Intraday return patterns and the extension of trading hours

Intraday return patterns and the extension of trading hours KOTARO MIWA # Tokio Marine Asset Management Co., Ltd KAZUHIRO UEDA The University of Tokyo Abstract Although studies argue that periodic market closure induces the well-known intraday price overreaction, namely, a negative association between intraday futures returns and the latest overnight returns, no study argues and examines whether the overreaction phenomenon is weaken or worsen by extending trading hours. In this current study, we empirically examine it by investigating two Japanese stock futures markets whose trading hours have been significantly and asynchronously extended by introducing extended sessions. We find that, the stronger overreaction is observed when an extended-hours trading session is longer and trading volume during the session is higher, indicating that such extended sessions induce the stronger overreaction. The results suggest that the intraday return patterns induced by periodic market closure are not easily and straightforwardly mitigated by an extension of trading hours. Keywords: intraday price overreaction; stock futures; opening price; extension of trading hours. JEL classifications: G14; G17; G2. 1. Introduction Most financial markets are closed overnight. Studies such as Glosten and Milgrom (1985), Kyle # Corresponding author, 1-3-1, Marunouchi, Chiyoda-ku, Tokyo, Japan, e-mail: miwa tfk@cs.c.u tokyo.ac.jp 3-8-1, Komaba, Meguro-ku, Tokyo, Japan,, e-mail: ueda@gregorio.c.u tokyo.ac.jp **The opinions expressed in this paper solely represent the views of the authors and do not reflect the opinions of the organizations to which the authors belong. 1

(1985), Foster and Viswanathan (1990), and Easlay and O Hara (1992) argue that public and private information accumulates overnight. Thus, market closures result in high information uncertainty at the open of trading sessions, which disturb efficient incorporation of information into prices and result in significant price concessions required by liquidity providers. This information uncertainty at the open of trading sessions could cause intraday return patterns. In accordance with this argument, several studies show that periodical market closures induce the well-known intraday return pattern, namely, the intraday overreaction phenomenon characterized by intraday price reversals following price changes at the market open. Atkins and Dyl (1990) find evidence of strong price reversals among common stocks after large price changes when a market opens. Fung et al. (2000) and Grant et al. (2005) find highly significant intraday price reversals in the US and HK stock index futures markets. Corte et al. (2015) show that such a reversal pattern can be observed in international stocks, equity indexes, interest rates, commodities, and currency futures. In terms of driver of these overreaction phenomenon, Ekman (1992) Daigler (1997) argue that the overreaction phenomenon is related to information uncertainty at the open, which is induced by periodic market closure. In addition, Corte et al. (2015) argue that the overreaction phenomenon is attributed to price concessions, increased by information uncertainty at the open. On the other hand, the extension of trading hours has increasingly been discussed in several markets (Osaki, 2014). Moreover, in the NYSE and NASDAQ, pre-market and after-hours trading sessions have already been introduced, while in the Tokyo Stock Exchange, the trading hours of stock futures (e.g., Nikkei 225 futures and TOPIX futures) have been significantly extended. Since periodic market closures induce the overreaction phenomenon, it would seem that the overreaction phenomenon is weaken by shorting market closure, namely, the extension of trading hours; for example, by introducing or expanding extended-hours sessions. However, the effect of extensions may not be so straightforward. Miwa and Ueda (2016) focus on the low liquidity features of asset prices during extended-hours sessions (Barclay and Hendershott, 2003). Their simulation-based analysis shows that an extension of trading-hours could disturb efficient price formation at the open because of low liquidity during the prior extended-hours session. In addition, 2

assets can be traded with high information uncertainty during an extended-hours session. For example, information uncertainty in stock futures can be higher during an extended-hours session (a night session) than during a regular session because the corresponding spot market is closed (thus, the corresponding spot index value is unavailable) during the extended-hours session. Higher information uncertainty induces erroneous pricing during the session which increases information uncertainty and required price concession at the opening of the subsequent regular session. Thus, it is possible that an extension of trading hours strengthens the intraday overreaction phenomenon. However, to the best of our knowledge, no study provides empirical evidence about whether the price overreaction phenomenon could be strengthened by an extension of trading hours. In this study, we empirically analyze whether the well-known price overreaction phenomenon can be made worse by extending trading hours. The analysis can achieves further understanding of not only the overreaction phenomenon but also the effect of the extension of trading hours. The difficulty of empirical analyses on the effect of the extension of trading hours is that there are few suitable samples with which to compare price behavior between a market with an extended-hours session and one without such an extension. Some studies examine the effect of extending trading hours on price volatility and trading volume. For example, Houston and Ryngaert (1992) find that reductions in NYSE trading hours had little effect on return volatility and trading volume during the week in which the reductions occurred. Further, Fan and Lai (2006) report that a significant change in the intraday pattern of return volatility and trading volume could not be observed after extending the trading session of the Taiwan Stock Exchange by 1.5 hours. Although these studies may indicate that asset pricing and trading are unaffected by a change in trading hours, the results may be due to an insufficient change in trading hours; thus, these studies cannot provide robust evidence regarding the effect of extending trading hours. However, recently, the trading hours of two representative futures of the Japanese stock market, namely Nikkei 225 futures and TOPIX futures, have been significantly extended. Indeed, trading had been extended by 11 hours for about 6 years through implementation of an extended-hours session called a night session. This significant extension enables us to perform time-series (before and after) 3

comparisons of the price overreaction phenomenon. Further, both extensions have not been introduced synchronously. There is a period during which the extended-hours session of Nikkei 225 futures were significantly longer than those of TOPIX futures. This circumstance enables us to perform a cross-sectional comparison; namely, a comparison of stock futures with different durations of an extended-hours session, in order to analyze whether the price overreaction phenomenon could be made worse by extending trading hours. In addition, the extension of the two Japanese stock futures can be considered the best sample for the following two additional reasons. First, stock futures are likely to be traded under a condition of higher information uncertainty during the night sessions because their corresponding spot markets (the Tokyo Stock Exchange and Osaka Stock Exchange) are closed during each session. These futures transactions that are made under a condition of high information uncertainty may increase the risk of increasing the price overreaction phenomenon. Second, high demand for the immediacy of the futures market causes the market to be designed to supply maximal immediacy of order execution at its opening (Grossman and Miller, 1988); consequently, illiquidity-based transaction costs are trivial at the opening of the futures market. Thus, in this study, we perform both time-series and cross-sectional comparisons on these Japanese stock futures to provide empirical evidence regarding the effect of extending trading hours on the well-known intraday return patterns. The findings can be summarized as follows. First, the time-series analysis shows that a longer night session results in a stronger negative association between overnight returns and subsequent intraday returns, indicating that implementing and extending a night session strengthens the price overreaction phenomenon. Second, the cross-sectional analysis shows that the price overreaction phenomenon for Nikkei 225 futures is weaker compared with TOPIX futures when there is no difference in trading hours between the futures. However, when trading hours (a night session) are significantly longer for Nikkei 225 futures than for TOPIX futures, the overreaction for Nikkei 225 futures is as strong as that for TOPIX futures. This result also indicates that a longer night session results in a stronger price overreaction phenomenon. Third, trading volume during a night session has additional predictive power for the price 4

overreaction phenomenon. Higher trading activity during the session induces a more negative association between overnight returns and subsequent intraday returns. This result indicates that frequent night-session transactions increase the price overreaction phenomenon. Last, consistent with the foregoing indication, the result reveals that night-session returns are negatively associated with subsequent intraday returns, indicating that price movement during a night session fails to reduce the price overreaction phenomenon. These results support the view that implementing and extending an extended-hours session (a night session) could increase information uncertainty and price concessions at the open which induce the intraday price overreaction phenomenon. We provide strong empirical evidence that an extension of trading hours carries a risk of increasing the intraday price overreaction phenomenon. Our result suggest that the intraday return patterns induced by periodic market closure are not easily and monotonically weakened by an extension of trading hours. The remainder of this paper is organized as follows. Section 2 presents the sample, methodologies, and results. Section 3 describes the robustness check and the additional analysis of the effect of extending trading hours. Finally, in section 4, we summarize the findings. 2. Empirical evidence 2.1. Sample construction I utilize TOPIX futures contracts and Nikkei 225 futures contracts traded on the Osaka Stock Exchange to test the intraday price overreaction. The sample spans January 2002 December 2015. We use transaction prices rather than bid ask prices because bid and ask prices are sometimes not updated as quickly as the trading prices move. Consequently, the day s closing price reflects the last transaction price rather than the settlement price. The expiration dates for TOPIX and Nikkei 225 futures are scheduled on a quarterly basis: the second Friday of March, June, September, and December. The futures are cash-settled contracts, with multiple contracts traded simultaneously on any given day. We utilize the values of the closest contract, 5

which is usually the most heavily traded. I exclude the following days from the analysis: the expiration days, since the opening prices of futures are quite volatile because of special quotation (SQ) events (calculating SQs for expired contracts); and the first trading day of each calendar year, since there is no extended-hours session for the prior (year-end day s) trading session. Regular trading hours for these futures are from 9:00 to 15:10 (15:15 after Jul. 20, 2010). Extended-hours sessions, called night sessions, 1 for Nikkei 225 futures and TOPIX futures were introduced on Sep. 17, 2007 and Jul. 16, 2008 respectively. Then, the extended-hours sessions were extended as shown in Table 1, panel (a). [Table 1] 2.2. Research methodology The intraday price overreaction, namely, intraday price reversals following price changes at the market open, can be identified by a negative association between overnight returns and subsequent intraday returns (Grant, 2005; Corte et al., 2015). At the start of each trading day t, the opening price (futures value at 9:00: P 9:00 ) and the closing price of the prior trading day s regular session (futures value at 15:10 on day t-1: P 15:10 1 ) are immediately available. An overnight return (denoted as R Overnight ) is defined as the natural logarithm of the division of the opening price (P 9:00 ) by the prior day s closing value (P 15:10 1 ) 2. Thus: R Overnight = log (P 9:00 /P 15:10 1 ) In terms of intraday returns, overnight returns are supposed to be reversed, especially when the corresponding spot market opens. The trading hours of the Tokyo Stock Exchange consist of a morning session and afternoon session. The morning session is from 9:00 to 11:00 (11:30 after Nov. 21, 2011) and the afternoon session is from 12:30 to 3:00. We specifically focus on return reversal during the 1 At first, the extended hours were called the evening session. 2 After Jul. 20, 2010, the regular market closed at 15:15. However, we utilize the price at 15:10 to maintain the consistency of the definition of overnight returns. Even if we utilize prices at 15:15 for calculating the overnight returns after Jul. 20, 2010, the implication of the result is unchanged. 6

morning session, namely, intraday future returns from 9:00 to 11:00 3. An intraday return, R Intraday, is defined as: R Intraday = log ( P 11:00 9:00 P ) 11:00 where P is the latest transaction price at 11:00; i=1 means Nikkei 225 futures; and i=2 means TOPIX futures. I evaluate the degree of the intraday overreaction phenomenon, namely intraday price reversals following price changes at the market open, by examining the association between the overnight return (R Overnight ) and the subsequent intraday return (R Intraday ). In order to examine whether the implementation of a night session mitigates or worsens the intraday overreaction phenomenon, we perform a time-series comparison for each futures and cross-sectional comparison between Nikkei 225 futures and TOPIX futures. 2.2.1. Time-series comparison Because the night sessions for Nikkei 225 and TOPIX futures were introduced and extended significantly, we can analyze the effect of the implementation of the night sessions through time-series comparison. We examine whether the association between overnight returns and subsequent intraday returns is affected by the implementation and extension of night sessions. If trading during a night session weakens (worsens) the intraday overreaction phenomenon, a longer night session should induce a weaker (stronger) negative association. Thus, we run the following regression: R Intraday = a i + b 1 i R Overnight + b 2 i T Night 1 R Overnight +b 3 i T Night 1 + e (1) where T Night denotes the length (hours) of a night session on day t, which is shown in Table 1, panel (b). 4 If the transactions during a night session mitigate (worsen) the intraday overreaction phenomenon, Night a longer T 1 should induce a weaker (stronger) negative relation between R Intraday and R Overnight 1. Thus, the coefficient of T Night 1 R Overnight (b i 2 ) should be positive (negative). 3 we also analyze the return reversal during the afternoon session, which is defined by the association between overnight returns and intraday returns during the subsequent afternoon session. The result is shown in Section 3.3. 4 Although the market is closed from the end of the regular-hour session until 16:30, we define T Night as the time from the end of the regular-hour session to the end of the night session because the news between the end of the regular-hour session and 16:30 is expected to be incorporated into prices during the subsequent night session. 7

In order to achieve greater understanding, we split the investigated period into three periods, on the basis of the length of the studied night sessions, and analyze the intraday overreaction phenomenon, namely the association between R Intraday and R Overnight, for each period. As shown in Table 1, panel (b), when T Night 1 =0, time t is included in period 1, which is called the no night-session period ; when 7 T Night 1 > 0, time t is included in period 2, which is called the short night-session period ; and when T Night 1 >7, time t is included in period 3, which is called the long night-session period. 2.2.2. Cross-sectional comparison The trading hours for Nikkei 225 futures and TOPIX futures are extended asynchronously. As shown in Table 1, panel (b), the trading hours of a prior trading day (T Night 1 ) are significantly longer for Nikkei 225 futures than for TOPIX futures from 7/20/2011 to 3/24/2014 (this period is denoted the Night different trading-hours period ). However, there is no difference in T 1 between them until 9/18/2007, from 6/17/2008 to 10/14/2008, and after 3/25/2014 (these periods are denoted overall as the same trading-hours period ). We perform panel data analysis by conducting the following panel regression analysis for the different trading-hours period and the same trading-hours period. R Intraday = a + b 1 R Overnight + b 2 NK i R Overnight + b 3 NK i + e (2) NK i is a dummy variable that takes one for Nikkei 225 futures and zero for TOPIX futures. The coefficient b 2 (the coefficient of NK i R Overnight ) represents the difference in the intraday overreaction phenomenon between TOPIX futures and Nikkei 225 futures. Since the more negative association between R Intraday and R Overnight means the stronger intraday overreaction phenomenon, positive (negative) b 2 means that the overreaction is weaker (stronger) for Nikkei 225 futures than for TOPIX futures. If night session trading mitigates the intraday overreaction phenomenon, the coefficient b 2 should be higher during the different trading-hours period than during the same trading-hours period because a night session of Nikkei 225 futures is longer than that of TOPIX futures during the different trading-hours period. However, if night session trading makes the intraday overreaction phenomenon worse, b 2 should be lower during the different trading-hours period than during the same trading-hours period. The different trading-hours period consists of three separate periods; namely, the period from 8

1/4/2002 to 9/18/2007, from 6/17/2008 to 10/14/2008, and from 3/25/2014 to 12/30/2015. Thus, we also perform a panel analysis for the different trading-hours period by adding dummy variables for inclusion in these periods as control variables. Thus: R Intraday = a + b 1 R Overnight + b 2 NK i R Overnight + b 3 T1 t R Overnight + b 4 T2 t R Overnight + b 5 NK i + b 6 T1 t +b 7 T2 t + e (3) where T1 t is a dummy variable that takes one if day t is between 6/17/2008 and 10/14/2008, and T2 t is a dummy variable that takes one if day t is between 3/25/2014 and 12/30/2015. During the same trading-hours period, the trading hours for TOPIX futures were extended as of 11/21/2011. Thus, we also perform a panel analysis for the same trading-hours period by adding a dummy variable T3 t, which takes one if day t is from 11/22/2011 to 3/25/2014, for inclusion as a control variable. Thus: R Intraday = a + b 1 R Overnight + b 2 NK i R Overnight + b 3 T3 t R Overnight + b 4 NK i + b 5 T3 t + e (4) While the result of the time-series analysis may be attributable to a time-varying macro event or other market structural change, the effect of these time-varying factors is less relevant for cross-sectional comparison; namely, the cross-sectional difference in the overreaction between Nikkei 225 futures and TOPIX futures. Thus, these cross-sectional analyses could provide more robust evidence regarding the effect of extended-hour session on the intraday overreaction phenomenon. 2.3. Results 2.3.1. Time-series comparison Table 2 shows the results of the time-series analysis. First, panel (a) reveals that the intraday overreaction phenomenon, identified by the negative association between R Intraday and R Overnight, is weakest during the no night-session period. Further, the negative association between R Intraday and R Overnight for Nikkei 225 futures during this period is insignificant. However, after the introduction of the night session, a stronger negative association can be observed for TOPIX and Nikkei 225 futures. [Table 2] Panel (b) of Table 2 reveals that the intraday overreaction phenomenon, namely intraday price 9

reversals following price changes at the market open, is observed for TOPIX and Nikkei 225 futures. In terms of the effect of night-session trading on the intraday overreaction phenomenon, the result reveals that the coefficient of T Night 1 R Overnight is significantly negative, indicating that a longer night session (higher T Night 1 ) induces a stronger negative relation between an overnight return (R Overnight ) and the subsequent intraday return (R Intraday ). These results indicate that a longer night session induces the stronger intraday overreaction phenomenon. 2.3.2. Cross-sectional comparison Table 3 shows the results of the cross-sectional comparison. The results reveal that the coefficient b 2 (the coefficient of NK i R Overnight ) for the same trading-hours period is significantly positive, indicating that the intraday overreaction phenomenon, namely intraday price reversals following price changes at the market open, is essentially weaker for Nikkei 225 futures than for TOPIX futures. [Table 3] The difference in the intraday overreaction phenomenon could be attributed to the difference in information uncertainty in the underlying spot market indexes of TOPIX and Nikkei 225 futures. The constituents of the Nikkei index are selected from stocks listed on the first section of the Tokyo Stock Exchange on the basis of liquidity, market size, visibility, and so on, while the constituents of the TOPIX index are all the stocks listed on the first section of the Tokyo Stock Exchange. Thus, the constituents of the Nikkei index consist of large and high visibility stocks, while the constituents of the TOPIX index include a considerable number of small and low visibility stocks. Actually, as shown in Table 4, the reciprocals of analyst coverage 5 and market values (billion yen), which are proxies of information uncertainty, are always higher for the TOPIX index than for the Nikkei 225 index. 6 In addition, the number of constituents is much larger for the TOPIX index (from 1500 to 2000) than for the Nikkei 225 index (essentially, 225). Thus, it is highly likely that information uncertainty is higher for TOPIX futures than for Nikkei 225 futures. Thus, the intraday overreaction phenomenon, which 5 Analyst coverage is defined by the number of earnings forecasts for the current fiscal year. We obtain a sample of analysts earnings forecasts for Japanese firms from the Factset Estimates. 6 The two proxies for information uncertainty are higher for the TOPIX index than for the Nikkei index during the same trading-hours period. 10

could be strengthened by information uncertainty, could be stronger for TOPIX futures than for Nikkei 225 futures. [Table 4] However, the results reveal that the coefficient b 2, which represents the difference in the intraday overreaction phenomenon between Nikkei 225 futures and TOPIX futures, is insignificant during the different trading-hours period. Further, the coefficient b 2 (the coefficient of NK i R Overnight ) is much smaller for the different trading-hours period than for the same trading-hours period. Although the intraday overreaction phenomenon is weaker for Nikkei 225 futures than for TOPIX futures during the same trading-hours period, the overreaction for Nikkei 225 futures is as strong as that for TOPIX futures when the length of the night session is longer for Nikkei 225 futures than for TOPIX futures. The two proxies for information uncertainty are higher for the TOPIX index than for the Nikkei index during both the different trading-hours period and the same trading-hours period. In addition, a difference in information uncertainty between the two futures is not smaller during the different trading-hours period than during the same trading-hours period. Thus, the stronger overreaction phenomenon for Nikkei 225 futures during the different trading-hours is not explained by information uncertainty. It is likely that the stronger overreaction for Nikkei 225 is attributed to a longer night session for Nikkei 225 futures. These results essentially support this study s view that a longer night session results in the stronger intraday overreaction phenomenon. 3. Robustness and additional analyses 3.1. Adjustment for market-wide uncertainty and bid-ask bounce In this section, in order to conduct a robustness check, we analyze the effect of implementing an extended-hours session on the intraday overreaction phenomenon after controlling for two effects: market-wide uncertainty and bid-ask bounce. Kyle (1985), Grossman and Miller (1988), and Nagel (2012) show that a short-term reversal strategy is positively associated with the proxy for market-wide uncertainty, namely the VIX index. 11

Corte et al. (2015) show that a change in levels of the VIX index adds explanatory power for the intraday overreaction phenomenon. Thus, we include VIX t 1 R Overnight 1 (and VIX t 1 ) as control variables, where VIX t denotes the change in close levels of the Nikkei stock average volatility index ( VIX t = VIX t VIX t 1 ) 7,8, as follows: R Intraday = a i + b 1 i R Overnight + b 2 i T Night 1 R Overnight +b 3 i T Night 1 + b 4 i VIX t 1 R Overnight +b 5 i VIX t 1 + e (5) In addition, we control for the effect of bid-ask bounce. A price change from close to open is more likely to occur as a result of bid-ask bounce than from an overnight change in true value (Corwin and Schultz, 2012). Thus, for an accurate identification of the intraday overreaction phenomenon, it may be necessary to control for overnight returns attributable to bid-ask bounce. To this end, as a control variable, we add Sign(R Overnight ) bidask 1, where bidask is defined by the bid-ask spread divided by the transaction price at the end of the regular session on day t. Further, the control variable Sign(R Overnight ) bidask 1 can be considered the overnight return that is attributable to the bid-ask bounce. We run the subsequent regression model as: R Intraday = a i + b 1 i R Overnight + b 2 i T Night 1 R Overnight +b 3 i T Night 1 + b 4 i Sign(R Overnight ) bidask 1 + e (6) In addition, we run the following regression model where both control variables are included: R Intraday = a i + b 1 i R Overnight + b 2 i T Night 1 R Overnight +b 3 i T Night 1 + b 4 i VIX t 1 R Overnight +b 5 i VIX t 1 + b 6 i Sign(R Overnight ) bidask 1 + e (7) negative. 2 Then, we examine whether the coefficient b i (the coefficient of T Night 1 R Overnight ) is still The results, shown in Table 5, reveal that even if we control for the effect of market-wide uncertainty and bid-ask bounce, the coefficient of T Night 1 R Overnight (b i 2 ) is significantly negative. Thus, the impact of night-session trading on the intraday overreaction phenomenon cannot be subsumed by the effect of market-wide uncertainty and bid-ask bounce. [Table 5] 7 Corte et al. (2015) utilize the change in close levels of the volatility index and the difference between the opening and prior close levels of the index. However, since the historical opening value of the Nikkei stock average volatility index is unavailable, we only utilize the change in close levels of the volatility index. 8 Since the full historical values of VIX for TOPIX are unavailable, we control for the Nikkei stock average volatility index when we analyze the intraday price overreaction of TOPIX futures. 12

3.2. Price reversal during an afternoon session In this study, we specifically focus on price reversal during a morning session. In this section, we examine whether the overnight return is still reversed during an afternoon session. We define the price reversal during an afternoon session by the association between overnight returns and intraday returns during the subsequent afternoon session. We utilize intraday future returns from 11:00 to 15:10, denoted as R Afternoon. R Afternoon is defined as: R Afternoon = log (P 15:10 /P 11:00 ) Overnight I examine the association between R and R Afternoon, and consider whether the association is affected by the length of the night session of the prior trading day (T Night 1 ). To this end, we perform a time-series analysis for R Afternoon by running the following regression: R Afternoon = a i + b 1 i R Overnight + b 2 i T Night 1 R Overnight +b 3 i T Night 1 + e (8) In addition, we conduct a cross-sectional comparison between Nikkei 225 futures and TOPIX futures by running the following panel analysis for the same trading-hours period and the different trading-hours period: R Afternoon = a + b 1 R Overnight + b 2 NK i R Overnight + b 3 NK i + e (9) The results of the time-series analysis and cross-sectional analysis, shown in Table 6, reveal that the coefficient of R Overnight is insignificant. This finding indicates that an intraday return during an afternoon session is not significantly associated with the overnight return of the prior day. [Table 6] In addition, the time-series analysis reveals that the coefficient of T Night Overnight 1 R Overnight insignificant. Further, the cross-sectional analysis reveals that the coefficient NK i R is is insignificant for the same trading-hours period and the different trading-hours period. These results indicate that the association between an overnight return and an intraday return during an afternoon session is not affected by the length of the prior night session. All these results suggest that the overnight return is no longer reversed during an afternoon session and the effect of a prior day s night session trading is not observed for the subsequent afternoon session. 13

3.3. Alternative indicator of the extension of trading hours Trading volume during a night session can be a proxy for the degree of the effect of extended-hours trading. Obviously, trading volumes during an extended-hours session are positively associated with the length of the session. In addition, higher trading volumes during a session can result in a greater effect of extended-hours trading on the overreaction phenomenon. If extended-hours transactions fail to reduce information uncertainty at the open of regular sessions, higher trading volumes during extended hours would result in greater intraday price reversals following price changes at the market open. In other words, intraday returns R Intraday can be more negatively associated with overnight returns R Overnight, when trading volume during extended-hours session is larger. Thus, in addition to analyzing the effect of the length of a night session on the intraday overreaction phenomenon, we analyze the effect of trading volume during a night session on such overreaction. Specifically, we utilize a turnover ratio OTURN Night 1, defined by trading volume during a night session denominated by 20 days moving median 9 of open interest (the total number of open or outstanding futures contracts). Trading volume tends to increase significantly from five days prior to the expiration date for investors demand to rollout their futures contracts. Thus, we control for these rolling-out demands by running the following regression: OTURN Night = α i + β s s i ET 5 s=1 + ε s where ET is a dummy variable that takes 1 when there is a night session for the future i, and day t is s-days prior to the expiration date of the latest future i. Adjusted turnover, TURN Night, is defined as: TURN Night = OTURN Night β s s i ET 5 s=1 I analyze the effect of TURN Night 1 on the association between R Intraday running the following regression: Overnight and R by 9 In order to control for the effect of the fluctuation of open interest (specifically, a decrease in open interest near the expiration date), a 20 median value is used as the denominator. 14

R Intraday = a i + b 1 i R Overnight + b 2 i TURN Night 1 R Overnight + b 3 i TURN Night 1 + e (10) 2 The negative b i (the negative coefficient of TURN Night 1 R Overnight ) means that larger transactions during a night session result in the stronger intraday overreaction phenomenon. The result, shown in Table 7, panel (a), reveals that the coefficient of TURN Night Overnight R (b i 2 ) is significantly negative, indicating that a larger amount of transactions during a night session induces a stronger negative relation between the overnight return (R Overnight ) and the subsequent intraday return (R Intraday ). This result indicates that higher transactions during a night session result in stronger intraday price reversals following price changes at the market open, namely the stronger intraday overreaction phenomenon. [Table 7] Compared with the effect of the length of the night session (T Night R Overnight ), TURN Night R Overnight seems to have more robust predictive power for the degree of the intraday overreaction phenomenon. Thus, to test the incremental predictive power of TURN Night, we run the following regression after controlling for T Night 1 R Overnight : R Intraday = a i + b 1 i R Overnight + b 2 i TURN Night 1 R Overnight + b 3 i TURN Night 1 + b 4 i T Night 1 R Overnight + b 5 i T Night 1 + e (11) The result, shown in Table 7, panel (b), reveals that the coefficient of TURN Night Overnight R (b i 2 ) is still significantly negative, indicating that TURN Night R Overnight has additional predictive power for the overreaction. Since a longer night session (larger T Night ) results in a higher TURN Night, TURN Night contains information regarding T Night. The incremental information of TURN Night to T Night could be the degree of trading activity per unit of time. Thus, the result suggests that the degree of trading activity per unit of time could have an additional predictive power for the overreaction. In other words, the overreaction phenomenon is associated not only with the length of the night session but also with the degree of trading activity during the session. The results in this section suggest that the overreaction phenomenon can be made worse by frequent trading during the extended-hours sessions. 3.4. Price movement during a night session 15

In this section, we analyze price discovery during a night session by testing whether price movements during such a session reduce information uncertainty at the open of a subsequent regular session which induces the overreaction phenomenon. To this end, we analyze the association between returns during a night session and the subsequent intraday returns. Specifically, we analyze the relation when a prior night session stays open until 3:00 (when futures have the longest night-session period). The investigated periods for Nikkei 225 futures and TOPIX futures range from 11/22/2011 to the end of 2015 and 3/25/2014 to the end of 2015 respectively. We decompose overnight returns, R Overnight, into the night-session return, R Night 1, and the opening return, R Opening. The night-session and opening returns are defined as: R Night = log (P 3:00 +1 /P 15:10 ) R Opening = log (P 9:00 /P 3:00 ) 3:00 Intraday where P is the latest transaction prices at 3:00. We examine the association between R and R Night 1 by running the following regression: R Intraday = a i + b 1 i R Night 1 +b 2 i R Opening + e (12) Table 8 reports the results of the regression. R Intraday is negatively and significantly associated not only with R Opening but also with R Night 1, indicating that price movements during a night session are reversed during a subsequent regular session. In other words, price movements during a night session strengthen the next day s intraday overreaction phenomenon. The result, at least, suggests that price movements during a night session fail to reduce information uncertainty at the open of a regular session which induces the intraday overreaction. [Table 8] 4. Conclusion Previous studies argue that periodic market closures induce the well-known intraday return pattern, namely, intraday price reversals following price changes at the market open. On the other hand, the extension of trading hours has increasingly been discussed in several markets. Although the effect of the extension of trading hours could be complex, there is no empirical study that examine whether and how 16

the extension of trading hours affects the intraday return pattern which is caused by period market closures. In this study, we provide empirical evidence by examining whether intraday price reversals following price changes at the market open is weaken or strengthened by extending trading hours. I investigate the extension of two representative Japanese stock index futures contracts. These can be considered the best sample for analyzing the effect of an extension for following reasons: the trading hours of these futures contracts have been extended significantly and asynchronously; the significant extensions enable us to perform a time-series (before and after) comparison regarding the intraday price reversals; and the asynchronous extensions enable us to perform comparisons of stock futures with different trading hours. Time-series analysis (the before and after comparison) shows that a longer extended-hours session (a longer night session) results in larger intraday price reversals following price changes at the market open for Nikkei 225 and TOPIX futures contracts. Cross-sectional analysis reveals that, although the intraday price reversals tends to be weaker for Nikkei 225 futures than for TOPIX futures during the same trading-hours period, the reversal for Nikkei 225 futures is as strong as that for TOPIX futures when the length of the night session is significantly longer for Nikkei 225 futures. Additional analysis shows that not only the length of a night session but also the trading volume during a session has predictive power for the degree of intraday price reversals following price changes at the market open; for example, higher trading volume induces a stronger reversal. Moreover, the results reveal that price movements during a night session are reversed during a subsequent regular session, indicating that price movements during a night session strengthen the next day s intraday price reversals. All these findings support the view that night session trading could strengthen intraday price reversals during a subsequent regular session, namely, the intraday price overreaction. We provide empirical evidence that the extension of trading hours actually strengthen the intraday overreaction phenomenon. The results suggest that the intraday return patterns induced by periodic market closure are not easily and straightforwardly mitigated by an extension of trading hours. Such evidence highlights the existence of the negative impact of the extension of trading hours. 17

In addition, the analyses raise another problem with implementing and extending an extended-hours session. Miwa and Ueda (2016) argue that the low liquidity feature of an extended-hours session lowers price efficiency and trading activity. However, Nikkei 225 futures and TOPIX futures both have enough liquidity during night sessions, and the analysis shows that higher trading activity of these futures during night sessions strengthens the intraday overreaction phenomenon. Considering that the corresponding spot markets are closed during the night sessions, it is likely that an increase in the intraday overreaction phenomenon can be attributed to high information uncertainty during these sessions. Thus, the finding shows that information uncertainty during an extended session is also a key reason for the negative impact of implementing an extended session. The findings suggest that not only liquidity during an extended-hours session but also information uncertainty during the session should be addressed before extending trading hours. References Atkins, B., and Dyl, A., 1990. Price reversals, bid ask spreads and market efficiency. Journal of Financial and Quantitative Analysis 25, 535 547. Barclay, M., and Hendershott, T., 2003. Price discovery and trading after hours. Review of Financial Studies 16, 1041 1073. Corte, D., Kosowski, R., and Wang, T., 2015. Market Closure and Short-Term Reversal, working paper. Corwin, A., and Schultz, P., 2012. A simple way to estimate bid-ask spreads from daily high and low prices. Journal of Finance 67, 719 759. Daigler, T., 1997. Intraday futures volatility and theories of market behavior. Journal of Futures Markets 17 (1), 45 74. Easlay, D., and O Hara, M., 1992. Time and the process of security price adjustment. Journal of Finance 47, 576 605. Ekman, P. D., 1992. Intraday patterns in the S&P 500 index futures market. Journal of Futures Markets 12, 365 381. Fan, J., and Lai, N., 2006. The intraday effect and the extension of trading hours for Taiwanese 18

securities. International Review of Financial Analysis 15, 328 347. Foster, D., and Viswanathan, S., 1990. A theory of intraday variation in volume, variance, and trading costs in securities markets. Review of Financial Studies 3, 593 624.Fung, W., Mok, D., and Lam, K., 2000. Intraday price reversals for futures in the US and Hong Kong. Journal of Banking & Finance 24, 1179 1201. Glosten, L., and Milgrom, P., 1985. Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. Journal of Financial Economics 14, 71 100. Grant, J., Wolf, A., and Yu, S., 2005. Intraday price reversals in the US stock index futures market: A 15-year study. Journal of Banking & Finance 29 (5), 1311 1327. Grossman, J., and Miller, M., 1988. Liquidity and market structure. Journal of Finance 43, 617 633. Houston, F., and Ryngaert, D., 1992. The links between trading time and market volatility. Journal of Financial Research 15, 91 100. Kyle, A., 1985. Continuous auctions and insider trading, Econometrica 53 (6), 1315 1335. Miwa, K., and Ueda, K., 2016. Is the extension of trading hours always beneficial? An artificial agent-based analysis. Computational Economics, in press. Nagel, S., 2012. Evaporating liquidity. Review of Financial Studies 25, 2005 2039. Osaki, S., 2014. TSE looking at extending cash trading hours again. NRI Financial Research Paper lakyara, 78. 19

Table 1 Trading hours of index futures Panel (a) shows the trading hours of the extended-hours sessions (the so-called night sessions ) for Nikkei 225 futures and TOPIX futures. Panel (b) shows the values of T Night, which represent the length of the night sessions, and the period categories, which are determined on the basis of the length of the night sessions. (a) The extended sessions of index futures Nikkei 225 TOPIX - 9/17/2007 Null Null 9/18/2007-2008/06/15 16:30~19:00 6/16/2008-10/13/2008 10/14/2008-7/19/2010 16:30~20:00 7/20/2010-7/18/2011 16:30~23:30 16:30~19:00 7/19/2011-11/20/2011 11/21/2011-3/23/2014 16:30~03:00 16:30~23:30 3/24/2014-16:30~03:00 (b) Values of T Night and period categories Nikkei 225 TOPIX Category (Nikkei 225) Category (TOPIX) - 9/17/2007 0 Period 1 0 9/18/2007-2008/06/15 4 6/16/2008-10/13/2008 Period 2 10/14/2008-7/19/2010 5 4 7/20/2010-7/18/2011 8.5 7/19/2011-11/20/2011 Period 3 11/21/2011-3/23/2014 12 8.5 3/24/2014-12 Period 1 Period 2 Period 3 20

Table 2 Time-series comparison Panel (a) shows the regression results regarding the association between the overnight returns (R Overnight ) and the intraday returns (R Intraday ) for period 1 (the no night-session period), period 2 (the short night-session period), and period 3 (the long night-session period). The results for the regressions in equation (1) in the text are shown in panel (b). The rows for Overnight return, Extension, and Overnight return x Extension show the coefficients of R Overnight, T Night 1, and T Night 1 R Overnight respectively. The figures in parentheses are t-statistics based on Newey and West standard errors. *, **, and *** indicate two-sided statistical significance at the 10%, 5%, and 1% levels respectively. (a) Opening price overreaction for each period Period 1 (No night-session period) Period 2 (Short night-session period) Period 3 (Long night-session period) Nikkei 225 Futures TOPIX Futures -0.022-0.056 *** (0.99) (3.08) -0.069 *** -0.165 *** (2.74) (4.92) -0.093 *** -0.122 *** (3.48) (4.27) (b) Overreaction and the length of the night sessions Intercept Overnight return Extension Overnight return x Extension Nikkei 225 Futures 0.000 TOPIX Futures 0.000 *** (1.41) (3.08) -0.037 ** -0.094 *** (2.01) (3.13) 0.000 ** 0.000 *** (2.29) (3.43) -0.005 ** -0.007 ** (2.18) (2.16) 21

Table 3 Cross-sectional comparison The results for the panel analyses in equations (2), (3), and (4) in the text are shown in this table. Panels (a) and (b) show the results for the same trading-hours period and the different trading-hours period respectively. The rows for Overnight return, NK, Overnight return x NK, T1, Overnight return x T1, T2, Overnight return x T2, T3, and Overnight return x T3 show the coefficients of R Overnight, NK i, NK i R Overnight, T1 t, T1 t T3 t R Overnight, T2 t, T2 t R Overnight, T3 t, and R Overnight respectively. The figures in parentheses are t-statistics based on Newey and West standard errors. *, **, and *** indicate two-sided statistical significance at the 10%, 5%, and 1% levels respectively. (a) The same trading-hours period Model (2) Model (3) 0.000 0.000 *** Intercept (1.08) (2.83) -0.114 *** -0.087 *** Overnight return (3.13) (3.32) 0.000 0.000 NK (0.42) (0.50) 0.091 ** 0.092 ** Overnight return x NK (2.27) (2.34) T1 0.001 (0.57) Overnight return x T1-0.055 (0.99) T2 0.001 *** (4.22) Overnight return x T2-0.056 * (1.68) (b) The different trading-hours period Model (2) Model (4) 0.000 0.000 Intercept (0.09) (0.12) -0.111 *** -0.175 *** Overnight return (4.64) (4.00) 0.000 0.000 NK (0.63) (0.63) 0.006 0.006 Overnight return x NK (0.15) (0.16) T3 0.000 (0.00) Overnight return x T3 0.090 * (1.78) 22

Table 4 Proxies of information uncertainty This table shows the weighted average of two information uncertainty indicators: reciprocals of analyst coverage and market values (billion yen). The columns headed 1/Coverage and 1/MV show the weighted averages of the reciprocals of analyst coverage and market values respectively. The table reports the values for TOPIX (the columns headed TOPIX ), the Nikkei index (the columns headed Nikkei ), and the difference between them (the columns headed Difference ) as of the end of each calendar year. 1/Coverage 1/MV TOPIX Nikkei Difference TOPIX Nikkei Difference 2002 22.6% 19.3% 3.2% 0.51% 0.24% 0.27% 2003 22.9% 18.2% 4.7% 0.61% 0.29% 0.33% 2004 24.5% 20.3% 4.3% 0.49% 0.23% 0.26% 2005 28.7% 22.9% 5.8% 0.45% 0.21% 0.24% 2006 27.7% 22.9% 4.9% 0.31% 0.14% 0.17% 2007 21.6% 18.5% 3.0% 0.27% 0.12% 0.15% 2008 19.5% 17.7% 1.8% 0.31% 0.13% 0.17% 2009 15.7% 12.3% 3.5% 0.53% 0.23% 0.30% 2010 15.7% 11.3% 4.5% 0.48% 0.19% 0.29% 2011 14.6% 10.6% 4.1% 0.46% 0.19% 0.27% 2012 12.5% 9.8% 2.7% 0.56% 0.23% 0.34% 2013 13.0% 9.7% 3.3% 0.48% 0.19% 0.29% 2014 13.1% 10.2% 2.9% 0.32% 0.12% 0.20% 2015 12.5% 9.2% 3.3% 0.30% 0.11% 0.19% 2002-2015 18.9% 15.2% 3.7% 0.44% 0.19% 0.25% 23

Table 5 Controlling for market uncertainty and bid-ask bounce This table shows the results for the regressions in equations (5), (6), and (7) in the text. Panels (a) and (b) show the results for Nikkei 225 futures and TOPIX futures respectively. The rows for Overnight return, Extension, VIX, Overnight return x Extension, Overnight return x VIX, and Bid-ask show the coefficients of R Overnight, T Night 1, VIX t 1, T Night 1 R Overnight, VIX t 1 R Overnight, and Sign(R Overnight ) bidask 1 respectively. The figures in parentheses are t-statistics based on Newey and West standard errors. *, **, and *** indicate two-sided statistical significance at the 10%, 5%, and 1% levels respectively. (a) Nikkei 225 futures Model(5) Model(6) Model(7) Intercept 0.000 0.000 0.000 (1.34) (1.47) (1.39) Overnight return -0.036 * -0.048 * -0.044 * (1.92) (1.95) (1.75) Extension 0.000 ** 0.000 ** 0.000 ** (2.28) (2.30) (2.29) VIX 0.005 * 0.005 * (1.95) (1.93) Overnight return x Extension -0.005 ** -0.005 ** -0.005 ** (2.17) (2.02) (2.05) Overnight return x VIX -0.255-0.246 (1.42) (1.34) Bid-ask 0.118 0.092 (0.90) (0.69) (b) TOPIX futures Model(5) Model(6) Model(7) Intercept 0.000 *** 0.000 *** 0.000 *** (3.06) (3.82) (3.78) Overnight return -0.092 *** -0.099 *** -0.095 *** (3.16) (4.00) (3.84) Extension 0.000 *** 0.000 *** 0.000 *** (3.46) (3.27) (3.33) VIX 0.009 *** 0.008 *** (3.33) (3.69) Overnight return x Extension -0.006 ** -0.007 ** -0.006 ** (2.11) (2.28) (2.41) Overnight return x VIX -0.329-0.209 (1.00) (0.75) Bid-ask 0.284 ** 0.248 ** (2.42) (2.12) 24

Table 6 Return reversal during afternoon sessions Panel (a) shows the time-series analysis regarding the association between the overnight returns and the intraday returns during afternoon sessions (the results for the regression in equation (8)). The rows for Overnight return, Extension, and Overnight return x Extension show the coefficients of R Overnight, T Night 1, and T Night 1 R Overnight respectively. Panel (b) shows the cross-sectional analysis regarding the association (the results for the regression in equation (9)). The rows for Overnight return, NK, and Overnight return x NK show the coefficients of R Overnight, NK i, and NK i R Overnight respectively. The figures in parentheses are t-statistics based on Newey and West standard errors. *, **, and *** indicate two-sided statistical significance at the 10%, 5%, and 1% levels respectively. (a) Time-series analysis Intercept Overnight return Extension Overnight return x Extension Nikkei 225 FuturesTOPIX Futures 0.000 0.000 (0.93) (1.03) 0.068 0.059 * (1.62) (1.81) 0.000 0.000 (0.35) (0.00) 0.003 0.006 (0.60) (1.05) (b) Cross-sectional analysis Intercept Overnight return NK Overnight return x NK The same The different trading-hours period trading-hours period 0.000 0.000 (0.67) (0.83) 0.068 * 0.067 * (1.73) (1.81) 0.000 0.000 (0.08) (0.53) -0.010 0.022 (0.17) (0.38) 25