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The inefficiency of Reuters foreign exchange quotes
Journal of Banking & Finance 22 (1998) 347±366
The ineciency of Reuters foreign exchange quotes Martin Martens
a,*
, Paul Kofman
b
a
b
Department of Accounting and Finance, Lancaster University, Lancaster, LA1 4YX, UK School of Banking and Finance, The University of New South Wales, Sydney, NSW 2052, Australia Received 18 April 1997; accepted 27 December 1997
Abstract Reuters foreign exchange (FXFX) page is the world wide predominant information source to foreign exchange traders. In this study we compare the indicative spot exchange rate quotes from Reuters with their matching futures exchange rates from the Chicago Mercantile Exchange. We ®nd that the indicative quotes on Reuters FXFX page are inecient and could be improved by incorporating information from the futures market. This casts doubt on the way banks determine these quotes, as well as on the informational content of these quotes as an indicator of the current exchange rate. Ó 1998 Elsevier Science B.V. JEL classi®cation: G14; G15 Keywords: Exchange rates; Futures; Eciency
1. Introduction The spot foreign exchange market is a 24 hours electronic market with brokers and traders around the world. Brokers display quotes to their customers.
* Corresponding author. Tel.: +44 1524 593623; fax: +44 1524 847321; e-mail: [email protected].
0378-4266/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 - 4 2 6 6 ( 9 8 ) 0 0 0 0 4 - 1
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These quotes are the best bid and ask price provided by a limited number of banks regularly contacted by the broker. Since there are many brokers each contacting their own circle of banks to obtain quotes and having their own customers, the natural question arises whether this market is informationally ecient. To date, no data sets have been available allowing for a direct test of the ef®ciency of the spot market in foreign exchange. Goodhart et al. (1996, 1997) study 7 hours of the Reuters-2000 electronic trading system, which at the time of sampling was still a relatively small broker in the spot market. Lyons (1995) studies one week of all transactions of a New York broker. Obviously, any data set on quotes from brokers will only re¯ect a part of the spot market. In fact, the only information source available to all traders around the world consists of indicative quotes, as provided by Reuters foreign exchange (FXFX) page, and those provided by its competitors Knight Ridder and Telerate. As such these quotes play an important role in the spot market, indicating the current foreign exchange rate. Though the quotes are only `indicative', studies using the quotes claim banks have reputation considerations and will most likely trade against their quotes if called within a short time after appearance on the Reuters FXFX page. This assumption is crucial for studies like De Jong et al. (1995) who study triangular arbitrage, Bollerslev and Domowitz (1993), and Dacorogna et al. (1993) who study the trading intensity and volatility patterns in the spot market, and Bollerslev and Melvin (1994) who study the relationship between the spreads and volatility. Similarly, Olsen and Associates who use these quotes to forecast the foreign exchange rate, started a boom in empirical research by releasing 1 year of Reuters quotes in 1994. In this study we further investigate the assumption that one can actually trade against the Reuters quotes. We compare these spot exchange rate quotes with their matching futures exchange rates traded at the Chicago Mercantile Exchange (CME). The futures market is a highly liquid market, but in value terms relatively small as compared to the spot market. Nevertheless, we ®nd that the futures market is leading the `quoted' spot market for up to 3 minutes. The results of a simple trading strategy show that pro®ts can be made from the futures lead, unless trading against the Reuters quotes is not (always) possible. This could (partly) explain our results, which we therefore interpret conditional on the possibility of trading against the Reuters quotes: (i) If one can trade against the Reuters quotes, then our results show that gains can be made and hence the spot market is inecient. (ii) If one cannot (always) trade against the Reuters quotes, our results can be (partly) explained by that fact. However, this implies that studies which made the assumption that one can trade against Reuters quotes were incorrect to do so. Their results will then have to be taken with care. In both cases banks displaying quotes on Reuters FXFX page can improve upon these quotes by paying more attention to the futures market. The futures
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price provides a more adequate re¯ection of the (true) current spot exchange rate than the Reuters quotes. The remaining part of this study is organised as follows. Section 2 discusses in further detail the functioning of the spot and futures markets. In Section 3 the data set is discussed. Section 4 describes the methodology, and Section 5 elaborates upon the results. Section 6 focuses on the eect of prescheduled news announcements and high volatility periods. In Section 7 the pro®tability of a simple trading strategy is tested. Finally, Section 8 will conclude. 2. Microstructure of foreign exchange markets The major dierence between the futures and the spot market in foreign exchange is the trading system. While the futures contracts at the CME are traded in an open outcry (OOC) market, the spot market is an electronic market with brokers and traders around the world. In addition to brokers setting quotes, market participants can also oer or obtain quotes via Reuters, Telerate or Knight Ridder. We will use Reuters FXFX data for the spot rates. These data consist of, mainly indicative, bid and ask quotes. Transaction prices are not available. Each trader can immediately submit quotes to Reuters FXFX page. In addition to Reuters FXFX page, traders have a screen displaying a very small spread often of a magnitude of only 1 tick (i.e., one hundredth of percentage point). This spread re¯ects the current best bid and ask provided by a broker. This broker just compares the available bids and asks of a number of banks (usually four or ®ve) by calling them at regular time intervals. In a normal market situation the spreads on Reuters screen will include the best bid and ask price. 1 Often banks are willing to trade only on one side of the bid±ask spread and they try to do so by setting a bid±ask hitting the currently best bid or ask and moving the other side away. 2 Results in Goodhart et al. (1996) suggest that the nature of the `indicative' spreads on Reuters FXFX page is dierent from the `®rm' spreads provided by brokers (derived from Reuters electronic broking system, D2000-2). However,
1 Most banks put quotes on the Reuters screen themselves. In addition, there are several brokers, each with their own limited circle of banks from which they obtain their quotes. As a result Reuters contains more updated information than the broker uses. The minimum spread, however, is 5 ticks on Reuters screen, while it can reduce to 1 tick for a broker using the best bid and ask. 2 For example, if for the DM/$ spot rate the current spread set by the broker is 1.6022±1.6023, a bank willing to sell US dollars could either do so by hitting the current best bid of 1.6022 or by setting a quote of, e.g., 1.6018±1.6023. In the latter case the quote on Reuters screen (1.6018± 1.6023) will be skewed to the left. Similarly a bank willing to buy US Dollars could set a quote of 1.6022±1.6032, skewing the spread to the right.
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an unresolved issue is the informational role of the `indicative' quotes as a re¯ection of the entire spot market which is available to all traders. Our results show that not only the nature of these indicative spreads is dierent, but also that the quoted prices are inecient. This does not necessarily imply pro®table trading opportunities. In a high-volatility situation, for example around news announcements, Reuters FXFX page might lag the current developments. Traders ®rst trade and only then update Reuters screen by setting new quotes. In that case the best bid and ask of the broker might be outside the spreads given on Reuters FXFX page. It will then also be impossible to trade against the bids and asks given on Reuters screen, simply because they are outdated and therefore no longer valid. In all other circumstances studies using Reuters FXFX quotes claim that reputation considerations will ensure that banks will trade at their quotes if requested within reasonable time after the appearance on Reuters. In this study we compare the Reuters quotes for the DeutscheMark/US Dollar (DM/$) exchange rate with the DM/$ futures contract traded on the CME. During our sample period most trading was still conducted by telephone and with many dierent brokers having a reasonable market share. Reuters FXFX page was therefore still the main source of publicly available information, while the individual broker's quotes were only known to the limited circle of his or her clients. 3. Data The data set consists of intraday Reuters quotations of the DM/$ exchange rate from the Olsen and Associates data set, and of futures prices of the DM/$ exchange rate for the September 1993 contract from the CME. The sample period covers June, July and August 1993. We choose to analyse the DM/$ exchange rate since it is the most liquid exchange rate in terms of number of contracts (futures market) and number of bid±ask quotes (spot market). The futures data contain the transaction price, the date and the time truncated to the minute (e.g. 8:370 4500 will be shown as 8:37). The Reuters quotations contain the date, a time stamp to the nearest second, the bid and ask price, the code for the bank, and the code for the country. The data set is an almost complete record of spot DM/$ quotations shown on Reuters FXFX page. Suspect quotations were ®ltered out using the methods of Dacorogna et al. (1993). Whereas Reuters FXFX data cover the entire day (24 hours), the futures data only cover the 7:20 a.m.±14:00 p.m. Chicago Standard Time (CST) period. In total we use 65 common trading intervals (i.e. days), during the trading hours of the CME. In this period we have about 3.2 quotations per minute for the futures market, and about 4.0 observations per minute for the spot market. The distribution of the number of observations over the trading hours of the CME is given in Fig. 1. The decrease in the number of spot quotes that
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Fig. 1. Total number of Reuters spot quotes and futures transaction prices for the DM/$ exchange rate for each minute during the trading hours of the Chicago Mercantile Exchange, 1 June±31 August 1993.
starts around 10:00 a.m. (CST) can be ascribed to the withdrawal of the European traders from the market. To allow for a fair comparison between the futures and the spot market, we con®ne the main part of our analysis to the 7:20± 10:00 a.m. CST window. We construct 1-min prices and returns to compare the futures exchange rates with the quotes on Reuters FXFX page. For the futures transaction prices the last available price in each minute is used, 3 and whenever there was no trade in a certain minute, the price in the previous minute is used. For the spot market the bid±asks are often skewed to one side, and this may alternate between the bid- and ask-side. This `skewing' results in negative autocorrelation (Goodhart and Figliuoli, 1991; Bollerslev and Domowitz, 1993) when using the bid±ask midpoints to generate spot returns. We propose, therefore, to extract spot prices from the Reuters data in two dierent ways. First, we will use the last available quote in each minute. From this bid±ask quote the midpoint is used as the price (from now on we call this panel A):
3 As noted before, the time stamp for the futures prices is truncated to the minute. As a result, e.g. the last observation with time label 0731 will be used to re¯ect the price at 07310 5900 .
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Table 1 Autocorrelation in the DM/$ spot and futures exchange rate returns Spot c Rtÿ1 Rtÿ2 Rtÿ3 Rtÿ4 Rtÿ5 Rtÿ6 Rtÿ7
Futures
Panel A
Panel B
)0.000347 )0.187 a 0.00244 0.0324 a 0.0359 a 0.0250 b
)0.000292 )0.0516 a 0.0448 a 0.0339 a 0.0249 b 0.0215 b
)0.000246 )0.0540 a 0.0442 a 0.0220 b 0.0275 a 0.0409 a )0.0259 a )0.0243 b
The results are obtained from an AR(p) process for the DM/$ spot and futures exchange rate returns. The sample period is June±August 1993, with for every day 1-min observations from 7:20± 10:00 a.m. CST. This results in 10,335 returns. Panel A uses the midpoint of the last spot quote each minute, Panel B uses also the previous two spot quotes (if within 15 seconds) to ®rst determine the best bid and ask and then calculate the midpoint. a Denotes signi®cance at 1% level. b Denotes signi®cance at 5% level.
st st;bid st;ask =2 ln st;bid ln st;ask =2;
1
where the log spot rate st is expressed in US dollars per DeutscheMark, like the futures price. Second, we will also use the two preceeding quotes, if within 15 seconds of the last available quote of the minute, and calculate the best bid and ask (from now on we call this panel B). Thus, we try to imitate what happens in practice, i.e., the broker searching for the currently best available bid and ask. 4 This latter approach will (partly) correct for the spread being usually skewed to one side. This can be observed in Table 1. The AR(1) coef®cient is )0.0516 for Panel B as opposed to )0.187 for Panel A. The negative ®rst order autocorrelation in the futures transaction prices can be attributed to the bid±ask bounce (Roll, 1984). 4. Methodology Having discussed the univariate data series, we can now proceed with their joint analysis based on the covered interest rate parity (CIRP). For the necessary US and German interest rates we obtained daily Eurocurrency rates from Datastream. We refrain from using intraday interest rates. First, they are not readily available. Second, foreign exchange transactions are not settled within 4
Obviously we cannot imitate exactly the broker(s), since the Reuters screen contains actually more spreads than the ones used by a broker. Furthermore, we cannot observe from our data whether a quote is still valid.
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the trading day but at the end of the trading day when the ®nal position in foreign currency is deposited at a bank oering the best rate. 5 Thus, the daily rates turn out to be the realised rates which had to be estimated by the traders during the day. For both the Eurodollar and the Euromark we have the midquotes (the bid- and ask-quotes are symmetric around the mid-quotes) for the 1-week, 1-month, 3-months and 6-months interest rate. From these data we construct midpoint series for the time-to-maturity of the futures contract using a standard polynomial (of order 6) interpolation. 6 The resulting series are rt;mid for the Eurodollar rate, and rft;mid for the Euromark rate. To evaluate the CIRP, Brenner and Kroner (1995) relate the cost-of-carry asset pricing model to the existence of cointegration between the spot and forward (futures) prices. They illustrate that cointegration depends on the time-series properties of the cost-of-carry. Since the interest rate dierential is likely to be stationary, the forward price and spot price in the FX markets should be cointegrated with vector (1 )1). Under certain assumptions given in Brenner and Kroner, a marking-to-market adjustment term, re¯ecting the dierence between futures and forward contracts, while being non-stochastic will have no eect on the cointegration relation. 7 For an extensive summary of the literature on cointegrating vectors for foreign exchange markets we refer to Table 2 in Brenner and Kroner. In our approach we de®ne the theoretical (log) futures price by f T ÿ d st ; ft ln Ft rd;mid ÿ rd;mid
2
where T is the maturity date of the futures contract, and t is the current time on day d. Hence for all prices within day d we make the same interest rate adjustment because the actual transactions in the spot market take place at the end of the trading day. This expression is based upon the CIRP, and it should therefore include an error term equal to the dierence between the forward and futures rate (see footnote 7). When using returns from minute to minute, this error term can be neglected. Furthermore, omitting overnight returns, a return in the theoretical futures price as de®ned by Eq. (2) will be equal to the spot return. The mispricing error is then de®ned as
5 Banks keep a record of all transactions during the day of their currency traders. Only at the end of the day all transactions are actually settled. The ®nal position in each currency has then to be deposited at the best available rates. 6 See for example Chambers et al. (1984), p. 236. It is assumed that the term structure of interest rates may be expressed as a simple polynomial of time. 7 More speci®cally, Brenner and Kroner derive for the (log) futures price
ft rt ÿ rtf T ÿ t st Qt;T ; where Qt;T is a non-stochastic marking-to-market adjustment term. This term will depend on the interest rate expectations of traders, which we cannot measure.
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Zt ft ÿ ft ;
3
where ft is the market observed futures price. If this mispricing variable is stationary (while the observed and theoretical futures prices are non-stationary), the prices will be cointegrated with a vector close to (1 )1). To facilitate the interpretation we will use this exact vector (1 )1). In Section 5 we formally test for cointegration. Engle and Granger (1987) show that if prices are cointegrated, the returns follow an error correction model. In this model the current price changes depend on how far the system was out of long-run equilibrium in the previous period. The traditional solution of ®rst dierencing the data imposes too many unit roots in the system, biasing parameter estimates and inference. Instead, we will estimate the following Vector Error Correction Model (VECM): DXt l
K X Ck DXtÿk ab0 Xtÿ1 et
4
k1
with Xt (ft ft )0 , b is restricted to (1 )1)0 (thus b0 > Xtÿ1 equals ztÿ1 ), l and a are (2 ´ 1) vectors of parameters, Ck are (2 ´ 2) matrices of parameters, et is a (2 ´ 1) error vector with mean zero and variance±covariance matrix X, and K is the lag-length which will be determined using the Schwarz (1978) criterion. Estimation of the model in Eq. (4) allows us to calculate impulse-response functions, and to determine the information share of both the spot and futures market by using the measure de®ned in Hasbrouck (1995), p. 1183. The VECM has a common trends representation (e.g. Johansen, 1991) Xt X 0 C
t X ei C Let ;
5
i1
where X0 is a constant (2 ´ 1) vector, and C(L) a matrix polynomial in the lag operator. C is the impact matrix which represents the long-run impact of a disturbance on each of the two prices. The impact matrix is related to Eq. (4) by the expression C b? a0? Wb? ÿ1 a0? ;
6
where a? (b? ) is a vector orthogonal to the vector a (b), and W is given by WIÿ
K X Ck Kab0 ;
7
k1
where I is the (2 ´ 2) identity matrix. By construction, C will have two identical rows, say c. If the price innovations between the spot and the futures market are correlated, X will not be diagonal. Let F be the Cholesky factorisation of X (F the lower triangular matrix such that X FF 0 ), then the market share of the innovation variance attributable to market j (j 1,2 for the futures and spot market, respectively) is equal to
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cF j 2 : 8 cXc0 The outcome depends on the stacking order of the prices in the vector Xt . The information share is maximised on the ®rst price in the vector. Therefore the information share will alternatively be calculated by putting the spot price (theoretical futures price) ®rst in the vector Xt . Then Eq. (8) will provide both a lower and upper bound for the information share of each market. One disadvantage of the VECM model is the multicollinearity problem between the explanatory variables, the lagged futures and spot returns, obscuring the length of the lead±lag relation, despite penalising the speci®cation of too many lags according to the Schwarz criterion. This multicollinearity eect is quite strong here due to negative autocorrelation in both return series and the positive impact of one market on the other market. This results in opposite signs of the parameters of the futures returns on the one hand and the parameters of the spot returns on the other hand. For this reason we will also calculate cross-correlations between the observed and theoretical futures returns. Finally, to address the impact of high volatility on the intertemporal relations set out above, we split our data set into two parts: high and low volatility. Since the futures market will turn out to be the most frequently updated market, we will employ the following ad hoc rule using the absolute futures returns as a proxy for the volatility: v u nN T T T X X u 1 X 1 1 1X 2 jDf1 j > jDft j P t jDft j ÿ jDft j : 9 N tn1 T t1 t ÿ 1 t1 T i1 Sj
Thus, we attribute each N-minute interval to the high volatility panel if the mean volatility during these N minutes is above the mean volatility of the total sample plus P percent of the standard deviation of the volatility of the total sample. For the majority of cross-correlations both the spot and the futures return will lie within the same N-minute interval. Volatility clustering is then taken into account as well by assigning intervals to the high or low volatility panel instead of single minutes. 5. Results In this section we will ®rst test for cointegration between the market observed futures prices and theoretical (spot-induced) futures prices based on the CIRP. Next, we will estimate the VECM speci®ed in Eq. (4). From this we will calculate impulse±response functions and the information share of both the futures and spot market. In Section 5.2 we investigate simple cross-correlations between the spot and futures returns to determine the lead±lag structure between the two markets.
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Table 2 Augmented Dickey Fuller tests and cointegration Panel A
Levels Dierences Cointegration Vector
a
Mispricing error
b
Panel B
Futures price
Theoretical futures price
Futures price
Theoretical futures price
)2.39 )37.9 )22.7 0.997
)2.37 )38.2 )22.7 1.00
)2.39 )37.9 )22.7 0.997
)2.36 )37.6 )22.7 1.00
)22.1
)22.0
Critical value )2.86 )2.86 )3.30 )2.86
Stationarity and cointegration tests for the DM/$ spot and futures prices. The sample period is June±August 1993, with for every day 1-min observations from 7:20±10:00 a.m. CST. Panel A uses the midpoint of the last spot quote each minute, Panel B uses also the previous two spot quotes (if within 15 seconds) to ®rst determine the best bid and ask and then calculate the midpoint. Theoretical futures prices are calculated using Eq. (2). For the stationarity tests the following equation is estimated using OLS: L X /i Ptÿi ÿ Ptÿiÿ1 et : i Pt ÿ Ptÿ1 h0 h1 Ptÿ1 i1
For both the levels and the ®rst dierences, the t-values of h1 are reported. Critical values are provided in the last column. The null hypothesis of non-stationarity is rejected if the t-value of h1 exceeds the critical value. a P1t c pP2t zt is estimated, ®rst with the futures price as the dependent variable (column `futures price'), second with the theoretical futures price as the dependent variable (column `theoretical futures price'). For the resulting error term, Eq. (i) is estimated. The t-value of h1 is reported here. b For the mispricing error (dierence between futures and theoretical futures price) Eq. (i) is estimated. The t-value of h1 is reported here.
5.1. Cointegration and error correction Table 2 provides the results of the test for cointegration. For both panel A and panel B the (theoretical) futures prices are non-stationary (row 1, labelled `levels'), while the returns are stationary (row 2, labelled `dierences'). Hence both the theoretical futures price and the market observed futures price have one unit root, which is the ®rst condition for cointegration. The estimated cointegration vector (row 4) is close to the expected vector (1)1), and the resulting residual is stationary as can be seen from row 3. Finally, the mispricing error as de®ned in Eq. (2) is stationary. To facilitate interpretation we will use this mispricing error. The results of the VECM model for both panel A and B are provided in Table 3. The mispricing error of the previous period, ztÿ1 , only has a signi®cant impact on spot price changes. Given the estimated coecients (e.g. in Panel A it is 0.215 for the spot equation and )0.0287 for the futures equation), the eect of the previous mispricing error is clearly stronger on the current spot price change. Since the results for Panel A and B are similar, we only report the impulse response functions resulting from the estimated VECM for Panel B. The im-
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Table 3 Vector error correction model for DM/$ spot and futures exchange rate returns Panel A Dftÿ1 Dftÿ2 Dftÿ3 Dftÿ4 Dftÿ5 Dftÿ6 Dftÿ7 Dftÿ8 Dftÿ9 Dftÿ10 Dftÿ11 Dstÿ1 Dstÿ2 Dstÿ3 Dstÿ4 Dstÿ5 Dstÿ6 Dstÿ7 Dstÿ8 Dstÿ9 Dstÿ10 Dstÿ11 ztÿ1 l Adj R2
Panel B
Dst
Dft
Dst
Dft
0.456 a 0.501 a 0.420 a 0.343 a 0.292 a 0.229 a 0.185 a 0.154 a 0.136 a 0.0955 a 0.0451 a )0.708 a )0.404 a )0.345 a )0.285 a )0.228 a )0.193 a )0.168 a )0.116 a )0.0894 a )0.0435 a )0.0146 0.215 a )0.00308 a
)0.0636 a 0.0498 a 0.0119 0.0151 0.0342 )0.0334 )0.0356 b )0.0151 0.00320 )0.0229 )0.0398 a 0.0574 a 0.0242 0.00359 0.00576 0.0100 0.00976 0.00903 0.00842 0.00619 )0.00864 )0.00263 )0.0287 )0.000026
0.403 a 0.507 a 0.401 a 0.322 a 0.283 a 0.224 a 0.189 a 0.151 a 0.134 a 0.0932 a 0.0454 a )0.611 a )0.374 a )0.321 a )0.274 a )0.222 a )0.181 a )0.175 a )0.115 a )0.0820 a )0.0354 a )0.00273 0.170 a )0.00243 a
)0.0669 a 0.0437 a )0.000281 0.00653 0.0294 )0.0312 )0.0272 )0.00460 0.00990 )0.0130 )0.0344 a 0.0812 a 0.0280 0.0180 0.00830 0.00172 0.00215 )0.00897 )0.00366 )0.00936 )0.00268 )0.00588 )0.0293 )0.000022
0.449
0.0137
0.467
0.0143
VECM for the DM/$ spot and futures returns, given in Eq. (4). The sample period is June±August 1993, with for every day 1-min observations from 7:20±10:00 a.m. CST. Panel A uses the midpoint of the last spot quote each minute, Panel B uses also the previous two spot quotes (if within 15 seconds) to ®rst determine the best bid and ask and then calculate the midpoint. Standard errors are usually around 0.01, while White errors are similar to the standard errors. a Denotes signi®cance at 1% level. b Denotes signi®cance at 5% level.
pulse response functions illustrate what happens to the system if there is a one standard deviation shock in either the spot or the futures market. The relevant impulse±response functions are given in Fig. 2. A shock in the futures market has clearly a much larger eect on the subsequent returns in the spot market than vice versa, i.e. the eect of a shock in the spot market on the futures returns. The upper and lower bounds of the information share of each market are calculated according to expression (8). For Panel A this implies an information share of 89.8±98.7% (Panel B: 88.1±98.6%) for the futures market, and 1.27± 10.2% for the spot market. Once again, the futures market is leading the quotes
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Fig. 2. Impulse response functions derived from the VECM results in Table 3. The graph shows the response of the futures returns to a shock in the spot returns (labelled `futures returns') and the response of the spot returns to a shock in the futures returns (labelled `spot returns').
Table 4 Cross-correlations between the DM/$ spot and futures exchange rate returns corr(Dfetÿ4 ,Dset ) corr(Dfetÿ3 ,Dset ) corr(Dfetÿ2 ,Dset ) corr(Dfetÿ1 ,Dset ) corr(Dfet ,Dset ) corr(Dfet ,Dsetÿ1 ) corr(Dfet ,Dsetÿ2 )
Full sample
June
July
August
0.00364 [0.016] 0.0764 a [0.016] 0.396 a [0.022] 0.311 a [0.032] 0.159 a [0.019] 0.0424 a [0.016] 0.00833 [0.014]
0.0228 [0.033] 0.0631 b [0.031] 0.398 a [0.028] 0.515 a [0.036] 0.101 a [0.036] 0.0709 b [0.028] 0.0213 [0.026]
0.00425 [0.021] 0.0905 a [0.025] 0.598 a [0.049] 0.0800 [0.046] )0.0144 [0.017] 0.00293 [0.021] )0.00969 [0.019]
)0.0271 [0.022] 0.0809 a [0.022] 0.159 a [0.025] 0.263 a [0.027] 0.451 a [0.026] 0.0438 [0.025] 0.00894 [0.021]
Dset and Dfet are the prewhitened DM/$ spot and futures returns, respectively, using an AR(p) ®lter. The sample period is June±August 1993, with for every day 1-min observations from 7:20± 10:00 a.m. CST. For the spot returns we employed Panel B. Panel B uses, in addition to the last quote in each minute, also the previous two quotes (if within 15 seconds) to ®rst determine the best bid and ask and then calculate the midpoint. Heteroscedasticity and autocorrelation consistent (HAC) errors inside brackets. a Denotes signi®cance at 1% level. b Denotes signi®cance at 5% level.
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on Reuters FXFX page and new information is incorporated much faster into the futures prices than into the spot quotes. 5.2. Cross-correlations Before calculating the cross-correlations, we ®rst prewhiten the time series using an AR(p) process following Pierce and Haugh (1977). 8 The results for Panel B are given in the ®rst column of Table 4 (the results for Panel A are similar; apparently, the direction of the skewing of the spot spreads is close to random and, therefore, does not aect the results, and the ®ltering procedures remove the dierent autocorrelation patterns). These results show that the futures market leads the spot quotes on Reuters FXFX page signi®cantly up to 3 min, while there is only a small signi®cant 1min lead the other way around. One possible explanation is that updating Reuters screen takes some time, another explanation is that one cannot actually trade against these quotes and as a result insucient eort is taken to make them ecient. Previous studies using Reuters quotes, however, claim that banks have reputation considerations, and for our sample period Reuters was the main information source available to all traders. The results for the subsamples June, July and August in columns 2±4 in Table 4 show that the general conclusions hold. The futures market is more ef®cient than the Reuters spot quotes. 6. The eect of high volatility periods In this section we split the sample into two parts: one where volatility is relatively high and one where volatility is at its normal level. In cases of high volatility or prescheduled news announcements, traders prefer ®rst to trade and only then update their Reuters quotes. However, traders will then also need to closely follow the current developments in the market. 6.1. Prescheduled news announcements Ederington and Lee (1993, 1995) investigate the volatility pattern surrounding news announcements for several futures markets. One of them is the DM/$ futures contract traded at the CME. In the period 7:30±7:31 a.m. CST there is a peak in the futures volatility, coinciding exactly with US macro-economic an-
8
For example for the ®rst column in Table 4 we use the estimated AR(p) processes from Table 1. We also experimented with time-varying AR(p) ®lters. This gives similar results as the ones provided here.
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Fig. 3. Average volatility spot (based on Reuters quotes) and futures exchange rates for the ®rst 40 min of trading in Chicago, 1 June±31 August 1993.
nouncements like GNP and employment rates. Using the absolute values of the futures and spot returns, the average taken over all trading days for each trading minute results in Fig. 3 (only the ®rst 40 min of CME trading are included). As expected, we observe in the period 7:30±7:31 a peak in the futures returns volatility. The peak in the spot returns volatility based on Reuters quotes occurs 1 min later. So, on average (the volatility in) the spot returns are lagging by 1 min in the case of prescheduled news announcements. The fact that there is only a 1 min lag is somewhat surprising given the 3 min lead we found earlier. It seems that the Reuters FXFX page is actually updated quite fast considering the fact that traders ®rst trade and only then update their quotes. Some traders may even temporarily withdraw from the market to wait until the volatile period has passed. To study the eect of prescheduled news announcements in greater detail, we analysed two occasions where the news announcement resulted in a major shock in the DM/$ exchange rate. On Friday, 4 June 1993, the announcement included an increase in US jobs for the month May with 209,000 (while the expectation was 155,000), and the unemployment rate had decreased slightly (while predicted to be stable). According to the news reports this apparently resulted in a fear for increased US in¯ation and an increase in the US interest rate, strengthened by the strong economic quarter compared to the ®rst quarter of 1993. In just a couple of minutes after the announcement the US dollar ap-
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preciated by 1 cent versus the Deutsche Mark. Our second news event took place on Friday, 2 July 1993, when the US dollar depreciated after an increase in non-agricultural employment of 13,000 instead of the expected 130,000. Since the futures prices are labelled up to the minute only, we divide the futures prices uniformly over each minute at equal time intervals (e.g. two futures observations in minute 7:33 a.m. will become 7:33:20 and 7:33:40 a.m.). The spot prices are multiplied by the cost-of-carry. This results in Fig. 4 where we also include the spot spread. On 4 June the futures market immediately reacted to the positive news in the same minute as the news was released, 1 min later followed by the spot quotes. Yet, quotes were still appearing on the Reuters FXFX page between 7:30 and 7:31 a.m. CST. Hence, the time-lag did not occur due to traders ®rst trading and only then posting new quotes. Also, it is surprising to see that the bid± ask spread only increases 1 min after the news release. One would expect spreads to increase before the news release. Second July gives a similar picture. The futures market is again the ®rst to react. In this case, however, it is obvious that the futures market overreacted, since even before the spot rate starts to decrease, the futures price moves up again. Once again there were spot quotes immediately after the release and the spread only increased 2 min after the release. 6.2. High volatility periods To investigate the eect of high volatility more formally, we divide our data according to the rule given in Eq. (9). We experimented with several values for the length of the intervals, N (5, 10 and 20 min), and the percentage of the standard deviation, P (20% and 40%). The results are similar. We therefore only give results for intervals of 5 min (N 5) and P equal to 20%, in Table 5. The spill-overs between the futures and the spot markets are signi®cantly stronger when volatility is high. This applies to both spill-over directions. The signi®cant 1 min lead of the Reuters spot quotes actually disappears in the low volatility panel, while it is larger in magnitude in the high volatility panel. One explanation is that in the case of high volatility related to news, one market might react faster, immediately followed by the other market. When there is no directly related news, the markets might follow each other, but this eect will be noticeably smaller. 9 9 Similar results are found when we split up the sample according to the time of the day, i.e. 7:20± 10:00 a.m. and 11:00 a.m.±14:00 p.m. CST. For the morning period we ®nd a 1-min signi®cant lead of the spot quotes in Table 4, while there is no spot lead left in the afternoon. The futures lead extends to 5 min for the afternoon period. From Fig. 1 it can be seen that trading activity decreases once the European markets are closed. The fact that there is no signi®cant spot lead in the afternoon period, can be attributed to the growing relative importance of the futures market once the European traders retreat from the spot market.
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Fig. 4. Prescheduled news announcements.
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Table 5 Cross-correlations between the DM/$ spot and futures exchange rate returns in high and low volatility periods corr(Dfetÿ4 ,Dset ) corr(Dfetÿ3 ,Dset ) corr(Dfetÿ2 ,Dset ) corr(Dfetÿ1 ,Dset ) corr(Dfet ,Dset ) corr(Dfet ,Dsetÿ1 ) corr(Dfet ,Dsetÿ2 )
Panel I: Low volatility
Panel II: High volatility
)0.0361 [0.014] 0.0218 [0.013] 0.296 a [0.016] 0.244 a [0.015] 0.107 a [0.014] 0.00117 [0.013] )0.0213 [0.012]
0.0349 [0.027] 0.117 a [0.026] 0.469 a [0.034] 0.359 a [0.052] 0.193 a [0.030] 0.0688 a [0.024] 0.0274 [0.020]
Dset and Dfet are the prewhitened DM/$ spot and futures returns, respectively, using an AR(p) ®lter. The sample period is June±August 1993, with for every day 1-min observations from 7:20± 10:00 a.m. CST. The data are split up according to the rule in Eq. (9), with P 0.20 and N 5. This results in 2935 observations in the high volatility panel and 7400 observations in the low volatility panel. For the spot returns we employed Panel B. Panel B uses, in addition to the last quote in each minute, also the previous two quotes (if within 15 seconds) to ®rst determine the best bid and ask and then calculate the midpoint. Heteroscedasticity and autocorrelation consistent (HAC) errors inside brackets. a Denotes signi®cance at 1% level. b Denotes signi®cance at 5% level.
7. A simple trading strategy Having established a statistically signi®cant lead of the futures market over the spot quotes, it is interesting to investigate its economic signi®cance. Of course the underlying test would be more reliable if we would have quotes from brokers at which we could certainly trade. On the other hand, Reuters FXFX page quotes usually include the broker's quotes, and thus the underlying strategy overvalues the trading costs. The spread of the broker can reduce to 1 tick, while the minimal spread on Reuters FXFX page is 5 ticks. For our sample period in many cases the spread is 10 ticks or even 15 ticks. Especially when the spread is skewed to one side, the test will overestimate the costs as compared to reality. In our test we employ the following simple trading strategy: Minute t Minute t 1
Minute t 3
Observe whether jDFt j P f Buy at St1;ask if DFt P f and St1;ask ÿ St1;bid 6 s case 1 Sell at St1;bid if DFt 6 ÿ f and St1;ask ÿ St1;bid 6 s case 2 Sell at St3;bid case 1 Profit: St3;bid ÿ St1;ask Buy at St3;ask case 2 Profit: St1;bid ÿ St3;ask: 10
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Thus, if it is observed at t that the absolute futures return exceeds a certain threshold f, then we buy/sell in the spot market at the ®rst observation in minute t + 1 appearing on Reuters screen if the spread is not too high, i.e., less than a threshold s. The position is liquidated by selling/buying in the spot market at the ®rst observation in minute t + 3, regardless of the spread. Applying this strategy to the total sample of three months for the 7:20± 10:00 a.m. CST window results in Table 6. The ®rst number in columns 2±4 indicates the total pro®t in DeutscheMarks per US dollar. Each time the strategy is applied, it is either ``winning'' or ``losing''. The ®rst number inside brackets denotes the number of times the strategy was winning, the second number denotes the number of times the strategy was losing. The results show that, despite the huge losses induced by the overestimated spot spreads, substantial gains could have been made (assuming one can always trade against the Reuters quotes immediately after appearance). For example, in the case of s equal to 0.0010 (10 ticks) and buying (selling) when the futures return is at least 5 ticks (is below )5 ticks), the above strategy would have earned 591 ticks in the spot market (winning 70 times, losing 34 times of the 104 times we apply the strategy). If the transaction size is 5 million US dollar each time, then 1 tick is worth 500 Deutsche Marks. Thus, 591 ticks amounts to 295,500 Deutsche Marks. The standard error inside parentheses show that this result is signi®cantly dierent from zero. This also applies to the majority of other entries in Table 6.
Table 6 Pro®ts from a simple strategy in the DM/$ exchange rate |DFt | P f
Spread 6 5 ticks
Spread 6 10 ticks
0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.0010
)0.0915 [53;209] (0.0127) )0.7897 [647;1920] (0.0404) )0.0084 [26;58] (0.0080) )0.0831 [399;686] (0.0283) 0.0099 [12;11] (0.0058) 0.0905 [195;162] (0.0214) 0.0067 [5;4] (0.0050) 0.0658 [85;42] (0.0174) 0.0055 [3;4] (0.0048) 0.0591 [70;34] (0.0168) 0.0059 [2;2] (0.0039) 0.0420 [31;11] (0.0116) )0.0003 [0;2] (0.0002) 0.0285 [21;5] (0.0092) 0.0000 [0;0] ()) 0.0260 [10;0] (0.0089) 0.0000 [0;0] ()) 0.0251 [9;0] (0.0088) 0.0000 [0;0] ()) 0.0199 [7;0] (0.0079)
Spread 6 15 ticks )1.6003 )0.3422 0.0660 0.1084 0.1010 0.0910 0.0657 0.0484 0.0489 0.0422
[845;3019] (0.0571) [612;1249] (0.0396) [321;346] (0.0293) [152;96] (0.0232) [131;77] (0.0222) [68;26] (0.0187) [40;15] (0.0166) [20;8] (0.0148) [19;7] (0.0147) [15;6] (0.0140)
Cumulative returns from the trading strategy in Eq. (10). A spot position in DM/$ is started based on the ®rst observation in the minute after a futures increase (decrease) and held for 2 min. Transaction costs are incurred by using the spot bid and ask quotes. Inside brackets the number of times the strategy won and the number of times the strategy lost, respectively. Inside parentheses the standard errors of the returns.
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8. Conclusion This study compares the DM/$ futures prices in Chicago with Reuters foreign exchange page displaying spot exchange rate quotes of many dierent banks. Even though Reuters' FXFX page is mainly indicative, reputation considerations might induce banks to trade at their quotes when asked to within reasonable time after the appearance on the screen. Also, broker's quotes are usually within the Reuter's quotes. Interestingly, we ®nd that the futures market is leading the quotes on Reuters FXFX page up to 3 min. There is only a small lead the other way around. This informational lead is supported by the information share as proposed by Hasbrouck (1995) showing that the information share of the futures market exceeds 89%. In the case of prescheduled news announcements the futures lead is reduced to approximately 1 min. Spot traders might then ®rst trade and only later update quotes on Reuters FXFX page. However, a few examples show that Reuters FXFX page still contains new quotes with spreads of at most 10 ticks immediately after the news release. Not only does this question the assumption that one can trade against the quotes on Reuters screen, it also suggests an alarming ineciency as an informational tool. Our results suggest that it deserves further attention to investigate whether spot traders should more closely watch the futures market. 10 Especially banks putting quotes on the Reuters FXFX page should take current developments in the futures market (if open) into consideration. Acknowledgements The authors would like to thank Yuan-chen Chang, Michel Dacorogna, Theo Nijman, Antoon Pelsser, Piet Sercu, Ton Vorst, Siegfried Trautmann, Casper de Vries, two anonymous referees, participants of the 13th International Conference of the French Finance Association in Geneva (1996), and participants of the 23rd European Finance Association meeting in Oslo (1996) for useful comments. We are also grateful to the ABN-AMRO bank for allowing us to visit their dealing-room in Amsterdam and speak with some of their trad-
10 Nowadays most trading occurs through the brokers, and Reuters claims that its electronic broking system D2000 has a still growing market share. In the Financial Times (30 June 1997) it was recently reported that over the ®rst quarter of 1997 Reuters had a daily average of 21,000 currency deals. Its main rival, EBS, had an average of 24,000 currency deals. Therefore, for future research it is interesting to obtain data from both these brokerage systems (up to now they seem hard to get for a reasonable period of time) and compare them with each other and with the futures market in Chicago.
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ers. The Erasmus Center for Financial Research is gratefully acknowledged for ®nancial support. All remaining errors are our own responsibility. References Bollerslev, T., Domowitz, I., 1993. Trading patterns and prices in the interbank foreign exchange market. Journal of Finance 48, 1421±1443. Bollerslev, T., Melvin, M., 1994. Bid±ask spreads and volatility in the foreign exchange market: an empirical analysis. Journal of International Economics 36, 355±372. Brenner, R.J., Kroner, K.F., 1995. Arbitrage, cointegration, and testing the unbiasedness hypothesis in ®nancial markets. Journal of Financial and Quantitative Analysis 30, 23±42. Chambers, D.R., Carleton, W.T., Waldman, D.W., 1984. A new approach to estimation of the term structure of interest rates. Journal of Financial and Quantitative Analysis 19, 233±252. Dacorogna, M.M., M uller, U.A., Nagler, R.J., Olsen, R.B., Pictet, O.V., 1993. A geographical model for the daily and weekly seasonal volatility in the foreign exchange market. Journal of International Money and Finance 12, 413±438. De Jong, F., Mahieu, R., Schotman, P., 1995. Price discovery in the foreign exchange market: an empirical analysis of the Yen/DMark rate. Unpublished manuscript, Department of Econometrics, Tilburg University. Ederington, L.H., Lee, J.H., 1993. How markets process information: news releases and volatility. Journal of Finance 48, 1161±1191. Ederington, L.H., Lee, J.H., 1995. The short-run dynamics of the price adjustment to new information. Journal of Financial and Quantitative Analysis 30, 117±134. Engle, R.F., Granger, C.W.J., 1987. Co-integration and error correction: representation, estimation and testing. Econometrica 55, 251±276. Goodhart, C.A.E., Figliuoli, L., 1991. Every minute counts in ®nancial markets. Journal of International Money and Finance 10, 23±52. Goodhart, C.A.E., Ito, T., Payne, R., 1996. One day in June, 1993: a study of the working of Reuters D2000-2electronic foreign exchange trading system. In: J. Frankel, G. Galli and A. Giovannini (Eds.), The Microstructure of Foreign Exchange Markets, University of Chicago press, Chicago. Goodhart, C.A.E., Chang, Y.C., Payne, R., 1997. Calibrating an algorithm for estimating transactions from FXFX exchange rate quotes. Journal of International Money and Finance 16, 921±930. Hasbrouck, J., 1995. One security, many markets: determining the contribution to price discovery. Journal of Finance 50, 1175±1199. Johansen, S., 1991. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551±1580. Lyons, R.K., 1995. Tests of microstructural hypotheses in the foreign exchange market. Journal of Financial Economics 39, 321±351. Pierce, D.A., Haugh, L.D., 1977. Causality in temporal systems: characterization and an survey. Journal of Econometrics 5, 265±293. Roll, R., 1984. A simple implicit measure of the eective bid±ask spread in an ecient market. Journal of Finance 39, 1127±1139. Schwarz, G., 1978. Estimating the dimension of a model. The Annals of Statistics 6, 461±464.
The ineciency of Reuters foreign exchange quotes Martin Martens
a,*
, Paul Kofman
b
a
b
Department of Accounting and Finance, Lancaster University, Lancaster, LA1 4YX, UK School of Banking and Finance, The University of New South Wales, Sydney, NSW 2052, Australia Received 18 April 1997; accepted 27 December 1997
Abstract Reuters foreign exchange (FXFX) page is the world wide predominant information source to foreign exchange traders. In this study we compare the indicative spot exchange rate quotes from Reuters with their matching futures exchange rates from the Chicago Mercantile Exchange. We ®nd that the indicative quotes on Reuters FXFX page are inecient and could be improved by incorporating information from the futures market. This casts doubt on the way banks determine these quotes, as well as on the informational content of these quotes as an indicator of the current exchange rate. Ó 1998 Elsevier Science B.V. JEL classi®cation: G14; G15 Keywords: Exchange rates; Futures; Eciency
1. Introduction The spot foreign exchange market is a 24 hours electronic market with brokers and traders around the world. Brokers display quotes to their customers.
* Corresponding author. Tel.: +44 1524 593623; fax: +44 1524 847321; e-mail: [email protected].
0378-4266/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 - 4 2 6 6 ( 9 8 ) 0 0 0 0 4 - 1
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These quotes are the best bid and ask price provided by a limited number of banks regularly contacted by the broker. Since there are many brokers each contacting their own circle of banks to obtain quotes and having their own customers, the natural question arises whether this market is informationally ecient. To date, no data sets have been available allowing for a direct test of the ef®ciency of the spot market in foreign exchange. Goodhart et al. (1996, 1997) study 7 hours of the Reuters-2000 electronic trading system, which at the time of sampling was still a relatively small broker in the spot market. Lyons (1995) studies one week of all transactions of a New York broker. Obviously, any data set on quotes from brokers will only re¯ect a part of the spot market. In fact, the only information source available to all traders around the world consists of indicative quotes, as provided by Reuters foreign exchange (FXFX) page, and those provided by its competitors Knight Ridder and Telerate. As such these quotes play an important role in the spot market, indicating the current foreign exchange rate. Though the quotes are only `indicative', studies using the quotes claim banks have reputation considerations and will most likely trade against their quotes if called within a short time after appearance on the Reuters FXFX page. This assumption is crucial for studies like De Jong et al. (1995) who study triangular arbitrage, Bollerslev and Domowitz (1993), and Dacorogna et al. (1993) who study the trading intensity and volatility patterns in the spot market, and Bollerslev and Melvin (1994) who study the relationship between the spreads and volatility. Similarly, Olsen and Associates who use these quotes to forecast the foreign exchange rate, started a boom in empirical research by releasing 1 year of Reuters quotes in 1994. In this study we further investigate the assumption that one can actually trade against the Reuters quotes. We compare these spot exchange rate quotes with their matching futures exchange rates traded at the Chicago Mercantile Exchange (CME). The futures market is a highly liquid market, but in value terms relatively small as compared to the spot market. Nevertheless, we ®nd that the futures market is leading the `quoted' spot market for up to 3 minutes. The results of a simple trading strategy show that pro®ts can be made from the futures lead, unless trading against the Reuters quotes is not (always) possible. This could (partly) explain our results, which we therefore interpret conditional on the possibility of trading against the Reuters quotes: (i) If one can trade against the Reuters quotes, then our results show that gains can be made and hence the spot market is inecient. (ii) If one cannot (always) trade against the Reuters quotes, our results can be (partly) explained by that fact. However, this implies that studies which made the assumption that one can trade against Reuters quotes were incorrect to do so. Their results will then have to be taken with care. In both cases banks displaying quotes on Reuters FXFX page can improve upon these quotes by paying more attention to the futures market. The futures
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price provides a more adequate re¯ection of the (true) current spot exchange rate than the Reuters quotes. The remaining part of this study is organised as follows. Section 2 discusses in further detail the functioning of the spot and futures markets. In Section 3 the data set is discussed. Section 4 describes the methodology, and Section 5 elaborates upon the results. Section 6 focuses on the eect of prescheduled news announcements and high volatility periods. In Section 7 the pro®tability of a simple trading strategy is tested. Finally, Section 8 will conclude. 2. Microstructure of foreign exchange markets The major dierence between the futures and the spot market in foreign exchange is the trading system. While the futures contracts at the CME are traded in an open outcry (OOC) market, the spot market is an electronic market with brokers and traders around the world. In addition to brokers setting quotes, market participants can also oer or obtain quotes via Reuters, Telerate or Knight Ridder. We will use Reuters FXFX data for the spot rates. These data consist of, mainly indicative, bid and ask quotes. Transaction prices are not available. Each trader can immediately submit quotes to Reuters FXFX page. In addition to Reuters FXFX page, traders have a screen displaying a very small spread often of a magnitude of only 1 tick (i.e., one hundredth of percentage point). This spread re¯ects the current best bid and ask provided by a broker. This broker just compares the available bids and asks of a number of banks (usually four or ®ve) by calling them at regular time intervals. In a normal market situation the spreads on Reuters screen will include the best bid and ask price. 1 Often banks are willing to trade only on one side of the bid±ask spread and they try to do so by setting a bid±ask hitting the currently best bid or ask and moving the other side away. 2 Results in Goodhart et al. (1996) suggest that the nature of the `indicative' spreads on Reuters FXFX page is dierent from the `®rm' spreads provided by brokers (derived from Reuters electronic broking system, D2000-2). However,
1 Most banks put quotes on the Reuters screen themselves. In addition, there are several brokers, each with their own limited circle of banks from which they obtain their quotes. As a result Reuters contains more updated information than the broker uses. The minimum spread, however, is 5 ticks on Reuters screen, while it can reduce to 1 tick for a broker using the best bid and ask. 2 For example, if for the DM/$ spot rate the current spread set by the broker is 1.6022±1.6023, a bank willing to sell US dollars could either do so by hitting the current best bid of 1.6022 or by setting a quote of, e.g., 1.6018±1.6023. In the latter case the quote on Reuters screen (1.6018± 1.6023) will be skewed to the left. Similarly a bank willing to buy US Dollars could set a quote of 1.6022±1.6032, skewing the spread to the right.
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an unresolved issue is the informational role of the `indicative' quotes as a re¯ection of the entire spot market which is available to all traders. Our results show that not only the nature of these indicative spreads is dierent, but also that the quoted prices are inecient. This does not necessarily imply pro®table trading opportunities. In a high-volatility situation, for example around news announcements, Reuters FXFX page might lag the current developments. Traders ®rst trade and only then update Reuters screen by setting new quotes. In that case the best bid and ask of the broker might be outside the spreads given on Reuters FXFX page. It will then also be impossible to trade against the bids and asks given on Reuters screen, simply because they are outdated and therefore no longer valid. In all other circumstances studies using Reuters FXFX quotes claim that reputation considerations will ensure that banks will trade at their quotes if requested within reasonable time after the appearance on Reuters. In this study we compare the Reuters quotes for the DeutscheMark/US Dollar (DM/$) exchange rate with the DM/$ futures contract traded on the CME. During our sample period most trading was still conducted by telephone and with many dierent brokers having a reasonable market share. Reuters FXFX page was therefore still the main source of publicly available information, while the individual broker's quotes were only known to the limited circle of his or her clients. 3. Data The data set consists of intraday Reuters quotations of the DM/$ exchange rate from the Olsen and Associates data set, and of futures prices of the DM/$ exchange rate for the September 1993 contract from the CME. The sample period covers June, July and August 1993. We choose to analyse the DM/$ exchange rate since it is the most liquid exchange rate in terms of number of contracts (futures market) and number of bid±ask quotes (spot market). The futures data contain the transaction price, the date and the time truncated to the minute (e.g. 8:370 4500 will be shown as 8:37). The Reuters quotations contain the date, a time stamp to the nearest second, the bid and ask price, the code for the bank, and the code for the country. The data set is an almost complete record of spot DM/$ quotations shown on Reuters FXFX page. Suspect quotations were ®ltered out using the methods of Dacorogna et al. (1993). Whereas Reuters FXFX data cover the entire day (24 hours), the futures data only cover the 7:20 a.m.±14:00 p.m. Chicago Standard Time (CST) period. In total we use 65 common trading intervals (i.e. days), during the trading hours of the CME. In this period we have about 3.2 quotations per minute for the futures market, and about 4.0 observations per minute for the spot market. The distribution of the number of observations over the trading hours of the CME is given in Fig. 1. The decrease in the number of spot quotes that
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Fig. 1. Total number of Reuters spot quotes and futures transaction prices for the DM/$ exchange rate for each minute during the trading hours of the Chicago Mercantile Exchange, 1 June±31 August 1993.
starts around 10:00 a.m. (CST) can be ascribed to the withdrawal of the European traders from the market. To allow for a fair comparison between the futures and the spot market, we con®ne the main part of our analysis to the 7:20± 10:00 a.m. CST window. We construct 1-min prices and returns to compare the futures exchange rates with the quotes on Reuters FXFX page. For the futures transaction prices the last available price in each minute is used, 3 and whenever there was no trade in a certain minute, the price in the previous minute is used. For the spot market the bid±asks are often skewed to one side, and this may alternate between the bid- and ask-side. This `skewing' results in negative autocorrelation (Goodhart and Figliuoli, 1991; Bollerslev and Domowitz, 1993) when using the bid±ask midpoints to generate spot returns. We propose, therefore, to extract spot prices from the Reuters data in two dierent ways. First, we will use the last available quote in each minute. From this bid±ask quote the midpoint is used as the price (from now on we call this panel A):
3 As noted before, the time stamp for the futures prices is truncated to the minute. As a result, e.g. the last observation with time label 0731 will be used to re¯ect the price at 07310 5900 .
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Table 1 Autocorrelation in the DM/$ spot and futures exchange rate returns Spot c Rtÿ1 Rtÿ2 Rtÿ3 Rtÿ4 Rtÿ5 Rtÿ6 Rtÿ7
Futures
Panel A
Panel B
)0.000347 )0.187 a 0.00244 0.0324 a 0.0359 a 0.0250 b
)0.000292 )0.0516 a 0.0448 a 0.0339 a 0.0249 b 0.0215 b
)0.000246 )0.0540 a 0.0442 a 0.0220 b 0.0275 a 0.0409 a )0.0259 a )0.0243 b
The results are obtained from an AR(p) process for the DM/$ spot and futures exchange rate returns. The sample period is June±August 1993, with for every day 1-min observations from 7:20± 10:00 a.m. CST. This results in 10,335 returns. Panel A uses the midpoint of the last spot quote each minute, Panel B uses also the previous two spot quotes (if within 15 seconds) to ®rst determine the best bid and ask and then calculate the midpoint. a Denotes signi®cance at 1% level. b Denotes signi®cance at 5% level.
st st;bid st;ask =2 ln st;bid ln st;ask =2;
1
where the log spot rate st is expressed in US dollars per DeutscheMark, like the futures price. Second, we will also use the two preceeding quotes, if within 15 seconds of the last available quote of the minute, and calculate the best bid and ask (from now on we call this panel B). Thus, we try to imitate what happens in practice, i.e., the broker searching for the currently best available bid and ask. 4 This latter approach will (partly) correct for the spread being usually skewed to one side. This can be observed in Table 1. The AR(1) coef®cient is )0.0516 for Panel B as opposed to )0.187 for Panel A. The negative ®rst order autocorrelation in the futures transaction prices can be attributed to the bid±ask bounce (Roll, 1984). 4. Methodology Having discussed the univariate data series, we can now proceed with their joint analysis based on the covered interest rate parity (CIRP). For the necessary US and German interest rates we obtained daily Eurocurrency rates from Datastream. We refrain from using intraday interest rates. First, they are not readily available. Second, foreign exchange transactions are not settled within 4
Obviously we cannot imitate exactly the broker(s), since the Reuters screen contains actually more spreads than the ones used by a broker. Furthermore, we cannot observe from our data whether a quote is still valid.
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the trading day but at the end of the trading day when the ®nal position in foreign currency is deposited at a bank oering the best rate. 5 Thus, the daily rates turn out to be the realised rates which had to be estimated by the traders during the day. For both the Eurodollar and the Euromark we have the midquotes (the bid- and ask-quotes are symmetric around the mid-quotes) for the 1-week, 1-month, 3-months and 6-months interest rate. From these data we construct midpoint series for the time-to-maturity of the futures contract using a standard polynomial (of order 6) interpolation. 6 The resulting series are rt;mid for the Eurodollar rate, and rft;mid for the Euromark rate. To evaluate the CIRP, Brenner and Kroner (1995) relate the cost-of-carry asset pricing model to the existence of cointegration between the spot and forward (futures) prices. They illustrate that cointegration depends on the time-series properties of the cost-of-carry. Since the interest rate dierential is likely to be stationary, the forward price and spot price in the FX markets should be cointegrated with vector (1 )1). Under certain assumptions given in Brenner and Kroner, a marking-to-market adjustment term, re¯ecting the dierence between futures and forward contracts, while being non-stochastic will have no eect on the cointegration relation. 7 For an extensive summary of the literature on cointegrating vectors for foreign exchange markets we refer to Table 2 in Brenner and Kroner. In our approach we de®ne the theoretical (log) futures price by f T ÿ d st ; ft ln Ft rd;mid ÿ rd;mid
2
where T is the maturity date of the futures contract, and t is the current time on day d. Hence for all prices within day d we make the same interest rate adjustment because the actual transactions in the spot market take place at the end of the trading day. This expression is based upon the CIRP, and it should therefore include an error term equal to the dierence between the forward and futures rate (see footnote 7). When using returns from minute to minute, this error term can be neglected. Furthermore, omitting overnight returns, a return in the theoretical futures price as de®ned by Eq. (2) will be equal to the spot return. The mispricing error is then de®ned as
5 Banks keep a record of all transactions during the day of their currency traders. Only at the end of the day all transactions are actually settled. The ®nal position in each currency has then to be deposited at the best available rates. 6 See for example Chambers et al. (1984), p. 236. It is assumed that the term structure of interest rates may be expressed as a simple polynomial of time. 7 More speci®cally, Brenner and Kroner derive for the (log) futures price
ft rt ÿ rtf T ÿ t st Qt;T ; where Qt;T is a non-stochastic marking-to-market adjustment term. This term will depend on the interest rate expectations of traders, which we cannot measure.
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Zt ft ÿ ft ;
3
where ft is the market observed futures price. If this mispricing variable is stationary (while the observed and theoretical futures prices are non-stationary), the prices will be cointegrated with a vector close to (1 )1). To facilitate the interpretation we will use this exact vector (1 )1). In Section 5 we formally test for cointegration. Engle and Granger (1987) show that if prices are cointegrated, the returns follow an error correction model. In this model the current price changes depend on how far the system was out of long-run equilibrium in the previous period. The traditional solution of ®rst dierencing the data imposes too many unit roots in the system, biasing parameter estimates and inference. Instead, we will estimate the following Vector Error Correction Model (VECM): DXt l
K X Ck DXtÿk ab0 Xtÿ1 et
4
k1
with Xt (ft ft )0 , b is restricted to (1 )1)0 (thus b0 > Xtÿ1 equals ztÿ1 ), l and a are (2 ´ 1) vectors of parameters, Ck are (2 ´ 2) matrices of parameters, et is a (2 ´ 1) error vector with mean zero and variance±covariance matrix X, and K is the lag-length which will be determined using the Schwarz (1978) criterion. Estimation of the model in Eq. (4) allows us to calculate impulse-response functions, and to determine the information share of both the spot and futures market by using the measure de®ned in Hasbrouck (1995), p. 1183. The VECM has a common trends representation (e.g. Johansen, 1991) Xt X 0 C
t X ei C Let ;
5
i1
where X0 is a constant (2 ´ 1) vector, and C(L) a matrix polynomial in the lag operator. C is the impact matrix which represents the long-run impact of a disturbance on each of the two prices. The impact matrix is related to Eq. (4) by the expression C b? a0? Wb? ÿ1 a0? ;
6
where a? (b? ) is a vector orthogonal to the vector a (b), and W is given by WIÿ
K X Ck Kab0 ;
7
k1
where I is the (2 ´ 2) identity matrix. By construction, C will have two identical rows, say c. If the price innovations between the spot and the futures market are correlated, X will not be diagonal. Let F be the Cholesky factorisation of X (F the lower triangular matrix such that X FF 0 ), then the market share of the innovation variance attributable to market j (j 1,2 for the futures and spot market, respectively) is equal to
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cF j 2 : 8 cXc0 The outcome depends on the stacking order of the prices in the vector Xt . The information share is maximised on the ®rst price in the vector. Therefore the information share will alternatively be calculated by putting the spot price (theoretical futures price) ®rst in the vector Xt . Then Eq. (8) will provide both a lower and upper bound for the information share of each market. One disadvantage of the VECM model is the multicollinearity problem between the explanatory variables, the lagged futures and spot returns, obscuring the length of the lead±lag relation, despite penalising the speci®cation of too many lags according to the Schwarz criterion. This multicollinearity eect is quite strong here due to negative autocorrelation in both return series and the positive impact of one market on the other market. This results in opposite signs of the parameters of the futures returns on the one hand and the parameters of the spot returns on the other hand. For this reason we will also calculate cross-correlations between the observed and theoretical futures returns. Finally, to address the impact of high volatility on the intertemporal relations set out above, we split our data set into two parts: high and low volatility. Since the futures market will turn out to be the most frequently updated market, we will employ the following ad hoc rule using the absolute futures returns as a proxy for the volatility: v u nN T T T X X u 1 X 1 1 1X 2 jDf1 j > jDft j P t jDft j ÿ jDft j : 9 N tn1 T t1 t ÿ 1 t1 T i1 Sj
Thus, we attribute each N-minute interval to the high volatility panel if the mean volatility during these N minutes is above the mean volatility of the total sample plus P percent of the standard deviation of the volatility of the total sample. For the majority of cross-correlations both the spot and the futures return will lie within the same N-minute interval. Volatility clustering is then taken into account as well by assigning intervals to the high or low volatility panel instead of single minutes. 5. Results In this section we will ®rst test for cointegration between the market observed futures prices and theoretical (spot-induced) futures prices based on the CIRP. Next, we will estimate the VECM speci®ed in Eq. (4). From this we will calculate impulse±response functions and the information share of both the futures and spot market. In Section 5.2 we investigate simple cross-correlations between the spot and futures returns to determine the lead±lag structure between the two markets.
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Table 2 Augmented Dickey Fuller tests and cointegration Panel A
Levels Dierences Cointegration Vector
a
Mispricing error
b
Panel B
Futures price
Theoretical futures price
Futures price
Theoretical futures price
)2.39 )37.9 )22.7 0.997
)2.37 )38.2 )22.7 1.00
)2.39 )37.9 )22.7 0.997
)2.36 )37.6 )22.7 1.00
)22.1
)22.0
Critical value )2.86 )2.86 )3.30 )2.86
Stationarity and cointegration tests for the DM/$ spot and futures prices. The sample period is June±August 1993, with for every day 1-min observations from 7:20±10:00 a.m. CST. Panel A uses the midpoint of the last spot quote each minute, Panel B uses also the previous two spot quotes (if within 15 seconds) to ®rst determine the best bid and ask and then calculate the midpoint. Theoretical futures prices are calculated using Eq. (2). For the stationarity tests the following equation is estimated using OLS: L X /i Ptÿi ÿ Ptÿiÿ1 et : i Pt ÿ Ptÿ1 h0 h1 Ptÿ1 i1
For both the levels and the ®rst dierences, the t-values of h1 are reported. Critical values are provided in the last column. The null hypothesis of non-stationarity is rejected if the t-value of h1 exceeds the critical value. a P1t c pP2t zt is estimated, ®rst with the futures price as the dependent variable (column `futures price'), second with the theoretical futures price as the dependent variable (column `theoretical futures price'). For the resulting error term, Eq. (i) is estimated. The t-value of h1 is reported here. b For the mispricing error (dierence between futures and theoretical futures price) Eq. (i) is estimated. The t-value of h1 is reported here.
5.1. Cointegration and error correction Table 2 provides the results of the test for cointegration. For both panel A and panel B the (theoretical) futures prices are non-stationary (row 1, labelled `levels'), while the returns are stationary (row 2, labelled `dierences'). Hence both the theoretical futures price and the market observed futures price have one unit root, which is the ®rst condition for cointegration. The estimated cointegration vector (row 4) is close to the expected vector (1)1), and the resulting residual is stationary as can be seen from row 3. Finally, the mispricing error as de®ned in Eq. (2) is stationary. To facilitate interpretation we will use this mispricing error. The results of the VECM model for both panel A and B are provided in Table 3. The mispricing error of the previous period, ztÿ1 , only has a signi®cant impact on spot price changes. Given the estimated coecients (e.g. in Panel A it is 0.215 for the spot equation and )0.0287 for the futures equation), the eect of the previous mispricing error is clearly stronger on the current spot price change. Since the results for Panel A and B are similar, we only report the impulse response functions resulting from the estimated VECM for Panel B. The im-
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Table 3 Vector error correction model for DM/$ spot and futures exchange rate returns Panel A Dftÿ1 Dftÿ2 Dftÿ3 Dftÿ4 Dftÿ5 Dftÿ6 Dftÿ7 Dftÿ8 Dftÿ9 Dftÿ10 Dftÿ11 Dstÿ1 Dstÿ2 Dstÿ3 Dstÿ4 Dstÿ5 Dstÿ6 Dstÿ7 Dstÿ8 Dstÿ9 Dstÿ10 Dstÿ11 ztÿ1 l Adj R2
Panel B
Dst
Dft
Dst
Dft
0.456 a 0.501 a 0.420 a 0.343 a 0.292 a 0.229 a 0.185 a 0.154 a 0.136 a 0.0955 a 0.0451 a )0.708 a )0.404 a )0.345 a )0.285 a )0.228 a )0.193 a )0.168 a )0.116 a )0.0894 a )0.0435 a )0.0146 0.215 a )0.00308 a
)0.0636 a 0.0498 a 0.0119 0.0151 0.0342 )0.0334 )0.0356 b )0.0151 0.00320 )0.0229 )0.0398 a 0.0574 a 0.0242 0.00359 0.00576 0.0100 0.00976 0.00903 0.00842 0.00619 )0.00864 )0.00263 )0.0287 )0.000026
0.403 a 0.507 a 0.401 a 0.322 a 0.283 a 0.224 a 0.189 a 0.151 a 0.134 a 0.0932 a 0.0454 a )0.611 a )0.374 a )0.321 a )0.274 a )0.222 a )0.181 a )0.175 a )0.115 a )0.0820 a )0.0354 a )0.00273 0.170 a )0.00243 a
)0.0669 a 0.0437 a )0.000281 0.00653 0.0294 )0.0312 )0.0272 )0.00460 0.00990 )0.0130 )0.0344 a 0.0812 a 0.0280 0.0180 0.00830 0.00172 0.00215 )0.00897 )0.00366 )0.00936 )0.00268 )0.00588 )0.0293 )0.000022
0.449
0.0137
0.467
0.0143
VECM for the DM/$ spot and futures returns, given in Eq. (4). The sample period is June±August 1993, with for every day 1-min observations from 7:20±10:00 a.m. CST. Panel A uses the midpoint of the last spot quote each minute, Panel B uses also the previous two spot quotes (if within 15 seconds) to ®rst determine the best bid and ask and then calculate the midpoint. Standard errors are usually around 0.01, while White errors are similar to the standard errors. a Denotes signi®cance at 1% level. b Denotes signi®cance at 5% level.
pulse response functions illustrate what happens to the system if there is a one standard deviation shock in either the spot or the futures market. The relevant impulse±response functions are given in Fig. 2. A shock in the futures market has clearly a much larger eect on the subsequent returns in the spot market than vice versa, i.e. the eect of a shock in the spot market on the futures returns. The upper and lower bounds of the information share of each market are calculated according to expression (8). For Panel A this implies an information share of 89.8±98.7% (Panel B: 88.1±98.6%) for the futures market, and 1.27± 10.2% for the spot market. Once again, the futures market is leading the quotes
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Fig. 2. Impulse response functions derived from the VECM results in Table 3. The graph shows the response of the futures returns to a shock in the spot returns (labelled `futures returns') and the response of the spot returns to a shock in the futures returns (labelled `spot returns').
Table 4 Cross-correlations between the DM/$ spot and futures exchange rate returns corr(Dfetÿ4 ,Dset ) corr(Dfetÿ3 ,Dset ) corr(Dfetÿ2 ,Dset ) corr(Dfetÿ1 ,Dset ) corr(Dfet ,Dset ) corr(Dfet ,Dsetÿ1 ) corr(Dfet ,Dsetÿ2 )
Full sample
June
July
August
0.00364 [0.016] 0.0764 a [0.016] 0.396 a [0.022] 0.311 a [0.032] 0.159 a [0.019] 0.0424 a [0.016] 0.00833 [0.014]
0.0228 [0.033] 0.0631 b [0.031] 0.398 a [0.028] 0.515 a [0.036] 0.101 a [0.036] 0.0709 b [0.028] 0.0213 [0.026]
0.00425 [0.021] 0.0905 a [0.025] 0.598 a [0.049] 0.0800 [0.046] )0.0144 [0.017] 0.00293 [0.021] )0.00969 [0.019]
)0.0271 [0.022] 0.0809 a [0.022] 0.159 a [0.025] 0.263 a [0.027] 0.451 a [0.026] 0.0438 [0.025] 0.00894 [0.021]
Dset and Dfet are the prewhitened DM/$ spot and futures returns, respectively, using an AR(p) ®lter. The sample period is June±August 1993, with for every day 1-min observations from 7:20± 10:00 a.m. CST. For the spot returns we employed Panel B. Panel B uses, in addition to the last quote in each minute, also the previous two quotes (if within 15 seconds) to ®rst determine the best bid and ask and then calculate the midpoint. Heteroscedasticity and autocorrelation consistent (HAC) errors inside brackets. a Denotes signi®cance at 1% level. b Denotes signi®cance at 5% level.
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on Reuters FXFX page and new information is incorporated much faster into the futures prices than into the spot quotes. 5.2. Cross-correlations Before calculating the cross-correlations, we ®rst prewhiten the time series using an AR(p) process following Pierce and Haugh (1977). 8 The results for Panel B are given in the ®rst column of Table 4 (the results for Panel A are similar; apparently, the direction of the skewing of the spot spreads is close to random and, therefore, does not aect the results, and the ®ltering procedures remove the dierent autocorrelation patterns). These results show that the futures market leads the spot quotes on Reuters FXFX page signi®cantly up to 3 min, while there is only a small signi®cant 1min lead the other way around. One possible explanation is that updating Reuters screen takes some time, another explanation is that one cannot actually trade against these quotes and as a result insucient eort is taken to make them ecient. Previous studies using Reuters quotes, however, claim that banks have reputation considerations, and for our sample period Reuters was the main information source available to all traders. The results for the subsamples June, July and August in columns 2±4 in Table 4 show that the general conclusions hold. The futures market is more ef®cient than the Reuters spot quotes. 6. The eect of high volatility periods In this section we split the sample into two parts: one where volatility is relatively high and one where volatility is at its normal level. In cases of high volatility or prescheduled news announcements, traders prefer ®rst to trade and only then update their Reuters quotes. However, traders will then also need to closely follow the current developments in the market. 6.1. Prescheduled news announcements Ederington and Lee (1993, 1995) investigate the volatility pattern surrounding news announcements for several futures markets. One of them is the DM/$ futures contract traded at the CME. In the period 7:30±7:31 a.m. CST there is a peak in the futures volatility, coinciding exactly with US macro-economic an-
8
For example for the ®rst column in Table 4 we use the estimated AR(p) processes from Table 1. We also experimented with time-varying AR(p) ®lters. This gives similar results as the ones provided here.
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Fig. 3. Average volatility spot (based on Reuters quotes) and futures exchange rates for the ®rst 40 min of trading in Chicago, 1 June±31 August 1993.
nouncements like GNP and employment rates. Using the absolute values of the futures and spot returns, the average taken over all trading days for each trading minute results in Fig. 3 (only the ®rst 40 min of CME trading are included). As expected, we observe in the period 7:30±7:31 a peak in the futures returns volatility. The peak in the spot returns volatility based on Reuters quotes occurs 1 min later. So, on average (the volatility in) the spot returns are lagging by 1 min in the case of prescheduled news announcements. The fact that there is only a 1 min lag is somewhat surprising given the 3 min lead we found earlier. It seems that the Reuters FXFX page is actually updated quite fast considering the fact that traders ®rst trade and only then update their quotes. Some traders may even temporarily withdraw from the market to wait until the volatile period has passed. To study the eect of prescheduled news announcements in greater detail, we analysed two occasions where the news announcement resulted in a major shock in the DM/$ exchange rate. On Friday, 4 June 1993, the announcement included an increase in US jobs for the month May with 209,000 (while the expectation was 155,000), and the unemployment rate had decreased slightly (while predicted to be stable). According to the news reports this apparently resulted in a fear for increased US in¯ation and an increase in the US interest rate, strengthened by the strong economic quarter compared to the ®rst quarter of 1993. In just a couple of minutes after the announcement the US dollar ap-
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preciated by 1 cent versus the Deutsche Mark. Our second news event took place on Friday, 2 July 1993, when the US dollar depreciated after an increase in non-agricultural employment of 13,000 instead of the expected 130,000. Since the futures prices are labelled up to the minute only, we divide the futures prices uniformly over each minute at equal time intervals (e.g. two futures observations in minute 7:33 a.m. will become 7:33:20 and 7:33:40 a.m.). The spot prices are multiplied by the cost-of-carry. This results in Fig. 4 where we also include the spot spread. On 4 June the futures market immediately reacted to the positive news in the same minute as the news was released, 1 min later followed by the spot quotes. Yet, quotes were still appearing on the Reuters FXFX page between 7:30 and 7:31 a.m. CST. Hence, the time-lag did not occur due to traders ®rst trading and only then posting new quotes. Also, it is surprising to see that the bid± ask spread only increases 1 min after the news release. One would expect spreads to increase before the news release. Second July gives a similar picture. The futures market is again the ®rst to react. In this case, however, it is obvious that the futures market overreacted, since even before the spot rate starts to decrease, the futures price moves up again. Once again there were spot quotes immediately after the release and the spread only increased 2 min after the release. 6.2. High volatility periods To investigate the eect of high volatility more formally, we divide our data according to the rule given in Eq. (9). We experimented with several values for the length of the intervals, N (5, 10 and 20 min), and the percentage of the standard deviation, P (20% and 40%). The results are similar. We therefore only give results for intervals of 5 min (N 5) and P equal to 20%, in Table 5. The spill-overs between the futures and the spot markets are signi®cantly stronger when volatility is high. This applies to both spill-over directions. The signi®cant 1 min lead of the Reuters spot quotes actually disappears in the low volatility panel, while it is larger in magnitude in the high volatility panel. One explanation is that in the case of high volatility related to news, one market might react faster, immediately followed by the other market. When there is no directly related news, the markets might follow each other, but this eect will be noticeably smaller. 9 9 Similar results are found when we split up the sample according to the time of the day, i.e. 7:20± 10:00 a.m. and 11:00 a.m.±14:00 p.m. CST. For the morning period we ®nd a 1-min signi®cant lead of the spot quotes in Table 4, while there is no spot lead left in the afternoon. The futures lead extends to 5 min for the afternoon period. From Fig. 1 it can be seen that trading activity decreases once the European markets are closed. The fact that there is no signi®cant spot lead in the afternoon period, can be attributed to the growing relative importance of the futures market once the European traders retreat from the spot market.
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Fig. 4. Prescheduled news announcements.
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Table 5 Cross-correlations between the DM/$ spot and futures exchange rate returns in high and low volatility periods corr(Dfetÿ4 ,Dset ) corr(Dfetÿ3 ,Dset ) corr(Dfetÿ2 ,Dset ) corr(Dfetÿ1 ,Dset ) corr(Dfet ,Dset ) corr(Dfet ,Dsetÿ1 ) corr(Dfet ,Dsetÿ2 )
Panel I: Low volatility
Panel II: High volatility
)0.0361 [0.014] 0.0218 [0.013] 0.296 a [0.016] 0.244 a [0.015] 0.107 a [0.014] 0.00117 [0.013] )0.0213 [0.012]
0.0349 [0.027] 0.117 a [0.026] 0.469 a [0.034] 0.359 a [0.052] 0.193 a [0.030] 0.0688 a [0.024] 0.0274 [0.020]
Dset and Dfet are the prewhitened DM/$ spot and futures returns, respectively, using an AR(p) ®lter. The sample period is June±August 1993, with for every day 1-min observations from 7:20± 10:00 a.m. CST. The data are split up according to the rule in Eq. (9), with P 0.20 and N 5. This results in 2935 observations in the high volatility panel and 7400 observations in the low volatility panel. For the spot returns we employed Panel B. Panel B uses, in addition to the last quote in each minute, also the previous two quotes (if within 15 seconds) to ®rst determine the best bid and ask and then calculate the midpoint. Heteroscedasticity and autocorrelation consistent (HAC) errors inside brackets. a Denotes signi®cance at 1% level. b Denotes signi®cance at 5% level.
7. A simple trading strategy Having established a statistically signi®cant lead of the futures market over the spot quotes, it is interesting to investigate its economic signi®cance. Of course the underlying test would be more reliable if we would have quotes from brokers at which we could certainly trade. On the other hand, Reuters FXFX page quotes usually include the broker's quotes, and thus the underlying strategy overvalues the trading costs. The spread of the broker can reduce to 1 tick, while the minimal spread on Reuters FXFX page is 5 ticks. For our sample period in many cases the spread is 10 ticks or even 15 ticks. Especially when the spread is skewed to one side, the test will overestimate the costs as compared to reality. In our test we employ the following simple trading strategy: Minute t Minute t 1
Minute t 3
Observe whether jDFt j P f Buy at St1;ask if DFt P f and St1;ask ÿ St1;bid 6 s case 1 Sell at St1;bid if DFt 6 ÿ f and St1;ask ÿ St1;bid 6 s case 2 Sell at St3;bid case 1 Profit: St3;bid ÿ St1;ask Buy at St3;ask case 2 Profit: St1;bid ÿ St3;ask: 10
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Thus, if it is observed at t that the absolute futures return exceeds a certain threshold f, then we buy/sell in the spot market at the ®rst observation in minute t + 1 appearing on Reuters screen if the spread is not too high, i.e., less than a threshold s. The position is liquidated by selling/buying in the spot market at the ®rst observation in minute t + 3, regardless of the spread. Applying this strategy to the total sample of three months for the 7:20± 10:00 a.m. CST window results in Table 6. The ®rst number in columns 2±4 indicates the total pro®t in DeutscheMarks per US dollar. Each time the strategy is applied, it is either ``winning'' or ``losing''. The ®rst number inside brackets denotes the number of times the strategy was winning, the second number denotes the number of times the strategy was losing. The results show that, despite the huge losses induced by the overestimated spot spreads, substantial gains could have been made (assuming one can always trade against the Reuters quotes immediately after appearance). For example, in the case of s equal to 0.0010 (10 ticks) and buying (selling) when the futures return is at least 5 ticks (is below )5 ticks), the above strategy would have earned 591 ticks in the spot market (winning 70 times, losing 34 times of the 104 times we apply the strategy). If the transaction size is 5 million US dollar each time, then 1 tick is worth 500 Deutsche Marks. Thus, 591 ticks amounts to 295,500 Deutsche Marks. The standard error inside parentheses show that this result is signi®cantly dierent from zero. This also applies to the majority of other entries in Table 6.
Table 6 Pro®ts from a simple strategy in the DM/$ exchange rate |DFt | P f
Spread 6 5 ticks
Spread 6 10 ticks
0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.0010
)0.0915 [53;209] (0.0127) )0.7897 [647;1920] (0.0404) )0.0084 [26;58] (0.0080) )0.0831 [399;686] (0.0283) 0.0099 [12;11] (0.0058) 0.0905 [195;162] (0.0214) 0.0067 [5;4] (0.0050) 0.0658 [85;42] (0.0174) 0.0055 [3;4] (0.0048) 0.0591 [70;34] (0.0168) 0.0059 [2;2] (0.0039) 0.0420 [31;11] (0.0116) )0.0003 [0;2] (0.0002) 0.0285 [21;5] (0.0092) 0.0000 [0;0] ()) 0.0260 [10;0] (0.0089) 0.0000 [0;0] ()) 0.0251 [9;0] (0.0088) 0.0000 [0;0] ()) 0.0199 [7;0] (0.0079)
Spread 6 15 ticks )1.6003 )0.3422 0.0660 0.1084 0.1010 0.0910 0.0657 0.0484 0.0489 0.0422
[845;3019] (0.0571) [612;1249] (0.0396) [321;346] (0.0293) [152;96] (0.0232) [131;77] (0.0222) [68;26] (0.0187) [40;15] (0.0166) [20;8] (0.0148) [19;7] (0.0147) [15;6] (0.0140)
Cumulative returns from the trading strategy in Eq. (10). A spot position in DM/$ is started based on the ®rst observation in the minute after a futures increase (decrease) and held for 2 min. Transaction costs are incurred by using the spot bid and ask quotes. Inside brackets the number of times the strategy won and the number of times the strategy lost, respectively. Inside parentheses the standard errors of the returns.
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8. Conclusion This study compares the DM/$ futures prices in Chicago with Reuters foreign exchange page displaying spot exchange rate quotes of many dierent banks. Even though Reuters' FXFX page is mainly indicative, reputation considerations might induce banks to trade at their quotes when asked to within reasonable time after the appearance on the screen. Also, broker's quotes are usually within the Reuter's quotes. Interestingly, we ®nd that the futures market is leading the quotes on Reuters FXFX page up to 3 min. There is only a small lead the other way around. This informational lead is supported by the information share as proposed by Hasbrouck (1995) showing that the information share of the futures market exceeds 89%. In the case of prescheduled news announcements the futures lead is reduced to approximately 1 min. Spot traders might then ®rst trade and only later update quotes on Reuters FXFX page. However, a few examples show that Reuters FXFX page still contains new quotes with spreads of at most 10 ticks immediately after the news release. Not only does this question the assumption that one can trade against the quotes on Reuters screen, it also suggests an alarming ineciency as an informational tool. Our results suggest that it deserves further attention to investigate whether spot traders should more closely watch the futures market. 10 Especially banks putting quotes on the Reuters FXFX page should take current developments in the futures market (if open) into consideration. Acknowledgements The authors would like to thank Yuan-chen Chang, Michel Dacorogna, Theo Nijman, Antoon Pelsser, Piet Sercu, Ton Vorst, Siegfried Trautmann, Casper de Vries, two anonymous referees, participants of the 13th International Conference of the French Finance Association in Geneva (1996), and participants of the 23rd European Finance Association meeting in Oslo (1996) for useful comments. We are also grateful to the ABN-AMRO bank for allowing us to visit their dealing-room in Amsterdam and speak with some of their trad-
10 Nowadays most trading occurs through the brokers, and Reuters claims that its electronic broking system D2000 has a still growing market share. In the Financial Times (30 June 1997) it was recently reported that over the ®rst quarter of 1997 Reuters had a daily average of 21,000 currency deals. Its main rival, EBS, had an average of 24,000 currency deals. Therefore, for future research it is interesting to obtain data from both these brokerage systems (up to now they seem hard to get for a reasonable period of time) and compare them with each other and with the futures market in Chicago.
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