Relative informational e ciency of cash, futures, and options markets: The case of an emerging market

Transcription

1 Journal of Banking & Finance 25 (2001) 355±375 Relative informational e ciency 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 b Department 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. 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 e ects and lower trading costs in index derivatives, - nancial economists often argue that returns on index futures or options lead * Corresponding author. Tel.: ; fax: address: wmfong@baf.msmail.cuhk.edu.hk (W.-M. Fong) /01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S (99)

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 e cient 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 e cient 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 e ciency 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 e ciency across emerging derivative markets at di erent 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 e ciency. 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.

3 R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355± 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 ine ciency 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 e ects 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 a ected 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.

4 358 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 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 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

5 R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355± 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 There are many di erent 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 e ects 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 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. 4 In our sample, there are 185 fu- 4 In Hong Kong Futures Exchange (1995, p. 4), the HKFE o cials 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''.

6 360 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 1994 a 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 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 di erence 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.

7 R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355± 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 a ected 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 coe cients (0.367 in the mornings and in the afternoons) and the numbers of coe cients 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 coe cients become close to zero and the numbers of coe cients that are signi cantly di erent from zero become trivial. 6 Bid and ask records before May 1996 are not available.

8 362 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 1994 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 a 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 5- minute 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.

9 Table 3 Autocorrelation of cash HSI returns, January±September 1994 a Lag R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355± Mean of coe cients Median of coe cients No. of signi cant coe cients + ) I. Cash HSI returns A. Mornings (n ˆ 185) )0.04 ) )0.124 ) )0.141 ) )0.101 ) B. Afternoons (n ˆ 184) ) II. HSI return innovations generated by an AR (1) model A. Mornings )0.073 ) )0.087 ) )0.087 ) )0.04 ) B. Afternoons )0.072 ) 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 coe cient of the AR (1) model to vary across di erent trading sessions. Reported are the means and medians of autocorrelation coe cients. The number of coe cients being signi cantly di erent 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 coe cients of longer lags/leads (4th or beyond) are small and insigni cant. Furthermore, the rst three lag/lead coe cients 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).

10 364 R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355±375 R s;t ˆ a X3 kˆ 3 b k R f ;t k e t ; 1 where R s;t is the 5-min cash index return and R f ;t is the 5-minute futures trade return at time t. For every morning, the rst three and the last three R s;t s are dropped because there are no corresponding lag or lead R f ;t s. For every afternoon, the rst three R s;t s are dropped because there are no corresponding lag R f ;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 coe cients b k with negative (positive) subscripts are lag (lead) coe cients. If the lag (lead) coe cients are signi cantly di erent from zero, the cash index lags (leads) the futures. 8 All the t-statistics for the coe cients are estimated with the generalized method of moments (Hansen, 1982; Chan, 1992, p. 133). 9 Because the HSI may su er 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 a ected 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 e ect of bid±ask bounce. 8 Previous studies such as Stoll and Whaley (1990) usually emphasize whether the lag/lead coe cients 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 coe cient 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 coe cient in model (1) might also be negative. The reason is that usually the contemporaneous coe cient 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 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 coe cients of the autoregressive models to vary across di erent trading sessions.

11 R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355± 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 di ers from one and it also di ers 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 11; 12 model: R s;t ˆ a c X4 kˆ 4 b k h c R c;t k t c;t ; c ˆ 1;...; M; t ˆ 1; ; T ; 2 where R c;t is the 5-minute trade return for a call contract c at time t, b k s the lag/ lead coe cients, h c 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 R s;t s during the morning )8 (the rst 4 and the last 4 R s;t s are dropped because there are no corresponding lag or lead R c;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 coe cients are always multiplied by h c, there is an indeterminacy that we resolve by normalizing the b k s so that P 4 kˆ 4 b k ˆ 1. As a result, only 8 b k s are independent from one another. In model (1), we can estimate the actual value of every coe cient. Now because of the normalization, we cannot estimate the actual value of each lag/lead coe cient, but we can still estimate the relative values across the coe cients (the sum of the relative values is one). By studying the relative values of the lag coe cient estimates versus the relative values of the lead coe cient 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 coe cient 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 coe cients of longer lags/leads (5th or beyond) are small and insigni cant. Furthermore, the rst 4 lag/lead coe cients 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).

12 366 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 1994 a b 4 b 3 b 2 b 1 b0 b 1 b 2 b 3 b 4 n R 2 A.I. With call trade returns (2.77) (8.96) (18.46) (23.14) (22.98) (18.08) (10.46) (3.85) A.II. With call quotation returns (2.91) (12.41) (26.14) (31.39) (30.41) (18.75) (8.78) (4.10) B.I. With put trade returns ) (2.67) (5.27) (17.29) (22.79) (23.13) (19.52) (11.31) (5.35) B.II. With put quotation returns (1.77) (10.80) (18.97) (27.40) (26.84) (21.01) (9.70) (2.74) a We run the following regression: Rs;t ˆ ao X4 kˆ 4 bkhoro;t k vo;t; o ˆ 1;...; 185; t ˆ 1;...; T ; X 4 kˆ 4 bk ˆ 1; 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 coe cient estimates with t-statistics in parentheses (* means signi cance at 0.1% level), the number of observations (n), and the average adjusted R 2 over the 185 call mornings or the 185 put mornings. Only the t-statistics of eight bks are reported, since the nine bks are normalized such that their sum is one and only eight bks are independent from one another.

13 R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355± 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 di erent 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 Panel A.I shows that cash returns lead call trade returns up to 15±20 minutes (b 1 through b 3 are signi cantly positive while b 4 is marginally so), and lag only by 10 minutes (b 1 and b 2 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 coe cients become smaller and the 4th one even becomes insigni cant, whereas the feedback of the puts on the cash re ected by b 2 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 As explained in Section 3.2, only eight normalized b k s are independent from one another. Thus, we only report the t-statistics of eight, not nine, b k s. With the same reasoning, Chan et al. (1993) only present six of the seven normalized coe cients in their model. Although the coe cient b 4 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 coe cients 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.

14 368 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 e cient 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 di erence 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 ine ciency 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 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.

15 R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355± 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 1994 a b 3 b 2 b 1 b 0 b 1 b 2 b 3 n R 2 A.I. With futures trade returns & HSI returns ) (2.66) (16.26) (36.61) (11.00) (10.54) (0.68) ()1.45) A.II. With futures quotation returns & HSI returns )0.016 ) (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 ) ) ()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 ) )0.028 ) ()7.41) ()2.32) (12.77) (25.72) (11.94) ()2.99) ()5.06) a We run the following regression: R s;t ˆ a X3 kˆ 3 b k R f ;t k e t ; where R s, t is the 5-minutes cash HSI return or innovation of HSI return tted to an AR (1) model, and R f, t is the 5-minutes futures trade return or quotation return calculated using the spot-month futures each day. Reported are the coe cient estimates with t-statistics in parentheses (* means signi cance at 0.1% level), the number of observations (n), and the adjusted R 2. 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 (b 1 and b 2 are signi cantly positive), and the cash only leads the futures by 5 minutes (b 1 is signi cantly positive). These suggest that the futures lead more than lag the spot index. The results in Panel A.II show that b 1, b 2, and b 3 are all signi cantly positive while b 1 is signi cantly positive and b 3 is signi cantly negative. 17 The magnitudes of the rst 2 17 The negative signi cance of the 3rd lead coe cient 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 coe cient estimate appears to be small relative to the magnitudes of the other positive coe cient 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 R s;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.)

16 370 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 1994 a Firms' names b 3 b 2 b 1 b 0 b 1 b 2 b 3 R 2 Hong Kong Telecommunications ) )0.046 ) ()0.63) (2.90) (6.16) (9.58) (4.74) ()1.25) ()1.40) HSBC Holdings ) (1.01) (0.36) (1.84) (5.49) (2.16) ()2.56) (0.77) Sun Hung Kai ) ) Properties ()1.25) (2.92) (7.30) (7.75) (5.21) (0.15) ()0.57) Hutchison ) ) Whampoa ()0.08) (5.28) (7.39) (12.71) (7.18) (0.46) ()1.47) Hang Seng Bank ) )0.021 ) ()0.43) (1.76) (4.48) (5.62) (3.69) ()0.43) ()1.89) Cheung Kong )0.017 ) (Holdings) (0.08) (4.26) (10.82) (16.40) (5.98) ()0.48) ()0.27) China Light & ) ) Power ()0.82) (2.59) (6.19) (5.89) (1.21) ()0.61) (1.04) Henderson Land ) Development (2.02) (4.25) (10.36) (9.91) (3.62) (0.15) ()1.46) Wharf (Holdings) ) (0.77) (3.73) (9.60) (8.29) (4.31) (0.74) ()0.77) Swire Paci c A ) (0.74) (3.49) (8.18) (8.55) (3.92) (0.14) ()1.39) Hong Kong Land ) Holdings (1.56) (2.26) (10.04) (11.29) (1.43) (0.82) ()0.54) Hong Kong ) )0.045 ) Electric Holdings ()0.23) (4.16) (6.71) (8.72) (3.91) ()1.38) ()2.12) CITIC Paci c ) (0.46) (5.68) (5.94) (8.05) (0.66) (1.05) ()2.16) Jardine Matheson ) Holdings (0.70) (0.49) (5.79) (5.42) (0.51) (1.14) ()1.57) New World Development (1.27) (5.31) (10.07) (9.60) (3.26) (0.53) (0.83) Cathay Paci c )0.016 ) Airways (2.75) (3.24) (6.72) (4.95) (0.21) ()0.37) ()0.45) Wheelock (0.56) (5.46) (11.76) (9.67) (1.92) (0.12) (0.86) Hopewell ) Holdings (1.16) (3.12) (6.13) (9.68) (3.11) (1.67) ()0.61) Hong Kong & )0.048 ) China Gas (2.51) (4.13) (5.53) (3.38) (3.81) ()1.16) ()0.09) Jardine Strategic )0.069 ) Holdings (1.70) (1.02) (3.80) (3.32) (3.07) ()1.34) ()1.99) Bank of East Asia ) ) ()0.21) (3.63) (6.14) (4.74) (0.73) (0.94) ()0.79) Hysan )0.040 ) Development (2.49) (5.01) (15.10) (8.31) (3.28) ()1.42) ()0.14)

17 Table 6 (Contined) Firms' names b 3 b 2 b 1 b 0 b 1 b 2 b 3 R 2 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 We run the following regression: R s;t ˆ a X3 R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355± kˆ 3 b k R f ;t k e t ; ) )0.092 ) (2.20) ()0.62) (3.02) (2.57) (0.66) ()1.72) ()0.06) ) (1.80) (8.50) (11.05) (11.87) (2.45) ()0.89) (0.21) (1.68) (3.28) (2.46) (0.38) (0.75) (0.29) (0.94) )0.024 ) (0.92) (4.37) (5.18) (4.42) ()0.50) ()0.63) (0.21) ) (2.40) (2.17) (4.04) (0.87) (0.53) (0.29) ()0.55) ) (3.22) (3.99) (11.36) (7.71) (1.34) (1.34) ()0.29) ) (2.29) (3.11) (3.31) (0.91) (1.92) (0.78) ()0.15) ) (1.17) (1.66) (4.58) (0.10) (1.56) (0.28) ()0.60) ) (1.65) (3.34) (4.18) (0.89) (0.44) (0.44) ()1.60) )0.069 ) (1.02) (3.77) (3.67) (1.19) ()1.80) ()0.97) (0.87) ) )0.018 )0.182 )0.001 (1.70) (2.85) ()0.36) (1.36) (1.00) ()0.25) ()1.43) where R s, t is the 5-minute trade return on stock s, and R f, t is the 5-minute futures quotation return calculated using the spot-month futures each day. Reported are the coe cient estimates with t- statistics in parentheses (* means signi cance at 0.1% level), and the adjusted R 2. The stocks are sorted by descending market capitalization. lag coe cients are larger than the rst 2 lead coe cients and the magnitude of the 3rd lag coe cient is similar to the 3rd lead coe cient. 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 e cient 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 e ciency. 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.

18 372 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 di erence 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 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 a ected 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 a ected 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.

19 R. Chiang, W.-M. Fong / Journal of Banking & Finance 25 (2001) 355± 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 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 futures. 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 monopolist 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 valueweighted index composed of 33 blue-chip stocks in Hong Kong. Our analysis sheds light on the relative informational e ciency across emerging derivative markets at di erent stages of development. We also examine the relative informativeness 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 e cient 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. 21 Sun Hung Kai is a major property developer in Hong Kong, while HSBC and Hang Seng Bank are major banks. Recently, Hong Kong Telecom has lost its monopolist status, since the government started to allow competition in the telecom industry.