Relative informational eciency of cash,
futures, and options markets: The case of an
emerging market
Raymond Chiang
a, Wai-Ming Fong
b,*a
Department of Accountancy, Hong Kong Ploytechnic University, Kowloon, Hong Kong bDepartment of Finance, Chinese University of Hong Kong, Shatin, N.T., Hong Kong
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.Ó2001 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
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*Corresponding author. Tel.: +852-2609-7903; fax: +852-2603-6586. E-mail address:wmfong@baf.msmail.cuhk.edu.hk (W.-M. Fong).
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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 op-tions traded on the Hong Kong Futures Exchange (HKFE). HSI is a value-weighted 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.2In 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.
2Related studies include Fung et al. (1997) and Bae et al. (1998), which examine the arbitrage
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 good-till-revision quotes replace trade prices in calculating option returns.3A 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. Con-sistent with this explanation, we observe that the HSI option quotes are up-dated 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 sur-prisingly, they are found to lead more than lag the cash index. One possible reason for the futuresÕlead 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 con-trasts 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
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 spe-cialists 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.
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 con-tract, one call concon-tract, 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 5-minute 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 1.4In our sample, there are 185
fu-4
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 dier-ence 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.5Many 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;
Table 1
HSI futures and options: Trading and quotation frequencies, January±September 1994a
Trade Bid Ask
I.Futures days
1. Percentage of 5-min intervals having trades/bids/asks
99.99 99.96 99.94
2. Average time of the last trade/ bid/ask in a 5-min interval
4.93 4.92 4.91
II.Option mornings A.The most active call 1. Percentage of 5-min intervals having trades/bids/asks
28.28 36.88 37.06
2. Average time of the last trade/ bid/ask in a 5-min interval
3.24 3.3 3.3
B.The most active put 1. Percentage of 5-min intervals having trades/bids/asks
23.84 31.85 30.84
2. Average time of the last trade/ bid/ask in a 5-min interval
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)).
5Afternoon trading sessions are too short and produce too few observations to be usable for the
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.6The ®le contains the time stamp, price, and volume for each trade. Ordering by market capitalization, Table 2 shows the stocksÕ trading fre-quencies 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 es-timate the return autocorrelation in each trading session (morning and after-noon 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 autocorrela-tion of the cash index return innovaautocorrela-tions 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.
Table 2
The component stocks of HSI: market value weight and trading frequency, January±September 1994a
HSBC Holdings plc 9.33 94.56 4.37 9009.7
Sun Hung Kai Properties 8.26 90.38 3.98 4404.6
Hutchison Whampoa 8.16 91.39 4.08 4443.3
Hang Seng Bank 6.48 89.82 4.02 2567.7
Cheung Kong (Holdings) 5.11 93.48 4.23 5302.4 China Light & Power 4.84 90.50 4.00 2574.5 Henderson Land Development 4.74 79.88 3.57 1588.8
Wharf (Holdings) 4.16 87.62 3.85 2362.7
Swire Paci®c A 3.63 82.23 3.65 2943.7
Hong Kong Land Holdings 3.18 90.53 4.05 2713.4 Hong Kong Electric Holdings 3.17 88.06 3.92 1491.6
CITIC Paci®c 2.95 90.52 4.00 2089.3
Jardine Matheson Holdings 2.94 75.70 3.48 2093.0 New World Development 2.63 90.32 4.00 2230.7
Cathay Paci®c Airways 2.17 71.11 3.33 578.2
Wheelock 2.12 85.37 3.73 1041.3
Hopewell Holdings 1.94 90.92 4.07 2010.4
Hong Kong & China Gas 1.86 89.44 3.98 1245.0 Jardine Strategic Holdings 1.83 67.11 3.27 856.3
Bank of East Asia 1.49 89.03 3.98 1464.0
Hysan Development 1.35 82.23 3.58 919.0
Dairy Farm International Hold-ings
1.13 70.94 3.35 616.1
Hang Lung Development Co 1.08 85.80 3.78 1062.3
Television Broadcasts 0.93 32.12 2.90 337.0
Hong Kong and Shanghai Ho-tels
0.76 52.41 3.08 271.6
Miramar Hotel & Investment 0.68 23.06 2.90 163.1
Great Eagle Holdings 0.61 79.47 3.45 574.8
Shun Tak Holdings 0.59 55.44 3.10 306.6
Mandarin Oriental International 0.44 47.55 3.02 169.5 Hong Kong Aircraft
Engineer-ing
0.41 45.02 3.02 239.4
Lai Sun Garment (International) 0.24 40.92 2.87 118.1 Winsor Industrial Corporation 0.17 42.46 2.88 136.5
aReported are the market value weights as on 30 September 1994 and trading frequencies of HSI
3. Methodology
3.1. Between spot and futures
Following Stoll and Whaley (1990) and Chan (1992), the lead±lag rela-tionship between the spot market and the futures market is investigated with the following model:7
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(n185)
1 0.367 0.382 96 0
2 0.131 0.14 4 0
3 )0.04 )0.038 0 1
4 )0.124 )0.125 0 1
5 )0.141 )0.14 0 0
6 )0.101 )0.111 0 1
B.Afternoons(n184)
1 0.253 0.284 13 0
2 )0.003 0.007 0 0
II.HSI return innovations generated by an AR(1)model A.Mornings
1 0.031 0.081 0 0
2 0.004 0.014 3 0
3 )0.073 )0.066 0 4
4 )0.087 )0.094 0 4
5 )0.087 )0.085 0 4
6 )0.04 )0.036 0 1
B.Afternoons
1 0.04 0.022 0 0
2 )0.072 )0.086 0 0
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.
7We ®nd that the coecients of longer lags/leads (4th or beyond) are small and insigni®cant.
Rs;ta X3
kÿ3
bkRf;tk et
; 1
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;ts are dropped because there are no corresponding lag or lead Rf;ts. For every afternoon, the ®rst three Rs;ts are dropped because there are no cor-responding lagRf;ts. 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 (posi-tive) subscripts are lag (lead) coecients. If the lag (lead) coecients are signi®cantly dierent from zero, the cash index lags (leads) the futures.8All 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 com-ponent stocks, model (1) is repeated with serially uncorrelated cash index re-turn 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 re-turns.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.
8Previous 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
Thet-statistics are calculated with standard error using GMM estimation in PROC MODEL of SAS, v. 6.09.
10
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;tac X4
kÿ4
bkhcRc;tk tc
;t; c1;. . .;M; t1; ;T; 2
whereRc;tis the 5-minute trade return for a call contractcat timet,bks the lag/ lead coecients, hc the delta value of the contract c and is assumed to be constant throughout the morning,Mthe number of call mornings (i.e., 185),T the number ofRs;ts during the morning)8 (the ®rst 4 and the last 4Rs;ts are dropped because there are no corresponding lag or lead Rc;ts). We study mornings only becauseTfor afternoons is too small for model (2) to be esti-mated. 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 byhc, there is an indeterminacy that we resolve by normalizing thebks so that
P4
kÿ4bk 1. As a result, only 8bks are independent from one another. In model (1), we can estimate the actual value of every coecient. Now because of the normaliza-tion, 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 normal-ized 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).
12We ®nd that the coecients of longer lags/leads (5th or beyond) are small and insigni®cant.
Table 4
The results of regressing HSI returns on leads and lags of HSI option returns, January±September 1994a
bÿ4 bÿ3 bÿ2 bÿ1 b0 b1 b2 b3 b4 n R
2
A.I.With call trade returns
0.006 0.022 0.073 0.156 0.227 0.225 0.161 0.094 0.036 3885 0.132
(2.77) (8.96) (18.46) (23.14) (22.98) (18.08) (10.46) (3.85)
A.II.With call quotation returns
0.000 0.019 0.079 0.183 0.259 0.234 0.130 0.065 0.031 3885 0.256
(2.91) (12.41) (26.14) (31.39) (30.41) (18.75) (8.78) (4.10)
B.I.With put trade returns
)0.013 0.019 0.046 0.152 0.224 0.228 0.184 0.107 0.053 3885 0.126
(2.67) (5.27) (17.29) (22.79) (23.13) (19.52) (11.31) (5.35)
B.II.With put quotation returns
0.001 0.014 0.080 0.143 0.242 0.248 0.170 0.078 0.024 3885 0.206
(1.77) (10.80) (18.97) (27.40) (26.84) (21.01) (9.70) (2.74)
a
We run the following regression:
Rs;tao
X4
kÿ4
bkhoRo;tkvo;t; o1;. . .;185; t1;. . .;T; X4
kÿ4
bk1;
whereRo,t is the 5-minute return at timetfor a call or put contractowith deltaho(we use the most active call and the most active put each morning, so
we have 185 call mornings and 185 put mornings), andTis the number of 5-min spot HSI return,Rs,t, during the morning)8. Reported are the coecient estimates witht-statistics in parentheses (* means signi®cance at 0.1% level), the number of observations (n), and the average adjustedR2 over the 185 call mornings or the 185 put mornings. Only thet-statistics of eightbks are reported, since the ninebks are normalized such that their sum
is one and only eightbks are independent from one another.
R.
Chiang,
W.-M.
Fong
/
Journal
of
Banking
&
Finance
25
(2001)
series regressions withTobservations in a pooled system ofMequations. It is estimated with iterated ordinary least-squares method.13
Model (2) is then repeated with serially uncorrelated cash index return in-novations to analyze the lead±lag behavior in the absence of the non-syn-chronous 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 inter-esting 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 proce-dure 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 4.14Panel A.I shows that cash returns lead call trade returns up to 15±20 minutes (b1 throughb3 are signi®cantly positive whileb4is marginally so), and lag only by 10 minutes (bÿ1 andbÿ2 are signi®cantly positive).15When 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 ap-pear 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 bybÿ2 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 normalizedbks are independent from one another.
Thus, we only report thet-statistics of eight, not nine,bks. With the same reasoning, Chan et al.
(1993) only present six of the seven normalized coecients in their model. Although the coecient bÿ4is presented in Table 4 without thet-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.
15We have nearly 4000 intraday observations. As Lindley (1957) points out, lower signi®cance
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 dier-ence 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 capi-talization. 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 good-till-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 re-solve 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 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 up-dated 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
(quotation) returns. The results in Panel A.I suggest that the futures lead the cash by up to 10 minutes (bÿ1andbÿ2 are signi®cantly positive), and the cash only leads the futures by 5 minutes (b1is signi®cantly positive). These suggest that the futures lead more than lag the spot index. The results in Panel A.II show thatbÿ1, bÿ2, and bÿ3 are all signi®cantly positive while b1 is signi®-cantly positive andb3is signi®cantly negative.17The magnitudes of the ®rst 2
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 b3 n R
2
A.I.With futures trade returns & HSI returns
0.026 0.140 0.298 0.314 0.153 0.016 )0.019 5917 0.565
(2.66) (16.26) (36.61) (11.00) (10.54) (0.68) (
)1.45)
A.II.With futures quotation returns & HSI returns
0.031 0.137 0.299 0.349 0.153 )0.016 )0.032 5917 0.588
(3.51) (15.74) (36.14) (37.51) (16.23) (
)1.93) ()3.93)
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)
aWe run the following regression:
Rs;ta X3
kÿ3
bkRf;tk
et;
whereRs,tis the 5-minutes cash HSI return or innovation of HSI return ®tted to an AR (1) model,
andRf,tis the 5-minutes futures trade return or quotation return calculated using the spot-month
futures each day. Reported are the coecient estimates witht-statistics in parentheses (* means signi®cance at 0.1% level), the number of observations (n), and the adjustedR2. Some mornings and
afternoons with problem in AR (1) estimation for cash HSI returns are deleted. Thus,nis smaller with HSI return innovations.
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 inRs;t, is dominated by the tendency
Table 6
The results of regressing HSI component stocksÕreturns on leads and lags of HSI futures returns, January±September 1994a
HSBC Holdings 0.063 0.024 0.130 0.391 0.154 )0.179 0.051 0.011
(1.01) (0.36) (1.84) (5.49) (2.16) (
)2.56) (0.77)
Sun Hung Kai Properties
)0.061 0.142 0.388 0.435 0.263 0.007 )0.032 0.037
()1.25) (2.92) (7.30) (7.75) (5.21) (0.15) ()0.57)
Hutchison Whampoa
)0.003 0.182 0.310 0.531 0.262 0.015 )0.048 0.099
()0.08) (5.28) (7.39) (12.71) (7.18) (0.46) ()1.47)
Hang Seng Bank )0.021 0.101 0.258 0.327 0.196 )0.021 )0.102 0.016
()0.43) (1.76) (4.48) (5.62) (3.69) ()0.43) ()1.89)
Cheung Kong (Holdings)
0.002 0.121 0.321 0.501 0.215 )0.017 )0.007 0.122
(0.08) (4.26) (10.82) (16.40) (5.98) (
)0.48) ()0.27)
China Light & Power
)0.039 0.146 0.320 0.274 0.075 )0.035 0.050 0.023
()0.82) (2.59) (6.19) (5.89) (1.21) ()0.61) (1.04)
Henderson Land Development
0.074 0.155 0.425 0.429 0.158 0.007 )0.057 0.082
(2.02) (4.25) (10.36) (9.91) (3.62) (0.15) (
)1.46)
Wharf (Holdings) 0.029 0.173 0.385 0.347 0.187 0.033 )0.032 0.055
(0.77) (3.73) (9.60) (8.29) (4.31) (0.74) (
)0.77)
Swire Paci®c A 0.027 0.162 0.377 0.365 0.168 0.007 )0.062 0.049
(0.74) (3.49) (8.18) (8.55) (3.92) (0.14) (
)1.39)
Hong Kong Land Holdings
0.059 0.085 0.357 0.445 0.067 0.026 )0.026 0.076
(1.56) (2.26) (10.04) (11.29) (1.43) (0.82) (
CITIC Paci®c 0.013 0.192 0.247 0.274 0.022 0.041 )0.075 0.058
(0.46) (5.68) (5.94) (8.05) (0.66) (1.05) (
)2.16)
Jardine Matheson Holdings
0.042 0.031 0.396 0.370 0.033 0.075 )0.090 0.013
(0.70) (0.49) (5.79) (5.42) (0.51) (1.14) (
)1.57)
New World Development
0.052 0.198 0.373 0.460 0.129 0.033 0.032 0.044 (1.27) (5.31) (10.07) (9.60) (3.26) (0.53) (0.83) Cathay Paci®c
Airways
0.099 0.125 0.267 0.222 0.009 )0.016 )0.016 0.037
(2.75) (3.24) (6.72) (4.95) (0.21) (
)0.37) ()0.45)
Wheelock 0.016 0.162 0.369 0.286 0.057 0.004 0.030 0.082 (0.56) (5.46) (11.76) (9.67) (1.92) (0.12) (0.86) Hopewell
Holdings
0.041 0.132 0.316 0.334 0.108 0.056 )0.024 0.059
(1.16) (3.12) (6.13) (9.68) (3.11) (1.67) (
)0.61)
Hong Kong & China Gas
0.100 0.170 0.256 0.151 0.160 )0.048 )0.004 0.019
(2.51) (4.13) (5.53) (3.38) (3.81) (
)1.16) ()0.09)
Jardine Strategic Holdings
0.082 0.054 0.191 0.174 0.182 )0.069 )0.117 0.010
(1.70) (1.02) (3.80) (3.32) (3.07) (
)1.34) ()1.99)
Bank of East Asia )0.011 0.228 0.351 0.276 0.044 0.052 )0.045 0.015
()0.21) (3.63) (6.14) (4.74) (0.73) (0.94) ()0.79)
Hysan Development
0.068 0.165 0.379 0.258 0.122 )0.040 )0.004 0.103
(2.49) (5.01) (15.10) (8.31) (3.28) (
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 op-tions markets, which both commenced on 2 May 1988, have similar informa-tional eciency. Thus, one likely explanation for our results is that the options
Table 6 (Contined)
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)
Television Broad-casts
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) Hong Kong and
Shanghai Hotels
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)
Miramar Hotel & Investment
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)
Great Eagle Hold-ings
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)
Shun Tak Hold-ings
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)
Mandarin Oriental International
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)
Hong Kong Air-craft Engineering
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)
Lai Sun Garment (International)
0.041 0.159 0.140 0.047 )0.069 )0.034 0.032 0.011
(1.02) (3.77) (3.67) (1.19) (
whereRs,tis the 5-minute trade return on stocks, andRf,tis the 5-minute futures 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), and the adjustedR2. The stocks are
sorted by descending market capitalization.
18The lead±lag relationship between the HSI futures and options has been analyzed with model
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 pre-vious 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
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 capitalization, are shown in Table 6.20 Several ®ndings are notable. First, the larger the market capitalization, the less the stock tends to lag the futures. Second, four of the biggest component stocks, especially HSBC, have more or less symmetric lead±lag relations with the fu-tures. These four stocks (Hong Kong Telecom, HSBC, Sun Hung Kai, and Hang Seng Bank) account for 34.7% of the index capitalization. Three of them are in the property development and banking sectors, while one is the mo-nopolist telecom company.21 In comparison with results for other countries such as Chan (1992) who ®nds that each MMI component stock lags the MMI futures, this ®nding could explain why the HSI futuresÕ lead over the cash market is less than the counterparts in other countries.
5. Conclusion
Using intraday data from January to September 1994, we study the lead±lag relations among the markets for the spot, futures (completely revamped after the 1987 market crash), and options (commenced in 1993) on the HSI, a value-weighted index composed of 33 blue-chip stocks in Hong Kong. Our analysis sheds light on the relative informational eciency across emerging derivative markets at dierent stages of development. We also examine the relative in-formativeness of the bids and asks for the futures and options, which are only good for immediate trade and non-lasting.
We ®nd that cash index returns lead more than lag option trade returns, even though the relatively active option contracts are used in our tests and even before the autocorrelation in the cash returns is purged. This suggests that the HSI options market is much less informationally ecient than the counterparts in other countries. A likely reason is that the options are thinly traded, so the prices are usually stale.
On the other hand, it seems that traders prefer to utilize the futures market, which is much more mature than the options market. The futures are very actively traded, yet their returns lead the cash index returns only before, but not after, the autocorrelation in the cash returns is purged. This suggests that
20
The results using futures trade returns are similar to the results using futures quotation returns that are reported here.
21Sun Hung Kai is a major property developer in Hong Kong, while HSBC and Hang Seng
the futuresÕ lead over the cash market is 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, 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 HSI component stocks have more or less sym-metric lead±lag relations with the futures.
Using bid±ask midpoints, we still ®nd that option returns lag cash returns. This contrasts with the ®ndings from markets where quotes are good-till-re-vision. On the other hand, we ®nd the futures quote returns lead the cash index returns before the autocorrelation in the cash returns is purged. A likely reason is that market makers focus on the quotes on the active futures market and update them frequently, whereas for the inactive options market the quotes are updated infrequently and thus are stale sometimes.
Our ®ndings have several implications. First, emerging derivatives marketsÕ
relative informational eciency seems to depend on the market maturity. Second, the relative informativeness of quotes that are only good for imme-diate trade also seems to depend on the market maturity. Third, though index derivatives oer leverage eects and lower trading costs, they may not lead the cash index (after the non-synchronous trading among the component stocks is considered) if the index is heavily aected by a few actively traded major stocks. The cash index can even lead the derivative securities if the derivatives are thinly traded.
Acknowledgements
We acknowledge the Earmarked Grant of the Research Grants Council of Hong Kong (CUHK 167/96H) for ®nancial support. Raymond Chiang also acknowledges the Direct Grant of The Chinese University of Hong Kong for ®nancial support. We thank Dennis Fan, The HKFE, HSI Services Limited, and The SEHK for the data. We thank Lawrence K.M. Fok, Larry Lang, Ivers Riley, the editor, and two anonymous referees for their helpful comments. The responsibility for any errors in this paper remains ours.
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