The trading mechanism, cross listed stocks: a comparison of the Paris Bourse and SEAQ- International

Transcription

1 Int. Fin. Markets, Inst. and Money 13 (2003) 401/417 The trading mechanism, cross listed stocks: a comparison of the Paris Bourse and SEAQ- International Patricia Chelley-Steeley * Accounting, Finance and Law Group, Aston Business School, University of Aston, Aston Triangle, Birmingham, UK Received 6 May 2001; accepted 6 November 2002 Abstract This paper studies the behaviour of returns for a sample of cross-listed stocks, listed on both the Paris Bourse and SEAQ-International in London. The aim of the paper is to discover which market adjusts to fundamental news more quickly, the home market of Paris or SEAQ- International. We find that prices in London adjust to changes in their fundamental value more slowly than Paris prices, despite the ability to quickly arbitrage between the two markets. We suggest that this finding may reflect the type of trading, which takes place in the two markets and differences associated with the reporting of large trades. We also estimate the amount of noise present in the two markets and show that the Paris market is more noisy than London. # 2003 Published by Elsevier B.V. Keywords: Cross listed stocks; Noise; Trading mechanism JEL classification: G15 1. Introduction In this paper, we show that the stock exchange trading mechanism can influence the speed that stock prices adjust to their fundamental value. We estimate the partial * Tel.: / ; fax: / address: pcs2@stir.ac.uk (P. Chelley-Steeley) /03/$ - see front matter # 2003 Published by Elsevier B.V. doi: /s (03)

2 402 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/417 adjustment model of Amihud and Mendelson (1987), and by using a Kalman filter, obtain estimates of both the partial adjustment parameter and the variance of noise. The use of a Kalman filter is an advance upon previous work that was unable to estimate simultaneously the partial adjustment coefficient and the variance of noise. Three main results are presented in this paper. First, we find that French stocks traded on the Paris Bourse adjust to their fundamental value more quickly than the same stocks traded on SEAQ-International (SEAQ-I) in London. Second, Paris price changes appear to be more noisy than London price changes, which is consistent with earlier findings by Pagano and Roell (1990), Madhavan (1992) and Biais (1993). Third, we present new evidence that shows that the speed with which prices adjust to intrinsic prices is time varying. The remainder of this paper is set out as follows. Section 2 reviews the literature which has linked the trading mechanism to the behaviour of stock returns. Section 3 compares the London and Paris trading systems. Section 4 describes the partial adjustment model of Amihud and Mendelson (1987) which will be applied in this paper. Section 5 describes the data that is used in this study and presents some summary information. Section 6 explains the Kalman Filter estimation process and provides the results. Section 7 considers how time variation may influence the speed of adjustment. Section 8 offers some conclusions to the paper. 2. Literature review Numerous studies, including those of Cohen et al. (1978) and Hasbrouck (1987) show that the trading mechanism of a stock exchange can exert a strong influence on the short run behaviour of equity prices and their volatility. The influence of the trading mechanism on the volatility of returns has also been noted in models by Amihud and Mendelson (1980, 1982), Biais (1993) and Handa and Schwartz (1996). Pioneering work by Amihud and Mendelson (1980, 1982) highlighted how a dealer can reduce stock price volatility by adjusting inventory in response to temporary imbalances in the order flow. The effect of the trading mechanism on return volatility is also considered by Biais (1993) who analyses the performance of fragmented and centralised markets, which have different levels of transparency. In the centralised market dealers compete with each other to attract the order flow, and observe the quotes and transactions of competitors. In the fragmented market, transactions arise as a result of bilateral negotiations, and market makers cannot observe their competitors quotes or the intensity of their desires to trade. The model shows that although the bid-ask spread is the same in both types of markets, the volatility of the spread in the centralised market is higher. More recently, Handa and Schwartz (1996) have shown that in a limit order trading system, when there is a shortage of orders, there is a rise in return volatility. All three models predict that dealer trading mechanisms generate less return volatility than auction markets. One way of comparing two trading mechanisms empirically is to use the approach suggested by Amihud and Mendelson (1987), who studied the volatility of returns from different trading mechanisms. Because the NYSE opens with a call auction but

3 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/ trades as a specialist dealer market thereafter, open to open returns reflect the influence of the opening auction while close to close returns reflect the influence of the specialist dealer market. Comparisons of opening and closing prices led Amihud and Mendelson (1987) and Stoll and Whaley (1990) to conclude that open to open returns are on average 20% more volatile than close to close returns. This research has encouraged the belief that call auctions have been a more noisy trading mechanism than continuous dealer markets. French and Roll (1986) have shown that there is a problem with the research that has studied the NYSE. They have shown that returns generated immediately following a market closure are characterised by increased volatility. This means that it is impossible to say whether opening NYSE returns are more volatile because of the trading mechanism or are more volatile because of the overnight closure. In our study of trading mechanisms we avoid the problem of the overnight closure by comparing the continuous dealer market SEAQ-I (SEAQ-International is the London trading system which executes deals in non UK shares) with the continuous auction market of the Paris Bourse. Since dually listed stocks have the same underlying intrinsic value in both markets, volatility caused by changes in value must be the same in both markets. Therefore, differences in return volatility must reflect the influence of the trading mechanism. A number of notable differences between SEAQ-I and the Paris Bourse have been noted previously. Extensive work on European markets by Pagano and Roell (1990) showed that for small trades, the Paris Bourse offered higher levels of liquidity than SEAQ-I. However, when trades were large, liquidity in London appeared higher. The Paris Bourse was essentially a tighter market, but SEAQ-I in London was deeper. It was argued by Pagano and Roell (1990) that differences in the two trading mechanisms contributed to these disparities. In particular, market maker systems like London, provide capital and trade immediacy to customers, unlike order driven systems such as those in Paris. Differences between the London and Paris markets were also observed by de Jong et al. (1995), who found that the effective spread in Paris was flat with respect to trade size, while in London, as the trade size increased, the spread tended to fall. A significant amount of research has also been devoted to study trade interdependancies between SEAQ-I and the Paris Bourse. Jacquillat and Gresse (1995, 1998) argued that block trades in French stocks, undertaken on SEAQ-I, were unwound in Paris rather than in London. This result is confirmed by Ellul (1999) who examined how quickly the Paris market adjusted to a block trade undertaken on SEAQ-I. It was found that a SEAQ-I block trade, undertaken on a French stock, was reflected in Paris prices within 1 h. The importance of intermarket links between Paris and SEAQ-I trades was also illustrated by Hamet (2002) who showed that trading volume in Paris was on average 40% lower if SEAQ-I was closed. The objective of this paper is to compare price adjustment speeds in Paris with those in London. Thus, our analysis considers bilateral adjustment speeds rather than the unilateral adjustment considered by Ellul (1999). The analysis is very general and considers the influence of all trades on the two markets rather than just

4 404 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/417 considering the effect of block trades. Unlike previous papers we also consider the importance of time variation on the partial adjustment process. 3. The London and Paris trading systems In 1985, the London Stock Exchange launched SEAQ-I, a dealer market consisting of competing market makers trading foreign stocks 1. For each stock trading on SEAQ-I, the system provides an electronic display of bid and ask prices quoted by the market makers registered for that equity. A listing on SEAQ-I can be obtained if at least one market maker is willing to make a market in the security. As indicated by de Jong et al. (1995), during the late 1980s to mid 1990s the market for French stocks in London was highly competitive 2. When SEAQ-I was introduced, registered market makers for French equities were required to provide firm quotes for trades up to Normal Market Size (NMS) 3 during the mandatory quote period (09:00/16:00 h London time). SEAQ-I market makers were not allowed to display prices on competing display systems that were better than those displayed on SEAQ-I 4. During the early to mid 1990s it was widely believed that up to 52% of the volume in French stocks was being traded in London on SEAQ-I 5. By contrast the Paris Bourse uses a centralised system for displaying and processing orders. The Coatation Assistee en Continu (CAC system), introduced in 1986, is an electronic order routing and execution mechanism. When the CAC system was first introduced the Paris market opened at 10:00 h with a call auction 6 thereafter continuous auction trading took place. Unlike SEAQ-I, the Paris Bourse has no market makers 7. Is a purely electronic system and is an example of a centralised market. In Paris the five best buy and sell prices are public information, which allows traders to assess the positions of competitors and the intensity at which they wish to trade more effectively than in London. SEAQ-I is an example of a fragmented market. Although SEAQ-I provides firm bid and ask quotes, a significant proportion of trades take place within the quoted spread, the consequence of bilateral telephone negotiations. Since these 1 Since October 1997 London has operated an electronic order book for the most heavily traded domestic stocks but SEAQ-I continued to operate as a dealer market. 2 During 1998, there was a substantial decline in the number of market makers quoting on the European sector of SEAQ-I. 3 NMS approximately reflects the size of the median transaction. 4 The best execution rule was introduced as part of the Big Bang regulations of Although, Jacquillat and Gresse (1995), in a paper commissioned by the Paris Bourse, argued that due to the way transactions were being recorded in London only 8% of trades were actually going through London. 6 de Jong et al. (1995) suggest that the call auction accounts for between 10 and 15% of trading volume. 7 A detailed account of the trading mechanism of the Paris Bourse can be found in Biais et al. (1995) or more recently by Muscarella and Piwowar (2001).

5 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/ negotiations are not observable to the rest of the market they contribute to reduced levels of pre-trade transparency 8. London and Paris have very different arrangements for the reporting of transactions and both markets have implemented significant changes to these during the 1990s. In the autumn of 1994 Paris amended its rules on block trading 9. The two most important features of these arrangements were that trades greater than 1 / normal block size (NBS) 10 were allowed to transact at any price within the weighted average spread. At the same time the reporting arrangements associated with block trades were relaxed. Trades larger than 1/NBS were able to be reported with a 2 h delay while trades larger than 5/NBS were allowed to be reported the next morning. All other trades continued to be published immediately. In London prior to 1996, immediate publication was required on all trades less than 3/NMS. Trades between 3 and 75/NMS were allowed a 90 min reporting delay while trades of 75/NMS or larger could be reported after 5 days. Since January 1996, the reporting requirements on SEAQ-I have been that trades not exceeding 6/NMS are published immediately. Trades between 6 and 75/NMS are published within 1 h, and trades larger than 75/NMS must be published within 5 days 11. In the aftermath of Big Bang SEAQ-I was a significant competitor for the Paris Bourse. During the 1990s SEAQ-I spreads increased considerably and by 1995 were no longer firm. Firm quotes were only available if market makers were contacted directly by telephone, enabling them to search for a counterparty before transacting. To curtail the rise in spreads, the London Stock Exchange imposed maximum spreads which could be quoted. From the mid 1990s onwards SEAQ-I also experienced a significant fall in the number of market makers willing to transact in French securities, contributing further to a decline in SEAQ-I business. Pagano and Steil (1995) argued that there was an increasing dichotomy between the two trading systems. London was increasingly only dealing in block trades, while Paris was capturing an enlarging share of remaining trades. More recently, the merger of the Paris, Brussels and Amsterdam exchanges created Euronext. Euronext provides a single order book, a unified trading platform and rule book for all three exchanges 12 and has provided a further challenge for SEAQ-I. In response to additional competition on the retail side of the market London introduced its international retail service in 2001, which is an order driven system trading the most liquid foreign stocks. Unlike SEAQ-I all orders executed on 8 A detailed discussion of SEAQ-I can be found in Pagano (1998). 9 From 1994 the Paris Bourse also abolished stamp duty payable by non-resident investors. 10 NBS is approximately 2.5% of average daily trading volume over the previous 3 months. 11 A detailed account of these changes can be found in Board and Sutcliffe (2000). 12 As well as changes to the trading times (the market is now open 09:00/17:30 h) two batch auctions take place for CAC 40 stocks, one at the open and one at the close with 5 min of trading at the last price after the closing auction. Continuous Trading takes place for CAC 40 stocks between the two batch auctions.

6 406 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/417 this system must be reported immediately. French stocks are now traded on this system. 4. The difference between noise and value In this section, the partial adjustment model of Amihud and Mendelson (1987) will be used to illustrate how the causes of return volatility can be decomposed into two elements, volatility caused by noise, and volatility caused by changes in firm value. One of the first papers to note the importance of noise was Black (1986). His paper demonstrated that stock prices could be driven away from their intrinsic value by errors in the analysis and interpretation of information or by noise trading. The distinction between noise and value was formally captured in a partial adjustment model by Amihud and Mendelson (1987). This model is shown below: P t P t1 g(v t P t1 )u t (1) 2g0 where, P t is the logarithm of observed prices and V t is the logarithm of the fundamental price. The {u t } are a white noise sequence of zero mean pricing errors which are iid with a finite variance, which can be denoted as s 2. The {u t } reflect the influence of noise, which pushes observed prices away from their intrinsic value. As noise increases, s 2 becomes progressively larger causing observed returns to become more volatile. Thus fragmentation, the size of bid ask spreads, the price cushioning effect of a dealer, and other effects of the trading mechanism could all influence the magnitude of s 2. The coefficient g is a partial adjustment parameter that captures the speed with which observed stock prices adjust to their fundamental value. When 0 B/g B/1, the current transaction price gradually adjusts towards the fundamental value of the stock, if g/0, then transaction prices do not adjust to changes in value. When g/1, there is full but noisy, price adjustment. When g /1 observed prices over-react to new information. In this model intrinsic prices, V t, follow a random walk with drift as shown below, V t V t1 e t m (2) where, m is the positive drift which reflects the magnitude of the daily expected return. The {e t } are a series of iid random variables, independent of u t, with a zero mean and finite variance, which can be denoted as v 2. Under these assumptions Amihud and Mendelson show that the variance of observed returns is given by: var(r) g 2 g v2 2 2 g s2 g where, 2 g v2 represents the contribution that the variation in the intrinsic price v 2

7 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/ makes to the observed variance, while 2 g s2 captures the influence that noise has on the observed variance. Thus the variance of observed returns is positively related to three factors, the variance of intrinsic prices, the amount of noise, and the magnitude of the partial adjustment coefficient. If 0B/g B/1 then the influence of the partial adjustment coefficient will dampen down the influence that noise has on the observed variance, because the partial adjustment process has a smoothing influence on observed returns. But, if g is greater than 1 (so that the market is over-reacting to new information), the price adjustment effect will be positive increasing the variance of observed returns. The first order serial correlation coefficient of observed returns, when they are explained by the partial adjustment model with noise can be shown to be: r 1 g(1 g)v2 gs 2 (4) gv 2 2s 2 Noise always has a negative influence on the first order serial correlation coefficient of observed returns. The price adjustment component, g(1/g)v 2, can have a positive or negative impact on r 1 depending on whether g is greater or less than 1. If estimated values of r 1 are positive, g will be less than 1, since the first term in the numerator is larger than the second term. If g is greater than 1 r 1 will be negative. Ambiguity in the sign of r 1 exists when g is less than 1 and price adjustments are noisy. The presence of negative serial correlation would suggest that either g is greater than 1 or that the influence of noise outweighs the influence of g being less than 1, that is g(1/g)v 2 is less than gs Data and summary results In this study, a sample of 27 stocks that trade both on SEAQ-I and the Paris Bourse are examined. All stocks trade in both markets between 6th of December 1994 and 4th of February During this period SEAQ-I quotes were made in French Franc. For each stock, the closing price in London and Paris was obtained from Datastream 13. Our sample ends in early 1998, because after this period the quotes of market makers may not have been competitive due to the decline in market makers operating on the European branch of SEAQ-I. The study of daily returns, rather than intraday returns provides a number of advantages. Since we are interested in comparing the speed of adjustment across two exchanges it is important for price observations to be sampled at approximately the same time. With high frequency data this is much more difficult because SEAQ-I is characterised by significantly fewer trades than the Paris Bourse. For example, Ellul 13 December 1994 is the earliest date SEAQ-I prices have been available on Datastream.

8 408 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/417 (1999) shows that on average for every one trade in London there are 17 in Paris. Additional benefits associated with using daily observations are that we can examine an enhanced number of companies over a much longer period of time. Our findings are, therefore, less likely to be an artifact of the sample period used. This is especially important since a large number of changes to both SEAQ-I and the Paris Bourse have taken place during the sample period. The names of each of the stocks included in the sample are listed in Table 1, along with their market value (in millions of Euro) during 1996 and other summary information. This table shows that market values range from 1957 million Euros for Bouygues to million Euros for L oreal. For all stocks there is no statistically significant difference between the return in London and the return in Paris. Table 2 reports the first order serial correlation coefficients, estimated from Paris and London returns. These are useful as they give a preliminary indication of the Table 1 Summary statistics This table contains the names of each of the cross listed stocks. The R L are the mean daily percentage returns for each stock calculated from daily closing prices quoted on SEAQ-International. The R P are the mean daily percentage returns for each stock calculated from Paris prices. R P R L are the daily percentage Paris returns less the daily percentage London returns. MV is the mean market value of each company in millions of Euro during Maximum and minimum are the highest and lowest daily returns in the sample.

9 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/ Table 2 Volatility and serial correlation This table presents volatility and first order serial correlation coefficients calculated from daily returns. The Var P is the daily percentage variance of Paris returns. The Var L is the percentage daily variance of London returns. The VR is the variance ratio statistic, which reflects the variance of Paris returns divided by the variance of daily London returns. The r P is the autocorrelation coefficient calculated using Paris returns while r L is the coefficient calculated using London returns, ** is a significantly significant coefficient at a 5% level of confidence, * refers to a statistically significant coefficient at a 10% level. magnitude of the partial adjustment coefficients. Since most of these coefficients are positive we should expect g to be predominantly less than 1 in both markets. In London, 18 of the serial correlation coefficients are significantly positive at a 5% level of confidence, while for stocks listed in Paris, only one is significantly positive. For Paris quoted stocks there are many more cases of negative serial correlation. Nine coefficients are negatively signed, although only three are significant at a 10% level of confidence, and none at a 5% level. For the London quoted stocks, only one company has a negatively signed serial correlation coefficient. The diversity of the serial correlations, when comparing London with Paris, suggests that the trading mechanisms in Paris and London may have a disparate influence on observed returns. Estimates of the variance of each stock return are also presented in Table 2 along with the variance ratio statistic (the variance of Paris returns divided by the variance of London returns). The mean variance ratio is and indicates that on average,

10 410 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/417 the returns of the cross listed stocks are about 37% more volatile in Paris. In the case of only three stocks, that of CCF, Michelin and Societe Generale, is volatility lower in Paris. The returns of over 20 of the stocks are at least 25% more volatile in Paris while, for seven stocks, Paris returns are more than 50% more volatile than in London. In order to establish whether the trading mechanism in Paris is really more noisy than the trading mechanism in London, it is necessary to compare both g, the partial adjustment coefficient, and s 2 across the two markets. In the next section, we show how the Kalman filter can be used to estimate both g and s Estimating g and s 2 using a Kalman filter The Kalman filter is an estimation method which is commonly used to estimate state space models. These class of models consist of two parts: the transition equation, which describes the evolution of a set of state variables, and the measurement equation, which describes how the data actually observed is generated from the state variables. A detailed account of the Kalman filter can be found in Harvey (1989). We can re-write the partial adjustment model, of Eq. (1), as follows: R t gv t gp t1 u t (5) where, R t is the observed stock return on day t, and all other variables are as previously defined. If we now re-define gv t as a t, we can write Eqs. (1) and (2) in state space form to provide the measurement and the transition equation as shown in Eqs. (6) and (7). R t a t gp t1 u t u t N(0; s 2 ) (6) where, a t is a time varying unobservable state variable. The u t reflects the influence that noise has on current returns which has a variance s 2. Since V t is a random walk with drift, the transition equation which describes the unobservable state variable a t through time can be written as: a t a t1 d n t n t N(0; s 2 n ) (7) where a t is gv t and is a random walk with drift, d, the positive drift g /m and n t is ge t which is a random variable with zero mean and finite variance. Thus the values of V t through time can be obtained by taking a t and dividing by g, the estimate of the partial adjustment coefficient. Within the flexible framework used in this study the partial adjustment parameter of each market is able to adjust to changes in the intrinsic process that originate in either the home market or London. This allows us to compare adjustment speeds in the two markets. Table 3 provides estimates of the constant partial adjustment coefficient. In this table the extent to which coefficients are statistically different from one provides evidence of under or over-reaction.

11 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/ Table 3 Estimates from the estimation of the constant partial adjustment model This table provides the results of the estimation of the following state space model using a Kalman Filter. R t a t gp t1 u t a t a t1 dn t In this table g P and g L are the partial adjustment coefficients estimated using daily London and Paris prices, respectively. The se(g) are the standard errors of the partial adjustment coefficient. The ** indicates that the g coefficient is significantly different from one at a 5% level of confidence except in the final column which indicates that the g coefficient in Paris is significantly different from the g in London at a 5% level of confidence. In the case of the Paris market 14 of the coefficients are significantly below 1, for London over 20 are significantly below 1. In both markets there appears to be a less than instant adjustment to changes in the fundamental value. In the final column of Table 3, we present values for the partial adjustment coefficient obtained from Paris returns, less the partial adjustment coefficient from London returns. For 14 of the stocks, Paris prices adjust to changes in the intrinsic process more quickly than London. These results suggest that prices in London appear to adjust to their fundamental value more slowly than Paris prices. This finding may reflect the characteristics of trading within the two markets. As discussed in Sections 2 and 3 large trades tend to be executed in London, while smaller trades tend to be executed in Paris. Ellul (1999) shows that although Paris undertakes as much as 17 times more

12 412 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/417 transactions than SEAQ-I, transactions on SEAQ-I are on average 20 times larger than in Paris. Thus a greater proportion of trades in London are subject to reporting delays 14. We also know that large trades contain a significant amount of new information, see Gemmill (1996). Thus a lack of reporting associated with large trades could cause a slower adjustment to fundamentals in London. There is also some evidence to suggest that London market makers adjust their inventory (pre-position) prior to a block trade, see Ellul (1999) 15. It has also been shown that a significant amount of this inventory adjustment takes place in the home market, and not on SEAQ-I, see Jacquillat and Gresse (1995, 1998) and Ellul (1999). This evidence means that the information content of large trades undertaken in London causes a price impact in Paris. Since one effect of pre-positioning is to cause information leakages, prices in the home market can adjust to the block trade even before it is reported on SEAQ-I. In Table 4 we report estimates of s 2, the variance of noise. Comparing s 2 across the two markets suggests that in most cases the price setting process is more noisy in Paris than in London. On average there is about three times more noise in the Paris returns than in the London returns. For a small number of stocks, the amount of noise present in Paris is several hundred percent more than in London. For only one stock is noise higher in London than Paris suggesting that prices tend to depart from their fundamental value by wider margins in Paris than in London. 7. Time variation in the model An important consideration is whether our conclusions would alter if we assumed that any of the model components had a time varying structure. It is well known for example, that stock return volatility is characterised by time variation 16. In particular, changing volatility has been shown to have an important role in influencing the adjustment speed of prices. Ross (1976) argues that volatility can be viewed as a measure of information flow because the variance of price changes is directly related to the flow of new information. Therefore, volatility increases arise when investors utilise new information that moves prices. More recently, Kim and Verrecchia (1991a,b, 1997) have also shown that the amount of volatility is related to the quality of the new information that arrives. The better the quality of information and the less pre announcement leakage that has taken place the greater the price 14 Board and Sutcliffe (1995) show that as much as 56% of turnover (by value) is reported with a delay in the pre-1996 reporting regime, although Board and Sutcliffe (2000) suggest this had fallen to approximately 30% in the post-1996 regime. 15 It should also be noted that differences across the two markets in the relative staleness of prices could give rise to a slower adjustment process in London. Although, since this study utilises daily data the effects of price staleness will be minimal. 16 See Bollerslev et al. (1992) for a survey of time varying volatility.

13 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/ Table 4 Estimates of noise The s 2 P and the s 2 L are the estimates of the percentage daily variances of noise for Paris and London prices, respectively /1000. The VR noise is the variance ratio of noise, this is the Paris estimate of noise divided by estimate of noise for London. impact and the more volatile returns become. The adjustment of prices towards the intrinsic price is likely to be influenced by these information changes and should be incorporated into our model. In particular, as the information quality improves and volatility rises we should expect a faster adjustment process, the result of greater investor consensus concerning the relevance of information. In an attempt to capture any such dynamics in the partial adjustment process, we estimate a second model in which the partial adjustment parameter is assumed to follow a random walk. This particular specification is chosen because it is able to reflect the random arrival of new information. This requires an amendment to the Kalman filter model that we outlined in Section 6. The measurement equation now has a time varying partial adjustment parameter g t as shown in Eq. (8) and the transition equation now has two components. The first component is Eq. (9) which describes the evolution of a t. The second transition equation models the evolution of g t as a random walk and is shown in Eq. (10). R t a t g t P t1 u t a t a t1 d n t (8) (9)

14 414 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/417 g t g t1 w t (10) where, g t is the time varying partial adjustment process and w t is a white noise series of errors which are assumed to be independent of u t and n t. E(w t )/0 and the variance of w t is w 2. All other terms are as previously defined. The results from the estimation of this model are shown in Tables 5 and 6. In Table 5, we report the average partial adjustment coefficient in each market for all stocks. Consistent with the results in Section 6, the London market tends to have lower partial adjustment parameters than the Paris market. On average the partial adjustment parameter in Paris is about 10% higher than in London. As these parameters are time varying minimum and maximum values along with their standard deviations are also reported. From these values we can see that the French market tends to have larger maxima than London. Over the sample period there is much more evidence of overreaction in France as many more of the coefficients rise above 1. Actually, 14 of the French stocks have coefficients that rise above 1 during the sample period, while in contrast London has only two stocks that appear to be characterised by overreaction at any time during the sample period. In Table 6, we report estimates of the variance of noise for each market assuming the partial adjustment parameter is time varying. This table shows that after adjusting for time variation in the partial adjustment parameter the overall amount of noise in each market declines but the differences across the two markets is accentuated. Overall Paris appears to have about four times the noise of London. 8. Summary and conclusions In this paper it is shown that French stocks, cross listed on SEAQ-I in London and on the Paris Bourse, adjust to their fundamental value at different speeds in the two markets. The partial adjustment model of Amihud and Mendelson (1987) is estimated using a Kalman filter to show that stock prices adjust to their fundamental value more quickly in Paris. We argue that the rate of adjustment in each market is influenced by the trading mechanism of the market. Within this framework it is not surprising that London adjusts at a slower rate than Paris because London allows a significant proportion of trades to be reported with a delay. The amount of noise present in the Paris and SEAQ-I returns is also estimated. It is found that there is more noise present in the Paris returns than in SEAQ-I returns. We argue that although noise from this model has not previously been calculated directly, the results are consistent with microstructure studies which have argued for some time that auction markets are more noisy than dealer markets. Whereas the findings of Amihud and Mendelson (1987) were treated cautiously, see for example Stoll and Whaley (1990) the evidence in this paper shows that the trading mechanism can have a very powerful impact on returns. Even when we compare two trading mechanisms at the same time of day discernible differences still emerge.

15 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/ Table 5 Estimates of the time varying partial adjustment coefficients This table provides the results of the estimation of the following state space model using a Kalman Filter. R t a t g t P t1 u t a t a t1 dn t g t g t1 w t In this table ḡ P and ḡ L are the mean values of the partial adjustment coefficients estimated using Paris and London prices, respectively. The VRḡ is the average of ḡ P divided by ḡ L : Min and Max are the minimum and maximum values of g t and the sg is the standard deviation of the partial adjustment coefficients.

16 416 P. Chelley-Steeley / Int. Fin. Markets, Inst. and Money 13 (2003) 401/417 Table 6 The estimates of noise from the time varying partial adjustment model This table provides the estimates of the variance of noise assuming that the partial adjustment parameter is time varying. The s 2 P is the percentage variance of noise in Paris /1000 while s 2 L is the percentage variance of noise in London /1000. Acknowledgements I would like to thank the editor, an anonymous referee and Jim Steeley for helpful comments they have made on this paper. Any mistakes or omissions are the fault of the author. References Amihud, Y., Mendelson, H., Dealership market: market-making with inventory. Journal of Financial Economics 8, 31/53. Amihud, Y., Mendelson, H., Asset price behaviour in a dealership market. Financial Analysts Journal 38, 50/59. Amihud, Y., Mendelson, H., Trading mechanisms and stock returns: an empirical investigation. Journal of Finance 62, 533/553. Biais, B., Price formation and equilibrium liquidity in fragmented and centralised markets, Journal of Finance 57/185.

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