Intraday price reversals for index futures in the US and Hong Kong

Transcription

1 Journal of Banking & Finance 24 (2000) 1179± Intraday price reversals for index futures in the US and Hong Kong Alexander Kwok-Wah Fung *, Debby M.Y. Mok, Kin Lam Department of Finance and Decision Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong, People's Republic of China Received 30 April 1998; accepted 9 June 1999 Abstract We observe intraday price reversals following large price changes at the opening of the S&P 500 Futures market and the HSI Futures market. We note that the magnitude of subsequent price reversals is positively related to the initial price changes, and that the price reversals are not caused by a bid±ask spread, or by panic among investors. We also note that such price reversals can be exploited to give rise to pro table opportunities after transaction costs, even though these may not be very signi cant. This study shows that investor overreaction may be a universal phenomenon and irrational investor behavior like overreaction may also exist among groups of sophisticated investors. Ó 2000 Elsevier Science B.V. All rights reserved. JEL classi cation: G14; G15 Keywords: Index futures; Overreaction; Market e ciency * Corresponding author. Tel.: ; fax: addresses: afung@hkbu.edu.hk (A.K.-W. Fung), mymok@hkbu.edu.hk (D.M.Y. Mok), kinlam@hkbu.edu.hk (K. Lam) /00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S (99)

2 1180 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179± Introduction There has been considerable interest on investorsõ possible overreaction in nancial markets since the publication of De Bondt and Thaler's (1985) research. According to their ``overreaction theory'', the tendency is for investors to overreact to new information, which results in exaggerated shift in price followed by price movements in the reverse direction. 1 De Bondt and Thaler (1985) also hypothesize that a ``magnitude e ect'' exists for the most extreme initial price movement, followed by the most extreme of subsequent price reversals. From a theoretical point of view, price reversals resulting from overreaction may challenge the assumption of investor rationality, which is fundamental to almost all nancial theories. On the practical side, trading strategies can be devised to pro t from market overreaction, assuming that the overreaction is of a magnitude which is economically signi cant. It is clear that extensive work is still needed in this area. Some say that the observed overreaction is awed. For example, Chan (1988) argues that after adjusting for risk, only small abnormal returns are found. However, Zarowin (1989) concludes in his study that risk adjustment alone is not able to explain the observed overreaction phenomena. Instead, he attributes the cause to rm size. Atkins and Dyl (1990) and Ball et al. (1995) point out that for short-term price reversals, the magnitude of the bid±ask spread for individual stocks results in severe bias in estimating the return in contrarian strategies. 2 According to Bremer et al. (1997), research on overreaction can be classi ed into three categories. Category 1 includes research on overreaction in the longer term in which reversals take as long as 3±5 years. Category 2 covers research on overreaction in the intermediate term in which the time scale considered is weeks or months. The nal category covers study of short-run price rebounds, which happen in the few days following large price movements. For a list of research publications as categorized above, one can refer to Bremer et al. (1997). We would like to add a fourth category to these three which studies price reversals that take place within the same day as that a big price swing occurs. The present study falls into this new category. 1 This is consistent with the ndings by studies in human overreaction in experimental psychology. Further evidence of long-horizon price reversal has also been observed in stock markets in other countries. See for example, Clare and Thomas (1995), da Costa (1994) and Fung (1996). 2 Conrad and Kaul (1993) follow through and observe that when the arithmetic average return is computed from the monthly return, the error due to the bid±ask spread accumulates. When the holding period return is used, they nd that overreaction disappears. They show that the overreaction e ect is indeed the price e ect since the e ect of the bid±ask spread is higher for lowpriced stocks.

3 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179± With the availability of intraday trading data, study of intraday price reversals becomes feasible. Stoll and Whaley (1990a) nd a negative correlation between overnight and following daytime returns in NYSE common stocks from 1982 to 1986, 3 implying the existence of price reversals in the morning trading session. Fabozzi et al. (1995) nd intraday price reversals for stocks on the NYSE and the AMEX during Gosnell (1995) also documents that the proportion of reversals is low near the opening of the market, but rapidly increases in the rst hour of trading. 4 The issue of intraday dynamics in the futures markets has also aroused some interest. Gay et al. (1994) nd that several commodity futures markets would overreact to bearish news in the Wall Street Journal at the opening of the market and then reverse during trading. Ederington and Lee (1993, 1995) nd weak evidence that the currency futures market tends to overreact to macroeconomic news. The empirical analysis on intraday price movements in the futures markets has a relatively short history and further exploration in this area is much needed. This study will investigate whether intraday price reversals occur in the index futures market. There are several reasons why the study of price reversals in the index futures market is meaningful: (1) While abnormal returns due to an overreaction in a longer time horizon can comfortably cover transaction costs, transaction costs become a crucial consideration for studies on overreaction within the same day. Since transaction costs are much higher in stock market than in a futures market, it is much easier to establish the economic signi cance of overreaction in a futures market, if there is any at all. As remarked by Park et al. (1997), ``the issue of overreaction in stock index futures is of particular interest because of its characteristics such as low capital requirements and low transaction costs''. 5 (2) Players in the futures markets are on an average better trained and better informed than stock market players as they may include more professional and institutional investors. Thus, it will be even more interesting if irrational behavior, even if only temporary, can be found among this group. (3) The study of the futures markets may add to our understanding of their microstructure, as explained in Section 2. Also, by studying more than one market (the US S&P 500 Futures market and Hong KongÕs HSIF market), we can tell whether overreaction is a general or marketspeci c phenomenon. 3 Amihud and Mendelson (1991) also uncover the negative correlation between overnight and following daytime returns in the Japanese stock market. 4 Gosnell (1995) examines the transaction price reversals of common stocks in the NYSE from October 1983 to August Park et al. (1997) investigate how the stock index futures prices react to the quarterly announcements of a macroeconomic variable, GNP, relative to the cash index prices. They used daily data and did not address intraday overreaction.

4 1182 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179± Overreaction at market opening and related issues We propose to study investor overreaction to information at market opening. If overreaction exists, there should be a price reversal when the futures market opens with a large change in price compared to the previous dayõs close. While Miller (1989) concludes that market specialists have a duty to maintain overnight price continuity, the futures markets under our study adopt an open out-cry trading system without market-maker participation. At opening, information gained overnight is not re ected in market prices. In the absence of market makers, there is a larger chance that the opening price may contain an error component. According to Amihud and Mendelson (1987), ``although not necessarily so, there may be a relationship between the size of the error in determining the price and the amount of accumulated information, leading to greater price dispersion in the opening''. This greater price dispersion on opening has been observed by studies in intraday volatility patterns in the futures market. 6 However, the direction of the error has yet to be made clear. The error may either be an underreaction or an overreaction to information as both can contribute to the higher volatility observed at market opening. The present study will address this point directly to ascertain whether the opening price in a futures market contains a systematic error, and if such error indeed exists, whether it represents a positive bias due to overreaction or a negative bias due to underreaction. The relationship between the size of the price error and the amount of accumulated information can then be tested. As overnight information is re ected in the price change between market close to market opening, such a test amounts to testing the second part of the ``overreaction hypothesis'' that the more extreme the initial price movement is, the greater the subsequent adjustment is. In order to rmly establish that the price reversal is actually a result of market overreaction, we need to ascertain that the reversal does not arise from the existence of a bid±ask spread. As pointed out by Kaul and Nimalendran (1990) and Atkins and Dyl (1990), the existence of a spread between bid and ask prices for common stocks may actually explain the short-run price reversals, because the reversals might simply be a shift from transactions at bid prices to transactions at ask prices. This problem will become more acute in the case of small stocks 7 and in the case of intraday price reversals. A methodology will be introduced in Section 3 for addressing the bid±ask-spread issue. 6 For some references of intraday volatility patterns in the futures markets, see for example, Ekman (1992), Daigler (1997) and Choi and Lam (1998). 7 In fact, Kaul and Nimalendran (1990) show that ``bid±ask errors in transaction prices are the predominant source of apparent price reversals in the short run for NASDAQ rms''. Using bid±ask quotes, they nd no evidence of market overreaction.

5 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179± Another issue that needs to be addressed is whether overreaction is caused by a few panicked investors who under the in uence of the nightõs news place rush orders at market opening. In Section 3 of this paper, we will attempt to clarify whether overreaction is restricted to a few panicked investors or whether it is a more widespread practice in the trading process. Finally, the issue of economical signi cance needs to be addressed. While the price reversals may be found to be statistically signi cant, their economical signi cance is of more interest. Only when economical signi cance is established will a contrarian intraday trading strategy be pro table. Thus, it is of practical interest to nd whether such reversals can be used to derive a trading pro t in a real trading environment. To consider this, we need to take into account transaction costs. In Section 3, a methodology is proposed to estimate trading pro ts in a real trading environment. 3. Data and methodology 3.1. Data The data in this study include daily opening and closing prices, and intraday tick-by-tick prices of the S&P 500 Futures from 1 September 1993 to 25 June 1996 and those of HSI Futures in Hong Kong from 18 March 1993 to 30 December Transaction prices are used here rather than bid±ask prices. The typical trading hours of the S&P 500 Futures are from 8:30 a.m. to 3:15 p.m. Chicago time. 8 The trading session for the Hang Seng Index Futures (HSIF) is from 10:00 a.m. to 12:30 p.m, and 2:30 p.m. to 4:00 p.m Cumulative abnormal return after market opening A standard methodology as used in event studies will be applied to study the price reversals at the opening. A marketõs opening return, denoted by OR, is de ned as the log di erence of the opening price and the previous dayõs closing price. Whenever the market opens with OR larger or smaller than a lter size f, the trading day is classi ed as an event day and the opening time is labeled as time zero in the event study. A range of lter sizes f will be used in both markets. The understanding is that a positive (negative) f refers to those event days whose opening return OR is larger (smaller) 8 From 6 October 1997 to 15 November 1997, the S&P 500 Futures opened 15 min before the NYSE in response to the competition of Dow Jones Industrial Index Futures. Subsequently, CME went back to the normal trading hours. During our data period, the S&P 500 Futures opened at the same time as the NYSE.

6 1184 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179±1201 than f. The use of a range of lter sizes will enable us to test the second hypothesis in the ``overreaction'' theory, i.e. the more extreme the initial price movement is, the greater the subsequent adjustment. Because volatility is higher in the HSIF market than in the S&P 500 Futures, the ranges of lter sizes chosen for our study are di erent in the two markets. For the HSIF, lter sizes of 0.10%, 0.20%, 0.30%, 0.40% and 0.50% will be studied. For the S&P 500 Futures, lter sizes of 0.10%, 0.15%, 0.20%, 0.25% and 0.30% will be studied. The reason why we do not study lter sizes with an absolute value larger than 0.5% for the HSIF market and 0.30% for the S&P 500 Futures is that the number of event days decrease for large lter sizes. Without a large number of event days, observed price movement patterns would have no reliability. The minute-by-minute return of the futures market will be calculated in all event days. The cumulative return of the index futures at time t (in min) during any event day i, denoted by CAR i;t, is de ned as the change in log prices over the time interval, from when market opens to time t, i.e. CAR i;t ˆ Log P i;t Log P i;0 ; 1 where P i;t and P i;0 are the traded futures prices on any event day i at time t and at market open, respectively. The traded price that happens just before time t and closest to time t is taken as the value of P i;t. The cumulative returns of the index futures at time t over all event days corresponding to a lter size f are averaged to obtain ACAR f t. The standard formula is given as follows: ACAR f t ˆ 1 X N CAR i;t ; N iˆ1 2 where N is the total number of event days corresponding to the lter size f. The sign of ACAR f t will be an indication of a market overreaction or underreaction. At a xed time point t, traditional t-test can be used to test whether ACAR f t is signi cantly greater than zero for event days with a large price drop, i.e. OR < f < 0, or is signi cantly lower than zero for event days with a large price rise, i.e. OR > f > 0. The test can decide whether there is a signi cant price reversal at t min after the market opens. The empirical ndings are reported in Sections 4.2 and 4.3. To verify the second part of the overreaction hypothesis, we can pre x a time point t and plot ACAR f t value against the lter size f. If it is indeed true that the more extreme the price movement is, the greater the subsequent movement, ACAR f t with xed t should decrease with f. In other words, a graph of ACAR f t against f should be downward sloping. Other than relying on a graphical display to con rm the second part of the hypothesis, more rigorous statistical tests can be carried out. In devising such a test, it is essential to note that there is an overlap in event days

7 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179± corresponding to two di erent lter sizes f 1 and f 2, i.e. ACAR f 1 t and ACAR f 2 t are dependent summary statistics. Hence, a statistical test on their di erence is not straightforward. In this study, we adopt the following method to test for the second part of the overreaction hypothesis. Days in which the opening returns whose absolute value are less than 0.1%, say, are deleted. Days deleted are non-event days. The remaining days are eventful and have absolute opening returns OR greater than 0.1%. According to the second part of the overreaction hypothesis, the larger OR is, the larger the subsequent adjustment. Thus, if the CAR t value in an event day is regressed on the dayõs OR value, a negative slope should occur. A regression analysis can then be carried out with various xed time point t to con rm whether the second part of the hypothesis really holds. The empirical results are reported in Section Other ways of calculating cumulative abnormal return 9 To consider whether the observed overreaction is due to the spread between the bid and ask prices, we calculate the overnight returns using the average price over the last ve trades of the day and the rst ve trades from the next morning. Also, intraday returns will be measured by the average of ve transaction prices at various points of time. By averaging the transaction prices, the di erences in the bid±ask prices tend to average out and we can tell whether the reversal is the result of a shift from bid-price transactions to ask-price transactions. Cumulative abnormal returns based on these average prices will be computed. The results of this analysis are presented in Section 4.5. To consider whether overreaction is a widespread phenomenon or is attributable to a few irrational traders, we can cumulate the abnormal return starting from the price at the rst (or second) minute of trading, and not from the single opening price. If overreaction indeed arises due to a few traders who overreact to the nightõs news, then the adjustment process will be rapid. In other words, average abnormal return cumulated from the rst (or second) minute of trading should not be signi cantly di erent from zero, although the abnormal return cumulated from the opening is signi cantly di erent from zero. The empirical results of this analysis are reported in Section 4.6. A practitioner may exploit the overreaction phenomenon by pro ting from a contrarian strategy. To estimate the actual pro t of such a contrarian strategy, we cannot rely on the abnormal return cumulated from the opening transaction. This is because the contrarian can only place a sell (buy) order 9 The analysis in this section was recommended by the referee.

8 1186 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179±1201 after the market is observed to open with a gap up (down). Since it takes time for an order to be executed, we cannot assume that the contrarian can trade at the opening price. It is therefore reasonable to allow a time lag of 1 (or 2) minute(s). Thus, the contrariansõ expected return is the average abnormal return cumulated starting from the rst (second) minute. In estimating actual pro t, we also need to deduct round-trip transaction costs. The results are reported in Section Empirical results 4.1. Event days The number of event days for each lter size is tabulated in Table 1 for the S&P 500 Futures and the HSIF. The average opening returns corresponding to each lter size are also tabulated. The total number of trading days in our study is 700 days for the S&P 500 Futures and is 919 days for the HSIF Rebound after overreaction The average cumulative returns ACAR f t of the S&P 500 Futures and the HSIF as t runs from 3 minutes to 2 hours, are graphed in Figs. 1 and 2. The amounts of rebound for a positive lter size f and a negative lter size )f are plotted in one single graph. Take Fig. 1 for the US market as an example. The lter sizes (f) involved are 0.1% and )0.1%. For f ˆ )0.1%, the opening return has an average value of )0.285%. Then the market rebounds to 0.016% in 3 minutes, 0.024% in 20 minutes, 0.020% in 1 hour and 0.039% in 2 hours. For f ˆ 0.1%, the opening return has an average value of %. The market continues to have a positive return of 0.003% in 3 minutes, reverses to )0.011% in 20 minutes, )0.033% in 1 hour and )0.018% in 2 hours. Although not shown here, the results for the S&P 500 Futures for lter sizes f ˆ 0.3% are similar but the reversals are of a greater magnitude in comparison to the case where f ˆ 0.1%. Fig. 2 shows the HSIF with lter sizes of 0.1%, and )0.1%. The results are similar to those for the US market. For f ˆ )0.1%, the opening return has an average value of )0.745%. Then the market return continues to be negative at )0.008% in 3 minutes, rebounds to 0.073% in 20 minutes, 0.143% in 1 hour and 0.079% in 2 hours. For f ˆ 0.1%, the opening return has an average value of %. The market continues to have a positive return of 0.016% in 3 minutes, reverses to )0.031% in 20 minutes, )0.049% in 1 hour and )0.002% in 2 hours. Again, with lter sizes of 0.5%, the results are similar but the reversals are of a greater magnitude in comparison to the case where f ˆ 0.1%. An inspection of Figs. 1 and 2 shows clearly that price reverals follow large price movements at market opening.

9 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179± Table 1 Event days in the S&P 500 Futures and the HSIF Panel A: S&P 500 Futures Filter size (%) )0.30 )0.25 )0.20 )0.25 ) Average OR (%) ) ) ) ) ) Event days Panel B: HSIF Filter size (%) )0.50 )0.40 )0.30 )0.20 ) Average OR (%) )1.179 )1.049 ) ) ) Event days

10 1188 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179±1201 Fig. 1. Average cumulative returns of S&P 500 Futures contracts with lter sizes of 0.1%. Fig. 2. Average cumulative returns of HSIF contracts with lter sizes of 0.1% Statistical signi cance of rebound Table 2 gives the results of statistical tests for the S&P 500 Futures. The ACAR f t values for xed f and t as well as the corresponding signi cance levels are tabulated. Table 3 gives the corresponding results for the HSIF. The large number of statistical signi cant ACAR f t values shows that intraday futures

11 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179± Table 2 Statistical signi cance of ACAR values (%) in the S&P 500 Futures a Filter size (%) )0.30 )0.25 )0.20 )0.15 ) minutes after opening ) (0.976) (0.862) (0.942) (0.482) (0.162) (0.204) (0.120) (0.132) (0.892) (0.186) 10 minutes after opening ) ) ) (0.774) (0.428) (0.402) (0.262) (0.956) (0.532) (0.368) (0.204) (0.802) (0.490) 20 minutes after opening ) ) ) ) ) (0.200) (0.676) (0.790) (0.514) (0.192) (0.558) (0.872) (0.624) (0.586) (0.590) 30 minutes after opening ) ) ) ) ) (0.416) (0.868) (0.768) (0.468) (0.248) (0.180) (0.336) (0.566) (0.136) (0.096) 1 hour after opening ) ) ) ) ) (0.506) (0.430) (0.620) (0.984) (0.558) (0.084) (0.122) (0.180) (0.102) (0.052) 2 hours after opening ) ) ) ) ) (0.092) (0.054) (0.184) (0.152) (0.166) (0.888) (0.674) (0.534) (0.406) (0.172) a The p-values are reported in parentheses. Consider a ˆ Prob > T signi cance probability for two-tailed test, then 0.05 < a 6 0.1().

12 1190 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179±1201 Table 3 Statistical signi cance of ACAR values (%) in the HSIF a Filter size (%) )0.50 )0.40 )0.30 )0.20 ) minutes after opening ) ) ) (0.100) (0.076) (0.056) (0.268) (0.264) (0.850) (0.272) (0.290) (0.714) (0.718) 10 minutes after opening ) (0.218) (0.216) (0.166) (0.648) (0.536) (0.882) (0.162) (0.836) (0.080) (0.008) 20 minutes after opening ) ) ) ) ) (0.10) (0.010) (0.008) (0.036) (0.058) (0.590) (0.094) (0.334) (0.060) (0.046) 30 minutes after opening ) ) ) ) ) (0.000) (0.000) (0.000) (0.000) (0.000) (0.536) (0.042) (0.316) (0.052) (0.098) 1 hour after opening ) ) ) ) ) (0.008) (0.004) (0.000) (0.000) (0.002) (0.328) (0.010) (0.066) (0.006) (0.014) 2 hours after opening ) ) ) ) ) (0.118) (0.110) (0.196) (0.196) (0.312) (0.058) (0.500) (0.982) (0.190) (0.280) a The p-values are reported in parentheses. Consider a ˆ Prob > T signi cance probability for two-tailed test, then a , ; 0.01 < a () ; 0.05 < a ().

13 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179± price reversal is common across these two markets. Hence, it is more likely to be a universal investorsõ behavior rather than just attributable to sample snooping. In order to see whether the result is due to some outliers, the proportion of ACAR that are consistent with overreaction hypothesis are tabulated in Table 4 for the US and Hong Kong markets with some lter sizes. The results are similar to those in Tables 2 and 3. Outliers do not seem to be a problem. A comparison of Tables 2 and 3 shows that the phenomenon of price reversals is stronger in Hong Kong than in the US. As observed by Lam et al. (1998), the US market is more e cient than the Hong Kong market. This may be due to the greater maturity of the US market, and also to the di erence in market microstructure. Although both markets have a similar opening mechanism, the oor o cials in the US market have more power than their Hong Kong counterparts in in uencing the bid and ask prices at opening. A more important reason for the di erence may be the existence of trading on GLO- BEX after normal trading hours in the US. The trading on GLOBEX stops 15 min before the S&P 500 Futures opens again. On the other hand, while Hong Kong stocks can be traded in London after the Hong Kong market closes, the trading in London stops many hours before the Hong Kong market reopens in the morning. The uncertainty involved in determining the opening price in the futures market is hence higher in the Hong Kong market. As a result, it is not surprising to nd that investor overreaction is more prominent in the Hong Kong market Second part of the overreaction hypothesis Amihud and Mendelson (1987) suspect that price error size at market opening may be proportional to the amount of information accumulated overnight. Assuming that the error will be corrected after trading starts, the larger the error size, the larger the subsequent price reversal. In Figs. 3 and 4, the values of ACAR f t are plotted against f for the US and the Hong Kong markets, respectively. The time t in ACAR f t is xed at 1 hour when the overreaction has settled down. A downward slope is observed in both the markets. This demonstrated that the larger the opening return, the more extreme the subsequent adjustment. The following regression is performed to formally test the second part of the overreaction hypothesis: CAR f t ˆ a t b t OR e t : 3 The regression is performed on days for which OR has an absolute value larger than a pre-speci ed critical lter size. The critical lter sizes are set at 0.1% and 0.15% for the US market, and at 0.1% and 0.2% for the Hong Kong market.

14 1192 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179±1201 Table 4 Proportions of ACAR values (%) in the S&P 500 Futures and the HSIF consistent with overreaction hypothesis a Filter size (%) S&P 500 Futures HSIF )0.30 ) )0.50 ) minutes from opening 40.98% 48.10% 45.31% 56.25% 52.66% 50.14% 45.37% 49.37% (0.913) (0.706) (0.925) (0.146) (0.237) (0.479) (0.972) (0.576) 10 minutes from opening 36.07% 46.67% 48.57% 52.50% 50.00% 48.74% 45.83% 46.44% (0.982) (0.829) (0.669) (0.337) (0.500) (0.682) (0.958) (0.862) 20 minutes from opening 47.54% 53.81% 53.88% 60.00% 54.26% 50.42% 54.40% 57.32% (0.645) (0.139) (0.117) (0.046) (0.126) (0.437) (0.034) (0.013) 30 minutes from opening 45.90% 49.52% 57.14% 60.00% 56.38% 50.14% 54.86% 57.74% (0.732) (0.554) (0.014) (0.046) (0.043) (0.479) (0.022) (0.009) 1 hour from opening 54.10% 50.48% 56.33% 63.75% 50.53% 50.42% 57.18% 59.83% (0.268) (0.446) (0.026) (0.010) (0.443) (0.437) (0.001) (0.001) 2 hours from opening 62.30% 53.33% 52.65% 58.75% 51.60% 47.34% 56.25% 58.58% (0.032) (0.171) (0.208) (0.070) (0.333) (0.841) (0.005) (0.004) a The p-values are reported in parentheses. The proportion is 0.5 in the null hypothesis. Consider a ˆ Prob > T signi cance probability for two-tailed test, then a < 0.01 () ; 0.01 < a < 0.05 () ; 0.05 < a < 0.1 ().

15 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179± Fig. 3. Average cumulative returns of S&P 500 Futures across di erent lter sizes. Fig. 4. Average cumulative returns of HSIF across di erent lter sizes. Table 5 shows the a t and b t values together with their p-values for various choices of t. The highly signi cant b values in Table 5 indicate that there is truth in the second part of the overreaction hypothesis, i.e. the more extreme the action, the larger the overreaction. Again, we can observe that the level of signi cance is more prominent in the Hong Kong market Bid±ask spread Even though the relative bid±ask spread for futures markets is generally smaller than that for stock markets, it does exist. In order to further reduce the

16 1194 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179±1201 Table 5 Regression tests results a S&P 500 Futures HIS Futures Removed )0.1% < OR < 0.1% Removed )0.15% < OR < 0.15% Removed )0.1% < OR < 0.1% Removed )0.2% < OR < 0.2% at bt at bt at1 bt at bt 5 minutes after opening ) ) ) (0.011) (0.050) (0.022) (0.086) (0.111) (0.010) (0.265) (0.011) 10 minutes after opening ) ) ) ) (0.194) (0.370) (0.275) (0.479) (0.161) (0.049) (0.391) (0.054) 20 minutes after opening ) ) ) ) (0.522) (0.211) (0.561) (0.360) (0.336) (0.000) (0.598) (0.000) 30 minutes after opening ) ) ) ) (0.975) (0.008) (0.977) (0.022) (0.035) (0.000) (0.121) (0.000) 1 hour after opening ) ) ) ) ) ) (0.547) (0.003) (0.415) (0.007) (0.107) (0.000) (0.435) (0.000) 2 hours after opening ) ) ) ) (0.576) (0.006) (0.681) (0.009) (0.162) (0.375) (0.441) (0.335) a The regression model is CAR f t ˆ at b t OR et where CAR f t is the cumulative return of the index futures at time t over all event days corresponding to a lter size f and OR is the opening return. The p-values are reported in parentheses. Consider a ˆ Prob > T signi cance probability for two-tailed test, then a () ; 0.01 < a () ; 0.05 < a ().

17 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179± e ect of the bid±ask spread, we calculate the overnight returns using the average price over the last ve trades of the day and the rst ve trades the next morning. As to the intraday returns, we use an average of ve trades at various points, two before and two after the trade closest to the time point. The results with selective lter sizes for the S&P 500 Futures and the HSIF are summarized in Table 6. Basically, the results are the same as Tables 2 and 3, only with slightly dampened magnitude, as expected. Take the HSIF for example. Where 11 out of 24 ACAR values reported in Table 6 are signi cant at the 10% level, the corresponding 24 ACAR values reported in Table 3 contain 12 signi cant values. Although we do not report the results for all lter sizes, this conclusion is generally consistent over a number of lter sizes. This shows that the bid±ask spread cannot explain away the reversal pattern Panic trading when market opens If indeed overreaction was due to a handful of investors, other rational investors would take advantage of the situation and hence, the reversal would have occurred very quickly. To see whether the overreaction persists beyond 1 minute, we present in Table 7 the ACAR values when cumulating is done starting from the rst minute. Here, the averages of ve transaction prices are also used so that the bid±ask e ect can also be addressed. It can be seen that the reversal pattern in Table 7 still resembles the reversal patterns in Tables 2 and 4. The results when cumulating is done starting from the second minute or for other lter sizes are similar, and strongly suggest that the reversal is not caused by just a few investors Economical signi cance of rebound Practitioners need to know whether the overreaction phenomena observed in this paper present any pro table opportunity. To consider this we look at the returns of the contrarian strategy. After observing the opening price, the trader needs some time to place the order and have the order executed. We assume that a contrarian trades at execution time lag of 1 or 2 minutes. Thus, the investorõs expected return is the ACAR value when the abnormal return is cumulated, starting from the rst minute. Hence the entries in Table 7 can be regarded as the expected trading pro t before transaction costs. Note that for a contrarian, a positive ACAR for the negative lter sizes represents a trading pro t. A positive ACAR for the positive lter sizes represents a trading loss. To accurately estimate potential pro t for a contrarian, the transaction costs must be deducted from the trading pro ts. Round-trip transaction costs used

18 1196 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179±1201 Table 6 ACAR values (%) in S&P 500 Futures and HSIF using average 5 trades a Filter size (%) S&P 500 Futures HSIF )0.30 ) )0.50 ) minutes from opening ) ) (0.940) (0.197) (0.295) (0.427) (0.100) (0.253) (0.497) (0.816) 10 minutes from opening ) ) (0.946) (0.824) (0.439) (0.806) (0.176) (0.407) (0.769) (0.062) 20 minutes from opening ) ) ) ) (0.135) (0.218) (0.500) (0.612) (0.022) (0.050) (0.508) (0.060) 30 minutes from opening ) ) ) ) (0.361) (0.304) (0.132) (0.075) (0.000) (0.000) (0.462) (0.090) 1 hour from opening ) ) ) ) (0.581) (0.674) (0.078) (0.049) (0.012) (0.001) (0.257) (0.012) 2 hours from opening ) ) ) (0.101) (0.180) (0.784) (0.166) (0.096) (0.213) (0.450) (0.398) a The p-values are reported in the parantheses. Consider a ˆ Prob > T signi cance probability for two-tailed test, then a () ; 0.01 < a () ; 0.05 < a ().

19 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179± Table 7 ACAR values (%) in the S&P 500 Futures and the HSIF using an average of ve trades and starting 1 min after market opening a Filter size (%) S&P 500 Futures HSIF )0.30 ) )0.50 ) minutes from opening ) ) ) ) minutes from opening ) ) ) ) minutes from opening ) ) ) ) minutes from opening ) ) ) ) hour from opening ) ) ) ) hours from opening ) ) ) ) a Consider a ˆ Prob > T signi cance probability for two-tailed test, then a () ; 0.01 < a () ; 0.05 < a ().

20 1198 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179±1201 Table 8 Trading pro ts of the contrarian trading strategies (in %) after transaction cost for the S&P 500 Futures and the HSIF (using an average of 5 trades) a Filter size (%) S&P 500 Futures HSIF )0.30 ) )0.50 ) minutes opening ) ) ) ) ) ) ) ) minutes opening ) ) ) ) ) ) ) ) minutes opening ) ) ) ) ) ) ) minutes opening ) ) ) ) ) ) hour opening ) ) ) hours opening ) ) ) ) ) a If the overnight return is negative, the trading pro t is the pro t of longing the futures at the one-minute price and unwinding the position at the time shown in the rst column. If the overnight return is positive, the trading pro t is the pro t of shorting the futures at the one-minute price and unwinding the position at the time shown in the rst column. Consider a ˆ Prob > T signi cance probability for two-tailed test, then a () ; 0.01 < a () ; 0.05 < a ().

21 A.K.-W. Fung et al. / Journal of Banking & Finance 24 (2000) 1179± are as suggested by a market practitioner, % for the US futures market and 0.125% for the Hong Kong futures market. These costs include commission and market-impact costs (bid±ask spread, etc.). If the opening price is lower (higher) than the previous dayõs closing price the contrarian will buy (sell) at the one-minute transaction price and then close out the position on the same day. The returns of this strategy are summarized in Table 8. To avoid confusion, the signs of the returns are adjusted so that a positive (negative) sign re ects pro t (loss). The results show that positive returns can be associated with this contrarian strategy after transaction costs and execution time lag are considered. For S&P Futures, pro t only shows up 1 hour after the market opens and with a lter size of 0.3%. The reversals for lower lter sizes ( 0.10%) are not strong enough to cover transaction costs, as expected. It takes at least 1 hour for the reversal in the S&P 500 Futures to cover transaction costs. The frequency of pro tability is higher for the HSIF. Pro ts show even when lter size is )0.10%, and as early as 30 minutes after the market opens with a lter size of )0.50%. However, only one case of shown pro t is statistically signi cant in the HSIF. Overall, the S&P 500 Futures and the HSIF are marginally e cient. The maximum gain is 0.093% per day, which is about 26% per year (with 250 trading days). The gain can be greater, however, for those traders who have made up their minds to sell (buy) futures on a day when prices open lower (higher). They could be advised not to rush a trade, during market opening. To wait and sell (buy) at a later time, they may save on an average 0.093% as well as the transaction costs which have been deducted from the calculation. For the Hong Kong market, this means a saving of 0.218% per trade. 5. Conclusion In this paper, we show that intraday futures price reversals following large changes in futures price occur at opening in both the S&P 500 Futures and the HSIF. Using a rigorous statistical test, the magnitude of subsequent price reversals is shown to be positively related to the initial price changes. Price reversals in the HSIF are found to be more prominent than in the S&P 500 Futures, both in terms of magnitude and statistical signi cance. The price reversals are not caused by bid±ask spread, nor by investor panic at market opening. Moreover, after transaction costs, pro table opportunities exist, even though not very signi cant, with a maximum annual return of 26% for the HSIF. This study shows that investor overreaction is a common phenomenon 10 Mr. Christoper Eoyand of Goldman Sachs in an ISI Cutting Edge Conference held in Hong Kong on 22 April 1997 and adjusted for day trade.

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