Is There Private Information in the FX Market? The Tokyo Experiment

Transcription

1 Is There Private Information in the FX Market? The Tokyo Experiment Takatoshi Ito Richard K. Lyons Michae T. Mevin This draft: January 1996 First draft: October 1995 Abstract It is a common view that private information in the foreign exchange market does not exist. This paper provides evidence against this view. The evidence comes from the opening of unch-hour trading in the Tokyo market: in December 1994 the restriction on interdeaer trading between 12:00 and 1:30 was aboished. We find that unch-hour voatiity is higher when the market is trading, impying the presence of private information (since the fow of pubic information did not change with the trading rues). In addition, the shift in regime is instructive because it induces interpretabe changes in the U-shape of voatiity over the trading day. We find that opening unch-hour trade changes the voatiity U-shape in three ways: the curve is (1) fatter, (2) tited upward, and (3) higher on average. These effects on the U-shape have impications for the nature of the private information invoved. JEL: F31 Keywords: Voatiity, Information, Microstructure. Correspondence Professor Richard K. Lyons Haas Schoo of Business, UC Berkeey Berkeey, CA Te: , Fax: E-mai: yons@haas.berkeey.edu Respective affiiations are Hitotsubashi University, IMF, and NBER; UC Berkeey and NBER; and Arizona State University. We thank Osen & Associates for generousy providing data. Lyons thanks the Nationa Science Foundation and the Berkeey Program in Finance for financia assistance.

2 Is There Private Information in the FX Market? The Tokyo Experiment 1. Introduction It is a common view that private information in the foreign exchange market does not exist. This paper evauates this view by examining how trading affects voatiity. In particuar, we examine the Tokyo foreign exchange (FX) market, which unti recenty was restricted from trading over the unch break from 12:00 to 1:30. For that ninety minutes, the Tokyo interbank market shut down. On December 22, 1994, this restriction was aboished. 1 The remova of the restriction thus provides a natura experiment regarding the effects of trading on voatiity. It is we known that the variance of equity returns is more than ten times arger when markets are open than when cosed (see Fama (1965), Odfied and Rogaski (1980), and French and Ro (1986), among others). French and Ro posit three possibe sources: (1) pubic information that arrives during business hours, (2) private information that enters price through trading, and (3) pricing errors that occur during trading. They examine stock market cosures during which there is no change in the fow of pubic information to determine the importance of the pubic information source. They find that return voatiity decreases significanty during these cosures, which is inconsistent with pubic information being the soe source of voatiity. Rather, private information appears to be the main source of high trading-time voatiity (they find ony a sma roe for pricing errors). The anaysis of this paper has two stages. The first stage is simiar in spirit to the equity anaysis of French and Ro (1986) in that we compare voatiity within a given interva across regimes. Our anaysis differs, however, in an important way: we are addressing a market whose information structure is more skewed toward pubic information. In fact, it is a common view that a participants in the FX market are projecting on the same pubic information set (except, perhaps, at times of centra bank intervention). Nevertheess, we find resuts simiar to French 1 This trading hour restriction was imposed by The Committee of Tokyo Foreign Exchange Market Customs, which is composed of representatives from commercia banks, foreign banks, and FX brokers. It was thus a vountary reguation by market participants rather than Ministry of Finance guidance. The restriction was introduced in 1972 after the yen exited the Bretton Woods system. The reason the restriction was aboished according to news reports was to regain the substantia voume that had migrated to other, unrestricted ocations (e.g., Singapore and Hong Kong). The decision to ift the restriction was made on December 21, and impemented on the foowing day. Restrictions on trading before 9 a.m. and after 3:30 p.m. were aso aboished on December 22. 1

3 striking. 2 The second stage of our anaysis moves beyond comparing unch-hour voatiity across and Ro s: unch-hour voatiity is twice as high with trading, without any change in the reease of pubic information. Given the perceived predominance of pubic information, this resut is regimes. In the second stage, we examine the regime shift s effect on the pattern of voatiity over the trading day. This aows us to ink our anaysis to the iterature on the U-shape of intraday voatiity. That work has estabished that voatiity over the day is U-shaped in many markets. 3 And recent theory in the area can rationaize the U-shape, most of it reying on some type of private information. 4 Empirica work, however, has ony recenty moved from documenting the phenomenon to determining if private information is indeed invoved. Here we address the ink between the U-shape and information by comparing the U-shape before and after the introduction of unch-hour trading. For exampe, most modes reying on private information predict a fattening of the U-shape: aowing trading induces greater reveation during the unch hour, with a smaer share remaining for the morning and afternoon. For concreteness, we offer a working definition of the term private information. By private information we mean any non-pubic information that is price reevant. Non-pubic information is any information that is not common knowedge in the usua sense. As for price reevance, we stress that price reevant information is not necessariy fundamenta. To understand this point, it is hepfu to estabish a taxonomy of information types that quaify as private by our definition. For the taxonomy, consider a standard two-period, three date trading mode in which trading occurs at t=0 and t=1, and at t=2 the fundamenta vaue F is reaized (e.g., fina payoffs occur). Now, by non-pubic fundamenta information we have in mind signas of the fina payoff F. We offer two possibiities in the context of FX. The first invoves (unsteriized) intervention: the deaer who receives a centra bank order has information that other market participants do not (see Peiers (1995)). The second invoves aggregation of information in orders tied to trade in goods: if a country s trade baance is a component of fundamenta vaue, then deaers receive signas of this component ong before pubished statistics are avaiabe (see Lyons (1995b)). 5 In contrast, by price reevant private information that is not fundamenta we have in 2 The fact that many markets exhibit reativey ow voatiity over the unch period does not weaken this resut since we are measuring the change in voatiity from the change in regime; we are not making a statement about the absoute eve, so controing for a natura decine over the unch period is not necessary. 3 Evidence of the U-shape pattern of intraday voatiity appears in Wood, McInish, and Ord (1985), Harris (1986), and Andersen and Boersev (1994), among many others. 4 See Admati and Pfeiderer (1988), Foster and Viswanathan (1990), and Hong and Wang (1995), among others. 5 A refinement that is reevant to both of these types of order-fow information ies in its distribution, for exampe its distribution across deaers. Since the transparency of FX trades is ow, order fow remains private information even after being conveyed to counterparties through trading (see, e.g., Lyons (1995b) and Romer (1993)). 2

4 mind information that is unreated to F but is reevant to the interim price at t=1. We offer two possibiities in the context of FX. The first invoves digestion effects that arise when risk sharing is incompete: for exampe, deaer positions uncorreated with F wi be price reevant if it is known that positions are cosed at day s end and that these (net) trades affect price (see Lyons (1995a)). The second invoves the presence of differentia prior beiefs in FX: Kraus and Smith (1994) show that beiefs about beiefs affect t=1 prices even when it is common knowedge that no participant has private information about fina payoffs at t=2. The two bodies of work most cosey reated to this paper are those concerning (i) voatiity dynamics in the FX market and (ii) voatiity effects of opening/cosing in other markets. The first emphasizes voatiity dynamics across both trading centers and time. 6 A centra resut is that voatiity generay propagates from one trading center to the next (e.g., a voatie Tokyo market is typicay foowed by a voatie New ork market the so-caed meteor shower effect). The semina work in the second area on opening/cosing effects is the French and Ro (1986) paper on the cosing of the NSE. One ater paper in this second area that is particuary reevant is Ito and Lin (1992). That paper examines the effects on stock price voatiity of the unch cosing of the Tokyo Stock Exchange. (Note that there is no change in the unch break in that case; the authors address the effects of its presence.) Surprisingy, they find no evidence of an intraday U-shape in voatiity. This is surprising because a U-shape is evident on the NSE, but the NSE does not break for unch. The rest of the paper is divided into four sections. Section 2 summarizes the reevant theory and information specifications. Section 3 describes the data. Section 4 presents our resuts. And Section 5 concudes. 6 See, e.g., Enge, Ito, and Lin (1990), Baiie and Boersev (1991), Ito, Enge, and Lin (1992), Dacorogna et a. (1993), and Hogan and Mevin (1994). 3

5 2. Experiment Design 2.a. Stage 1: Testing for the presence of private information The first stage of our anaysis is in the spirit of French and Ro (1986). In this first stage we test whether FX voatiity is caused soey by pubic information. To do this, we test whether unch-hour voatiity is affected by the introduction of trading. If there is no change in the fow of pubic information at the time the restriction is removed, then voatiity shoud not be affected as ong as voatiity is caused soey by pubic information. The aternative is that this market is not driven purey by pubic information, in which case voatiity shoud increase with the introduction of trading. Ceary, an important concern in interpreting the resuts is whether the fow of pubic information changed across the two regimes. If it does, and if the change over the unch-hour is an increase, then an increase in voatiity might be spuriousy attributed to private information. We offer three arguments that the fow of pubic information did not change with the regime shift. First, the decision to aboish the restrictions on trading was not part of a broader poicyreform package; rather, it was an isoated change in regime. Second, the decision was not the work of the Ministry of Finance (MOF). It came from The Committee of Tokyo Foreign Exchange Market Customs (see footnote 1). It is thus difficut to argue that it might have correated with MOF initiatives more broady. Finay, we have reviewed the schedue for pubic reease of reevant macro data and find no changes within our sampe either toward or away from the midday period. 7 To summarize our first hypothesis, its test, and the aternative, we have: H.1: Voatiity in the FX market is caused soey by pubic information. Test: V ( cosed) = V ( open) AH.1: V ( cosed) < V ( open) where V is the return variance of the yen/doar rate over the unch period from 12:00-1:30, Tokyo time. The cosed sampe corresponds to the period before remova of the trading 7 For exampe, we checked the number of news reports over the 12-1:30 period on the Reuters Money Market Headine News screen. In the thirty trading days before the unch-hour opening, there were 18.5 reports on average. In the thirty trading days after the unch-hour opening, there were 17.5 reports on average (precise dates correspond to our samping convention, described beow). 4

6 restriction (i.e., before December 22, 1994). The open sampe corresponds to the period after remova of the restriction. Our second stage-one hypothesis is directed at the fact that the Tokyo experiment is not a pure regime shift (cosed to open) since there were aternative markets where Tokyo participants coud trade during the restricted ninety minutes. Singapore, in particuar, is open during the Tokyo trading day, and can execute FX transactions originating in Tokyo over the unch break. 8 Nevertheess, under the restriction overa depth in yen/doar was sharpy ower over the break. If depth went to zero over the break, our test woud be more powerfu. That depth does not go to zero does not, however, bias our test. There is a way to measure this power oss, and at the same time check the robustness of our test of hypothesis 1. Note that in Tokyo yen/doar trading is much higher reative to mark/doar trading than in Singapore or Hong Kong (data provided beow). This reative importance provides a way to measure the importance of Singapore and Hong Kong as aternative trading venues. Per above, the power of our test depends on the degree to which depth drops from the Tokyo break. Taking Tokyo off ine causes a much sharper drop in the depth of yen/doar than in the depth of mark/doar (since Tokyo trading in far more yen/doar intensive). Though we expect the effect on voatiity in these two markets to have the same sign, the magnitude shoud be greater in the case of yen/doar. To summarize our second hypothesis and test, we have: H.2: If voatiity is induced from trading, then mark/doar voatiity over the unch-hour shoud increase when the Tokyo market opens, but by ess than the increase in yen/doar voatiity. M M Test: V ( cosed) < V ( open) and M M V ( cosed) V ( open) > V ( cosed) V ( open) where V M is the return variance of the mark/doar rate over the unch period from 12:00-1:30, Tokyo time. 8 Japanese newspapers report that there was indeed migration of unch-hour trading to Singapore and Hong Kong before the restriction was aboished. 5

7 2.b. Stage 2: Identifying types of private information from changes in the U-shape The second stage of our anaysis moves beyond simpy documenting higher unch-hour voatiity. The objective of this stage is to discriminate between the types of private information that might cause the voatiity effects we find in testing hypotheses 1 and 2. We do this by examining how the U-shape of intraday voatiity is affected by the introduction of unch-hour trading. There are three key dimensions to shifts in the U-shaped curve: (1) does the curve fatten or cur? (2) does the curve rise or fa? and (3) does the curve tit up or down? The answers to these questions provide vauabe evidence regarding the nature of the private information invoved. Our third hypothesis and test summarizes the impications of recent theory with respect to fattening the U-shape: H.3: If voatiity is caused by the reveation of information in the trading process, then opening unch-hour trading shoud fatten the U-shape of intraday voatiity. Test: V ( cosed) V ( cosed) < V ( open) V ( open) m and V ( cosed) V ( cosed) < V ( open) V ( open) a m a where V m and V a are the yen/doar return variances over the morning and afternoon periods, respectivey (10:30-12:00 and 1:30-3:00, Tokyo time). The second way the U-shaped curve might shift is in its overa eve. A recent paper that introduces a hepfu taxonomy here is Romer (1993). Romer distinguishes between interna news, which must be aggregated by the trading process, and externa news, which is refected in price without trading. We add to this the distinction between short-ived and ong-ived information. Private information can be short-ived if a future pubic signa is expected to revea it. This induces a front oading of informed trading within a given trading period. In contrast, ong-ived private information produces a more even trading pattern, as in Kye (1985). Our fourth hypothesis empoys these information categories to generate impications for the average eve of voatiity over the day. 6

8 H.4: If voatiity is caused by the reveation of information in the trading process, and that information is whoy short-ived interna news, then opening unch-hour trading shoud not effect average voatiity over the day. Test: V ( cosed) = V ( open) AH.4: If the information reveaed by the trading process is party ong-ived interna news, then opening unch-hour trading shoud increase voatiity over the day. where V is the yen/doar return variance over a three subperiods (10:30-3:00, Tokyo time). The fifth and ast of our hypotheses addresses the third way in which the U-shaped curve might shift: titing either up or down. If voatiity is redirected toward the afternoon, we shoud find a titing up; if it is redirected toward the morning, a titing down. H.5: If the information reveaed by the trading process is party short-ived, then opening unch-hour trading shoud raise afternoon voatiity reative to morning voatiity, titing the U-shape upward. Test: V ( cosed) V ( cosed) > V ( open) V ( open) m a m a 2.c. An additiona consideration There is a compication that derives from the date of the reguatory change (December 22). Traditionay, the Christmas week is one of the east representative since most businesses and currency deaers take vacation (from just before Christmas through New ear s day). Hence, a standard before-versus-after comparison is not a cean test because there is a strong seasona in the hoiday period foowing the change in regime in our data. We use two methods to correct for this seasona. With the first, we omit from the after sampe the business days between December 22 and January 2. In the end, we find no substantive effect on our resuts from this correction. (This is the correction used for our reported resuts.) The second method we examined is comparing before and after resuts over intervas exacty one year apart. Though this ceary eiminates the seasona, the resuting arger gap between the sub-sampes introduces other factors that are difficut to contro. In any case, unchhour voatiity is significanty higher in the after sampe using this method as we. 3. Data 7

9 3.a. Exchange rate data The yen/doar and mark/doar rates we use are the indicative spot quotes posted on the Reuters FXFX screen between 29 September 1994 and 28 March 1995 (the first and ast dates of our ongest samping interva). Our source for these series is Osen & Associates (Zurich). Each bid-offer quote is time stamped to the second. (For more detais regarding the capture and ceaning of the data, see Dacorogna et a. (1993). For more on their indicative nature, see Goodhart (1989) and Goodhart, Ito, and Payne (1996)). Though the indicative quotes have their shortcomings, our method of use minimizes our exposure. Specificay, the variance ratios require ony the exchange rate series themseves (bidoffer midpoint). This is the dimension of the data that Goodhart, Ito, and Payne (1996) find provides the most accurate measure of the underying market anaogue (cf the series for the indicative spread and the frequency of quote entry). 3.b. The Tokyo and Singapore markets According to the tri-annua survey of the Bank for Internationa Settements (BIS), the daiy turnover of the Tokyo FX market in the month of Apri 1995 was $161 biion. Of this, roughy 80 percent was interbank (i.e., interdeaer), either done directy or through brokers (the remaining 20% being customer-deaer trades). 9 By currency, yen/doar accounts for 76% and the mark/doar accounts for 12%. In Singapore, the daiy turnover was $105 biion over the same period. By currency, yen/doar accounts for 30% and mark/doar accounts for 32% We write roughy 80% because the BIS report incudes a third category of participant caed other financia institutions. This category incudes nonreporting banks, which in many countries incudes investment banks, some of which are important in deaing. That deaers are incuded in this category is evidenced by the significant brokered trading of this category: ony deaers have access to brokers in this market. 10 Singapore s currency breakdown is from the 1992 BIS Survey (the 1995 resuts for the breakdown in Singapore are not yet avaiabe to us). 8

10 4. Resuts and Discussion 4.a. Stage 1 resuts: The voatiity effects from the regime shift Our stage one anaysis incudes the testing of hypotheses 1 and 2. The test of hypothesis 1 is a test of whether voatiity rises over the unch hour from 12 to 1:30 after the opening of trade (i.e., after the remova of the restriction on 22 December 1994). We test this by cacuating the ratio of the unch-hour variance when open to the unch-hour variance when cosed, and testing whether this ratio is greater than one. Tabe 1 presents the resuts. The first coumn presents the number of trading days in both the cosed and open sampes (i.e., the before and after sampes). For exampe, the dates of the 20 day before sampe are the weekdays from November 24 to December 21, 1994 and the dates of the 20 day after sampe are the weekdays from January 4, 1995 to January 31, 1995 (hoiday week omitted see section 2.c.). Note that 20 trading days corresponds roughy to one trading month. The second coumn presents the variance ratios, open to cosed. The variance ratios are cacuated from returns measured as the change in the og of the bid-offer midpoint. P-vaues for the nu that the variance ratios equa one are not incuded because in a three cases they are zero to two decima paces (i.e., ess than 0.5%). These resuts are strong evidence that unch-hour voatiity does indeed rise with the opening of trade. In fact, return variance roughy doubes. This is a cear rejection of the nu that voatiity in FX is caused soey by pubic information. Our test of hypothesis 2 is a test of whether mark/doar voatiity aso rises over the unch hour, but by ess than the rise of yen/doar voatiity. Reca that this impication is motivated by the presence of aternative trading venues avaiabe during the Tokyo market cosure. We expect a smaer rise in mark/doar voatiity because mark/doar is reativey unimportant in Tokyo, impying a smaer effect from bringing Tokyo back on ine. Tabe 2 presents the resuts. As in Tabe 1, the first coumn presents the number of trading days in both the cosed and open sampes. The second coumn presents the variance ratios, open to cosed, in the case of mark/doar over the unch hour. P-vaues for the nu that these ratios equa one are in parentheses. The ast coumn presents the difference between the corresponding ratio from Tabe 1 for the yen/doar rate and the ratio for the mark/doar rate in coumn two. (P-vaues are not presented for this coumn because the resuting statistic is the difference between two F-statistics, requiring Monte Caro methods, which we have not yet performed). 9

11 Note that voatiity aso rises significanty in the case of mark/doar, but by ess than yen/doar. Thus, we cannot reject hypothesis 2, providing further evidence that voatiity is induced from trading, and that the source is not pubic information. 4.b. Stage 2 resuts: The pattern of voatiity over the day Stage 2 of our anaysis moves beyond showing that unch-hour voatiity rises with the opening of trade. Here, we examine how the U-shape of voatiity over the day is affected by the unch-hour opening. There are three questions we address: (1) does the curve fatten or cur? (2) does the curve rise or fa? and (3) does the curve tit up or down? The answers to these questions provide evidence regarding the type of private information invoved. Our third hypothesis concerns the first of these questions. If voatiity is caused by the reveation of information in the trading process, then opening unch-hour trading shoud fatten the U-shape of intraday voatiity. Tabe 3 presents our resuts. This tabe presents reative variance ratios for the yen/doar rate over three intraday periods: morning, unch, and afternoon (10:30-12:00, 12:00-1:30, and 1:30-3:00 Tokyo time, respectivey). The second coumn presents the unch-to-morning variance ratio after the opening reative to the unch-to-morning variance ratio before the opening. The third coumn presents the unch-to-afternoon variance ratio after the opening reative to the unch-to-afternoon variance ratio before the opening. P-vaues for the ratio=1 nu are zero to two decima paces for the component variance ratios (i.e., ess than 0.5%). The resuts ceary indicate a fattening of the U-shape. To see this, note that the denominators impy that unch return variance is substantiay ess than both morning and afternoon variance in the cosed sampe (i.e., the before sampe). After trade is opened, however, unch variance rises reative to both morning and afternoon variance, as indicated by the numerators being higher than the denominators in a cases. Because the numerators remain ess than one, the U-shaped curve is not fattened competey. Our fourth hypothesis concerns whether the intraday voatiity curve rises or fas on average. In formuating it, we referred to information types that have different impications for the average eve of voatiity over the day. Specificay, if the information driving trading-time voatiity is whoy short-ived interna news, then opening unch-hour trading shoud not effect average voatiity over the day. In contrast, if the information reveaed by the trading process is party ong-ived interna news, then opening unch-hour trading shoud increase voatiity over the day. Tabe 4 presents our resuts. 10

12 The second coumn impies that the U-shaped voatiity curve does rise on average. This coumn presents the return variance ratio for the yen/doar rate over a three periods (10:30-3:00 Tokyo time). In a cases, the P-vaue for the nu that the ratio equas one is zero to two decima paces. (Note, however, that these reative increases in variance are much smaer than those that occur over the unch hour, per Tabe 1.) Thus, we have evidence that short-ived information is not the whoe story, at east to the extent that the opportunity to profit from such information is dissipated by the end of the trading day. Our fifth hypothesis concerns whether the intraday voatiity curve tits up or down with the opening of unch-hour trade. If voatiity is redirected toward the afternoon, we shoud find a titing up; if it is redirected toward the morning, a titing down. For interpretation, if the information reveaed by the trading process is party short-ived, then opening unch-hour trading shoud raise afternoon voatiity reative to morning voatiity, titing the U-shape upward. Tabe 5 presents our resuts. Coumns two and three indicate that the U-shaped voatiity curve does indeed tit upward. Coumn two presents the morning variance ratio. Coumn three presents the afternoon variance ratio. Note from coumn two that there is evidence that the morning variance actuay fas sighty after opening unch-hour trade. In contrast, the afternoon variance ceary rises after opening unch-hour trade. This resut, in conjunction with the previous resut, suggests that short-ived information is indeed being reveaed in the trading process, though it is not the ony type of information being reveaed as interna news (in the sense of Romer (1993)). 4.c. Discussion So how do these resuts inform us about trading in FX? Consider three ways of thinking about the stage one resuts. One view regards FX as perfecty competitive, driven by pubic information, and neary infinitey deep (order fow has virtuay no price impact). Order fow is iquidity-motivated under this view, coming from customers and from deaers trading for inventory contro purposes. In this case, opening midday trade in Tokyo does not affect voatiity. A second view admits a roe for private information in FX, but considers the drop in depth as resuting primariy from ess iquidity trading in Tokyo since the informed woud simpy choose to route their trades to Singapore over the break. With itte decine in informed trading midday, the opening of midday trade in Tokyo shoud have itte impact on voatiity. A third view aso admits a roe for private information, but regards the drop in depth as argey from reduced trading by the informed. (An exampe is information that is communicated in biatera 11

13 transaction patterns among famiiar payers. In this case, transactions in Tokyo are inherenty different from transactions in Singapore, and the informed may not trade in Singapore because of unfamiiarity with the counterparties.) This reduction in the trading of the informed over the unch break reduces voatiity. Our resuts support this third view. 12

14 5. Concusions We reject the view that private information in FX does not exist. Our strong rejection comes from the fact that unch-hour return variance roughy doubes after the opening of trade. Thus, the view that traders of FX project excusivey on the same pubic information needs to be reaxed. Reaxing this view is made easier by recognizing that private, price-reevant information need not be private fundamenta information (per our introduction). Examining the regime shift s effect on the U-shape of voatiity over the day yieds further resuts. In particuar, we find that opening unch-hour trade aters the U-shape in three ways: the curve is (1) fatter, (2) tited upward, and (3) higher on average. The fattening of the curve is supportive of the presence of private information that must be aggregated in the trading process (or interna news, in the sense of Romer (1993)). The fattening occurs because aowing trading induces greater reveation during the unch hour, with a smaer share remaining for the morning and afternoon. The fact that the curve tits sharpy upward is supportive of a predominant roe for short-ived private information. The tit upward occurs because opening trade over unch reduces the incentive to front-oad informed trading in order to avoid a unch-hour signa that dissipates its vaue. Finay, the raising of voatiity on average suggests that at east some of the private information being aggregated through trading is ong-ived. Here, by ong-ived we mean information whose vaue is not fuy dissipated at the end of the trading day by the arriva of pubic information (see, e.g., Foster and Viswanathan (1990)). 13

15 Tabe 1 Lunch-Hour en/doar Variance Ratio This tabe presents the return variance ratio for the yen/doar rate over the unch-hour (12-1:30 Tokyo time). The numerator of the ratio is the unch-hour return variance after the unch market opened (i.e., after December 22, 1994); the denominator is the unch-hour return variance before the opening. The returns are cacuated as the change in the og of the bid-offer midpoint. The eft-hand coumn describes the ength of the before and after sampes. For exampe, the dates of the 20 day before sampe are the weekdays from November 24 to December 21, 1994 and the dates of the 20 day after sampe are the weekdays from January 4, 1995 to January 31, 1995 (hoiday week omitted). P-vaues for the ratio=1 nu are zero to two decima paces in a cases (i.e., ess than 0.5%). en Variance Ratio: Sampe Open/Cosed 20 days days days

16 Tabe 2 Lunch-Hour Mark/Doar Variance Ratio This tabe presents the return variance ratio for the mark/doar rate over the unch-hour (12-1:30 Tokyo time). The numerator of the ratio is the unch-hour return variance after the unch market opened (i.e., after December 22, 1994); the denominator is the unch-hour return variance before the opening. The returns are cacuated as the change in the og of the bid-offer midpoint. The eft-hand coumn describes the before and after sampes. For exampe, the dates of the 20 day before sampe are the weekdays from November 24 to December 21, 1994 and the dates of the 20 day after sampe are the weekdays from January 4, 1995 to January 31, 1995 (hoiday week omitted). The second coumn presents the variance ratio for the mark/doar rate. The third coumn presents the difference between the corresponding ratio from Tabe 1 for the yen/doar rate and the ratio for the mark/doar rate in coumn two. P-vaues for the ratio=1 nu are in parentheses. Mark Variance Ratio: Sampe Open/Cosed en Ratio - Mark Ratio 20 days 1.11 (0.01) 40 days 1.23 (0.00) 60 days 1.96 (0.00) = = =

17 Tabe 3 Does Lunch-Hour Trading Fatten the U-Shape? This tabe presents reative variance ratios for the yen/doar rate over three intraday periods: morning, unch, and afternoon (10:30-12:00, 12:00-1:30, and 1:30-3:00 Tokyo time, respectivey). The returns are cacuated as the change in the og of the bid-offer midpoint. The eft-hand coumn describes the before and after sampes. For exampe, the dates of the 20 day before sampe are the weekdays from November 24 to December 21, 1994 and the dates of the 20 day after sampe are the weekdays from January 4, 1995 to January 31, 1995 (hoiday week omitted). The second coumn presents the unch-to-morning variance ratio after the unch-hour market opened reative to the unch-to-morning variance ratio before the opening. The third coumn presents the unch-to-afternoon variance ratio after the unch-hour market opened reative to the unch-to-afternoon variance ratio before the opening. P-vaues for the ratio=1 nu are zero to two decima paces for the component variance ratios (i.e., ess than 0.5%). Sampe Lunch/Morning Open Lunch/Morning Cosed Lunch/Afternoon Open Lunch/Afternoon Cosed 20 days 0.64 / 0.22 = / 0.38 = days 0.66 / 0.26 = / 0.37 = days 0.67 / 0.32 = / 0.32 =

18 Tabe 4 Does Lunch-Hour Trading Raise the U-Shape? This tabe presents the return variance ratio for the yen/doar rate over a three periods (10:30-3:00 Tokyo time). The numerator of the ratio is the return variance after the unch-hour market opened (i.e., after December 22, 1994); the denominator is the return variance before the opening. The returns are cacuated as the change in the og of the bid-offer midpoint. The eft-hand coumn describes the ength of the before and after sampes. For exampe, the dates of the 20 day before sampe are the weekdays from November 24 to December 21, 1994 and the dates of the 20 day after sampe are the weekdays from January 4, 1995 to January 31, 1995 (hoiday week omitted). P-vaues for the ratio=1 nu are zero to two decima paces in a cases (i.e., ess than 0.5%). A-Period Variance Ratio: Sampe Open/Cosed 20 days days days

19 Tabe 5 Does Lunch-Hour Trading Tit the U-Shape? This tabe presents the return variance ratio for the yen/doar rate over the morning and afternoon periods (10:30-12:00 and 1:30-3:00 Tokyo time, respectivey). The numerator of the ratio is the return variance after the unch-hour market opened (i.e., after December 22, 1994); the denominator is the return variance before the opening. The returns are cacuated as the change in the og of the bid-offer midpoint. The efthand coumn describes the before and after sampes. For exampe, the dates of the 20 day before sampe are the weekdays from November 24 to December 21, 1994 and the dates of the 20 day after sampe are the weekdays from January 4, 1995 to January 31, 1995 (hoiday week omitted). The second coumn presents the variance ratio for the morning period. The third coumn presents the variance ratio for the afternoon period. P-vaues for the ratio=1 nu are in parentheses. Sampe Morning Variance Ratio: Open/Cosed Afternoon Variance Ratio: Open/Cosed 20 days 0.77 (0.00) 40 days 0.81 (0.00) 60 days 1.01 (0.41) 1.59 (0.00) 1.22 (0.00) 1.35 (0.00) 18

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