An empirical examination of the intraday volatility in euro dollar rates

The Quarterly Review of Economics and Finance 44 (2004) 44 57 An empirical examination of the intraday volatility in euro dollar rates Ken B. Cyree a, Mark D. Griffiths b,, Drew B. Winters c a Texas Tech University, Lubbock, TX, USA b Thunderbird, The American Graduate School of International Management, 15249 North 59th Avenue, Glendale, AZ 85306, USA c University of Central Florida, Federal Reserve Bank of St. Louis, St. Louis, MO, USA Received 22 May 2002; received in revised form 4 October 2002; accepted 25 November 2002 Abstract We examine hourly observations of one-month euro dollar rates using the GARCH model from Baillie and Bollerslev (1990) and find an intraday volatility pattern with two important components. First, intraday volatility is largest during regular business hours in the Asian markets and smallest during regular business hours in the U.S. This result is in contrast to the previously identified intraday volatility patterns in the currency exchange rates. Second, we find volatility spikes at the beginning of the business day in Tokyo, London, and New York. Currency exchanges rates also show volatility spikes at the beginning of the business day in Tokyo, London, and New York. We interpret these results as support for the model by Hong and Wang (2000) which suggests that volatility clusters at the beginning and end of the regular business day, even in the absence of market closures, if most traders are not active during regular non-business hours. 2003 Board of Trustees of the University of Illinois. All rights reserved. JEL classification: G15, G21, G28 Keywords: Intraday volatility; Empirical; Currency exchange rate Part of this research was done while Winters was a visiting scholar at the Research Department of the Federal Reserve Bank of St. Louis during 2002. The views expressed are the authors alone and are not necessarily those of the Federal Reserve Bank of St. Louis or the Federal Reserve System. Corresponding author. Tel.: +1-602-978-7612; fax: +1-602-843-6143. E-mail address: griffitm@t-bird.edu (M.D. Griffiths). 1062-9769/$ see front matter 2003 Board of Trustees of the University of Illinois. All rights reserved. doi:10.1016/s1062-9769(03)00002-4

1. Introduction K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 45 Baillie and Bollerslev (1990) examine intraday volatility in the 24-hour currency exchange markets and find a consistent intraday volatility pattern in exchange rates. They examine the intraday volatility of exchange rates in the markets for U.S. dollars exchanged into British pounds, German marks, Japanese yen and Swiss francs. They find several regularities within the 24-hour intraday pattern of exchange rate volatilities. First, the U.S. market is the most volatile while the Asian market is the least volatile. Second, the most volatile time of the day is during the U.S. morning trading hours when both the U.S. and European markets are active. Third, there is a volatility spike at the beginning of the regular business day in Tokyo, London, and New York. Andersen and Bollerslev (1998) extend Baillie and Bollerslev and find the same basic 24-hour intraday volatility pattern in exchange rates in a different sample period. Baillie and Bollerslev (1990) and Andersen and Bollerslev (1998) identify a clear and persistent intraday volatility pattern in 24-hour currency exchange markets. Our objective is to test for a 24-hour intraday volatility pattern in U.S. dollar-based short-term interest rates and compare the result to the pattern in exchange rates. However, before we begin our empirical analysis we provide an analytical discussion of our expectations for any relation between the intraday volatility in exchange rates and intraday volatility in short-term interest rates, since dollar-based exchange rates and dollar-based interest rates are both part of the interest rate parity condition. We discuss that markets linked through interest rate parity need not have the same intraday volatility effect. Then, we replicate the empirical model from Baillie and Bollerslev to identify the intraday volatility pattern in short-term interest rates and compare that result to the known pattern in exchange rates to identify similarities and differences. 1 We then discuss the comparison as to how it adds to our understanding of intraday volatility. For a 24-hour analysis, standard domestic short-term debt markets, such as the U.S. T-bill market, are not appropriate since they are not active around the clock. However, euro currency deposit markets do trade continuously. Since Baillie and Bollerslev (1990) and Andersen and Bollerslev (1998) focus on U.S. dollar exchange, we chose to analyze the market for one-month euro dollar deposits. 2 We find that euro dollar rates are most volatile during regular business hours in the Asian market and least volatile during regular business hours in the U.S. market, which is markedly different from the previously identified volatility patterns in exchange rates. Nonetheless, we find volatility is highest in euro dollar rates in Tokyo, London, and New York at the beginning of the business day in each market, which is consistent with the intraday volatility in currency exchange rates at the beginning of the regular business day in these major markets. Our results provide two contributions to the literature. First, we show that currency exchange markets and short-term debt markets linked through interest rate parity need not display the same intraday volatility pattern. Second, we show that the volatility in both short-term interest rates and currency exchange rates are highest at the beginning of the business day in the major markets around the world. Tse (1999a) finds a similar volatility spike in Japanese government bond futures at the beginning of trading in London and suggests a home bias exists in international markets. Tse concludes (p. 1856) that London traders act as though they cannot trade until the London market opens even though an almost identical contract is available in the Tokyo market. Hong and Wang (2000) offer an explanation for how a home bias in international markets creates

46 K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 volatility clustering at the open. They suggest that if most traders only trade during their regular local business hours then volatility will cluster at the beginning of the local business day as traders start each day by adjusting their portfolios for the arrival of new information over the preceding non-business day hours. 2. Interest rate parity, euro dollar market background, data, and methods 2.1. Interest rate parity and covered interest arbitrage Exchange rates and short-term risk-free interest rates both appear in the interest rate parity condition. Hence, these rates are linked through the covered interest arbitrage opportunities available when interest rate parity is violated. Accordingly, the relevant questions are: in which market (s) will the price pressures created by volatility in spot exchange rates appear as investors attempt to take advantage of covered interest arbitrage and, will that price pressure transfer the known intraday volatility effect in spot exchange rates on to short-term interest rates? One common representation of interest rate parity is: X forward X spot = 1 + r foreign 1 + r domestic (1) where X is an exchange rate for foreign currency per unit of domestic currency. Baillie and Bollerslev use U.S. dollar exchange rates and Rhee and Chang (1992) use euro dollar rates as the domestic short-term interest rate. Accordingly, we use U.S. dollars as the domestic currency. We start by assuming that markets are frictionless and that interest rate parity holds. Thus, any change in the spot exchange rate will cause a violation in the parity condition and create a covered interest arbitrage opportunity. Covered interest arbitrage requires borrowing in one country, investing in the second country, and entering in a forward (futures) exchange rate contract to unwind the transactions at a future date. The transactions in the three different markets create price pressures in each market. However, when we remember the size of the euro dollar market and its foreign counterpart, it seems unlikely that a covered interest arbitrage opportunity would be of sufficient size and duration to move interest rates. Instead, it seems much more likely that the price pressure necessary to return the markets to the parity condition would occur in the forward/futures exchange rate market. 3 We now relax the assumption of frictionless markets and introduce bid/ask spreads in the various markets. Rhee and Chang (1992) show that the introduction of bid/ask spreads changes interest rate parity from one condition (see Eq. (1)) to two conditions that must hold simultaneously. 4 Using the two conditions discussed by Rhee and Chang, it is relatively straight forward to show that high volatility in the spot exchange rate market need not create high volatility in the domestic interest rate market, even when everything else is held constant. In summary, even though exchange rates and short-term interest rates are both part of the interest rate parity condition, it appears unlikely that a volatility regularity in exchange rates will create a similar volatility regularity in short-term domestic interest rates. Thus, any 24-hour intraday volatility regularity in short-term euro dollar rates becomes strictly an empirical

K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 47 question without any prior expectation based on a link to the 24-hour intraday volatility pattern of exchange rates. 2.2. The euro dollar market This section discusses the various local markets in the 24-hour market for euro dollar deposits. The focus of the discussion will be on the importance and trading times of the various local markets. 5 The euro dollar market starts its day between 8:00 a.m. and 9:00 a.m. local time in the Far East markets of Tokyo, Singapore, and Hong Kong. The Tokyo market accounts for more than half of the euro dollar activity in the Far East. However, when compared to London and New York, the activity in the Tokyo market is relatively thin. As the day progresses, the next set of major euro dollar markets to open are in Europe. London is the dominant European market but, U.K. traders generally start their day early to catch the end of business in the Far East markets (8:00 a.m. London standard time is 5:00 p.m. Tokyo time). Historically, London was the largest euro dollar market to the point where, in the late 1970s, New York banks ran their euro dollar trading desk on London time. However, in recent years, London has given way to New York as the dominant euro dollar market. Currently, there is good liquidity during the morning session in London. The final major euro dollar market to become active is New York. New York has gained dominance for two reasons. The first reason is the development of Caribbean branches by New York banks to take off-shore dollar deposits. The second reason is the development of a successful euro dollar futures contract by the International Monetary Market (IMM) Division of the Chicago Mercantile Exchange. The best liquidity in the euro dollar market occurs during periods of IMM futures trading (8:20 a.m. to 3:00 p.m. New York time). The current importance of the New York market is such that Japanese euro dollar traders often work during the morning in New York. After the end of business in New York, there is a brief lull in the euro dollar market until the beginning of the next business day in the Far East. Euro dollars are available for trade in San Francisco during this time, but volume is very thin. 2.3. Data The data comprise hourly-sampled, offer-side broker quotes for one-month euro dollar rates. 6 The rates are the prices in this market since one-month euro dollar deposits are time deposits that trade at face value with an interest payment. The data are provided by the IMM Division of the Chicago Mercantile Exchange. The IMM collects rates hourly from 7:00 a.m. Monday in Tokyo to 4:00 p.m. Friday in New York and records these rates in their daily logs. We were able to obtain the data for the period from September 24, 1990 to January 1, 1996. Baillie and Bollerslev (1990) and Andersen and Bollerslev (1998) find volatility changes at the beginning of the business day in each of the major trading regions for foreign exchange, so it is important to identify the start of the business day in the major (Tokyo, London, and New York) euro dollar markets around the world. Table 1 provides a time reference based on Greenwich Mean Time (GMT) with labels for the 8:00 a.m. and 5:00 p.m. standard time in

48 K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 Table 1 Standard New York time and the corresponding time for London and Tokyo Greenwich Mean Time Business day times 2300 8:00 a.m. Tokyo 2400 0100 0200 0300 0400 0500 0600 0700 0800 5:00 p.m. Tokyo 8:00 a.m. London 0900 1000 1100 1200 1300 8:00 a.m. New York 1400 1500 1600 1700 5:00 p.m. London 1800 1900 2000 2100 2200 5:00 p.m. New York Tokyo, London, and New York. We start the table with 8:00 a.m. Tokyo time, because that is the beginning of the business day. Using standard time, Tokyo is 9 hours ahead of London and New York is 5 hours behind London. We use the 24-hour clock based on GMT to label the hourly variables in our model. In addition, we note (but do not present in Table 1) that New York and London observe daylight savings time during the summer while Tokyo does not. We adjust our data for daylight savings time when appropriate for our empirical tests. Table 2 provides some summary statistics on the data. Panel A presents rate levels across the day, while Panel B presents rate changes. Panel A reports the mean, standard deviation (S.D.), minimum, and maximum of the rates at each hour of the day. There are two principal results to note from these statistics. First, the mean and S.D. are quite similar across the hours. Second, the lowest maximum rates are at the New York open and the highest maximum rates are in the morning in Tokyo. Recall that in Section 2.2 we note that New York is the dominate market for euro dollars and, on a relative basis, Tokyo has the thinnest market in euro dollars. Panel B also suggests abnormal activity at the beginning of the business day with rates rising in Tokyo and falling in London. This is likely the result of the relative liquidity at these times in these markets. 7 The summary statistics in Table 2 suggest the existence of abnormal rate changes and volatility at the beginning of the business day in the major financial markets around the world. However, previous work has shown persistent time-series characteristics in short-term interest rates, which

K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 49 Table 2 Summary statistics for one-month euro dollar rates reported hourly based on New York [Eastern] time Greenwich Mean Time Mean S.D. Minimum Maximum Panel A: Rate levels 2300 (8:00 a.m. Tokyo) 4.777 1.405 3.00 10.00 2400 4.786 1.407 3.03 10.00 0100 4.806 1.409 3.03 10.53 0200 4.811 1.410 3.03 10.50 0300 4.818 1.410 3.03 10.00 0400 4.823 1.410 3.05 10.00 0500 4.825 1.407 3.05 9.87 0600 4.819 1.405 3.06 10.12 0700 4.807 1.409 3.06 10.12 0800 (8:00 a.m. London) 4.788 1.408 3.00 9.87 0900 4.787 1.405 3.03 9.56 1000 4.786 1.405 3.00 9.25 1100 4.786 1.405 3.00 9.25 1200 4.784 1.394 3.03 9.12 1300 (8:00 a.m. New York) 4.742 1.356 3.00 9.12 1400 4.840 1.421 3.03 10.00 1500 4.849 1.430 3.03 10.00 1600 4.847 1.430 3.03 10.00 1700 (5:00 p.m. London) 4.847 1.427 3.00 10.00 1800 4.843 1.424 3.03 10.00 1900 4.851 1.426 3.03 10.00 2000 4.846 1.425 3.03 10.00 2100 4.846 1.425 3.03 10.00 2200 (5:00 p.m. New York) 4.777 1.406 3.03 10.00 Panel B: Rate changes (r t r t 1 ) 2300 (8:00 a.m. Tokyo) 0.001 0.011 0.12 0.17 2400 0.010 0.053 0.81 0.44 0100 0.019 0.089 1.25 1.12 0200 0.005 0.076 0.38 1.31 0300 0.006 0.074 0.50 0.91 0400 0.005 0.046 0.31 0.69 0500 0.002 0.045 0.25 0.88 0600 0.005 0.057 0.69 0.31 0700 0.012 0.060 0.94 0.57 0800 (8:00 a.m. London) 0.020 0.063 0.47 0.31 0900 0.001 0.066 1.00 0.97 1000 0.001 0.048 0.43 0.37 1100 0.001 0.037 0.31 0.25 1200 0.003 0.048 0.25 0.43 1300 (8:00 a.m. New York) 0.005 0.046 0.37 0.31 1400 0.005 0.052 0.68 0.31 1500 0.002 0.034 0.30 0.24 1600 0.001 0.036 0.30 0.81 1700 (5:00 p.m. London) 0.001 0.027 0.25 0.27 1800 0.001 0.018 0.28 0.18 1900 0.001 0.012 0.13 0.19 2000 0.000 0.012 0.13 0.18 2100 0.000 0.010 0.13 0.13 2200 (5:00 p.m. New York) 0.002 0.036 0.87 0.19 Notes: The number of observations at each hour of the day has a range of 1223 (1300 h) to 1342 (1600 h) with the most hours having approximately 1250 rate observations. The range in the number of observations at each hour is due to missing values.

50 K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 suggests that we must utilize controls to isolate the time-of-the-day effects in the one-month euro dollar market. The model used by Baillie and Bollerslev contain controls for time-series effects and, its use will allow for the direct comparison of our intraday volatility pattern in euro dollar rates to the intraday volatility pattern they identify in exchange rates. 2.4. Methods We implement the GARCH model from Baillie and Bollerslev to allow for direct comparison of the results. The model is: y day,hour = (R day,hour R day,hour ) 100 (2) y day,hour = µ 0 + θ 1 ε day,hour 1 + ε day,hour (3) ε day,hour ψ day,hour 1 N(0,σ 2 day,hour ) (4) σday,hour 2 = γ hour + α 1 (ε 2 day,hour 1 γ hour 1) + α 2 (σday,hour 1 2 γ hour 1) + δ 1 V + η 1 ε 2 day 1,hour (5) where R day,hour is the one-month euro dollar rate with day denoting the day in the time-series and hour denoting the time within a day; V, a 0/1 dummy variables that equals 1 for the hour after a business closed holiday and 0 otherwise. The second and third terms of the conditional variance remove any conditioning effects in γ hour from the previous hour so that, apart from any deterministic effects of market closed holidays (V), γ hour is the unconditional variance for hour t. Baillie and Bollerslev refer to the final term in the conditional variance equation as a seasonal ARCH term. It captures trends in the error at the current hour from the previous day. 3. Results In this section, we present our results from estimating the model defined in Eqs. (3) and (5). After presenting our results, we compare the intraday euro dollar rate volatility to the intraday volatility pattern identified by Baillie and Bollerslev (1990). We conclude this section with a brief discussion of some additional tests intended to determine the robustness of the basic intraday pattern in euro dollar rates. 3.1. GARCH model parameter estimates Table 3 contains the results from the estimation of Eqs. (3) and (5) above as developed by Baillie and Bollerslev. The ARCH (α 1 ) parameter estimate and the GARCH (α 2 ) parameter estimate are both positive and significant at better than the 1% level. Significant ARCH and GARCH terms suggest that the variance is conditional. Specifically, a positive ARCH term suggests that trends exist in the variance and a positive GARCH term suggests that shocks to the variance are persistent. These results suggest that the hourly-sampled one-month euro dollar

K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 51 Table 3 Results from estimating the Baillie and Bollerslev model on hourly one-month euro dollar rates Variables Parameter estimates p-values γ hour size ranks µ 0 (intercept) 0.0192 <0.0001 θ 1 0.1839 <0.0001 α 1 (ARCH) 0.5070 <0.0001 α 2 (GARCH) 0.2309 <0.0001 δ 1 (vacation) 0.9692 <0.0001 η 1 (seasonal ARCH) 0.1318 <0.0001 γ 1 5.6578 <0.0001 1 γ 2 4.1262 <0.0001 9 γ 3 3.6757 <0.0001 γ 4 5.2990 <0.0001 2 γ 5 4.6423 <0.0001 5 γ 6 4.3329 <0.0001 7 γ 7 3.7573 <0.0001 γ 8 4.8540 <0.0001 4 γ 9 4.5742 <0.0001 6 γ 10 4.9226 <0.0001 3 γ 11 4.2172 <0.0001 8 γ 12 3.7756 <0.0001 10 γ 13 3.2472 <0.0001 γ 14 3.0794 <0.0001 γ 15 2.6668 <0.0001 γ 16 2.6323 <0.0001 γ 17 2.5779 <0.0001 γ 18 2.5128 <0.0001 γ 19 2.5218 <0.0001 γ 20 2.7183 <0.0001 γ 21 2.5201 <0.0001 γ 22 2.4343 <0.0001 γ 23 3.1919 <0.0001 γ 24 2.7184 <0.0001 Mean equation: y day,hour = µ 0 + θ 1 ε day,hour 1 + ε day,hour Variance equation: σ 2 day,hour = γ hour + α 1 (ε 2 day,hour 1 γ hour 1) + α 2 (σ 2 day,hour 1 γ hour 1) + δ 1 V + η 1 ε 2 day 1,hour with variables as defined in Section 2.4. rates have time-series characteristics that must be controlled to isolate the hourly effects in euro dollar rate volatility. 3.2. Hourly time-of-the-day results Baillie and Bollerslev refer to the γ hour parameters in their model as the unconditional variance for each hour of the day. In other words, after removing the time-series effects the γ hour parameters provide the volatility effect based on the time of the day.

52 K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 In the conditional variance equation, all 24 γ hour parameters are positive and significant at better than the 1% level. Accordingly, we will focus on the magnitude of the parameter estimate, so in the last column of Table 3 we identify the 10 largest γ hour estimates. The largest γ hour estimate is at 10:00 a.m. Tokyo time (recall that the Asian markets start their day between 8 a.m. and 9:00 a.m., so our 10:00 a.m. estimates represents the first full hour of the regular business day) and, 6 of the 10 largest γ hour estimates occur during regular Tokyo business hours suggesting that the Tokyo market is the most volatile. The least volatile market is the New York market. None of the 10 largest γ hour estimates occurs between 8:00 a.m. and 5:00 p.m. New York time making New York the only major market without one of the 10 largest γ hour estimates. Recall, our discussion of the euro dollar market in Section 2.2 indicated that the best liquidity in the euro dollar market occurs during IMM euro dollar future trading, which occurs from 8:20 a.m. to 3:00 p.m. New York time, and high liquidity should reduce volatility. 8 Interestingly, London is highly volatile in its morning hours before regular New York business hours, but becomes substantially less volatile when regular business hours in London and New York overlap. Further, the largest γ hour estimates in each major market are at the beginning of the business day. The largest γ hour estimate during regular Tokyo business hours (and overall) is at 10 a.m. (covering the time from 9:00 a.m. to 10:00 a.m.). The largest γ hour estimate between 8:00 a.m. and 5:00 p.m. London time occurs at 10:00 a.m. London time. However, recall that London traders often start early to catch the last hour of the regular business day in Tokyo. The γ 8 estimate covers this hour of the day. The γ 8 estimate is the fourth largest γ hour estimate overall and is larger than any of the γ hour estimates between 8:00 a.m. and 5:00 p.m. London time. The largest γ hour estimate between 8:00 a.m. and 5:00 p.m. New York time is the γ 14 estimate which covers the hour from 8:00 a.m. to 9:00 a.m. In summary, the γ hour estimates suggest high volatility across the day in Tokyo, during the London morning hours before the beginning of regular business hours in New York, and at the beginning of the business day in each of the major euro dollar markets. 3.3. Comparison to the intraday exchange rate volatility pattern Having identified the intraday volatility pattern in hourly one-month euro dollar rates, we now compare our results to the previously identified pattern in exchange rates. The purpose is to determine the similarities and differences in the intraday volatility patterns. Baillie and Bollerslev (1990) examine intraday volatility in the foreign exchange markets of U.S. dollars for British pounds, West German deutsche marks, Swiss francs, and Japanese yen, and find a consistent result across the four currencies. They find large increases in volatility around the open of trading in London and New York and, persistent high volatility throughout the morning hours in New York during the time when regular business hours overlap in London and New York. Using a different sample period, Andersen and Bollerslev (1998) find the same intraday volatility pattern in the deutsche mark/u.s. dollar exchange market. This does not match our results for intraday volatility in the euro dollar market. To show the difference in intraday volatility patterns between the exchange rate markets and the euro dollar deposit rate market, we provide Figs. 1 and 2. Our Fig. 1 is a reproduction of Fig. 2 from Baillie and Bollerslev (1990, p. 575). The figure presents the intraday volatility of the deutsche mark/u.s.

K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 53 Fig. 1. dollar exchange rate and is representative both, of all the intraday volatility patterns presented by Baillie and Bollerslev and, of the intraday volatility pattern for deutsche mark/u.s. dollar exchange rates presented by Andersen and Bollerslev (1998) in their Fig. 4. Fig. 2 plots our γ hour estimates from the conditional variance equation reported in Table 3. We divide our γ hour estimates by 100 and fix the range of the y-axis from 0.00 to 0.08 to provide as direct a comparison as possible with the figure from Baillie and Bollerslev. Fig. 1 shows high exchange rate volatility at the hours of 0800 and 0900 (8:00 a.m. and 9:00 a.m. London time) and for the hours1300 to 1900 (8:00 a.m. to 2:00 p.m. New York time). The intraday pattern during U.S. market hours forms an inverted U pattern with volatility increasing across the U.S. morning hours with a peak at 12 noon New York time (5:00 p.m. London time) and then declining in the afternoon. Fig. 1 also shows a spike at 0100 (10:00 a.m. Tokyo time), but the spike during Asian market hours is smaller than the morning volatility in either London or New York. The Asian market hours appear to be the low volatility time of the day in exchange rates. Fig. 2.

54 K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 Our results for euro dollars presented in Fig. 2 shows the largest volatility spike at the 0100 (10:00 a.m. Tokyo time) hour with additional large hourly volatility across the Tokyo business day (hours 2300 to 0800) in direct contrast to the currency exchange markets. Fig. 2 shows additional high volatility for hours 0900 to 1200 (9:00 a.m. to 12:00 noon London time), which covers regular business hours only in the London market. The London afternoon, which overlaps with the New York morning, is a period of declining volatility. The volatility pattern in euro dollar rates during regular London business hours again is in stark contrast to the volatility pattern in exchange rates. Finally, both figures show that volatility is highest near the beginning of the regular business day in each of the major markets. We use the exchange rate results in Baillie and Bollerslev (1990) for comparison to our euro dollar rate results even though their sample period predates our sample period. However, the exchange rate regularity identified in Baillie and Bollerslev is consistent with that reported in Andersen and Bollerslev. The sample period covered in this latter study (October 1, 1992 to September 30, 1993) is contained within our sample period. Since our data period contains the Andersen and Bollerslev sample period, we believe that any difference in the intraday pattern between exchange rates and euro dollar deposit rates would not be the result of different sample periods. 3.4. Robustness checks for the identified intraday volatility pattern Andersen and Bollerslev (1998) extend the hourly dummy variable model in Baillie and Bollerslev (1990) to include other timing effects for volatility. In addition, verifying the identified 24-hour volatility pattern in exchange rates, they find significant volatility effects in exchange rates: at U.S. economic announcements, at Bundesbank meetings, at the beginning of business in Tokyo, at market closed holidays, and for the summer shift to daylight savings time. Numerous studies also find quarter-end and year-end effects in the various short-term debt markets (see, for example, Allen and Saunders, 1992; Hamilton, 1996; Griffiths and Winters, 1997; Musto, 1997). Ederington and Lee (2001) find day-of-the-week effects in euro dollar futures contracts. Finally, Ederington and Lee (2001) in euro dollar futures contracts and Tse (1999b) in stock index futures contracts also find volatility spikes around U.S. macro-economics news announcements. Accordingly, we need to verify that our intraday volatility pattern is not the result of these other effects. After controlling for these other effects, we find no evidence to suggest a qualitative change in our intraday volatility pattern for one-month euro dollar rates. 9 4. Implications of our results We began our analysis by suggesting that it was unlikely that any link of the currency exchange markets and the short-term debt markets through interest rate parity would cause the same intraday volatility pattern in exchange markets and the short-term debt market. Our empirical results indicate that the intraday volatility patterns are quite different in these two markets. Thus, as expected, we find no evidence of commonality in intraday volatility between these markets operating through interest rate parity. However, we do find that euro dollar rate

K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 55 volatility is highest at the beginning of the regular business day in each of the major markets and that this is common to the exchange markets. We believe the high volatility at the beginning of the regular business day across these markets has important implications for the understanding of the intraday volatility clustering identified in the market micro-structure literature that we discuss below. 4.1. The importance of volatility clustering at the beginning of the business day A large and growing body of literature identifies a U-shaped intraday volatility pattern in markets that close daily. Attempts to explain the U-shaped intraday volatility pattern fall into two basic groups: (1) asymmetric private information (Admati and Pfleiderer, 1988; Slezak, 1994) and (2) market closures (Brock and Kleidon, 1992). Recently, Cyree and Winters (2001) show that asymmetric private information is not a necessary condition for a U-shaped intraday volatility pattern and suggest that market closures is a sufficient condition to create volatility clustering at the open and close of the trading day. However, Hong and Wang (2000) suggest that markets need not close to create volatility clustering. Instead, they suggest that having most traders cease trading during regular non-business hours is sufficient to create volatility clustering at the beginning and end of the regular business day. That is, Hong and Wang suggests that traders in local markets have regular business hours during which they conduct their activities. At the end of the regular business hours these traders cease trading for the day when they have achieved positions with which they are comfortable for the overnight period. Then, the local traders resume trading at the beginning of the regular business hours on the next business day adjusting their positions for the information that arrived during their non-business hours. This activity during the regular business day can create volatility clustering at the beginning and ending of the day even in the absence of an official market closure. We interpret the volatility spikes in euro dollar rates and currency exchange rates at the beginning of the regular business in the major markets around the world as support for Hong and Wang (2000). Our lack of high volatility at the end of the regular business day may result from the fact that, without market closure, local traders who do not hold their desired end-of-business-day position can continue to trade thereby spreading any end-of-the-day trading pressure over a longer period. 5. Conclusion We examine hourly-sampled one-month euro dollar rates using the model by Baillie and Bollerslev (1990) to determine if a 24-hour intraday volatility pattern exists in short-term interest rates. We find euro dollar rates are most volatile during the Asian business hours and least volatile during the U.S. business hours. We note that this pattern contrasts with the known pattern in the currency exchange rates, which are most volatile during U.S. business hours and least volatile during Asian business hours. In addition, we find high volatility at the beginning of the regular business day in Tokyo, London, and New York. We note that volatility is also high at the beginning of the business day in Tokyo, London, and New York for the currency exchange rates. We conclude that the common spikes at the beginning of regular business day

56 K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 in Tokyo, London, and New York have important implications for the understanding of intraday volatility clustering and suggest that high volatility at the beginning of the business in the major global financial markets supports the model by Hong and Wang (2000) that suggests volatility will cluster at the beginning and end of the regular business day if, most traders do not trade during non-business hours. The implication of our empirical results in the context of Hong and Wang s model is that although financial markets may become more global, they are likely to retain local components associated with regular local business hours. Notes 1. Note that to model the interaction between exchange rates and interest rates explicitly, every exchange rate and interest rate would have to be modeled simultaneously due to triangular arbitrage. This is beyond the scope of this paper. 2. We note that Rhee and Chang (1992) use euro dollar rates as the short-term domestic interest rate in their analysis of interest rate parity and covered interest arbitrage. 3. Kyriacou and Sarno (1999) find strong evidence of significant simultaneity between spot-market volatility and derivative trading. Also, Fung, Leung, and Xu (2001) state that they use financial futures contracts to study information flows because of the relative ease of arbitrage using futures. 4. The parity conditions from Rhee and Chang (1992) with bid/ask spreads are and F a S b [ 1 + rb 1 + r a F b S a [ 1 + ra 1 + r b ] ] where a, ask rate; b, bid rate; F y, forward exchange rate; S y, spot exchange rate; r y, euro dollar interest rate (as a proxy for domestic short-term default-free interest rate); and ry, euro foreign currency interest rate, where y = a or b as appropriate. 5. Our discussion of the euro dollar market draws heavily from Stigum (1990), Chapter 18. 6. We do not have access to spread data, nor do we know of any source of spread data that covers the large sample period covered by our data. In addition, comparisons with the existing exchange rate literature, such as Baillie and Bollerslev (1990) and Andersen and Bollerslev (1998), is more direct using a time series of rates instead of the bid/ask spread. 7. Fung, Leung, and Xu (2001) find that 76.2% of U.S. dollar yen trading occurs in Japan. 8. One definition of liquidity is the ability to trade at the equilibrium price, which means a highly liquid market can absorb high volume without large price movements. Thus, we associate the most liquid euro-dollar market with low volatility. 9. Not reported in the interest of brevity but available upon request.

Acknowledgments K.B. Cyree et al. / The Quarterly Review of Economics and Finance 44 (2004) 44 57 57 We thank Bruce Frost of IMM Division of the Chicago Mercantile Exchange for making available the data used in this paper. We also thank Campbell Harvey for insightful comments. References Allen, L., & Saunders, A. (1992). Bank window dressing: Theory and evidence. Journal of Banking and Finance, 16, 585 623. Admati, A., & Pfleiderer, P. (1988). A theory of intraday patterns: Volume and price variability. Review of Financial Studies, 1, 3 40. Andersen, T., & Bollerslev, T. (1998). Deutsche mark dollar volatility: Intraday activity patterns, macroeconomic announcements, and longer run dependencies. Journal of Finance, 53(1), 219 265. Baillie, R., & Bollerslev, T. (1990). Intra-day and inter-market volatility in foreign exchange rates. Review of Economic Studies, 58, 565 585. Brock, W., & Kleidon, A. (1992). Periodic market closure and trading volume: A model of intraday bids and asks. Journal of Economic Dynamics and Control, 16, 451 489. Cyree, K., & Winters, D. (2001). An intraday examination of the federal funds market: Implications for the theories of the reverse-j pattern. Journal of Business, 74, 535 556. Ederington, L., & Lee, J. (2001). Intraday volatility in interest-rate and foreign-exchange markets: ARCH, announcement, and seasonality effects. Journal of Futures Markets, 21, 517 552. Fung, H., Leung, W., & Xu, X. (2001). Information role of US futures trading in a global financial market. Journal of Futures Markets, 21, 1071 1090. Griffiths, M., & Winters, D. (1997). On a preferred habitat for liquidity at the turn-of-the-year: Evidence from the term-repo market. Journal of Financial Services Research, 12, 21 38. Hamilton, J. (1996). The daily market for federal funds. Journal of Political Economy, 104, 26 56. Hong, H., & Wang, J. (2000). Trading and returns under periodic market closures. Journal of Finance, 55, 297 354. Kyriacou, K., & Sarno, L. (1999). The temporal relationship between derivative trading and spot market volatility in the UK: Empirical analysis and Monte Carlo evidence. Journal of Futures Markets, 19, 245 270. Musto, D. (1997). Portfolio disclosures and year-end price shifts. Journal of Finance, 52, 1563 1588. Rhee, S., & Chang, R. (1992). Intra-day arbitrage opportunities in foreign exchange and eurocurrency markets. Journal of Finance, 47, 363 379. Slezak, S. (1994). A theory of the dynamics of security returns around market closures. Journal of Finance, 49, 1163 1211. Stigum, M., 1990. The money market. Homewood, IL: Dow Jones-Irwin. Tse, Y. (1999a). Round-the-clock market efficiency and home bias: Evidence from the international Japanese government bonds futures markets. Journal of Banking and Finance, 23, 1831 1860. Tse, Y. (1999b). Market microstructure of FT-SE 100 index futures: An intraday empirical analysis. Journal of Futures Markets, 19, 31 58.