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A note on weekday, intraday, and overnight patterns in the interbank foreign exchange and listed currency options markets
Journal
of Banking
and
Finance
16 (1992)
1159-l 171. North-Holland
A note on weekday, intraday, and overnight patterns in the interbank foreign exchange and listed currency options markets* Jimmy E. Hilliard Vniversiry
of Georgia,Athens, GA 30602, USA
Alan L. Tucker Temple University, Philadelphia, PA 19122, USA Received April 1991, final version received
February
1992
Transactions data are used to investigate returns patterns for close-to-close, close-to-open, and intraday long positions in spot currency (interbank) and currency put options (listed) for the years 1983 through 1988. Both trading-day and calendar-day hypotheses are investigated. Under the former, spot market returns are found to be significantly higher from Friday close to Monday close and from Friday close to Monday open. Under the calendar-day hypothesis, however, no significant close-to-close pattern emerges, and the Friday close to Monday open effect is reversed. Finally, spot (put) market returns are found to be significantly lower (higher) for Tuesday and Friday afternoons.
1. Introduction
Empirical research over the last decade has documented persistent patterns of return and their volatilities for several financial assets, especially common stock. See Flannery and Protopapadakis (1988) for a bibliography. Trading day effects in foreign exchange prices have been studied by McFarland et al. (1982) and Levi (1978). These studies focus on empirical regularities of asset returns and their volatilities in order to develop better equilibrium asset pricing models and to examine issues related to the efficiency of securities markets. Continuing in this spirit, this study undertakes an investigation of weekly, intraday, and Correspondence to: Professor Jimmy E. Hilliard, G. Herman and Mary Virginia Terry Chair of Business, Banking and Finance Department, University of Georgia, Athens, GA 30602, USA. Tel. (706) 542-3646. *We thank Larry Lockwood, David Peterson, and two anonymous referees for helpful comments. 0378-4266,‘92/.%05.00
C 1992-Elsevier
Science Publishers
B.V. All rights reserved
1160
J.E. Hilliard and AL. Tucker, Patterns in the interbank foreign exchange markets
overnight returns patterns in the foreign exchange market and, relatedly, the currency options market, while utilizing transactions data for the US dollar price of three foreign currencies for the calendar years 1983 through 1988. This investigation is undertaken with respect to both the trading-day hypothesis, which treats Friday to Monday returns in an identical manner to other weekday or overnight retutns, and the calendar-day hypothesis, which recognizes that the return on an asset is a function of both the calendar time over which the investment is made and the risk borne over that period of time. It is particularly interesting to examine intraweek returns in the interbank market, because of the market’s current and unique practice of settling all transactions on the same day that they occur. Thus, any particular weekday or overnight pattern found in this market under the trading-day hypothesis would suggest that similar patterns documented in other securities markets are likely not solely attributable to their delayed settlement procedures [cf. Lakonishok and Levi (1982)l.l Under the trading-day hypothesis, percentage changes in spot interbank exchange rates are found to exhibit discernible weekday, interday, and overnight patterns. Specifically, dollar-foreign currency returns are significantly higher from Friday close to Monday close than for other weekdays, returns are significantly higher from Friday close to Monday opening than for other overnight periods, and returns are significantly lower for some late intraday periods, especially on Fridays. Together, these patterns support the ‘safe dollar hypothesis’ of McFarland et al., which contends that there is a flow into dollars before the weekend because the dollar is a safe short term store of value. We do not find any other particular weekday or overnight effects, suggesting that the high Wednesday and low Thursday returns documented by McFarland et al. and Levi were indeed attributable to settlement procedures that existed in the interbank market prior to October 1981. For our sample period, all interbank currency transactions are settled the same day. Thus, foreign exchange rates no longer reflect the fact that, before October 1981, dollars moving through the payment system became usable a trading day later than other currencies. Returns for currency put options generally exhibit consistent patterns, further attesting to the documented inextricable linkages between derivative securities and their underlying assets [cf. Bhattacharya (1987)]. significant Under the calendar-day hypothesis, however, no statistically weekday pattern emerges, and the high Friday close to Monday open effect IThere are other interesting reasons for investigating seasonaiity in the foreign exchange market. For instance, examining exchange rates and currency option prices guards against data snooping, that is. the possibility that reported findings for equities results merely from extensive and repeated analyses of the same data (CRSP tapes) [see Lakonishok and Smidt (1988)]. In addition, determining whether seasonal patterns are similar for currency and other assets should provide insight into hypotheses regarding the origins of the patterns.
J.E. Hilliard and A.L. Tucker, Patterns in the interbank foreign
exchange
markets
1161
is reversed. Of course, the intraday patterns reported under the trading-day hypothesis are unaffected. This evidence strongly suggests that other investigations of anomalous intraweek effects [e.g. McFarland et al. (1982)] may have to be reinterpreted under the calendar-day hypothesis. This study proceeds as follows. Section 2 describes the data used, while empirical results are provided in section 3 (trading-day hypothesis) and section 4 (calendar-day hypothesis). Section 5 offers a brief conclusion.
2. Data The major data source is the Philadelphia Stock Exchange (PHLX) currency options data base, which lists every option from December 1982 (the start of trading) through December 1988 for up to seven major trading currencies, including the Japanese yen, British pound, and German mark. There are nearly 500,000 records of transactions which are time and date stamped (to the minute), each indicating the number of contracts traded, the underlying currency, and the option’s premium, exercise price, and expiration date. Also recorded for each transaction are the underlying spot, bid, and ask exchange rates. The bid and ask exchange rates are provided by Telerate and represent the last interbank quotes available before the option’s transaction time. The ‘spot’ exchange rate is internally generated at the PHLX, and represents an average of the last five or six bid and ask rates provided by Telerate prior to the recorded transaction time. Over the sample period, the trading session opened at 8:OOa.m. and closed at 2:OOp.m. eastern time. For the purpose of constructing intraday spot market returns for each currency, we define three intraday periods: (1) opening option trade (approximately 8:OOa.m.) to approximately 10:OOa.m.; (2) approximately 10:OOa.m. to approximately 12:00 noon; and (3) approximately 12:00 noon to closing option trade (approximately 2.30p.m.). For the purpose of constructing these returns, any option trade occurring near the designated times will suffice, since the variable of interest is the recorded underlying interbank exchange rate. For weekday returns (close-to-close), the exchange rates underlying the closing options trades are employed, while for overnight returns (close-to-open), the exchange rates underlying the closing and subsequent opening option trades are employed. If no currency option trades within ten minutes of 8:OOa.m.. lO:OOa.m., 12:OOnoon, or 2:30p.m., the corresponding return measures are omitted from the analysis. This occurs infrequently, however, since an average of nearly 15 option trades occur per hour over the sample period. Trading days following holidays are excluded from the sample, ensuring weekday returns being measured over (approximately) 24-hour or 72-hour periods, and overnight returns being measured over (approximately) 17.5-hour of 65.5-hour per-
J.B.F.-
F
1162
J.E. Hilliard and A.L. Tucker. Patterns in the interbank foreign
exchange markers
iods.’ When computing all interbank spot market returns, the spot rates as generated internally at the PHLX are employed. Nearly identical results obtain when using the average of the recorded bid and ask exchange rates provided by Telerate.3 Computing returns for currency option holdings is more complicated because the same option series (i.e., options with the same underlying currency, exercise price and expiration date) must be employed. We compute weekday, intraday, and overnight returns separately for all possible long positions in yen, pound, and mark put options, provided that options of the same series are available within ten minutes of the designated trading times. Options with less than one week to expiration are never employed, and observations are omitted if the required option series is unavailable. As expected, this occurs more frequently than with the computation of spot market returns, since the additional constraint of using the same option series is imposed. Finally, the reported option premium is the actual trade price, and it is not possible to discern if the trade emanated from an order to buy or sell. 3. Empirical results: Trading-day
hypothesis
Under the trading-day hypothesis, weekend returns (Friday close to Monday close and Friday close to Monday open) are treated in an identical manner as other weekday and overnight returns. To investigate this hypothesis, for each time interval examined, mean returns and their standard deviation are computed. Further, various patterns of intertemporal returns are tested through progressing returns on a set of dummy variables. 3.a.
Weekday
returns
Panel A in table 1 reports weekday (close-to-close) results for long positions in spot currencies and currency put options for the sample period. All mean spot (option) returns are positive (negative), due to the substantial decline in the dollar’s value from 1983 through 1988. For example, during this six-year period, the dollar depreciated by more than fifty percent against the yen. Assuming 250 trading days per year, the (compounded) appreciation of the yen was nearly 0.0008 per day for the sample period, implying positive (negative) returns to investors with long positions in spot yen (yen puts). The dollar also depreciated against the pound and mark. For spot yen, the Friday close to Monday close mean return (0.00091) is higher than the other weekday returns. This result is corroborated by the F5 zPeriod adjustments associated with changes in daylight savings time are not considered. 3For other studies that employ intraday foreign exchange rate data. see Engle et al (1990), Goodhart and Figliuoli (1991). Muller et al. (1990). and Wasserfallen and Zimmerman (1985).
J.E. Hilliard
and A.L. Tucker,
Patterns
in the interhank
Table Returns Friday to Monday
security Panel
A: Weekday
Spot yen Yen puts
Monday to Tuesday
-0.00961 (1.831) 0.0056 (0.284)
0.00055 (0.240) -0.00318 (1.607) 0.00037 (0.233) -0.00216 (1.738)
puts
- 0.00608 ( 1.974)
Spot marks
o.c0O73 (0.304)
0.00043 (0.25 1)
- 0.00764 (1.739)
- 0.00257 ( 1.509)
Pound
Mark
puts
Panel
B: Overnight
Spot yen Yen puts Spot pounds
the trading-day Tuesday to Wednesday
hypothesis, Wednesday to Thursday
0.00042 (0.247) -0.00612 (1.692) 0.00030 (0.239) -0.00388 (1.740) 0.00034 (0.249) -0.00439 (1.607)
O.OQO46 (0.231) -0.00581 (1.658)
Thursday to Friday
Test statistics F\
Fi
F;
6.36*
0.58
1.02
3.82’
1.14
3.78.
6.22’
0.69
1.11
4.04*
1.20
3.78’
6.02’
0.55
0.91
3.47*
1.23
6.49’
1X02*
1.29
2.95*
7.00
1.91
4.21’
9.63*
1.08
2.86’
5.71’
1.46
0.00044 (0.209)
6.31’
10.54;
1.38
- 0.00408 ( 1.622)
2.69,
6.44*
1.83
0.00039 (0.239)
0.00026 (0.23 1)
- 0.00374 ( 1.697)
-0.00381 (1.686)
o.ooo37 (0.240)
0.00033 (0.242)
- 0.00449 (1.581)
-0.00417 (1.520)
4.01
l
(close-to-open)
O.cQ114’ (0.241)b -0.00712 (1.741) 0.00050 (0.237)
0.00082 (0.180) - 0.00209 (1.409)
o.wO69 (0.197) -0.00416 ( I .685)
0.0006 (0.205) - 0.00488 (1.733)
o.OQO3I (0.206)
0.00032 (0.195)
0.00027 (0.191)
- 0.0022 1 (1.422)
- 0.00309 (1.491)
- 0.00296 (1.400)
Spot marks
0.0092 (0.247)
O.ocQ66 (0.196)
0.00058 (0.205)
0.00049 (0.213)
puts
1163
1983-1988.
-0.00539 (1.599)
0.00028 (0.277)
-0.00513 (1.627)
Mark
markets
1
puts
Pound
exchange
(close-to-close)
0.00091’ (0.299)b
Spot pounds
under
foreign
-0.00572 (1.807)
-0.00166 (1.312)
-0.00358 I 1.505)
‘Mean return. bStandard deviation in parentheses. ‘Fs is the F-statistic testing the difference dfM is the F-statistic testing the difference ‘F, is the F-statistic testing the difference *Significant at the 0.05 level.
-0.00391 (1.591)
I
o.oGO52 (0.204) -0.00526 (1.624) 0.00028 (0.193) -0.00310 ( 1.466)
in means across the live days. in means for Monday from other days. in means for across Tuesday through Friday.
1164
J.E. Hilfiard and AL. Tucker, Patterns in the interbank foreign exchange markets
test statistic (4.01) and the F, test statistic (6.36).’ Similar results obtain for the pound and mark. Higher Monday returns for dollar-denominated foreign exchange long positions were also found by Levi (1978) and McFarland et al. (1982). The latter study also found a Wednesday-Thursday effect that the authors associate with settlement procedures that existed in the foreign market during their sample period. Specifically, dollars moving through the payment system became usable a trading day later than other currencies prior to October 1981. Since it then took two trading days to clear a foreign currency, purchases of foreign currency on Wednesday were delivered on Fridays, but purchases of dollars on Wednesdays were not delivered until the next Mondays. Thus, purchasers of dollars were giving sellers a longer, fiveday interest-free loan on Wednesdays than on the other weekdays, implying a lower dollar price on Wednesdays to compensate dollar purchasers. However, our F, test statistics suggest that there are no significant differences in mean returns across Tuesday through Friday for any currency for our sample period. Currently, all interbank currency trades are cleared on the same day through the Clearing House Interbank Payment System (CHIPS). The weekday results for long yen put positions are consistent with spot market results, with Monday returns (-0.00961) relatively lower than other weekdays (F,=3.82). As expected, the standard deviations of put returns are substantially greater than those of spot returns. Similar resufts obtain for the pound and mark. Consistent with results related to other financial markets (cf. Harris (1986) and Peterson (1990)], Friday close to Monday close return volatility is greater than for other weekdays for both spot and option markets.
3.6. Uvernjgh~ returns
Panel B in table 2 reports analogous results for overnight (close-to-open) positions. For spot yen, the Friday close to Monday open (weekend) return is signi~cantly higher (0.~114~ than for other overnight periods (F,=6.49 and F,= 12.02). Thus, the higher Monday return reported in panel A is largely attributable to a higher weekend return. The Tuesday through Friday overnight returns are insignificantly different (F,= 1.29). and the weekend return volatility (0.241) in generalfy greater than that of other overnight ‘The test statistic F, is derived from a regression of returns on five dummy variables, each representing a weekday. FM is derived from a regression of returns on two dummy variables, one representing Monday and the other Tuesday through Friday. F, is derived from a regression OF returns on four dummy variables, with Monday returns omitted. Results and inferences for the option market should be interpreted cautiously since option returns are bounded below, implying that returns are skewed and that normal distribution theory may not be applicable.
and A.L. Tucker, Patterns in the interbank foreign exchange markets
J.E. Hilliard
Table Intraday
spot returns
1165
2
( x 100).1983-1988. Test statistics
Interval
Mondav
Panel A: Japanese
Tuesdav
Wednesday
Thursday
Friday
FE,
Fljj
F;
yen puts
1. Open-IO:00
0.00275’ (0.323)b
0.00201 (0.442)
0.00191 (0.459)
0.00239 (0.352)
0.00256 (0.360)
1.61
2.89.
1.49
2. lO:OO-12:oO
0.00316 (0.275)
0.00238 (0.410)
0.00213 (0.430)
O.OQ280 (0.3 19)
0.00228 (0.346)
1.40
2.38’
0.94
3. 12:O&Close
0.00270 (0.3 IO)
0.00087 (0.706)
0.0022 (0.429)
0.00247 (0.407)
O.ooO77 (0.879)
3.22”
5.01.
3.06*
I
FrALL
0.55
3.19*
1.00
I .40
3.70’
F:
0.37
1.32
0.70
1.19
2.13’
F:
0.34
1.18
0.48
1.42
1.17
p,
0.30
3.19*
0.99
0.78
5.29,
Panel
B: British pounds
1. Open-IO:00
0.00184 (0.3 17)
0.00136 (0.364)
0.00125 (0.371)
0.00157 (0.331)
0.00170 (0.351)
1.47
2.63.
1.22
2. lO:OO-12:00
0.00212 (0.251)
0.00160 (0.331)
0.00144 (0.358)
0.00174 (0.299)
0.00147 (0.329)
1.18
2.29’
0.90
3. 12:~Close
0.00181 (0.298)
O.OC060 (0.582)
0.00117 (0.361)
0.00161 (0.364)
0.00052 (0.707)
2.96,
4.82’
2.90.
0.00215 (0.35 1)
1.42
2.76’
1.35
F ALL
0.42
2.91.
0.92
1.27
4.02* 2.36
F,
0.29
I.21
0.66
1.09
F,
0.3
I .05
0.4
1.35
1.09
FJ
0.25
3.00*
1.03
0.64
5.28’
I
1
Panel C: German marks 1. Open-IO:00
0.00224 (0.361)
0.00171 (0.470)
0.00157 (0.488)
0.00196 (0.370)
2. lO:OO-12:OO 0.00253 (0.294)
0.00191 (0.436)
0.00174 (0.397)
0.0024 (0.305)
1
0.00191 (0.330)
1.29
2.228
0.90
3. IZ:OO-CIose
o.OOlN5 (0.836)
0.00177 (0.441)
0.0020 (0.388)
I
0.00089 (0.724)
3.04’
4.02’
2.73’
0.00206 (0.334)
F ALL.
0.79
3.728
1.16
1.26
3.21*
F,
0.40
1.41
0.89
0.94
2.30;
F,
0.38
1.26
0.43
1.11
1.09
F,
0.38
3.48;
1.00
0.77
4.77.
‘Mean return ( x 100). %tandard deviation in parentheses. ‘F, is the F-statistic testing the digerence in means across the five days. “F, is the F-statistic testing the difference in means for Monday from other days. ‘F, is the F-statistic testing the difference in means for across Tuesday through Friday. testing the difference in means across three time intervals. ‘F*U_ is the F-statistic sF, is the F-statistic testing the diITerence in means for interval 1 from intervals 2 and 3. “F‘, is the F-statistic testing the diNerence in means for interval 2 from intervals 1 and 3. ‘F, is the F-statistic testing the difference in means for interval 3 from intervals I and 2. *SigniIicant at the 0.05 level.
1166
J.E. Hilliard
and A.L.
Tucker,
Patterns
in the interbank
foreign
exchange
markets
periods. Returns for long positions in yen put options are generally consistent with overnight returns in the spot market. Weekend option returns (-0.00712) are significantly lower (F, =2.95 and F, = 7.00), while Tuesday through Friday overnight returns are not significantly different at the 0.10 level (F,= 1.91). Again, similar results obtain for the pound and mark. Finally, a comparison of the corresponding standard deviations reported in table 1 suggests that close-to-close returns are slightly more volatile than close-to-close returns in both markets.
3.~. Intrada_v returns Intraday results for spot currencies and currency puts are reported in tables 2 and 3, respectively. For spot yen, Monday intraday returns tend to be relatively higher than corresponding intraday returns for other weekdays. The F, test statistics are 2.89 (interval l), 2.38 (interval 2), and 5.01 (interval 3). This result suggests that not all of the Monday effect reported in table 1, panel A is attributable to the weekend return (panel B). Also, interval 3 (12:00-close) returns tend to differ by weekday (F,=3.22 and F,=3.06). This result is likely due to the unusually low Tuesday and Friday interval 3 returns. For Tuesday, the F,,, test statistic is 3.19 and the FJ test statistic is 3.19, indicating that afternoon returns are lower than for earlier intraday periods.’ For Friday, FALL= 3.70 and F,=5.29, indicating that Friday afternoon returns are significantly lower than earlier intraday returns, at the 0.05 level. Once again, similar results obtain for the pound and mark. Both of these currencies exhibit higher Monday intraday returns and lower Tuesday and Friday afternoon returns. Finally, a comparison of standard deviations within each weekday suggests that volatility takes on a U-shaped pattern for each currency, with standard deviations generally higher during intervals 1 and 3. Such a U-shaped intraday volatility pattern is also found in the stock market [cf. Harris (1986) and Lockwood and Linn (199O)J Regarding long put positions (table 3), returns are generally lower for all Monday intraday intervals, and returns are also significantly higher (less negative) for Tuesday and Friday afternoons. However, some inconsistency between spot and option returns exists, particularly in Fridays. For example, Friday interval 1 yen put returns are unusually high (F, =3.30), as are Friday interval 2 put returns (F2 = 2.95). The same inconsistencies appear for the pound and mark. These results are not attributable to Friday expiration
‘The test statistic FALL is derived from a regression of returns on three dummy variables, each representing an intraday time interval. The F-statistics F,, F,, and F, are derived from a regression of returns on two dummy variables.
I.E. Hilliard and A.L. Tucker. Patterns in the interbank foreign exchange markets Table Intraday
option
1167
3
returns
( x 100).1983-1988.
Wednesday
Thursday
Test statistics Interval
Mondav
Tuesday
Friday
F:
Fd,
F:
Panel A: Japanese yen puts I. Open-IO:00
-0.01125” (0.747)b
- 0.00972 (0.940)
2. 10:0&12.:00
-0.01207 (0.772)
- 0.0094 (0.611)
3. 12:~Close
-0.01380 (0.912)
F ALL
I
-0.00871 (0.904)
- 0.00462 (0.810)
1.58
1.71
2.47’
- 0.00!309 (0.8 17)
- 0.00773 (0.812)
- 0.00500 (0.807)
1.08
1.63
1.55
- 0.00620 (1.053)
-0.00798 (1.11)
- 0.00905 (1.012)
-0.00601 (1.277)
4.12’
4.13’
5.04;
0.90
3.17*
1.69
1.11
4.13’
Ff
0.66
1.79
1.6i
0.99
3.30*
F:
0.50
1.97
1.71
1.43
2.95;
F;
0.72
3.12’
1.17
1.78
5.098
- 0.00632 (1.10-l)
- 0.00579 (0.871)
-0.00317 (0.792)
1.36
1.50
2.39;
- 0.0094 (1.132)
I
Panel 5: British pound puts I. Open-IO:00
-0.00751 (0.729)
2. 10::0&12:00
-0.00802 (0.756)
-0.00617 (0.714)
-0.00581 (0.809)
-0.00501 (0.814)
-0.00385 (0.797)
0.95
1.60
1.48
3. IZ:OO-Close
-0.00925 (0.904)
-0.00433 (1.102)
-0.00536 (1.035)
-0.00613 (0.961)
- 0.00404 (1.192)
3.64*
3.70;
4.36’
1.33
1.48
2.19.
0.0064 1 (0.9 18)
F ALL
0.97
2.96*
1.52
1.04
3.88,
F,
0.58
1.74
1.46
0.87
3.048
F,
0.46
1.88
1.59
1.32
2.76;
F,
0.70
3.07’
1.09
1.60
4.75;
-0.00737 (0.821)
-0.00753 (0.965)
- 0.00638 (0.871)
- 0.00404
Panel C: German mark purs I. Open-IO:00
0.00871 (0.692)
(0.934)
2. lO:Wl2:CXl
-0.00961 (0.713)
-0.00701 (0.537)
-0.00635 (0.729)
- 0.00604 (0.813)
- 0.00420 (0.933)
1.01
1.39
1.29
3. 12:OWZlose
- 0.01027 (0.809)
- 0.00541 (0.963)
-0.00571 ( 1.030)
-0.00741 (0.98 1)
- 0.00582 (1.177)
3.64’
3.50*
4.26’
F ALL
0.82
2.83;
1.52
1.02
3.09*
FL
0.54
1.61
1.40
1.01
2.76*
FZ
0.51
1.75
1.57
1.19
2.72;
0.63
2.48*
0.94
1.30
4.188
F3
“Mean return (x 100). %tandard deviation in parentheses. ‘Fs is the F-statistic testing the dilTerence in means across the five days. dF, is the F-statistic testing the di&rence in means for Monday from other days. ‘F, is the F-statistic testing the difference in means for across Tuesday through Friday. testing the difference in means the three across three time intervals. ‘FALL is the F-statistic #F, is the F-statistic testing the difference in means for interval 1 from intervals 2 and 3. ‘F, is the F-statistic testing the difference in means for interval 2 from intervals 1 and 3. ‘F, is the F-statistic testing the difference in means for interval 3 from intervals 1 and 2. *Signilicant at the 0.05 level.
1168
J.E. Hilliard and A.L. Tucker, Patterns in the interbank foreign
day effects, as our sample remaining to maturity.6
excludes
4. Empirical results: Calendar-day
options
exchange
markets
with less than
one week
hypothesis
The return on any asset is a function of both the calendar time over which the investment is made and the risk borne over that period of time. Since risk over the weekend is only slightly greater than risk over a weekday but calendar time over the weekend is roughly three times greater than the calndar time over a weekday, the apparently anomalous weekday results reported in the previous section may be explained away by adjusting the premium for risk versus the premium for time. In this section, we investigate this calendar-day hypothesis by conducting the same tests described earlier, but where the Friday close to Monday close returns are divided by 3 (72/24) and the Friday close to Monday open returns are divided by 3.743 (65.5,‘17.5).
4.a.
Weekday
returns
Panel A in table 4 reports the weekday (close-to-close) returns under the calendar-day hypothesis. This table is analogous to panel A in table 1, but where Friday close to Monday close returns are divided by 3. As a consequence, currency spot (option) returns now tend to be lower (higher) from Friday to Monday than for other weekdays. However, as indicated by the reported F-statistics, the null of equal weekday returns cannot be rejected at traditional significance levels, Thus, no weekend effect appears under the calendar-day viewpoint.
4.h. Overnight
returns
Panel B in table 4 reports the overnight returns under the calendar-day hypothesis. This table is analogous to panel B in table 1, but where Friday close to Monday open returns are divided by 3.743. As a consequence, currency spot (option) returns now tend to be lower (higher) from Friday close to Monday open than for other overnight periods. The F, and FM 61f no data were censored and continuous observations were possible, it would follow that the mean close-to-close returns (table I) would equal the corresponding mean close-to-open returns (table 2) plus the corresponding intraday returns (tables 3 and 4). This mathematical absolute is violated, however, because a record for close-to-close is not necessarily duplicated for close-toopen and.‘or the corresponding intraday return since a currency option might not trade during the first or last few minutes of these subperiods.
J.E. Hilliard and A.L. Tucker, Parterns in rhe inrerbank Jiireign exchange markets
Table Returns
Security
under
the calendar-day
1169
4 hypothesis,
1983-1988.
Friday
Monday
Tuesday
Wednesday
Thursday
to
to
to
to
to
Test statistics
Monday
Tuesday
Wednesday
Thursday
Friday
Ff
Fi
F;
0.00039
1.62
1.28
0.58
1.17
1.24
1.14
1.26
1.53
0.69
1.43
1.68
1.20
1.35
1.71
0.55
1.26
1.50
1.23
2.27’
5.26’
1.29
2.12.
3.14;
1.91
2.97*
3.49*
1.08
2.54*
3.07’
1.46
2.79’
4.04*
1.38
2.12’
2.88;
1.83
Panel A: Weekduy (close-to-close) Spot yen Yen puts Spot pounds Pound
puts
Spot marks Mark
puts
o.OOQ3(r (O.OlO)b - 0.00320 (0.610) o.COO19 (0.095) - 0.00203 (0.658) 0.00024 (0.101) -0.00255 (0.580)
0.00055 (0.240) -0.00318 (1.607) 0.00027 (0.233) -0.00216 (1.738) 0.00043 (0.251) -0.00257 (1.509)
0.00042 (0.23 1) -0.00612 ( 1.692) o.Of3030 (0.239)
0.00046 (0.239) -0.00581 (1.658) 0.00028 (0.227)
- 0.00388 (1.740)
- 0.00374 (1.697)
0.00034 (0.249)
0.00037 (0.240)
- 0.00439
- 0.00449 (1.581)
( 1.607)
-0.Ofx39 ( 1.599) 0.00026 (0.231) -0.00381 ( 1.686) 0.00033 (0.242) -0.00417 ( I .520)
Panel B: Overnight (close-to-open) Spot yen Yen puts Spot pounds Pound
puts
Spot marks Mark
puts
0.00030” (0064)b -0.00190 (0.465) 0.#013 (0.063) -0.00137 (0.435) O.OOG25 (0.066) -0.00153 (0.483)
0.00082 (0.180) - 0.00209 ( 1.409) o.ooo3 1 (0.206) -0.00221 ( 1.422) 0.00066 (0.196) -0.00166 (1.312)
‘Mean return. “Standard deviation in parentheses. ‘f, is the F-statistic testing the difference dfh, is the F-statistic testing the difference ‘P, is the F-statistic testing the difference *Significant at the 0.05 level.
0.00069 (0.197) -0.00416 (1.685)
0.00061 (0.205) - 0.00488 (1.733)
0.00032 (0.195)
0.00027 (0.191)
- 0.00309 (1.491)
- 0.00296 (1.400)
0.00058 (0.205) - 0.00358 (1.505)
o.cQO49 (0.213) -0.00391 (1.591)
0.00052 (0.204) -0.00526 ( 1.624) 0.00028 (0.193) -0.00310 ( 1.466) O.ooo44 (0.209) -0.00408 ( 1.622)
in means across the live days. in means for Monday from other in means across Tuesday through
days. Friday.
1170
J.E. Hiiliard and A.L. Tucker. Patterns in the inrerbankforeign
exchange markets
statistics are significant for each currency and, thus, the weekend overnight pattern reported under the trading-day hypothesis (table 2) is reversed under the calendar-day viewpoint. 5. Conclusion
Using transactions data for listed currency options that include underlying interbank spot exchange rates, we document the weekday, intraday, and overnight returns and return volatilities patterns that existed for long spot currency and currency put options positions for the period 1983 through 1988. Under the trading-day hypothesis, spot (option) returns are found to be significantly higher (lower) from Friday close to Monday close and significantly higher (lower) from Friday close to Monday open. For the interbank spot market, this weekend pattern is not attributable to a float effect since all transactions are settled the same day. For the listed options market, this weekend pattern may be attributable, in part, to next-day settlement at the PHLX. However, such settlement is unlikely to fully explain the weekend option pattern. Under a calendar-day viewpoint, the anomalous weekend close-to-close effect no longer appears, and the anomalous weekend close-to-open effect is actually reversed. Although some anomalous intraday effects were observed, our results show that processes generating currency returns are reasonably ‘well-behaved’ when time is measured by calendar days. This suggests, for example, that the time unit when measuring time-to-expiration for currency options should be calendar days, not trading days. References Bhattacharya, M., 1987, Price changes of related securities: The case of call options and stock. Journal of Financial and Quantitative Analysis 22, March, l-15. Engle, R., T. Ito and W. Lin,.1990, Meteor showers or heat waves? Heteroskedastic intra-daily volatilitv in the foreian exchange market. Econometrica 58, May, 525542. Flannery, M. and A. Protopapadakis, 1988, From T-bills to common stocks: Investigating the generality of intra-week return seasonality, Journal of Finance 43, June, 431-450. Goodhart, C. and L. Figliuoli, 1991, Every minute counts in financial markets, Journal of International Money and Finance IO, March, 23-52. Harris, L., 1986, A transaction data study of weekly and intradaily patterns in stock returns, Journal of Financial Economics 16, May, 99-117. Lakonishok, J. and M. Levi, 1982, Weekend effects on stock returns: A note, Journal of Finance 37, June, 883-889. Lakonishok, J. and S. Smidt, 1988, Are seasonal anomalies real? A ninety-year perspective, Review of Financial Studies I, Winter, 403-425. Levi, M., 1978, The weekend game: Clearing house vs. Federal funds. Canadian Journal of Economics 11, Nov., 750-757. Lockwood, L. and S. Linn. 1990, An examination of stock market return volatility during overnight and intraday periods, 1964-1989, Journal of Finance 45, June, 591-601. McFarland, J., R. Pettit and S. Sung, 1982, The distribution of foreign exchange price changes: Trading day effects and risk measurement, Journal of Finance 37, June, 693-715.
J.E. Hilliard
and A.L.
Tucker.
Patterns
in the interbank
foreign
exchange
markets
1171
Muller, U., M. Dacorogna, R. Olsen, 0. Pictet, M. Schwarz and C. Morgeuegg, 1990, Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis, Journal of Banking and Finance 14, Dec., 1189-1208. Peterson, D., 1990, A transaction data study of day-of-the-week and intraday patterns in option returns, Journal of Financial Research 13, Summer, 117-131. Wasserfallen. W. and H. Zimmerman, 1985, The behavior of intra-daily exchange rates, Journal of Banking and Finance 9, March, 55-72.
of Banking
and
Finance
16 (1992)
1159-l 171. North-Holland
A note on weekday, intraday, and overnight patterns in the interbank foreign exchange and listed currency options markets* Jimmy E. Hilliard Vniversiry
of Georgia,Athens, GA 30602, USA
Alan L. Tucker Temple University, Philadelphia, PA 19122, USA Received April 1991, final version received
February
1992
Transactions data are used to investigate returns patterns for close-to-close, close-to-open, and intraday long positions in spot currency (interbank) and currency put options (listed) for the years 1983 through 1988. Both trading-day and calendar-day hypotheses are investigated. Under the former, spot market returns are found to be significantly higher from Friday close to Monday close and from Friday close to Monday open. Under the calendar-day hypothesis, however, no significant close-to-close pattern emerges, and the Friday close to Monday open effect is reversed. Finally, spot (put) market returns are found to be significantly lower (higher) for Tuesday and Friday afternoons.
1. Introduction
Empirical research over the last decade has documented persistent patterns of return and their volatilities for several financial assets, especially common stock. See Flannery and Protopapadakis (1988) for a bibliography. Trading day effects in foreign exchange prices have been studied by McFarland et al. (1982) and Levi (1978). These studies focus on empirical regularities of asset returns and their volatilities in order to develop better equilibrium asset pricing models and to examine issues related to the efficiency of securities markets. Continuing in this spirit, this study undertakes an investigation of weekly, intraday, and Correspondence to: Professor Jimmy E. Hilliard, G. Herman and Mary Virginia Terry Chair of Business, Banking and Finance Department, University of Georgia, Athens, GA 30602, USA. Tel. (706) 542-3646. *We thank Larry Lockwood, David Peterson, and two anonymous referees for helpful comments. 0378-4266,‘92/.%05.00
C 1992-Elsevier
Science Publishers
B.V. All rights reserved
1160
J.E. Hilliard and AL. Tucker, Patterns in the interbank foreign exchange markets
overnight returns patterns in the foreign exchange market and, relatedly, the currency options market, while utilizing transactions data for the US dollar price of three foreign currencies for the calendar years 1983 through 1988. This investigation is undertaken with respect to both the trading-day hypothesis, which treats Friday to Monday returns in an identical manner to other weekday or overnight retutns, and the calendar-day hypothesis, which recognizes that the return on an asset is a function of both the calendar time over which the investment is made and the risk borne over that period of time. It is particularly interesting to examine intraweek returns in the interbank market, because of the market’s current and unique practice of settling all transactions on the same day that they occur. Thus, any particular weekday or overnight pattern found in this market under the trading-day hypothesis would suggest that similar patterns documented in other securities markets are likely not solely attributable to their delayed settlement procedures [cf. Lakonishok and Levi (1982)l.l Under the trading-day hypothesis, percentage changes in spot interbank exchange rates are found to exhibit discernible weekday, interday, and overnight patterns. Specifically, dollar-foreign currency returns are significantly higher from Friday close to Monday close than for other weekdays, returns are significantly higher from Friday close to Monday opening than for other overnight periods, and returns are significantly lower for some late intraday periods, especially on Fridays. Together, these patterns support the ‘safe dollar hypothesis’ of McFarland et al., which contends that there is a flow into dollars before the weekend because the dollar is a safe short term store of value. We do not find any other particular weekday or overnight effects, suggesting that the high Wednesday and low Thursday returns documented by McFarland et al. and Levi were indeed attributable to settlement procedures that existed in the interbank market prior to October 1981. For our sample period, all interbank currency transactions are settled the same day. Thus, foreign exchange rates no longer reflect the fact that, before October 1981, dollars moving through the payment system became usable a trading day later than other currencies. Returns for currency put options generally exhibit consistent patterns, further attesting to the documented inextricable linkages between derivative securities and their underlying assets [cf. Bhattacharya (1987)]. significant Under the calendar-day hypothesis, however, no statistically weekday pattern emerges, and the high Friday close to Monday open effect IThere are other interesting reasons for investigating seasonaiity in the foreign exchange market. For instance, examining exchange rates and currency option prices guards against data snooping, that is. the possibility that reported findings for equities results merely from extensive and repeated analyses of the same data (CRSP tapes) [see Lakonishok and Smidt (1988)]. In addition, determining whether seasonal patterns are similar for currency and other assets should provide insight into hypotheses regarding the origins of the patterns.
J.E. Hilliard and A.L. Tucker, Patterns in the interbank foreign
exchange
markets
1161
is reversed. Of course, the intraday patterns reported under the trading-day hypothesis are unaffected. This evidence strongly suggests that other investigations of anomalous intraweek effects [e.g. McFarland et al. (1982)] may have to be reinterpreted under the calendar-day hypothesis. This study proceeds as follows. Section 2 describes the data used, while empirical results are provided in section 3 (trading-day hypothesis) and section 4 (calendar-day hypothesis). Section 5 offers a brief conclusion.
2. Data The major data source is the Philadelphia Stock Exchange (PHLX) currency options data base, which lists every option from December 1982 (the start of trading) through December 1988 for up to seven major trading currencies, including the Japanese yen, British pound, and German mark. There are nearly 500,000 records of transactions which are time and date stamped (to the minute), each indicating the number of contracts traded, the underlying currency, and the option’s premium, exercise price, and expiration date. Also recorded for each transaction are the underlying spot, bid, and ask exchange rates. The bid and ask exchange rates are provided by Telerate and represent the last interbank quotes available before the option’s transaction time. The ‘spot’ exchange rate is internally generated at the PHLX, and represents an average of the last five or six bid and ask rates provided by Telerate prior to the recorded transaction time. Over the sample period, the trading session opened at 8:OOa.m. and closed at 2:OOp.m. eastern time. For the purpose of constructing intraday spot market returns for each currency, we define three intraday periods: (1) opening option trade (approximately 8:OOa.m.) to approximately 10:OOa.m.; (2) approximately 10:OOa.m. to approximately 12:00 noon; and (3) approximately 12:00 noon to closing option trade (approximately 2.30p.m.). For the purpose of constructing these returns, any option trade occurring near the designated times will suffice, since the variable of interest is the recorded underlying interbank exchange rate. For weekday returns (close-to-close), the exchange rates underlying the closing options trades are employed, while for overnight returns (close-to-open), the exchange rates underlying the closing and subsequent opening option trades are employed. If no currency option trades within ten minutes of 8:OOa.m.. lO:OOa.m., 12:OOnoon, or 2:30p.m., the corresponding return measures are omitted from the analysis. This occurs infrequently, however, since an average of nearly 15 option trades occur per hour over the sample period. Trading days following holidays are excluded from the sample, ensuring weekday returns being measured over (approximately) 24-hour or 72-hour periods, and overnight returns being measured over (approximately) 17.5-hour of 65.5-hour per-
J.B.F.-
F
1162
J.E. Hilliard and A.L. Tucker. Patterns in the interbank foreign
exchange markers
iods.’ When computing all interbank spot market returns, the spot rates as generated internally at the PHLX are employed. Nearly identical results obtain when using the average of the recorded bid and ask exchange rates provided by Telerate.3 Computing returns for currency option holdings is more complicated because the same option series (i.e., options with the same underlying currency, exercise price and expiration date) must be employed. We compute weekday, intraday, and overnight returns separately for all possible long positions in yen, pound, and mark put options, provided that options of the same series are available within ten minutes of the designated trading times. Options with less than one week to expiration are never employed, and observations are omitted if the required option series is unavailable. As expected, this occurs more frequently than with the computation of spot market returns, since the additional constraint of using the same option series is imposed. Finally, the reported option premium is the actual trade price, and it is not possible to discern if the trade emanated from an order to buy or sell. 3. Empirical results: Trading-day
hypothesis
Under the trading-day hypothesis, weekend returns (Friday close to Monday close and Friday close to Monday open) are treated in an identical manner as other weekday and overnight returns. To investigate this hypothesis, for each time interval examined, mean returns and their standard deviation are computed. Further, various patterns of intertemporal returns are tested through progressing returns on a set of dummy variables. 3.a.
Weekday
returns
Panel A in table 1 reports weekday (close-to-close) results for long positions in spot currencies and currency put options for the sample period. All mean spot (option) returns are positive (negative), due to the substantial decline in the dollar’s value from 1983 through 1988. For example, during this six-year period, the dollar depreciated by more than fifty percent against the yen. Assuming 250 trading days per year, the (compounded) appreciation of the yen was nearly 0.0008 per day for the sample period, implying positive (negative) returns to investors with long positions in spot yen (yen puts). The dollar also depreciated against the pound and mark. For spot yen, the Friday close to Monday close mean return (0.00091) is higher than the other weekday returns. This result is corroborated by the F5 zPeriod adjustments associated with changes in daylight savings time are not considered. 3For other studies that employ intraday foreign exchange rate data. see Engle et al (1990), Goodhart and Figliuoli (1991). Muller et al. (1990). and Wasserfallen and Zimmerman (1985).
J.E. Hilliard
and A.L. Tucker,
Patterns
in the interhank
Table Returns Friday to Monday
security Panel
A: Weekday
Spot yen Yen puts
Monday to Tuesday
-0.00961 (1.831) 0.0056 (0.284)
0.00055 (0.240) -0.00318 (1.607) 0.00037 (0.233) -0.00216 (1.738)
puts
- 0.00608 ( 1.974)
Spot marks
o.c0O73 (0.304)
0.00043 (0.25 1)
- 0.00764 (1.739)
- 0.00257 ( 1.509)
Pound
Mark
puts
Panel
B: Overnight
Spot yen Yen puts Spot pounds
the trading-day Tuesday to Wednesday
hypothesis, Wednesday to Thursday
0.00042 (0.247) -0.00612 (1.692) 0.00030 (0.239) -0.00388 (1.740) 0.00034 (0.249) -0.00439 (1.607)
O.OQO46 (0.231) -0.00581 (1.658)
Thursday to Friday
Test statistics F\
Fi
F;
6.36*
0.58
1.02
3.82’
1.14
3.78.
6.22’
0.69
1.11
4.04*
1.20
3.78’
6.02’
0.55
0.91
3.47*
1.23
6.49’
1X02*
1.29
2.95*
7.00
1.91
4.21’
9.63*
1.08
2.86’
5.71’
1.46
0.00044 (0.209)
6.31’
10.54;
1.38
- 0.00408 ( 1.622)
2.69,
6.44*
1.83
0.00039 (0.239)
0.00026 (0.23 1)
- 0.00374 ( 1.697)
-0.00381 (1.686)
o.ooo37 (0.240)
0.00033 (0.242)
- 0.00449 (1.581)
-0.00417 (1.520)
4.01
l
(close-to-open)
O.cQ114’ (0.241)b -0.00712 (1.741) 0.00050 (0.237)
0.00082 (0.180) - 0.00209 (1.409)
o.wO69 (0.197) -0.00416 ( I .685)
0.0006 (0.205) - 0.00488 (1.733)
o.OQO3I (0.206)
0.00032 (0.195)
0.00027 (0.191)
- 0.0022 1 (1.422)
- 0.00309 (1.491)
- 0.00296 (1.400)
Spot marks
0.0092 (0.247)
O.ocQ66 (0.196)
0.00058 (0.205)
0.00049 (0.213)
puts
1163
1983-1988.
-0.00539 (1.599)
0.00028 (0.277)
-0.00513 (1.627)
Mark
markets
1
puts
Pound
exchange
(close-to-close)
0.00091’ (0.299)b
Spot pounds
under
foreign
-0.00572 (1.807)
-0.00166 (1.312)
-0.00358 I 1.505)
‘Mean return. bStandard deviation in parentheses. ‘Fs is the F-statistic testing the difference dfM is the F-statistic testing the difference ‘F, is the F-statistic testing the difference *Significant at the 0.05 level.
-0.00391 (1.591)
I
o.oGO52 (0.204) -0.00526 (1.624) 0.00028 (0.193) -0.00310 ( 1.466)
in means across the live days. in means for Monday from other days. in means for across Tuesday through Friday.
1164
J.E. Hilfiard and AL. Tucker, Patterns in the interbank foreign exchange markets
test statistic (4.01) and the F, test statistic (6.36).’ Similar results obtain for the pound and mark. Higher Monday returns for dollar-denominated foreign exchange long positions were also found by Levi (1978) and McFarland et al. (1982). The latter study also found a Wednesday-Thursday effect that the authors associate with settlement procedures that existed in the foreign market during their sample period. Specifically, dollars moving through the payment system became usable a trading day later than other currencies prior to October 1981. Since it then took two trading days to clear a foreign currency, purchases of foreign currency on Wednesday were delivered on Fridays, but purchases of dollars on Wednesdays were not delivered until the next Mondays. Thus, purchasers of dollars were giving sellers a longer, fiveday interest-free loan on Wednesdays than on the other weekdays, implying a lower dollar price on Wednesdays to compensate dollar purchasers. However, our F, test statistics suggest that there are no significant differences in mean returns across Tuesday through Friday for any currency for our sample period. Currently, all interbank currency trades are cleared on the same day through the Clearing House Interbank Payment System (CHIPS). The weekday results for long yen put positions are consistent with spot market results, with Monday returns (-0.00961) relatively lower than other weekdays (F,=3.82). As expected, the standard deviations of put returns are substantially greater than those of spot returns. Similar resufts obtain for the pound and mark. Consistent with results related to other financial markets (cf. Harris (1986) and Peterson (1990)], Friday close to Monday close return volatility is greater than for other weekdays for both spot and option markets.
3.6. Uvernjgh~ returns
Panel B in table 2 reports analogous results for overnight (close-to-open) positions. For spot yen, the Friday close to Monday open (weekend) return is signi~cantly higher (0.~114~ than for other overnight periods (F,=6.49 and F,= 12.02). Thus, the higher Monday return reported in panel A is largely attributable to a higher weekend return. The Tuesday through Friday overnight returns are insignificantly different (F,= 1.29). and the weekend return volatility (0.241) in generalfy greater than that of other overnight ‘The test statistic F, is derived from a regression of returns on five dummy variables, each representing a weekday. FM is derived from a regression of returns on two dummy variables, one representing Monday and the other Tuesday through Friday. F, is derived from a regression OF returns on four dummy variables, with Monday returns omitted. Results and inferences for the option market should be interpreted cautiously since option returns are bounded below, implying that returns are skewed and that normal distribution theory may not be applicable.
and A.L. Tucker, Patterns in the interbank foreign exchange markets
J.E. Hilliard
Table Intraday
spot returns
1165
2
( x 100).1983-1988. Test statistics
Interval
Mondav
Panel A: Japanese
Tuesdav
Wednesday
Thursday
Friday
FE,
Fljj
F;
yen puts
1. Open-IO:00
0.00275’ (0.323)b
0.00201 (0.442)
0.00191 (0.459)
0.00239 (0.352)
0.00256 (0.360)
1.61
2.89.
1.49
2. lO:OO-12:oO
0.00316 (0.275)
0.00238 (0.410)
0.00213 (0.430)
O.OQ280 (0.3 19)
0.00228 (0.346)
1.40
2.38’
0.94
3. 12:O&Close
0.00270 (0.3 IO)
0.00087 (0.706)
0.0022 (0.429)
0.00247 (0.407)
O.ooO77 (0.879)
3.22”
5.01.
3.06*
I
FrALL
0.55
3.19*
1.00
I .40
3.70’
F:
0.37
1.32
0.70
1.19
2.13’
F:
0.34
1.18
0.48
1.42
1.17
p,
0.30
3.19*
0.99
0.78
5.29,
Panel
B: British pounds
1. Open-IO:00
0.00184 (0.3 17)
0.00136 (0.364)
0.00125 (0.371)
0.00157 (0.331)
0.00170 (0.351)
1.47
2.63.
1.22
2. lO:OO-12:00
0.00212 (0.251)
0.00160 (0.331)
0.00144 (0.358)
0.00174 (0.299)
0.00147 (0.329)
1.18
2.29’
0.90
3. 12:~Close
0.00181 (0.298)
O.OC060 (0.582)
0.00117 (0.361)
0.00161 (0.364)
0.00052 (0.707)
2.96,
4.82’
2.90.
0.00215 (0.35 1)
1.42
2.76’
1.35
F ALL
0.42
2.91.
0.92
1.27
4.02* 2.36
F,
0.29
I.21
0.66
1.09
F,
0.3
I .05
0.4
1.35
1.09
FJ
0.25
3.00*
1.03
0.64
5.28’
I
1
Panel C: German marks 1. Open-IO:00
0.00224 (0.361)
0.00171 (0.470)
0.00157 (0.488)
0.00196 (0.370)
2. lO:OO-12:OO 0.00253 (0.294)
0.00191 (0.436)
0.00174 (0.397)
0.0024 (0.305)
1
0.00191 (0.330)
1.29
2.228
0.90
3. IZ:OO-CIose
o.OOlN5 (0.836)
0.00177 (0.441)
0.0020 (0.388)
I
0.00089 (0.724)
3.04’
4.02’
2.73’
0.00206 (0.334)
F ALL.
0.79
3.728
1.16
1.26
3.21*
F,
0.40
1.41
0.89
0.94
2.30;
F,
0.38
1.26
0.43
1.11
1.09
F,
0.38
3.48;
1.00
0.77
4.77.
‘Mean return ( x 100). %tandard deviation in parentheses. ‘F, is the F-statistic testing the digerence in means across the five days. “F, is the F-statistic testing the difference in means for Monday from other days. ‘F, is the F-statistic testing the difference in means for across Tuesday through Friday. testing the difference in means across three time intervals. ‘F*U_ is the F-statistic sF, is the F-statistic testing the diITerence in means for interval 1 from intervals 2 and 3. “F‘, is the F-statistic testing the diNerence in means for interval 2 from intervals 1 and 3. ‘F, is the F-statistic testing the difference in means for interval 3 from intervals I and 2. *SigniIicant at the 0.05 level.
1166
J.E. Hilliard
and A.L.
Tucker,
Patterns
in the interbank
foreign
exchange
markets
periods. Returns for long positions in yen put options are generally consistent with overnight returns in the spot market. Weekend option returns (-0.00712) are significantly lower (F, =2.95 and F, = 7.00), while Tuesday through Friday overnight returns are not significantly different at the 0.10 level (F,= 1.91). Again, similar results obtain for the pound and mark. Finally, a comparison of the corresponding standard deviations reported in table 1 suggests that close-to-close returns are slightly more volatile than close-to-close returns in both markets.
3.~. Intrada_v returns Intraday results for spot currencies and currency puts are reported in tables 2 and 3, respectively. For spot yen, Monday intraday returns tend to be relatively higher than corresponding intraday returns for other weekdays. The F, test statistics are 2.89 (interval l), 2.38 (interval 2), and 5.01 (interval 3). This result suggests that not all of the Monday effect reported in table 1, panel A is attributable to the weekend return (panel B). Also, interval 3 (12:00-close) returns tend to differ by weekday (F,=3.22 and F,=3.06). This result is likely due to the unusually low Tuesday and Friday interval 3 returns. For Tuesday, the F,,, test statistic is 3.19 and the FJ test statistic is 3.19, indicating that afternoon returns are lower than for earlier intraday periods.’ For Friday, FALL= 3.70 and F,=5.29, indicating that Friday afternoon returns are significantly lower than earlier intraday returns, at the 0.05 level. Once again, similar results obtain for the pound and mark. Both of these currencies exhibit higher Monday intraday returns and lower Tuesday and Friday afternoon returns. Finally, a comparison of standard deviations within each weekday suggests that volatility takes on a U-shaped pattern for each currency, with standard deviations generally higher during intervals 1 and 3. Such a U-shaped intraday volatility pattern is also found in the stock market [cf. Harris (1986) and Lockwood and Linn (199O)J Regarding long put positions (table 3), returns are generally lower for all Monday intraday intervals, and returns are also significantly higher (less negative) for Tuesday and Friday afternoons. However, some inconsistency between spot and option returns exists, particularly in Fridays. For example, Friday interval 1 yen put returns are unusually high (F, =3.30), as are Friday interval 2 put returns (F2 = 2.95). The same inconsistencies appear for the pound and mark. These results are not attributable to Friday expiration
‘The test statistic FALL is derived from a regression of returns on three dummy variables, each representing an intraday time interval. The F-statistics F,, F,, and F, are derived from a regression of returns on two dummy variables.
I.E. Hilliard and A.L. Tucker. Patterns in the interbank foreign exchange markets Table Intraday
option
1167
3
returns
( x 100).1983-1988.
Wednesday
Thursday
Test statistics Interval
Mondav
Tuesday
Friday
F:
Fd,
F:
Panel A: Japanese yen puts I. Open-IO:00
-0.01125” (0.747)b
- 0.00972 (0.940)
2. 10:0&12.:00
-0.01207 (0.772)
- 0.0094 (0.611)
3. 12:~Close
-0.01380 (0.912)
F ALL
I
-0.00871 (0.904)
- 0.00462 (0.810)
1.58
1.71
2.47’
- 0.00!309 (0.8 17)
- 0.00773 (0.812)
- 0.00500 (0.807)
1.08
1.63
1.55
- 0.00620 (1.053)
-0.00798 (1.11)
- 0.00905 (1.012)
-0.00601 (1.277)
4.12’
4.13’
5.04;
0.90
3.17*
1.69
1.11
4.13’
Ff
0.66
1.79
1.6i
0.99
3.30*
F:
0.50
1.97
1.71
1.43
2.95;
F;
0.72
3.12’
1.17
1.78
5.098
- 0.00632 (1.10-l)
- 0.00579 (0.871)
-0.00317 (0.792)
1.36
1.50
2.39;
- 0.0094 (1.132)
I
Panel 5: British pound puts I. Open-IO:00
-0.00751 (0.729)
2. 10::0&12:00
-0.00802 (0.756)
-0.00617 (0.714)
-0.00581 (0.809)
-0.00501 (0.814)
-0.00385 (0.797)
0.95
1.60
1.48
3. IZ:OO-Close
-0.00925 (0.904)
-0.00433 (1.102)
-0.00536 (1.035)
-0.00613 (0.961)
- 0.00404 (1.192)
3.64*
3.70;
4.36’
1.33
1.48
2.19.
0.0064 1 (0.9 18)
F ALL
0.97
2.96*
1.52
1.04
3.88,
F,
0.58
1.74
1.46
0.87
3.048
F,
0.46
1.88
1.59
1.32
2.76;
F,
0.70
3.07’
1.09
1.60
4.75;
-0.00737 (0.821)
-0.00753 (0.965)
- 0.00638 (0.871)
- 0.00404
Panel C: German mark purs I. Open-IO:00
0.00871 (0.692)
(0.934)
2. lO:Wl2:CXl
-0.00961 (0.713)
-0.00701 (0.537)
-0.00635 (0.729)
- 0.00604 (0.813)
- 0.00420 (0.933)
1.01
1.39
1.29
3. 12:OWZlose
- 0.01027 (0.809)
- 0.00541 (0.963)
-0.00571 ( 1.030)
-0.00741 (0.98 1)
- 0.00582 (1.177)
3.64’
3.50*
4.26’
F ALL
0.82
2.83;
1.52
1.02
3.09*
FL
0.54
1.61
1.40
1.01
2.76*
FZ
0.51
1.75
1.57
1.19
2.72;
0.63
2.48*
0.94
1.30
4.188
F3
“Mean return (x 100). %tandard deviation in parentheses. ‘Fs is the F-statistic testing the dilTerence in means across the five days. dF, is the F-statistic testing the di&rence in means for Monday from other days. ‘F, is the F-statistic testing the difference in means for across Tuesday through Friday. testing the difference in means the three across three time intervals. ‘FALL is the F-statistic #F, is the F-statistic testing the difference in means for interval 1 from intervals 2 and 3. ‘F, is the F-statistic testing the difference in means for interval 2 from intervals 1 and 3. ‘F, is the F-statistic testing the difference in means for interval 3 from intervals 1 and 2. *Signilicant at the 0.05 level.
1168
J.E. Hilliard and A.L. Tucker, Patterns in the interbank foreign
day effects, as our sample remaining to maturity.6
excludes
4. Empirical results: Calendar-day
options
exchange
markets
with less than
one week
hypothesis
The return on any asset is a function of both the calendar time over which the investment is made and the risk borne over that period of time. Since risk over the weekend is only slightly greater than risk over a weekday but calendar time over the weekend is roughly three times greater than the calndar time over a weekday, the apparently anomalous weekday results reported in the previous section may be explained away by adjusting the premium for risk versus the premium for time. In this section, we investigate this calendar-day hypothesis by conducting the same tests described earlier, but where the Friday close to Monday close returns are divided by 3 (72/24) and the Friday close to Monday open returns are divided by 3.743 (65.5,‘17.5).
4.a.
Weekday
returns
Panel A in table 4 reports the weekday (close-to-close) returns under the calendar-day hypothesis. This table is analogous to panel A in table 1, but where Friday close to Monday close returns are divided by 3. As a consequence, currency spot (option) returns now tend to be lower (higher) from Friday to Monday than for other weekdays. However, as indicated by the reported F-statistics, the null of equal weekday returns cannot be rejected at traditional significance levels, Thus, no weekend effect appears under the calendar-day viewpoint.
4.h. Overnight
returns
Panel B in table 4 reports the overnight returns under the calendar-day hypothesis. This table is analogous to panel B in table 1, but where Friday close to Monday open returns are divided by 3.743. As a consequence, currency spot (option) returns now tend to be lower (higher) from Friday close to Monday open than for other overnight periods. The F, and FM 61f no data were censored and continuous observations were possible, it would follow that the mean close-to-close returns (table I) would equal the corresponding mean close-to-open returns (table 2) plus the corresponding intraday returns (tables 3 and 4). This mathematical absolute is violated, however, because a record for close-to-close is not necessarily duplicated for close-toopen and.‘or the corresponding intraday return since a currency option might not trade during the first or last few minutes of these subperiods.
J.E. Hilliard and A.L. Tucker, Parterns in rhe inrerbank Jiireign exchange markets
Table Returns
Security
under
the calendar-day
1169
4 hypothesis,
1983-1988.
Friday
Monday
Tuesday
Wednesday
Thursday
to
to
to
to
to
Test statistics
Monday
Tuesday
Wednesday
Thursday
Friday
Ff
Fi
F;
0.00039
1.62
1.28
0.58
1.17
1.24
1.14
1.26
1.53
0.69
1.43
1.68
1.20
1.35
1.71
0.55
1.26
1.50
1.23
2.27’
5.26’
1.29
2.12.
3.14;
1.91
2.97*
3.49*
1.08
2.54*
3.07’
1.46
2.79’
4.04*
1.38
2.12’
2.88;
1.83
Panel A: Weekduy (close-to-close) Spot yen Yen puts Spot pounds Pound
puts
Spot marks Mark
puts
o.OOQ3(r (O.OlO)b - 0.00320 (0.610) o.COO19 (0.095) - 0.00203 (0.658) 0.00024 (0.101) -0.00255 (0.580)
0.00055 (0.240) -0.00318 (1.607) 0.00027 (0.233) -0.00216 (1.738) 0.00043 (0.251) -0.00257 (1.509)
0.00042 (0.23 1) -0.00612 ( 1.692) o.Of3030 (0.239)
0.00046 (0.239) -0.00581 (1.658) 0.00028 (0.227)
- 0.00388 (1.740)
- 0.00374 (1.697)
0.00034 (0.249)
0.00037 (0.240)
- 0.00439
- 0.00449 (1.581)
( 1.607)
-0.Ofx39 ( 1.599) 0.00026 (0.231) -0.00381 ( 1.686) 0.00033 (0.242) -0.00417 ( I .520)
Panel B: Overnight (close-to-open) Spot yen Yen puts Spot pounds Pound
puts
Spot marks Mark
puts
0.00030” (0064)b -0.00190 (0.465) 0.#013 (0.063) -0.00137 (0.435) O.OOG25 (0.066) -0.00153 (0.483)
0.00082 (0.180) - 0.00209 ( 1.409) o.ooo3 1 (0.206) -0.00221 ( 1.422) 0.00066 (0.196) -0.00166 (1.312)
‘Mean return. “Standard deviation in parentheses. ‘f, is the F-statistic testing the difference dfh, is the F-statistic testing the difference ‘P, is the F-statistic testing the difference *Significant at the 0.05 level.
0.00069 (0.197) -0.00416 (1.685)
0.00061 (0.205) - 0.00488 (1.733)
0.00032 (0.195)
0.00027 (0.191)
- 0.00309 (1.491)
- 0.00296 (1.400)
0.00058 (0.205) - 0.00358 (1.505)
o.cQO49 (0.213) -0.00391 (1.591)
0.00052 (0.204) -0.00526 ( 1.624) 0.00028 (0.193) -0.00310 ( 1.466) O.ooo44 (0.209) -0.00408 ( 1.622)
in means across the live days. in means for Monday from other in means across Tuesday through
days. Friday.
1170
J.E. Hiiliard and A.L. Tucker. Patterns in the inrerbankforeign
exchange markets
statistics are significant for each currency and, thus, the weekend overnight pattern reported under the trading-day hypothesis (table 2) is reversed under the calendar-day viewpoint. 5. Conclusion
Using transactions data for listed currency options that include underlying interbank spot exchange rates, we document the weekday, intraday, and overnight returns and return volatilities patterns that existed for long spot currency and currency put options positions for the period 1983 through 1988. Under the trading-day hypothesis, spot (option) returns are found to be significantly higher (lower) from Friday close to Monday close and significantly higher (lower) from Friday close to Monday open. For the interbank spot market, this weekend pattern is not attributable to a float effect since all transactions are settled the same day. For the listed options market, this weekend pattern may be attributable, in part, to next-day settlement at the PHLX. However, such settlement is unlikely to fully explain the weekend option pattern. Under a calendar-day viewpoint, the anomalous weekend close-to-close effect no longer appears, and the anomalous weekend close-to-open effect is actually reversed. Although some anomalous intraday effects were observed, our results show that processes generating currency returns are reasonably ‘well-behaved’ when time is measured by calendar days. This suggests, for example, that the time unit when measuring time-to-expiration for currency options should be calendar days, not trading days. References Bhattacharya, M., 1987, Price changes of related securities: The case of call options and stock. Journal of Financial and Quantitative Analysis 22, March, l-15. Engle, R., T. Ito and W. Lin,.1990, Meteor showers or heat waves? Heteroskedastic intra-daily volatilitv in the foreian exchange market. Econometrica 58, May, 525542. Flannery, M. and A. Protopapadakis, 1988, From T-bills to common stocks: Investigating the generality of intra-week return seasonality, Journal of Finance 43, June, 431-450. Goodhart, C. and L. Figliuoli, 1991, Every minute counts in financial markets, Journal of International Money and Finance IO, March, 23-52. Harris, L., 1986, A transaction data study of weekly and intradaily patterns in stock returns, Journal of Financial Economics 16, May, 99-117. Lakonishok, J. and M. Levi, 1982, Weekend effects on stock returns: A note, Journal of Finance 37, June, 883-889. Lakonishok, J. and S. Smidt, 1988, Are seasonal anomalies real? A ninety-year perspective, Review of Financial Studies I, Winter, 403-425. Levi, M., 1978, The weekend game: Clearing house vs. Federal funds. Canadian Journal of Economics 11, Nov., 750-757. Lockwood, L. and S. Linn. 1990, An examination of stock market return volatility during overnight and intraday periods, 1964-1989, Journal of Finance 45, June, 591-601. McFarland, J., R. Pettit and S. Sung, 1982, The distribution of foreign exchange price changes: Trading day effects and risk measurement, Journal of Finance 37, June, 693-715.
J.E. Hilliard
and A.L.
Tucker.
Patterns
in the interbank
foreign
exchange
markets
1171
Muller, U., M. Dacorogna, R. Olsen, 0. Pictet, M. Schwarz and C. Morgeuegg, 1990, Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis, Journal of Banking and Finance 14, Dec., 1189-1208. Peterson, D., 1990, A transaction data study of day-of-the-week and intraday patterns in option returns, Journal of Financial Research 13, Summer, 117-131. Wasserfallen. W. and H. Zimmerman, 1985, The behavior of intra-daily exchange rates, Journal of Banking and Finance 9, March, 55-72.