This ®nding contrasts sharply with the results for other countries such as Chan
(1992) who ®nds that each MMI component stock lags the MMI futures.
The rest of the paper is organized as follows. In Section 2, we describe our
data. Our methodology is explained in Section 3. We present our ®ndings in
Section 4. The paper is concluded in Section 5.
2. Data
The HSI, a value-weighted index, is the most commonly used benchmark for
Hong KongÕs stock market. Its 33 component stocks account for more than
70% of the total market capitalization. All of the component stocks are traded
on the Stock Exchange of Hong Kong (SEHK), which is open from Monday to
Friday, from 10:00 to 12:30 and from 14:30 to 15:45 (15:30 before July 1994).
Trading on the market is conducted by an order-driven system, the Automatic
Order Matching and Execution System (AMS), without the services of specialists or designated market makers.
The HSI futures contracts were introduced on 6 May 1986 by the HKFE
and completely revamped after the 1987 market crash. As the stock market
began to rise in 1992, futures trading became active again. In 1994, the average
daily volume was about 17,000 contracts. The contract size is the HSI futures
price times HK $50. The last trading day is the second last business day of the
maturity month. The delivery (expiration) months include the spot month, the
next calendar month, and the next two calendar quarter months. The market
opens from Monday to Friday, from 10:00 to 12:30 and from 14:30 to 16:00
(15:45 before July 1994), so the afternoon market close is 15 minutes later than
the stock market. Trading on the futures market is conducted by the open
outcry system.
The HSI option contracts were launched on 5 March 1993 by the HKFE.
The contracts are European in nature. At expiration, the contracts are cash
settled if they are in-the-money. The contract cycle and trading hours are the
same as the HSI futures contracts. The trading was thin in 1993, with a daily
average of only several hundred lots. The contracts gained more popularity in
1994, and the average daily volume was about 2500 contracts. Similar to the
futures, trading on the options market is conducted by the open outcry
system.
Our data on the HSI are provided by HSI Services. The data set consists of
minute-by-minute data on the index from January to September 1994. Each
trading day is divided into 5-minute trading intervals. Consequently, the ®rst
(last) trading interval in the morning ends at 10:05 (12:30) and the ®rst (last)
trading interval in the afternoon ends at 14:35 (15:30 before July 1994 and
15:45 otherwise). Because we exclude overnight return (over-the-lunch-break
return), the ®rst 5-minute return of every morning (afternoon) is computed as
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
359
the logarithmic ratio between the HSI at 10:10 (14:40) and the HSI at 10:05
(14:35).
The data on the HSI futures and options trades and quotations are provided
by the HKFE. The data set consists of all time-stamped records of trades, bids,
and asks, and all records of opening prices and closing prices of all HSI futures
and options contracts for each trading day during January±September 1994.
There are many dierent contracts of futures and options available for trading
each day. To mitigate thin trading problem, we focus on more frequently
traded futures and options contracts. Since trading occurs mainly in the nearby
contracts, the data from the spot-month contracts are used; ®ve trading days
before expiration, the contracts are rolled over to the next-month to mitigate
the expiration eects documented elsewhere. For futures, there is only one
spot-month contract each day. For calls and puts, there are many strike prices
per delivery month; each day we use the data from the most frequently traded
call and the most frequently traded put (by number of trades during the day).
Thus, for each of the 185 sample trading days, we focus on one futures contract, one call contract, and one put contract.
The data are then divided into 1-minute trading intervals such that the ®rst
(last) trading interval in the morning ends at 10:01 (12:30) and the ®rst (last)
trading interval in the afternoon ends at 14:31 (15:45 before July 1994 and
16:00 otherwise). For each of the futures, call, and put contracts, we keep the
data on the last price, bid, and ask for each trading interval. If there is no trade
(bid quotation or ask quotation) in the interval, the last price (bid or ask) is
regarded as missing.
Using the above minute-by-minute data set, 5-minute returns for every
contract are computed as follows. First, each trading day is divided into 5minute trading intervals. We then keep the data on the last available price, bid,
and ask for each trading interval. If there is missing price (bid or ask) in the
interval, the price (bid or ask) of the previous interval is used. Finally, we
compute the 5-minute trade return in every interval as the logarithmic ratio
between the price of the interval and that of the previous interval. Quotation
returns are computed with the bid±ask midpoints of the intervals. We exclude
overnight returns and over-lunch-break returns.
In the absence of accurate data on intraday transaction volume from the
HKFE, we report trading (quotation) frequency in terms of the frequency of
intervals having trades (quotes) in Table 1. 4 In our sample, there are 185 fu-
4
In Hong Kong Futures Exchange (1995, p. 4), the HKFE ocials wrote: ``The price reporting
system is designed to report prices on a real time basis, but not volume. Under the open outcry
system, the price reporting sta members can report the volume only after a trade is concluded.
Hence, they will input the estimated volume based on initial observation and then update it from
time to time during the day in accordance with the actual volume entered into the clearing system''.
360
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Table 1
HSI futures and options: Trading and quotation frequencies, January±September 1994a
I. Futures days
1. Percentage of 5-min intervals
having trades/bids/asks
2. Average time of the last trade/
bid/ask in a 5-min interval
II. Option mornings
A. The most active call
1. Percentage of 5-min intervals
having trades/bids/asks
2. Average time of the last trade/
bid/ask in a 5-min interval
B. The most active put
1. Percentage of 5-min intervals
having trades/bids/asks
2. Average time of the last trade/
bid/ask in a 5-min interval
Trade
Bid
Ask
99.99
99.96
99.94
4.93
4.92
4.91
28.28
36.88
37.06
3.24
3.3
3.3
23.84
31.85
30.84
3.19
3.19
3.21
a
Reported are trading and quotation frequencies of the spot-month futures each day, of the most
active call and the most active put each morning. Trading and quotation frequencies are expressed
in terms of the percentage of 5-minute intervals having trades/bids/asks and the average time of the
last trade/bid/ask in a 5-minute interval (if the last trade/bid/ask is observed in the 4th (5th) minute,
the time is recorded as 4 (5)).
tures days; and as illustrated in Panel I, practically all the intervals have trades
and quotes. For every interval having trades (or quotes), we take the time when
the last trade (or quote) is observed as the time of observation. For example, if
the last trade is observed in the 4th minute, the time of observation is 4. The
average observation time for intervals with trades (bids and asks) displayed in
Panel I is 4.93 (4.92 and 4.91). In other words, the last trade and the last quotes
for the futures are observed mainly during the 5th minute of each interval.
Given the timing of the last trade and quotes are almost identical, any dierence in ®ndings between futures trade returns and quote returns should arise
from bid±ask bounce in trade prices.
The trading and quotation frequencies during morning for the calls and the
puts are displayed in Panel II. 5 Many of the 185 call mornings and 185 put
mornings in our sample actually experience thin trading. For the calls, only
28.28% of the intervals have trades. We fare better with quotes: there are
observations about 37% of the time. The puts are even less active than the calls;
5
Afternoon trading sessions are too short and produce too few observations to be usable for the
later tests.
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
361
the frequency is 23.84%, 31.85%, and 30.84%, respectively, for trades, bids, and
asks. Furthermore, the time of observing the trade and quotes for the calls
(3.24, 3.30, and 3.30) is also closer to the 5-minute mark than that for the puts
(3.19, 3.19, and 3.21). Thus, it seems that the market makers pay less attention
to the put quotes and update them less frequently. One likely reason is that the
put contracts are less actively traded than the calls, such that the market
makers have less incentive to update put quotes. Overall, the trading and
quotation frequencies and the average timing of the last trade/quotes for these
calls and puts are nowhere near those for futures contracts. As a result, we
expect information to be re¯ected in the futures prices and quotes better than
the options.
One key factor of the lead±lag relation between the spot market and the
futures (options) market is the trading frequency of the index component
stocks. We thus examine the trading frequency of the component stocks. Our
data for the component stocks are from the trade record ®le provided by the
SEHK. 6 The ®le contains the time stamp, price, and volume for each trade.
Ordering by market capitalization, Table 2 shows the stocksÕ trading frequencies in terms of percentage of 5-minute intervals having trades and average
time of the last trade in a 5-minute interval. The average 5-minute volume is
also reported. Note that the HSI is aected heavily by the stocks of big ®rms.
These big ®rms are in the infrastructure, property development, and banking
sectors, which dominate the Hong Kong economy. Also note that trading
frequency tends to increase with the stockÕs capitalization. Smaller stocks are
not actively traded, yet only one of them (Miramar Hotel, which accounts for
less than 0.7% of the index capitalization) is less actively traded than the 185
call mornings and the 185 put mornings. On the other hand, all the component
stocks are less actively traded than the 185 futures days.
As the smaller stocks are less liquid, the non-synchronous trading among the
component stocks may lead to autocorrelation in index returns. We thus estimate the return autocorrelation in each trading session (morning and afternoon separately) and present the summary statistics in Table 3. The
autocorrelation is signi®cant in the ®rst order (see Panel I): both the means of
the coecients (0.367 in the mornings and 0.253 in the afternoons) and the
numbers of coecients that are signi®cantly positive (96 out of the 185
mornings and 13 out of the 184 afternoons) are sizable. Higher orders of
autocorrelation, however, are not detected. Panel II displays the autocorrelation of the cash index return innovations generated by an AR (1) model ®tted
to the return series. As depicted in the panel, the means of the coecients
become close to zero and the numbers of coecients that are signi®cantly
dierent from zero become trivial.
6
Bid and ask records before May 1996 are not available.
362
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Table 2
The component stocks of HSI: market value weight and trading frequency, January±September
1994a
a
Firms' names
Market
value
weight in
HSI (%)
5-minute
intervals
having
trades (%)
Average time
of the last
trade in a
5-minute
interval
Average volume in a
5-minute
interval (in
$1000)
Hong Kong Telecommunications
HSBC Holdings plc
Sun Hung Kai Properties
Hutchison Whampoa
Hang Seng Bank
Cheung Kong (Holdings)
China Light & Power
Henderson Land Development
Wharf (Holdings)
Swire Paci®c A
Hong Kong Land Holdings
Hong Kong Electric Holdings
CITIC Paci®c
Jardine Matheson Holdings
New World Development
Cathay Paci®c Airways
Wheelock
Hopewell Holdings
Hong Kong & China Gas
Jardine Strategic Holdings
Bank of East Asia
Hysan Development
Dairy Farm International Holdings
Hang Lung Development Co
Television Broadcasts
Hong Kong and Shanghai Hotels
Miramar Hotel & Investment
Great Eagle Holdings
Shun Tak Holdings
Mandarin Oriental International
Hong Kong Aircraft Engineering
Lai Sun Garment (International)
Winsor Industrial Corporation
10.65
90.70
4.05
3326.3
9.33
8.26
8.16
6.48
5.11
4.84
4.74
4.16
3.63
3.18
3.17
2.95
2.94
2.63
2.17
2.12
1.94
1.86
1.83
1.49
1.35
1.13
94.56
90.38
91.39
89.82
93.48
90.50
79.88
87.62
82.23
90.53
88.06
90.52
75.70
90.32
71.11
85.37
90.92
89.44
67.11
89.03
82.23
70.94
4.37
3.98
4.08
4.02
4.23
4.00
3.57
3.85
3.65
4.05
3.92
4.00
3.48
4.00
3.33
3.73
4.07
3.98
3.27
3.98
3.58
3.35
9009.7
4404.6
4443.3
2567.7
5302.4
2574.5
1588.8
2362.7
2943.7
2713.4
1491.6
2089.3
2093.0
2230.7
578.2
1041.3
2010.4
1245.0
856.3
1464.0
919.0
616.1
1.08
0.93
0.76
85.80
32.12
52.41
3.78
2.90
3.08
1062.3
337.0
271.6
0.68
0.61
0.59
0.44
0.41
23.06
79.47
55.44
47.55
45.02
2.90
3.45
3.10
3.02
3.02
163.1
574.8
306.6
169.5
239.4
0.24
0.17
40.92
42.46
2.87
2.88
118.1
136.5
Reported are the market value weights as on 30 September 1994 and trading frequencies of HSI
component stocks sorted by descending market capitalization. Trading frequency is expressed in
terms of the percentage of 5-minute intervals having trades, the average time of the last trade in a 5minute interval (if the last trade is observed in the 4th (5th) minute, the time is recorded as 4 (5)),
and the average 5-minute volume.
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
363
Table 3
Autocorrelation of cash HSI returns, January±September 1994a
Lag
Mean of
coecients
Median of
coecients
No. of signi®cant coecients
+
)
I. Cash HSI returns
A. Mornings (n 185)
1
0.367
2
0.131
3
)0.04
4
)0.124
5
)0.141
6
)0.101
0.382
0.14
)0.038
)0.125
)0.14
)0.111
96
4
0
0
0
0
0
0
1
1
0
1
B. Afternoons (n 184)
1
0.253
2
)0.003
0.284
0.007
13
0
0
0
II. HSI return innovations generated by an AR (1) model
A. Mornings
1
0.031
0.081
2
0.004
0.014
3
)0.073
)0.066
4
)0.087
)0.094
5
)0.087
)0.085
6
)0.04
)0.036
0
3
0
0
0
0
0
0
4
4
4
1
B. Afternoons
1
2
0
0
0
0
0.04
)0.072
0.022
)0.086
a
We estimate the autocorrelation of HSI returns and innovations of HSI returns ®tted to an AR (1)
model in each trading session (morning and afternoon separately). We allow the coecient of the
AR (1) model to vary across dierent trading sessions. Reported are the means and medians of
autocorrelation coecients. The number of coecients being signi®cantly dierent from zero at 2
standard deviations or higher is also reported. There are 184, not 185, afternoons because trading
was closed for the afternoon just prior to the Chinese New Year Eve.
3. Methodology
3.1. Between spot and futures
Following Stoll and Whaley (1990) and Chan (1992), the lead±lag relationship between the spot market and the futures market is investigated with
the following model: 7
7
We ®nd that the coecients of longer lags/leads (4th or beyond) are small and insigni®cant.
Furthermore, the ®rst three lag/lead coecients are found to be robust whether the longer lags/
leads are included or not. Thus for model parsimony, we use three lags/leads in model (1).
364
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Rs;t a
3
X
bk Rf ;tk et ;
1
kÿ3
where Rs;t is the 5-min cash index return and Rf ;t is the 5-minute futures
trade return at time t. For every morning, the ®rst three and the last three
Rs;t s are dropped because there are no corresponding lag or lead Rf ;t s. For
every afternoon, the ®rst three Rs;t s are dropped because there are no corresponding lag Rf ;t s. This means that we examine the lead±lag relation based
on the middle parts of morning and afternoon only, and the results may not
apply to the market open or close. The coecients bk with negative (positive) subscripts are lag (lead) coecients. If the lag (lead) coecients are
signi®cantly dierent from zero, the cash index lags (leads) the futures. 8 All
the t-statistics for the coecients are estimated with the generalized method
of moments (Hansen, 1982; Chan, 1992, p. 133). 9
Because the HSI may suer from non-synchronous trading among component stocks, model (1) is repeated with serially uncorrelated cash index return innovations to analyze the lead±lag behavior after the non-synchronous
trading bias is mitigated (Chan, 1992, p. 134). The return innovations are
generated by an autoregressive model ®tted to the series of cash index returns. 10 Unlike trade returns, quotation returns are not aected by bid±ask
bounce. Given the non-lasting nature of futures quotes and that the time of
observation is virtually the same for trade prices and quotes, repeating model
(1) with futures quotation returns allows us to investigate the eect of bid±ask
bounce.
8
Previous studies such as Stoll and Whaley (1990) usually emphasize whether the lag/lead
coecients are signi®cantly positive to infer the lead±lag relation between the futures and the spot
markets. Yet a signi®cantly negative lag or lead coecient could also have implications for the
lead±lag relation (we thank an anonymous referee for suggesting this). For example, if the spot
return series on average exhibit negative autocorrelation in the third lag (this is the case for HSI as
shown by Table 3), the third lead coecient in model (1) might also be negative. The reason is that
usually the contemporaneous coecient in the model would be large suggesting substantive
comovement between futures returns and spot returns, thus any reversal in the spot returns would
likely be associated with an analogous reversal in the futures returns.
9
The t-statistics are calculated with standard error using GMM estimation in PROC MODEL of
SAS, v. 6.09.
10
We will report the results using the return innovations generated by a parsimonious AR (1)
model. The results are robust even if we have used the return innovations generated by an AR (2)
model. We allow the coecients of the autoregressive models to vary across dierent trading
sessions.
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
365
3.2. Between spot and options
Unlike the futures, a factor of the relation between option returns and spot
returns is the optionÕs delta. OptionÕs delta usually diers from one and it also
diers across various option contracts. Based on Chan et al. (1993, pp. 1957±
1958, 1960±1961), the lead±lag relationship between the spot market and the
call market is investigated with the following non-linear system equation
model: 11; 12
Rs;t ac
4
X
bk hc Rc;tk tc;t ;
c 1; . . . ; M;
t 1; ; T ;
2
kÿ4
where Rc;t is the 5-minute trade return for a call contract c at time t, bk s the lag/
lead coecients, hc the delta value of the contract c and is assumed to be
constant throughout the morning, M the number of call mornings (i.e., 185), T
the number of Rs;t s during the morning )8 (the ®rst 4 and the last 4 Rs;t s are
dropped because there are no corresponding lag or lead Rc;t s). We study
mornings only because T for afternoons is too small for model (2) to be estimated. This means that we examine the lead±lag relation based on the middle
part of morning only, and the results may not apply to afternoon, or morningÕs
open or close. Since the lag/lead coecients are always multiplied P
by hc , there is
an indeterminacy that we resolve by normalizing the bk s so that 4kÿ4 bk 1.
As a result, only 8 bk s are independent from one another. In model (1), we can
estimate the actual value of every coecient. Now because of the normalization, we cannot estimate the actual value of each lag/lead coecient, but we
can still estimate the relative values across the coecients (the sum of the
relative values is one). By studying the relative values of the lag coecient
estimates versus the relative values of the lead coecient estimates, we can infer
whether the spot returns lag the option returns more than they lead. With a
similar reasoning, Chan et al. (1993) infer whether the stock option returns lag
the stock returns more than they lead from the relative values of the normalized lag/lead coecient estimates. Model (2) can be thought of as single time
11
This non-linear multivariate regression model is ®rst used in ®nance by Gibbons (1982). This
approach is simple and requires little information to be implemented (e.g., it can be used without
knowing the dividend ex-date). Yet Chan et al. (1993) show that this simple approach can replicate
the results generated using more complicated approaches (e.g., the approach of computing implied
stock prices through inverting the Black and Scholes or another option-pricing equation (Stephan
and Whaley, 1990)). For more details on this approach, see Gibbons (1982) and Chan et al. (1993).
12
We ®nd that the coecients of longer lags/leads (5th or beyond) are small and insigni®cant.
Furthermore, the ®rst 4 lag/lead coecients are found to be robust whether the longer lags/leads are
included or not. Thus, for model parsimony, we use 4 lags/leads in model (2).
366
bÿ4
a
bÿ3
bÿ2
2
bÿ1
b0
b1
b2
b3
b4
n
R
A.I. With call trade returns
0.006
0.022
0.073
(2.77)
(8.96)
0.156
(18.46)
0.227
(23.14)
0.225
(22.98)
0.161
(18.08)
0.094
(10.46)
0.036
(3.85)
3885
0.132
A.II. With call quotation returns
0.000
0.019
0.079
(2.91)
(12.41)
0.183
(26.14)
0.259
(31.39)
0.234
(30.41)
0.130
(18.75)
0.065
(8.78)
0.031
(4.10)
3885
0.256
B.I. With put trade returns
)0.013
0.019
0.046
(2.67)
(5.27)
0.152
(17.29)
0.224
(22.79)
0.228
(23.13)
0.184
(19.52)
0.107
(11.31)
0.053
(5.35)
3885
0.126
B.II. With put quotation returns
0.001
0.014
0.080
(1.77)
(10.80)
0.143
(18.97)
0.242
(27.40)
0.248
(26.84)
0.170
(21.01)
0.078
(9.70)
0.024
(2.74)
3885
0.206
We run the following regression:
Rs;t ao
4
X
kÿ4
bk ho Ro;tk vo;t ;
o 1; . . . ; 185;
t 1; . . . ; T ;
4
X
bk 1;
kÿ4
where Ro ,t is the 5-minute return at time t for a call or put contract o with delta ho (we use the most active call and the most active put each morning, so
we have 185 call mornings and 185 put mornings), and T is the number of 5-min spot HSI return, Rs ,t , during the morning )8. Reported are the
coecient estimates with t-statistics in parentheses (* means signi®cance at 0.1% level), the number of observations (n), and the average adjusted R2
over the 185 call mornings or the 185 put mornings. Only the t-statistics of eight bk s are reported, since the nine bk s are normalized such that their sum
is one and only eight bk s are independent from one another.
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Table 4
The results of regressing HSI returns on leads and lags of HSI option returns, January±September 1994a
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
367
series regressions with T observations in a pooled system of M equations. It is
estimated with iterated ordinary least-squares method. 13
Model (2) is then repeated with serially uncorrelated cash index return innovations to analyze the lead±lag behavior in the absence of the non-synchronous trading bias. In addition, we repeat model (2) with call quotation
returns to investigate the informativeness of the quotes. Given the non-lasting
nature of these open outcry quotes and that the time of observation (3.30, see
Panel II, Table 1) is substantially dierent from 5, this will provide an interesting contrast to the ®ndings for markets with good-till-revision quotes. To
investigate the lead±lag relationship between the spot market and the put
market and to study the informativeness of the put quotes, the whole procedure is repeated with the 185 put mornings.
4. Results
4.1. Between spot and options
The results on the lead±lag relation between cash HSI returns and call trade
and quotation returns are displayed in Panels A.I and A.II, Table 4. 14 Panel
A.I shows that cash returns lead call trade returns up to 15±20 minutes (b1
through b3 are signi®cantly positive while b4 is marginally so), and lag only
by 10 minutes (bÿ1 and bÿ2 are signi®cantly positive). 15 When we look at the
results using call quotation returns in Panel A.II, the lead±lag pattern seems to
be more or less the same as Panel A.I.
The relationship between the cash and puts is presented in Panels B.I and
B.II. The put returns based on trade prices lag the cash by 20 minutes and lead
only by 10 minutes. When we look at the put quotation returns, the puts appear to lag the cash slightly less than when we use the put trade returns: the 2nd
and the 3rd lead coecients become smaller and the 4th one even becomes
insigni®cant, whereas the feedback of the puts on the cash re¯ected by bÿ2 is
larger.
13
Our procedure is similar to that of Chan et al. (1993), but we replace the outdated PROC
SYSNLIN with PROC MODEL in SAS, v. 6.09.
14
As explained in Section 3.2, only eight normalized bk s are independent from one another.
Thus, we only report the t-statistics of eight, not nine, bk s. With the same reasoning, Chan et al.
(1993) only present six of the seven normalized coecients in their model. Although the coecient
bÿ4 is presented in Table 4 without the t-statistic, this should not cause major problems as we can
see that it is the smallest (in magnitude) among all the normalized coecients and our conclusion
that the option returns lag the spot returns more than they lead is robust.
15
We have nearly 4000 intraday observations. As Lindley (1957) points out, lower signi®cance
should be required for large samples. All the tests in this table use the 0.1% signi®cance level as the
rejection criterion, instead of conventional levels of signi®cance.
368
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
To summarize, cash index returns lead more than lag option trade returns
even before the non-synchronous trading bias in the cash returns is purged. 16
It seems that the HSI options market is much less informationally ecient than
the counterparts in other countries where cash index returns lag more than lead
option returns. For example, Fleming et al. (1996) ®nd that due to the dierence in trading costs, S&P 500 futures lead S&P 100 options, which in turn lead
the spot index. It is nevertheless not too surprising that the HSI options lag the
spot index. We have observed that the option contracts are inactive; even the
relatively popular contracts (Panel II, Table 1) are less actively traded than 32
of the 33 HSI component stocks, which account for 99.3% of the index capitalization. Thus, their prices could be stale as compared to the HSI component
stocks, leading to the result that option trade returns lag the spot index returns.
Further, the results using option quotation returns suggest that the relative
informational ineciency of the option bid±ask quotes is quite similar to the
possibly stale prices. This contrasts with other markets where quotes are goodtill-revision. For example, when Stephan and Whaley (1990) ®nd that stocks
lead stock options using trade prices to calculate returns, Chan et al. (1993)
suspect that it is probably caused by stale option prices. They proceed to resolve the puzzle using good-till-revision quotes to calculate option returns.
They then ®nd that stocks no more lead the options. Unlike trade price, goodtill-revision quote has to re¯ect market conditions until the next quote. It
cannot be stale, otherwise the market maker may incur loss. On the other hand,
we observe that the HSI option quotes from the open outcry system are updated infrequently, so they could be stale (Panel II, Table 1). A likely reason is
that even though the market makers update infrequently their quotes, unlike
the case of good-till-revision quotes, traders cannot take advantage of these
stale non-lasting quotes.
4.2. Between spot and futures
In Table 5, we examine the lead±lag relation between cash HSI returns and
futures returns. Panel A.I (A.II) shows the results when we use futures trade
16
To mitigate the thin trading problem in options, we repeat our tests using 40 call mornings and
23 put mornings, each of which has at least 40% of its 5-minute intervals with trades. The results,
not reported here, show that the calls and puts still lag more than lead the spot index. Alternatively,
if we lengthen the intraday time interval to 10 or more minutes, there will be less intervals with no
trade for the option mornings. However, the number of intervals per morning will also decrease,
causing problems in estimating model (2). Furthermore, when we repeat the analysis with serially
uncorrelated HSI return innovations from an AR (1) model to mitigate the non-synchronous
trading bias in the spot index, the results, not reported here, show as expected that the calls and
puts only lag the cash more.
369
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Table 5
The results of regressing HSI returns (or innovations of HSI returns ®tted to an AR (1) model) on
leads and lags of HSI futures returns, January±September 1994a
bÿ3
bÿ2
bÿ1
b0
b1
b2
2
b3
n
R
A.I. With futures trade returns & HSI returns
0.026
0.140
0.298
0.314
0.153
(2.66)
(16.26) (36.61) (11.00) (10.54)
0.016
(0.68)
)0.019
()1.45)
5917
0.565
A.II. With futures quotation returns & HSI returns
0.031
0.137
0.299
0.349
0.153
(3.51) (15.74) (36.14) (37.51) (16.23)
)0.016
()1.93)
)0.032
()3.93)
5917
0.588
B.I. With futures trade returns & HSI return innovations generated by an AR (1) model
)0.071
)0.018
0.120
0.235
0.120
0.002
)0.028
5862
0.297
()7.48) ()1.95)
(12.80) (11.25)
(8.47)
(0.10)
()1.84)
B.II. With futures quotation returns & HSI return innovations generated by an AR (1) model
)0.065
)0.022
0.122
0.257
0.130
)0.028
)0.044
5862
0.318
()7.41) ()2.32)
(12.77) (25.72) (11.94) ()2.99)
()5.06)
a
We run the following regression:
Rs;t a
3
X
bk Rf ;tk et ;
kÿ3
where Rs ,t is the 5-minutes cash HSI return or innovation of HSI return ®tted to an AR (1) model,
and Rf ,t is the 5-minutes futures trade return or quotation return calculated using the spot-month
futures each day. Reported are the coecient estimates with t-statistics in parentheses (* means
signi®cance at 0.1% level), the number of observations (n), and the adjusted R2 . Some mornings and
afternoons with problem in AR (1) estimation for cash HSI returns are deleted. Thus, n is smaller
with HSI return innovations.
(quotation) returns. The results in Panel A.I suggest that the futures lead the
cash by up to 10 minutes (bÿ1 and bÿ2 are signi®cantly positive), and the cash
only leads the futures by 5 minutes (b1 is signi®cantly positive). These suggest
that the futures lead more than lag the spot index. The results in Panel A.II
show that bÿ1 , bÿ2 , and bÿ3 are all signi®cantly positive while b1 is signi®cantly positive and b3 is signi®cantly negative. 17 The magnitudes of the ®rst 2
17
The negative signi®cance of the 3rd lead coecient is consistent with the negative
autocorrelation in the 3rd lag of HSI as shown by Table 3. The substantive co-movement between
futures returns and spot returns means that any reversal in the spot returns would likely be
associated with an analogous reversal in the futures returns. On the other hand, the magnitude of
this negative coecient estimate appears to be small relative to the magnitudes of the other positive
coecient estimates. This is consistent with the supposition that any tendency for the (spot and)
futures to reverse after 15 or so minutes, following a change in Rs;t , is dominated by the tendency
for spot and futures returns to move in the same direction, contemporaneously and across other
lags. (We thank an anonymous referee for suggesting this.)
370
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Table 6
The results of regressing HSI component stocksÕ returns on leads and lags of HSI futures returns,
January±September 1994a
Firms' names
bÿ3
bÿ2
Hong Kong Telecommunications
HSBC Holdings
)0.019
()0.63)
0.063
(1.01)
)0.061
()1.25)
)0.003
()0.08)
)0.021
()0.43)
0.002
(0.08)
)0.039
()0.82)
0.074
(2.02)
0.029
(0.77)
0.027
(0.74)
0.059
(1.56)
)0.007
Sun Hung Kai
Properties
Hutchison
Whampoa
Hang Seng Bank
Cheung Kong
(Holdings)
China Light &
Power
Henderson Land
Development
Wharf (Holdings)
Swire Paci®c A
Hong Kong Land
Holdings
Hong Kong
Electric
Holdings
CITIC Paci®c
Jardine Matheson
Holdings
New World
Development
Cathay Paci®c
Airways
Wheelock
Hopewell
Holdings
Hong Kong &
China Gas
Jardine Strategic
Holdings
Bank of East Asia
Hysan
Development
()0.23)
0.013
(0.46)
0.042
(0.70)
0.052
(1.27)
0.099
(2.75)
0.016
(0.56)
0.041
(1.16)
0.100
(2.51)
0.082
(1.70)
)0.011
()0.21)
0.068
(2.49)
bÿ1
b0
2
b1
b2
b3
R
0.111
0.214
0.330
(2.90)
(6.16) (9.58)
0.024
0.130
0.391
(0.36)
(1.84)
(5.49)
0.142
0.388
0.435
(2.92)
(7.30) (7.75)
0.182
0.310
0.531
(5.28) (7.39) (12.71)
0.101
0.258
0.327
(1.76)
(4.48) (5.62)
0.121
0.321
0.501
(4.26) (10.82) (16.40)
0.146
0.320
0.274
(2.59)
(6.19) (5.89)
0.155
0.425
0.429
(4.25) (10.36) (9.91)
0.173
0.385
0.347
(3.73) (9.60) (8.29)
0.162
0.377
0.365
(3.49) (8.18) (8.55)
0.174
(4.74)
0.154
(2.16)
0.263
(5.21)
0.262
(7.18)
0.196
(3.69)
0.215
(5.98)
0.075
(1.21)
0.158
(3.62)
0.187
(4.31)
0.168
(3.92)
)0.046
()1.25)
)0.179
()2.56)
0.007
(0.15)
0.015
(0.46)
)0.021
()0.43)
)0.017
()0.48)
)0.035
()0.61)
0.007
(0.15)
0.033
(0.74)
0.007
(0.14)
)0.049
()1.40)
0.051
(0.77)
)0.032
()0.57)
)0.048
()1.47)
)0.102
()1.89)
)0.007
()0.27)
0.050
(1.04)
)0.057
()1.46)
)0.032
()0.77)
)0.062
()1.39)
0.036
0.085
0.357
0.445
(2.26) (10.04) (11.29)
0.164
0.237
0.293
0.067
(1.43)
0.120
(4.16) (6.71)
0.192
0.247
(5.68) (5.94)
0.031
0.396
(0.49)
(5.79)
0.198
0.373
(5.31) (10.07)
0.125
0.267
(3.24) (6.72)
0.162
0.369
(5.46) (11.76)
0.132
0.316
(3.12)
(6.13)
0.170
0.256
(4.13) (5.53)
0.054
0.191
(1.02)
(3.80)
0.228
0.351
(3.63) (6.14)
0.165
0.379
(5.01) (15.10)
(3.91)
0.022
(0.66)
0.033
(0.51)
0.129
(3.26)
0.009
(0.21)
0.057
(1.92)
0.108
(3.11)
0.160
(3.81)
0.182
(3.07)
0.044
(0.73)
0.122
(3.28)
(8.72)
0.274
(8.05)
0.370
(5.42)
0.460
(9.60)
0.222
(4.95)
0.286
(9.67)
0.334
(9.68)
0.151
(3.38)
0.174
(3.32)
0.276
(4.74)
0.258
(8.31)
0.011
0.037
0.099
0.016
0.122
0.023
0.082
0.055
0.049
0.026 )0.026 0.076
(0.82) ()0.54)
)0.045 )0.063 0.049
()1.38)
0.041
(1.05)
0.075
(1.14)
0.033
(0.53)
)0.016
()0.37)
0.004
(0.12)
0.056
(1.67)
)0.048
()1.16)
)0.069
()1.34)
0.052
(0.94)
)0.040
()1.42)
()2.12)
)0.075
()2.16)
)0.090
()1.57)
0.032
(0.83)
)0.016
()0.45)
0.030
(0.86)
)0.024
()0.61)
)0.004
()0.09)
)0.117
()1.99)
)0.045
()0.79)
)0.004
()0.14)
0.058
0.013
0.044
0.037
0.082
0.059
0.019
0.010
0.015
0.103
371
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
Table 6 (Contined)
Firms' names
bÿ3
Dairy Farm International Holdings
Hang Lung Development
Television Broadcasts
Hong Kong and
Shanghai Hotels
Miramar Hotel &
Investment
Great Eagle Holdings
Shun Tak Holdings
Mandarin Oriental
International
Hong Kong Aircraft Engineering
Lai Sun Garment
(International)
Winsor Industrial
Corporation
a
bÿ2
bÿ1
b0
b1
b2
b3
2
R
0.138 )0.040
0.209
0.198
0.042 )0.092 )0.004 0.004
(2.20) ()0.62)
(3.02)
(2.57)
(0.66) ()1.72) ()0.06)
0.049
0.243
0.346
0.331
0.074 )0.032
0.007 0.096
(1.80)
(8.50) (11.05) (11.87) (2.45) ()0.89)
(0.21)
0.062
0.102
0.075
0.014
0.034
0.010
0.028 0.007
(1.68)
(3.28) (2.46)
(0.38)
(0.75)
(0.29)
(0.94)
0.042
0.193
0.282
0.176 )0.024 )0.027
0.008 0.026
(0.92)
(4.37) (5.18) (4.42) ()0.50) ()0.63)
(0.21)
0.062
0.063
0.106
0.022
0.014
0.007 )0.014 0.007
(2.40)
(2.17)
(4.04) (0.87)
(0.53)
(0.29) ()0.55)
0.144
0.174
0.461
0.303
0.059
0.058 )0.012 0.055
(3.22) (3.99) (11.36) (7.71) (1.34)
(1.34) ()0.29)
0.077
0.127
0.127
0.033
0.072
0.030 )0.005 0.007
(2.29)
(3.11)
(3.31) (0.91)
(1.92)
(0.78) ()0.15)
0.069
0.106
0.309
0.006
0.097
0.020 )0.042 0.005
(1.17)
(1.66)
(4.58) (0.10)
(1.56)
(0.28) ()0.60)
0.048
0.121
0.135
0.027
0.012
0.014 )0.062 0.014
(1.65)
(3.34) (4.18) (0.89)
(0.44)
(0.44) ()1.60)
0.041
0.159
0.140
0.047 )0.069 )0.034
0.032 0.011
(1.02)
(3.77) (3.67) (1.19) ()1.80) ()0.97)
(0.87)
0.154
0.159 )0.081
0.316
0.063 )0.018 )0.182 )0.001
(1.70)
(2.85) ()0.36)
(1.36)
(1.00) ()0.25) ()1.43)
We run the following regression:
Rs;t a
3
X
bk Rf ;tk et ;
kÿ3
where Rs ,t is the 5-minute trade return on stock s, and Rf ,t is the 5-minute futures quotation return
calculated using the spot-month futures each day. Reported are the coecient estimates with tstatistics in parentheses (* means signi®cance at 0.1% level), and the adjusted R2 . The stocks are
sorted by descending market capitalization.
lag coecients are larger than the ®rst 2 lead coecients and the magnitude of
the 3rd lag coecient is similar to the 3rd lead coecient. Again, these results
suggest that the spot index lags more than leads the futures.
Comparing the above results with Table 4, the options trade prices (quotes)
seem to be less informationally ecient than the futures trade prices
(quotes). 18 In Finland, Puttonen (1993) ®nds that the FOX futures and options markets, which both commenced on 2 May 1988, have similar informational eciency. Thus, one likely explanation for our results is that the options
18
The lead±lag relationship between the HSI futures and options has been analyzed with model
(2) using both trade and quotation returns. The results, not reported here, show as expected the
futuresÕ lead over the options.
372
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
market is much less mature than the futures market, such that traders prefer to
trade futures rather than options and market makers focus on their futures
quotes. As shown in Table 1, the options are much less actively traded than the
futures, so their prices could be stale as compared to futures prices. It also
seems that the non-lasting futures quotes are updated together with the intense
trading activities to re¯ect market conditions. On the other hand, for the much
less active options market, it seems that the market makers simply do not
bother to update their non-lasting quotes.
Non-synchronous trading among the index component stocks might have
caused part of the HSI futuresÕ lead over the cash index. Thus, in Panels B.I
and B.II of Table 5, we repeat the analysis with serially uncorrelated cash index
return innovations. There is one marked dierence between the results in
Panels B.I and B.II and those in Panels A.I and A.II: the lead±lag relationship
between the cash and futures markets now becomes more or less symmetric.
Thus, it seems that after the non-synchronous trading bias in the cash index
returns is purged, the futures no longer lead more than lag the index. 19
4.3. Between HSI component stocks and futures
To summarize, the futures lead the spot index only before the cash return
non-synchronous trading bias is considered. This contrasts sharply with previous studies for other countries. For example, Chan (1992) shows that index
futures lead more than lag the cash index even after the non-synchronous
trading bias in the cash index returns is considered. While the staleness of
option prices and quotes may explain the cash lead over the options, the HSI
futures are very active. They are even more actively traded than all the HSI
component stocks. Then why does their lead over the cash market appear to be
less than the counterparts in other countries? One likely explanation is that the
HSI is value-weighted and aected heavily by a few major stocks. These major
stocks are nearly as actively traded as the futures, and are in the infrastructure,
property development, and banking sectors, which dominate the Hong Kong
economy. If the HSI futures only have little lead over these stocks, their lead
over the cash index would be dampened and less than the counterparts in other
countries. To investigate this, we examine the lead±lag relationship between the
futures and each of the component stocks.
19
To investigate the possibility that the futures lead more when the market is bearish than when
the market is bullish because of short-sale restrictions in the spot market, we have repeated the
analysis in Table 5 with trading sessions sorted into 4 quartiles by the sign and size of HSI returns.
The results, not reported here, suggest that the lead±lag relation between the futures and cash is not
aected by whether the market is bullish or bearish. These results are similar to those of Chan
(1992), and suggest that marginal traders have long positions in the stocks and are not constrained
by the short-sale restrictions.
R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375
373
Model (1) is repeated with returns of individual component stock replacing
HSI returns. For each stock, we generate 5-minute returns from trade prices,
which are also used by HSI Services in computing the HSI. The results, sorted
by individual stockÕs market