Two months in the life of several gilt-edged market makers on the London Stock Exchange

Journal of International Financial Markets, Institutions and Money 8 (1998) 299 – 324

Two months in the life of several gilt-edged market makers on the London Stock Exchange Paolo Vitale * London School of Economics, Department of Accounting and Finance, Houghton Street, London WC2A 2AE, UK Received 30 June 1998; accepted 31 July 1998

Abstract We investigate the micro structure of the UK gilt market studying the behaviour of several gilt-edged market makers on the London Stock Exchange. Through a structural model of the price process we can test different microstructural hypotheses, concerning information asymmetries, transaction and inventory carrying costs, and market liquidity. Our results suggest that inventories do not alter the price process in the gilt market. Moreover, in contrast to customer orders, inter-dealer transactions possess an information content. Transaction costs in the inter-dealer market are also substantially smaller than those for external customers. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Liquidity, Micro structure, UK gilt market JEL classification: G10; G15; G19

1. Introduction The past 10 years have seen a large number of contributions analysing the micro structure of securities markets (see Goodhart and O’Hara, 1997 and O’Hara, 1995). However, a striking aspect of this strand of research is that nearly all the analysis has concentrated on equity markets. In particular, despite the size and the importance of bond markets, there are virtually no empirical or theoretical studies of

* Corresponding author. Tel.: + 44-171-955-7230; Fax: +44-171-955-7420; e-mail: [email protected]. 1042-4431/98/$ - see front matter © 1998 Elsevier Science B.V. All rights reserved. PII: S 1 0 4 2 - 4 4 3 1 ( 9 8 ) 0 0 0 3 8 - 9

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their micro structure1. A reason for this omission might be the lack of proper data sources — most bond markets do not have a centralised structure, which impedes the collection of the necessary transaction data. Furthermore, the presumption that in these markets inventory and asymmetric information effects do not play an important role may have contributed to a lack of interest in the micro structure of bond markets among researchers. We take an opposite view and argue that this lack of interest is completely unjustified. In fact, given their specific organisation, bond markets may shed light on the controversial relation between market structure and the price process. The only other study of the UK gilt market was recently carried out by Proudman (1995). He tested a series of classical predictions of market microstructure theory by applying the VAR approach of Hasbrouck (1991). In this paper we suggest a rather different strategy, which takes account of the institutional differences between the UK gilt market and the New York Stock Exchange (NYSE) for which the VAR approach was originally proposed. While the NYSE possesses a completely centralised trading organisation, a multiple dealer system operates in the UK gilt market. Since its dealers do not reveal their transactions to other traders, the market is not transparent. As a result, an analysis of the type suggested by Lyons (1995) for the foreign exchange market, which is similar in many respects to a bond market, is more appropriate: instead of estimating an unrestricted VAR model for the transaction price and the signed order size of the entire market a study of individual dealers is undertaken. Our analysis of the price process suggests some interesting results. Firstly, inventory carrying costs are limited and do not affect the transaction price in the gilt market. Secondly, inter-dealer transactions seem to carry information, as opposed to customer orders. Thirdly, trading costs are very small, indicating that this market is extremely deep. Finally, inter-dealer transactions are executed at more favorable prices. The paper is organised as follows. In Section 2, we briefly discuss the institutional arrangements regulating the UK gilt market, presenting a preliminary analysis of its characteristics and regularities. In Section 3, a general structural model for the determination of the price process is introduced. This model captures both inventory and asymmetric information effects and takes account of the decentralised structure of the market. In Section 4, the results of the estimation of the model are discussed. In Section 5, we study the possibility that non-linear components play an important role for the price process. In Section 6, the structural model is used to derive estimates of the effective bid-ask spread and investigate the relationship between the volume of trading, the price volatility and the cost of trading. Section 7 completes the paper.

1

See Fleming and Remolona (1997) for an exception.

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2. The structure of the UK gilt market The UK gilt market is a continuous multiple dealer quote-driven market2. In this market, several dealers, gilt-edged market-makers (GEMMs), quote on request bids and asks for a number of different bonds, which differ by maturity and type. In this activity GEMMs are facilitated by three inter-dealer brokers (IDBs), who allow them to unwind inventory imbalances anonymously and rapidly, and by eight Stock Exchange money brokers (SEMBs), which may lend bonds to a GEMM when he receives a large market order from a client. GEMMs have exclusive access to IDBs and SEMBs, whilst other members of the Stock Exchange, dealer-brokers, and simple customers can only trade amongst themselves and with GEMMs. The market does not have official starting and closing times and dealers are not required to post firm quotes, though they must stand ready to trade. Moreover, dealers do not have to disclose their trading activity, although they do have to report any transaction they complete to the London Stock Exchange (LSE). As a consequence, dealers cannot observe other GEMMs order flows directly3, so the market remains opaque. The UK government securities market is very large, but its activity is not intense, if compared with the equity market. In particular, in October and November 1994 the total turn-over in UK gilts was £244.4 billion (£5.68 billion per day) compared to £91.9 billion (£2.1 billion per day) in the domestic equity market, while the average transaction size was £1.6 million versus £68 thousand in 1994. However, the daily number of trades is much lower (2500 versus 31 000)4. Proudman’s estimates of effective spreads suggest that the larger size of the gilt market is translated into lower trading costs than in the equity market. Despite these differences, the pattern of intra- and inter-day trading in gilts does not seem to differ substantially from those observed in other markets5. In fact, Proudman finds the usual U-shaped form for the intra-day volume and larger turn-over in mid-week. He also concludes that there is a positive relationship between spreads and turn-over, in contrast to popular models of asymmetric information, notably Admati and Pfleiderer (1988) and Foster and Viswanathan (1990), but in line with empirical studies of other markets (Hsieh and Kleidon, 1992; Mc Inish and Wood, 1993 and Foster and Viswanathan, 1993). 2

This description refers to 1994, the year for which data is available. See British Go6ernment Securities: The Market in Gilt-Edged Securities, 1993, Bank of England and Dattels (1995), who also describes other similar Government Securities Markets. 3 In fact, there is a significant difference between reporting data to a central office and revealing it to the rest of the market. Even if the LSE publishes at the end of any trading day statistics on the volume and the prices of transactions, this is not sufficient to make the market transparent. 4 See Quality of Markets Monthly Fact Sheet, London Stock Exchange, October and November 1994 and London Stock Exchange Quarterly, Spring 1995. 5 See Jain and Joh (1988), Mc Inish and Wood (1993), Foster and Viswanathan (1993), Gerety and Mulherin (1992) for the NYSE, Chan et al. (1995) for the NASDAQ, De Jong et al. (1995) for the SEAQ International and Hsieh and Kleidon (1992) for the foreign exchange market.

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In synthesis, it appears that the UK gilt, apart from its larger size, its peculiar structure and regulation, is not significantly different from other securities markets. In order to examine this in more detail, though, we need to investigate the price process for gilts. The database of gilt transactions kept by the Quality of Markets Group (QMG) of the LSE has been used to do this.

2.1. The data All transactions in gilts completed on the LSE are reported to its QMG. We use this dataset for the period October to November 1994. It records the time (to the minute) and date, size, price and value of all trades completed on the LSE. It also reports codes which permit individuating the counter-parties involved in any trade, which of the two is buying (selling), if they are market-makers, dealer-brokers, or simply customers, i.e. traders which are not members of the LSE. In the case of transactions between market-makers, the dataset determines if they are through an inter-dealer broker or direct, whilst when trades are amongst members of the LSE, we can also determine if these are operating on their own or on behalf of a client. When two members of the LSE complete a transaction directly, they both report it to the QMG. Similarly, an indirect inter-dealer transaction is recorded four times, since both market-makers report a trade with a broker, while he communicates the trade to the QMG as two separate deals. This allows cross-checking for errors. On the other hand, when a member of the LSE transacts with a non-member the latter does not communicate the trade, so that there will be less certainty on the accuracy of that report. This gain in the quality of the data has a high cost in terms of data processing. In fact, preliminary to any analysis, double reports have to be matched in order to obtain a sequence of individual trades. This exercise can be problematic, since reports can have significant time lags or differences in prices and values, especially for indirect inter-dealer trades6. Furthermore, the dataset contains contra-trades— that is, artificial trades which counteract mistakes. In these cases, we have to affiliate the contra-trades with the original ones and delete them from the dataset. For the analysis which follows we have decided to concentrate on only one gilt: the 6% Treasury Stock 1999 (6% TL 99). This security has been selected because it was by far the most actively traded in 1994 (Proudman, 1995) The 6% TL 99 was first issued with an auction face value of £3.5 billion on 28 October 1993 and successively tapped on 28 December 1993 and on 10 October 1994 for the face value of 0.4 and £0.25 billion, respectively. The decentralised organisation of a securities market poses an important question regarding the diffusion of information about dealers order flows. Most empirical research on decentralised markets implicitly assumes that when a market-maker receives an order, this is immediately known by the rest of the market so that all 6

When there is a time difference, the moment the transaction was first reported is taken as the time of the trade. Likewise, if differences in prices and values exist simple arithmetic means are used. Notice, however, that the share of trades with these differences is minimal.

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dealers instantaneously adjust their quotes. However, this in practice is unlikely to be true in the gilt market, as most transactions are the result of private bilateral meetings among traders the outcome of which is not observable by other market participants. This means that the transaction price for the market as a whole may not adjust to orders in the way described by theory. So examining the trading activity of all market participants may result in too much ‘noise’ in the price. Consequently, we have decided to consider the activity of individual market-makers for the 6% TL 99 gilt. In particular, we have chosen to study the behaviour of only six of the existing 21 GEMMs. These dealers are the most active and account for more than 60% of all the trades in the 6% TL 99 gilt for the period covered by our dataset. Concentrating on a relatively small, but important, sample of GEMMs permits conducting a significant econometric analysis of the price process in the UK gilt market.

2.2. Descripti6e statistics A preliminary analysis of our dataset confirms at an individual level the general picture of the gilt market we observe in an aggregate study. Table 1 contains some statistics on the transactions by the six market makers we selected. It clearly indicates that the activity of GEMMs in the 6% TL 99 gilt is sparse, since the daily number of trades is small for all dealers. Conversely, their sizes are very large, with individual averages ranging from 1.29 to £4.60 million. A rough measure of the liquidity of the market is given by the maximum size of the orders GEMMs can execute. As Table 1 shows, this almost reaches £100 million, indicating a very deep market. The LSE dataset allows us to determine which side of any trade our market-makers take. Thus, in Table 2 we can distinguish between transactions in which the Table 1 Comparative statistic: trades and turn-over Dealer Panel Total Daily Daily Daily

1

2

b

4

1013 23.6 39 10

1145 26.6 45 17

5

6

A: number of trades average maximum minimum

484 11.3 30 1

Panel B: turn-o6er (in pounds) Totala 2.23 Trade average sizeb 4.60 Trade maximum sizeb 45.2 Trade minimum size 1979 a

3

Billions of pounds. Millions of pounds.

369 8.6 23 1 1.62 4.38 45.6 2300

1.88 1.85 44.9 452

2.36 2.06 81.3 398

503 11.7 30 1 2.72 5.40 88.3 1979

1140 26.5 58 10 1.47 1.29 90.5 614

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Table 2 Comparative statistic: trade sign decomposition Dealer

1

Panel A: number of trades Buy orders 224 Sell orders 260 Panel B: trade size (in pounds) Buy average sizea 4.53 Sell average sizea 4.68 Buy maximum sizea 45.2 Sell maximum sizea 31.6 Buy minimum size 1979 Sell minimum size 9019 a

2

211 158 3.80 5.16 45.6 22.6 2300 9125

3

4

779 234

899 246

1.08 4.44 31.8 44.9 722 452

1.35 4.67 81.3 81.3 800 398

5

240 263 5.51 5.31 54.0 88.3 1979 9019

6

904 236 0.76 3.35 90.5 45.6 830 614

Millions of pounds.

counter-parties of the GEMMs buy from those in which they sell. Another distinct feature of the behaviour of these six dealers emerges from this Table. In fact, whilst the number of buy and sell trades are roughly the same for dealers one, two and five, GEMMs three, four and six received far more buy orders than sell ones. Likewise, while for the former group of dealers buy and sell trades have broadly the same magnitude for the latter sell trades are on average much larger than buy trades. This asymmetry in the distribution of the sign of trades for the gilt contradicts the general intuition that liquidity traders are more likely to be sellers than buyers in a securities market7, but a simple phenomenon seems to be at work here. Table 3 clearly indicates that most trades with clients, that is agents which are non-members of the LSE, were buy orders, whilst transactions with other GEMMs and dealer-brokers were equally divided between sells and buys8. In effect, in the UK gilt market GEMMs buy gilts in large quantities when these are auctioned by the Bank of England and then unwind their positions selling to investors and institutions. In support of this interpretation notice that the asymmetry in the number of sales and purchases is particularly relevant for dealers three, four and six, who mostly trade with non-members of the LSE. In Fig. 1 the distribution of the size of trades is presented. For the second group of GEMMs (i.e. dealers three, four and six) this distribution is clearly bimodal, while there is a single mode for the first. The break-up of the distribution according to the counter-party type shows that trades with other market-makers are larger. This feature is of particular interest, because of the debate in the literature about

7

See Allen and Gorton (1992). The LSE dataset reports whether a dealer–broker transacting with a GEMM is acting on behalf of a customer or not. In the first case the transaction is classified as a trade between the market-maker and a client. 8

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whether block trades have a greater information content. In the analysis to come, we study the price process distinguishing between customer and dealer orders and between large and small trades, so that we will be able to address this question. In Fig. 2 we decompose the volume of trading and the price volatility of transactions involving the six GEMMs according to the time of the day. The upper panels present the share of total turnover per trading hour from 8:00 to 17:00, whilst the lower panels reproduce the dynamics of the standard deviation of the transaction price over the same period. For all dealers we find the usual U-shaped pattern in the volume of trading observed in most markets and reported by

Table 3 Comparative statistic: trades by counter-partya Dealer

1

2

3

4

5

6

Panel A: total Clients 164 Gemms 291 Dealers 29

229 133 7

792 201 20

954 172 19

198 273 32

949 158 33

Panel B: buy orders Clients 74 Gemms 137 Dealers 13

149 58 4

684 88 7

814 73 12

98 126 16

822 71 11

Panel C: sell orders Clients 90 Gemms 154 Dealers 16

80 75 3

108 113 13

140 99 7

100 147 16

127 87 22

Panel D: turn-o6er Clientsb 0.79 Gemmsb 1.24 Dealersb 0.20

0.92 0.66 0.04

0.96 0.82 0.10

1.50 0.81 0.04

1.30 1.25 0.16

0.65 0.63 0.20

Panel E: trade mean size Clientsc 4.81 Gemmsc 4.27 Dealersc 6.75

4.00 4.96 6.17

1.21 4.08 5.02

1.58 4.73 2.32

6.58 4.58 5.13

0.68 3.97 6.04

Panel F: buy orders mean size Clientsc 4.31 Gemmsc 4.28 Dealersc 8.38

3.44 4.58 6.27

0.71 3.65 4.63

1.04 4.73 1.49

6.35 4.92 5.01

0.41 4.20 4.43

Panel G: sell orders mean size Clientsc 5.22 Gemmsc 4.27 Dealersc 5.43

5.04 5.25 6.03

4.38 4.41 5.24

4.58 4.73 3.75

6.81 4.30 5.25

2.44 3.79 6.85

a

‘Dealers’ stands for dealer-brokers, ‘clients’ for non-members of the LSE. Billions of pounds. c Million of pounds. b

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Fig. 1. Distribution of transaction size in October – November 1994.

Proudman, with most activity concentrated in the initial hours of the day. Turning to the dynamics of the price volatility, we do not have a clear picture, even if we notice some evidence of clustering around lunchtime.

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The existing literature on market micro structure suggests that regularities in the intra-day dynamics of the price volatility and the trading volume can emerge if some source of asymmetric information is relevant in the activity of market

Fig. 2. Volume and volatility in October – November 1994.

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participants. In this respect, the structural model of the price process we develop and estimate in the following sections will help establish if the usual paradigm of market microstructure theory applies to the UK gilt market.

3. A structural model of the price process In market microstructure theory four different factors can account for the cost of trading. First of all, market-makers can charge an order processing cost, since they provide immediacy to their clients. An investor, which desires to trade in a security, may find it inconvenient to post a limit order with a broker, whose execution may be uncertain or slow. Using a market-maker on the other hand will guarantee the deal will be executed rapidly (Demsetz, 1968). Secondly, since the dealer absorbs any momentary imbalance between total demand and supply he faces the risk of accumulating an undesired short or long position in the security. Then, he may set his bid and ask prices in order to return his inventory to an optimal level. In other words, the bid-ask spread is an instrument market-makers use to force their flow of orders in a determined direction (Ho and Stoll, 1983). Thirdly, when some clients have superior information on the fundamental value of the security, by imposing a bid-ask spread dealer’s may transfer losses with informed traders to other customers (Glosten and Milgrom, 1985; Kyle, 1985). Finally, since dealers may possess monopoly power on their order flow, they can charge a fee even when other factors are not at work (Copeland and Galai, 1983; Leach and Madhavan, 1992, 1993; Perraudin and Vitale, 1996). In practice, there are two main ways we can investigate these four factors. Hasbrouck (1991) suggests that a simple VAR approach should be used, arguing that under the assumption that the relations between prices, trades and inventories are captured by an unconstrained system of auto and cross-correlations, they can be studied within a general vector autoregressive model. The alternative is a structural model, which, despite its loss of generality, allows the disentangling of the aforementioned micro-structural factors in the determination of the price process. Moreover, using this approach it is easy to test the relevance of different market microstructure hypotheses. While Proudman (1995) follows Hasbrouck’s suggestion, we will consider a general structural model of the price process (Lyons, 1995), which encompasses several others (Ho and Macris, 1984; Roll, 1984; Glosten and Harris, 1988; Foster and Viswanathan, 1990 and Madhavan and Smidt, 1991) and takes account of the decentralised organisation of the UK gilt market. As we proceed with the description of the structural model, the specific reasons why we prefer this to a VAR model will be clarified.

3.1. The price process model In a specialist market, a structural model for the price process can be formulated along the lines proposed by Madhavan and Smidt (1991). They assume that in the

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market for a risky security traders transact with a specialist at times t= 1, 2,…, T. The liquidation value of the security at time T, fT, is the sum of T+ 1 ‘dividends’, fT =STt = 0dt. These ‘dividends’ are independent and identically distributed random variables with zero expected value. Thus, the fundamental value of the security at time t is given by fT =Stt = 0di. Then, assuming transaction and inventory carrying costs exist, the pricing rule of the specialist at time t will be linear in his expected fundamental value, m st , the deviation of his inventory with respect to an optimal position, It −Io, and the direction of the customer order, Ct :9 pt =m st −g(It −Io ) +cCt

(1)

where Ct =1 if the order is a buy and −1 if it is a sell. Before any transaction with a trader, the specialist receives a public signal on the fundamental value, s pu t : pu s pu t = ft +e t

where e pu is an idiosyncratic shock of variance s 2pu. Simultaneously, a trader t pu observes s t and a private signal, s pr t , also. This is given by: pr s pr t = ft + e t 2 where e pr t is also an idiosyncratic shock of variance s pr. Then, under the assumption of normality and independence of the errors, the trader will use the projection theorem to update her expectation of the fundamental value, m tr t : pr pu m tr t = us t +(1 −u)s t ,

where u=

s 2pu s 2pu +s 2pr

Finally, if she maximises a mean variance utility, given Eq. (1), her market order, tr q tr t , will be a function of the security mix-pricing, m t − pt. Nevertheless, an l 2 unpredictable liquidity component, et, of variance s l is also present in her order, so that this becomes: tr l q tr t = a(m t −pt ) + e t

(2) pu t

The specialist employs the public signal, s , and the ‘information’ contained in the client order to update his expectations of the fundamental value of the security and fix the transaction price. Madhavan and Smidt prove that the corresponding changes in the transaction price respect the following structural model: g c Dpt =A + lq tr t − It +gIt − 1 + Ct − cCt − 1 + ht, p p

(3)

9 Note that Eq. (1) is not derived from the solution of any utility maximisation problem, so that the authors refer to it as a prototypical formulation, although it can be proved that under a very general specification the optimal pricing strategy of the specialist is in fact given by Eq. (1). See Madhavan and Smidt (1993).

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where A= −g(1 −1/p)Io, l=

1 −p ap

and p is a coefficient which depends on the various parameters of the model. The coefficient p determines the information content of the market orders of the traders: for p small (l large) traders have a large informational advantage, that is reflected in a relevant impact of trades on the transaction price. Conversely, for p large (l small) the market orders do not convey any new information. In synthesis, in Eq. (3) the coefficients of q tr t , It − 1 and Ct − 1 capture three different factors accounting for the cost of trading: l measures the information content of the customer orders received by the specialist, whilst c and g are the transaction and inventory carrying costs, respectively. In particular, g will be positive if dealers are risk-averse and inventory-carrying costs are relevant, while c accounts for all fixed transaction costs. This means that using this model we can verify directly the relevance of the various market micro-structure hypotheses on the price process, by testing for the significance of the coefficients in Eq. (3). Madhavan and Smidt apply this model to the NYSE, which is a fully centralised market, because the specialist can observe all transactions and orders. As mentioned above, this is not the case for the UK gilt market. Therefore, an application of this structural model is only possible with respect to the activity of individual market-makers, since they can only partially observe the order flows of other dealers. In particular, through the connection with inter-dealer brokers they can also obtain information on all trades between market-makers which are not direct. Lyons (1995) has proposed a modified version of the Madhavan and Smidt model which can be applied to decentralised markets with inter-dealer brokers. In this version, several market-makers deal in the same risky security amongst themselves and with customers. For the price process of a single dealer, m, a model similar to that discussed by Madhavan and Smidt applies, with the difference that the selected market-maker will observe before any trade both a public signal and one on the total volume of inter-dealer trading, q bt which is given by: q bt = %q dt +y bt , d

where y is an idiosyncratic shock of variance s 2n, which accounts for some noise in the electronic communication system dealers are attached to, and q dt indicates a single transaction between dealers completed through a broker. Lyons assumes that these dealers have received informative orders from other traders and that they place market orders similar to those of customers. In other words, if a market-maker d posts an order with a broker, this is given by the following expression: d t

q dt = a(m dt −pt ) +e id t ,

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where m dt is his expectation of the fundamental value and e id t is the usual idiosyncratic liquidity shock of variance s 2id. Lyons then proves that the structural model for the transaction price modifies in the following way: g c Dpt =A + fq bt +lq tr t − It +gIt − 1 + Ct − cCt − 1 + ht p p

(4)

Here the coefficient of q bt , f, is the equivalent of l for the inter-dealer transactions: when other market makers possess superior information on the value of the security, these transactions (q bt ) convey a signal and influence the transaction price.

4. Model estimation for the gilt market We can now consider the estimation of Eq. (4) for the gilt we have analysed in Section 2. In order to do so, we need first to prepare the data. In particular, we need to determine the direction of all trades, that is if transactions are buyer or seller initiated. Trades between market-makers and customers are straightforward to assign, because they are necessarily started by the latter. Thus, since our dataset reports for any transaction if our GEMMs are buying or selling, when a transaction is with a client the determination of the corresponding direction of trade is automatic: if the client is recorded as the buyer, the trade is buyer initiated and vice versa if the client is the seller. However, the determination of the direction of inter-dealer trades is not so simple, since it is always possible that our GEMMs initiate trades with other market-makers. When quotes from market-makers are recorded, the direction of inter-dealer trades can be determined using the method put forward by Lee and Ready (1991), which is based on a comparison between the transaction price and the prevailing best quotes. For the gilt market no information on quotes is available and we therefore have to rely on the tick test. In the application of the tick test inter-dealer trades are isolated, so that the comparison between transaction prices is carried out using only trades amongst market-makers. In other words, to classify the direction of a trade we compare the current transaction price with that of the previous trade that involve market-makers. The reason for this is simple: spreads in the inter-dealer market are generally smaller than those for normal customers, so that when applying the tick test, if we used all the transactions we would undergo a systematic error in the classification of the direction of trades. In the inter-dealer market, transactions are often mediated by an IDB10. In this case, it could be possible to detect the direction of trades from the record of different times the three parties involved, the dealers and the broker, report the transaction. If the market-maker posting a limit order with a broker reported it first, it would be possible to determine which of the two dealers initiated the 10

Dattels (1995) found that 96% of inter-dealer trades in the UK gilt market are through an IDB.

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corresponding trade. But, as market participants in the UK gilt market have 15 min (5 min for block trades) to communicate a trade to the QMG, the timing of the reports is not useful in determining the direction of trades. In practice, we often observe in the dataset that the broker communicates a transaction between marketmakers before the counter-parties do. Another important transformation of the data we need before estimating our structural model concerns transactions reported at the same moment. Since we use transaction time rather than calendar time in the formulation of the model, the observations we use have to be filed in the sequential order that trades are completed. Thus, when in our dataset two trades are time-stamped in the same minute we cannot determine which one comes first. As a consequence, they do not represent distinct transactions and hence they are consolidated, in that a unique total transaction is derived using the average price and the total signed order. Finally, we had to eliminate changes in the price that occur during the night, because our model concerns only the intra-day price process. Thus, after excluding trades at the beginning of any day, trades among dealers in which our GEMMs act as clients, and consolidating transactions reported in the same minutes, we ended up with six files for the six dealers containing 215, 203, 773, 900, 223 and 816 observations, respectively. Notice that, inter-dealer trades are still used to determine the inventory positions of the selected market-makers. This mitigates the problem of multi-collinearity in the estimation of Eq. (4), because their inventories change both when the GEMMs act as clients and as market-makers. Each file contains the change in the transaction price charged by the GEMM, Dpt, the direction and the signed quantity of any customer trade, Ct and q tr t , where is positive (negative) for a buy (sell) order, the total signed quantity of q tr t inter-dealer trading since last customer order excluding trades with our selected market-maker, q bt , his inventory position, It, the time any customer trade is completed and a dummy variable indicating if the client is another dealer or not. When we turn to the estimation of model (4) we need to consider the properties of its error term, ht. It is not difficult to see that ht follows an MA(1) process. Thus, the OLS estimator is not efficient and the maximum likelihood method should be used to estimate the coefficients of the model11. In Table 4 we report the results of the estimations of model (4) for the six GEMMs. We indicate the estimated coefficients along side some specification statistics, as the corrected coefficient of multiple correlation, R( 2, the Durbin – Watson statistic, DW, for the error term, ht, and other diagnostic tests. In Table 4 the MA(1) coefficient is significant and, as suggested, negative for all regressions, apart from dealer one, while the presence of negative serial correlation of, ht, is also signalled by the high values of the Durbin–Watson statistic. As we 11

Given the ergodicity of the process and the large number of observations, we can use a quasi-maximum likelihood method based on the Gauss–Newton algorithm (Harvey, 1989). Notice that for the efficiency of the estimator we need to start the Gauss – Newton algorithm from consistent estimates of the coefficients and then just run one iteration. The OLS estimator of the coefficients of an MA(1) model is not efficient but consistent, so we can use it as a starting point.

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Table 4 Quasi-maximum likelihood estimation of the linear model with MA(1) errorsa,b,c Dealer

1

2

b0 b1 b2 b3 b4 b5 b6 b7

0.9688** 0.1577** −0.1072** −0.0856** 0.0910** 1.3886** −1.0316** 0.0242**

0.8850** 0.1994** −0.2303** −0.0350** 0.0303** 4.7932** −2.6575** −0.0560**

0.081 1.859 15.56 3.179** 20.06** 0.606

0.257 2.113 12.94 2.16* 16.32** 0.993

Diagnostic tests R( 2 DW Serial correlation Skewness Kurtosis Heteroscedasticity a

3 −0.5534** 0.1319** −0.0722** −0.0869** 0.0842** 4.0380** −1.9859** −0.8315** 0.002 3.003 198** 207** 2574** 93.4**

4

5

0.3874** 0.1459** −0.0219** 0.0103** −0.0080* 2.9880** −2.8114** −0.2233**

1.83** 0.1205** −0.0012 −0.0320** 0.0366** −0.0651 −0.5592** −0.0879**

0.165 2.399 39.34** 13.85** 130.8** 6.592*

6

0.031 2.117 8.180 5.015** 13.85** 0.120

0.3409** 0.1166** 0.5478** 0.1587** −0.1527** 2.8533** −3.6374** −0.4790** 0.231 2.804 138.4** 7323.4** 412.6** 186.5**

Dpt = b0+b1q bt +b2q tr t +b3It+b4It−1+b5Ct+b6Ct−1+ht pu ht =h pu t +b7e t−1.

The coefficients b1, b2, b3 and b4 are multipled by 106. Prices are in pence. * Indicates a significance level at 5%. ** Indicates a significance level at 1%.

b c

incorporate in the model a transaction cost term, a negative value for the MA(1) coefficient b7 cannot be the consequence of the bid-ask bounce. On the contrary, if the specification of the model is correct, b7 measures the degree of asymmetry between public and private information. So the larger value of b7 for dealers three, four and six signals a higher level of information asymmetries. Notice that these dealers are exactly those who trade the most with external customers. However, the diagnostic tests for the Gaussian linear model with MA(1) errors clearly casts some doubts on the validity of the estimates of the coefficients of Eq. (4). In fact, if the assumption of Section 3.1 were correct the error term, ht, should not present serial correlation beyond the second lag. Yet, the Portamentau test clearly shows that serial correlation up to the tenth lag is significant for some of the regressions. Furthermore, the usual tests of the departure from indicate both skewness and kurtosis. This sugthe normality of the shock e pu t gests the presence of fat tails in the distribution of e pu t , a very common phenomenon in financial time series. The same argument applies for the heteroscedasticity we detect in e pu t . In our dataset observations are not equally spaced in calendar time, which may be one reason why we observe the departure from homoscedasticity.

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Provided that the specification of model (4) is correct, even if its error term does present serial correlation and heteroscedasticity, the OLS method is more appropriate and inference on the model coefficients can be carried out using the Newey– West heteroscedasticity and auto correlation consistent estimator of their standard errors. In Table 5 we report these OLS estimates. Their standard errors, which have been estimated assuming that the maximum order of serial correlation in the errors is ten, are generally much larger than those of in Table 4. The regression results of Table 5 propose some interesting conclusions. All in all, we do not reject the following restrictions on the model coefficients: b0 = 0, b2 = 0, b3 =0 and b4 =0. Although, we do reject the null hypothesis of b1 = 0 against the alternative of b1 \0. Likewise, we can reject the combined null hypothesis that b5 =0 and b6 =0. In practice, these results are consistent with the following values for the underlying parameters of the structural model: p =1, g= 0, f \ 0, c \ 0. Thus, Table 5 suggests that the inventory effect is not detected for any GEMM in our sample, i.e. g =0. This result is in line with those of Madhavan and Smidt (1991) and Proudman (1995) and might be explained by the existence of various instruments to hedge large inventory imbalances. In particular, GEMMs can trade in future markets and sell (buy) bonds to (from) SEMBs, they can also combine opposite inventories in strongly correlated bonds. Although, if the optimal level of the inventory, Io, varies over time we can obtain insignificant values for b3 and b4

Table 5 OLS estimation with Newey–West standard errorsa,b,c Dealer

1

2

3

4

5

6

b0 b1 b2 b3 b4 b5 b6 R( 2 DW F-Test

0.9838 0.1577** −0.1028 −0.0863** 0.0916** 1.3556*** −1.0260* 0.081 1.860 4.159***

0.8690 0.1980*** −0.2265 −0.0294 0.0247 4.8704*** −2.6796*** 0.257 2.107 12.65***

−0.1818 0.1848*** −0.0010 0.0685 −0.0704 4.0640*** −2.8639*** 0.003 3.003 1.39

0.3827 0.1634*** −0.0141 0.0219 −0.0195 2.8781*** −2.7123*** 0.166 2.392 30.80***

1.8298*** 0.1109** −0.0131 −0.0278 0.0333 1.590 −0.5746 0.032 2.095 2.215**

1.4804 0.1178*** 0.8120* −0.1035 0.1009* 1.9609*** −3.3210*** 0.264 2.626 49.6***

a

Dpt = b0+b1q bt +b2q tr t +b3It+b4It−1+b5Ct+b6Ct−1+ht.

The coefficients b1, b2, b3 and b4 are multipled by 106. Prices are in pence. * Indicate levels of significance at 10%. ** Indicate levels of significance at 5%. *** Indicate levels of significance at 1%.

b c

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even when an inventory effect is at work (i.e. g\ o).12 Snell and Tonks (1995, 1996) allowing for changes in Io find some evidence of inventory effects on the LSE. Table 5 also signals the absence of an information content in customer orders. This result is in contrast with findings of several empirical investigations for the NYSE (for instance Hasbrouck, 1991; Madhavan and Smidt, 1991), but is not dissimilar from those of Snell and Tonks (1995) for the UK equity market. Although, even here, we can observe an insignificant value of b2 when p" 1, because of a time-varying optimal inventory level13. An alternative explanation, which does not involve speculative motives, is that block trades have an information content while small trades do not. We will investigate this possibility in Section 5, where we study non-linear components in the price process. In his analysis of the UK gilt market Proudman has considered the market as a whole. Assuming that GEMMs trade among themselves merely to adjust their inventory positions, he stripped out all inter-dealer trades. Our regressions suggest that this may lead to a loss of valuable information: the positive value of b1 indicates that inter-dealer trading may be an effective way for market-makers to ‘sell’ information to each other. In this situation, as Perraudin and Vitale (1996) suggest, decentralisation may increase the speed with which information is disseminated in the market, since informative inter-dealer trades may stimulate price experimentation on the part of dealers. This thesis contrasts with that of other researchers, notably Flood (1994), who claim that decentralisation brings about inefficiency and distortion. A problem with this interpretation is that it is not clear why orders from market-makers are informative, but customer orders are not. According to the market micro-structure literature, inter-dealer trades are informative only insofar as they reflect information dealers have previously gathered from customer orders.

12 Suppose in model (4) the market-maker sets the optimal level of the inventory for speculative reasons. Hence Io varies with the value of the security,Iot =v(m m t −pt ) and Eq. (1) becomes:

pt = m m t − g%It + c%Ct, where g% =g/(1+gv), c% =c/(1+ gv) So in Eq. (4) the constant disappears and b4 underestimates g. Moreover, an error-in-the-variable problem can also plague our estimates and standard errors, in that, because the data is not available, we do not know the initial inventory position of our GEMMs. 13 tr Suppose, in fact, that Iot = v(m m t − mt ), then the coefficient of the customer order in Eq. (4), q t , becomes: l=

(1−p) (1− ag) ap a

Thus, for g close to 1/a we can have a zero value for l even when p is different from 1.

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Nevertheless, dealers can gather information from other private sources: for example, transactions in related derivatives products or proprietary trading.

5. Analysis of non-linear components Another issue which has been debated in the market microstructure theory concerns the effect of block trades on the transaction price and the cost of trading. In fact, while Demsetz (1968) suggests that transaction costs decrease with the order size, Easley and O’Hara (1987) claim that informed traders have an incentive to place large market orders, so that block trades have a more pronounced information content and a larger impact on the transaction price. A unified method to assess the relevance of non-linearities in the price process does not exist: researchers have used different strategies. Holthausen et al. (1987), Gemmill (1996), Board and Sutcliffe (1995) and Proudman (1995) employ an event-study approach to see if block trades have permanent effects on the transaction price. Hasbrouck (1991) and Proudman (1995) consider quadratic terms in the specification of their VAR models. Madhavan and Smidt (1991) and Breedon (1993) analyse piecewise linear functions of the order size, while Easley et al. (1994) estimate an extended version of the original model discussed by Easley and O’Hara (1987). Since so far we have used a structural model to investigate the price process, the application of a piecewise linear function is a natural candidate for the analysis of block trades. In this respect, we estimate the following extension of Eq. (4) H

tr − tr Dpt =b0 +b1q bt +b2q tr t + % dhxh (q t − q h )+ b3It + b4It − 1 + b5Ct h=1

+b6Ct − 1 +ht

(5)

where q¯ tr h indicates a knot of the piecewise linear relation, H is the number of knots tr ¯ tr and xh an indicative function, in that for q¯ tr h positive xh = 1 if q h \ q h and zero tr tr tr otherwise, for q¯ h negative xh =1 if q h B q¯ h and zero otherwise. In Table 6 we report the OLS estimates of the coefficients of model (5) with Newey–West standard errors for the six GEMMs. In these regressions two knots have been included in order to capture the difference between large and small, buy and sell orders. The selected knots for the regressions are q¯ tr 1 = − £1 million and =£1 million face value. The selection of these knots is based on the distribution q¯ tr 2 of the order size of the trades with other dealers: as Fig. 1 indicates, in our dataset most of the transactions with other GEMMs are larger than £1 million face value. This selection is probably a reasonable way to distinguish between large and small orders, although regressions with other choices of the knots give similar results. Table 6 contains some interesting results. Firstly, most of the conclusions regarding model (4) hold even when non-linear components are inserted. Thus, the inventory effect remains insignificant. At the same time, the coefficients of the

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Table 6 OLS estimation of spline model with Newey–West standard errorsa,b,c Dealer

1

2

3

4

5

6

b0 b1 b2 b1 b2 b3 b4 b5 b6 R( 2 DW F-Test

1.5505* 0.1612*** −2.6488 2.6905 2.4756 −0.0848* 0.0890** 3.4615** −1.1073** 0.082 1.893 3.385***

2.1658*** 0.1965*** −1.0237 1.1476 0.4632 −0.0253 0.0213 5.1473*** −2.6666*** 0.285 2.079 11.07***

0.4699 0.1821*** 0.2083 −0.0401 −0.4273 0.0828 −0.0852 3.6858*** −2.9139*** 0.001 3.002 1.09

0.7500 0.1685*** −2.2937** 2.7588*** 2.2773** 0.0228 −0.0189 2.9020*** −2.6559*** 0.190 2.362 27.28***

2.1646*** 0.1115** −0.7355 0.7765 0.6497 −0.0304 0.0340 0.8930 −0.6004 0.028 2.092 1.794*

−0.7010 0.0982** −5.5253*** 5.7511*** 6.8101*** −0.0931* 0.0888* 5.0057*** −3.5815*** 0.343 2.341 54.1***

a

tr Dpt = b0+b1q bt +b2q tr ¯ tr t +%hdhxh (q t −q t )+b3It+b4It−1+b5Ct+b6Ct−1+ht

The coefficients, b1, b2, b3 and b4 are multipled by 106. Prices are in pence. * Indicate levels of significance at 10%. ** Indicate levels of significance at 5%. *** Indicate levels of significance at 1%. b

c

direction of trades, b5 and b6, are significant and have the right sign for the regressions apart from that of dealer five. The coefficient of the signed quantity of inter-dealer trading, bl, is also always positive and significant. Secondly, new results emerge. In particular, when we introduce the terms ¯ tr dhxh (q tr t −q h ) in the regressions for dealers four and six, we observe that b2 becomes significantly smaller than zero, while the coefficients of the non-linear terms, dl and d2, are significantly larger than zero. For other dealers this is not true and, therefore, introducing non-linearities does not improve the fitting of the model. tr the impact on the transaction Now, in model (5) for a buy order exceeding q − 2 tr tr tr price is b2q t +d2(q t −q¯ 2 ). This means that block trades have a larger effect on the transaction price if d2 \0. An analogous argument applies to sell orders. Breedon (1993) and Gemmill (1996) find evidence that block trades have a greater impact on prices for the UK equity market, while Proudman (1995) obtains contrasting conclusions in the gilt market. Our results are clearly mixed and might suggest different styles of market making on the part of our GEMMs. We can interpret the values of the coefficient b2, d1 and d2 for dealers four and six as suggesting that large customer orders have an information content, but small ones do not. Thus, for small trades transaction costs are decreasing in the order size, while for large ones asymmetric information augments the cost of trading. However, if dealers act strategically and engage in price experimentation, they

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might find it convenient to offer discounts to informed customers when these place small orders, as suggested in the literature by Leach and Madhavan (1992, 1993), Naik et al. (1994), Perraudin and Vitale (1996). Hansch and Neuberger (1996) find that dealers act strategically on the LSE, supporting this thesis. Moreover, dealers four and six trade mostly with external customers who might have a smaller bargaining power and to which GEMMs can impose larger transaction costs. Finally, Table 6 indicates for all dealers that dl is not significantly different from d2. This means that we do not observe significant asymmetries between purchases and sales. This is rather surprising, since it is common opinion that buy orders are potentially more informative than sell ones. Before we employ our structural model to investigate other aspects of the micro structure of the gilt market, we need to stress an important aspect of our regressions. Only part of the volatility of the transaction price for the six GEMMs is captured by our models (4) and (5). In particular, the values of the coefficient of multiple determination, R( 2, for dealers three and five are extremely low and in general, for all regressions, at least 2/3 of the variability of the dependent variable remains unexplained. In other words, there are other factors behind the determination of the transaction price in these markets we do not take into account. This is however common to most of the empirical research on market micro structure (Madhavan and Smidt, 1991; Lyons, 1995). Another point regarding our structural model is worth making before we turn to its applications. While there has been a lot of discussion on the information content of market orders and their impact on the transaction price, they do not seem to contribute a great deal to the fit of our regressions. In fact, even if the corresponding coefficients are significant, when we eliminate the order size term from the regressions of Tables 5 and 6 we do not observe a large reduction in R( 2. Madhavan and Smidt (1991) discuss a number of institutional features of the NYSE which may cause a downward bias in the estimation of the coefficient of the order size. Even if these features are also at work on the UK gilt market, we should still conclude that information asymmetries are not so relevant in its functioning. Consequently, the decentralisation of the UK gilt market should not have any important effect on its performance.

6. Applications

6.1. The effecti6e cost of trading The estimation of the effective cost of trading represents a question of great interest regarding the micro structure of securities markets. In principle trading costs in a dealer market are measured by the difference between ask and bid prices. Anyway, in measuring spreads it is important to distinguish between quoted and effective (or realised) spreads, since dealers quotes are not firm and actual prices generally fall well within quotes (Reiss and Werner, 1994; Board and Sutcliffe, 1995). As a result,

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even when quoted spreads are observable, they do not necessarily represent an unbiased estimator of the effective costs of trading. In the past several ways to estimate the effective bid-ask spread have been suggested. Roll (1984) proposed a very simple estimator based on the first order autocovariance of price returns. This estimator is unbiased only if the spread represents the cost of immediacy. When spreads are affected by inventory and asymmetric information costs (Stoll, 1989), this estimator can be corrected using the conditional probabilities that consecutive trades are in the same direction (Choi et al., 1988). But even when corrected, this estimator can be very noisy, if the fundamental value of the security is subject to idiosyncratic shocks (Harris, 1990). Using our structural model we can derive a simple measure of the effective bid-ask spread. According to a common definition, this is given by the cost of an immediate round-trip transaction, which is a buy order followed by a sell order of the same size. Since this measure depends on the order size, we actually define an estimator of a function, s(q tr) = p(q tr) −p(− q tr). While for normal size orders this is given both in model (4) and (5) by: s(q tr) = 2(b5 +b2q tr), for large trades we will have in the second case: tr ¯ tr s(q tr) = 2(b5 +b2q tr) +d1(q tr +q¯ tr 1 )+ d2(q − q 2)

In Table 7 we report the estimates of s(q tr) for several values of q tr t . These are obtained using model (4) for dealers one, two, three and five, and model (5) for dealers four and six. We also report simple estimates obtained using the method suggested by Roll (1984). Table 7 shows that Rolls estimate clearly underestimates the effective cost of trading and confirms that the gilt market presents very small trading costs: in fact, the estimates of the effective spread are very close to 2/32. Table 7 Estimation of the Effective Spread Dealer

1

Madha6an and Smidt’s estimate a 10th percentilec 0.0284 25th percentile 0.0268 50th percentile 0.0186 75th percentile 0.0141 Average trade size 0.0174

2

3

4

5

6

0.1076 0.1065 0.0945 0.0737 0.0846

0.0899 0.0899 0.0899 0.0899 0.0899

0.0640 0.0637 0.0630 0.0135 nab

0.0329 0.0295 0.0208 0.0006 0.0015

0.1101 0.1096 0.1084 0.0435 na

0.0086

0.0157

0.0106

0.0032

0.0138

Roll’s estimator a 0.0025 a

As percentage of the average size. na indicates a negative spread. c From the distribution of the trade size. b

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Table 8 The dynamics of the spread during the daya Dealer

1

2

3

4

5

6

8:00–11:30 11:30–14:30 14:30–17:00

nab 0.0200 0.0074

0.0459 0.0109 0.0068

0.0449 0.0463 0.0549

0.1001 0.0203 0.0481

na na 0.0143

0.1442 0.0885 0.0553

a b

As percentage of the average price, calculated for the median order size. na indicates a negative spread.

Apart from dealer three, we observe a limited decline in the spread with the order size. However, for dealers four and six, for which model (5) applies, extremely large trades will be executed at less favourable prices and transaction costs will be increasing with size. Moreover, despite the common decline of transaction costs with the order size, Table 7 also indicates a substantial difference in the cost of transacting charged by the six GEMMs. Again, we notice that the dealers who mostly trade with external customers tend to charge larger transaction costs.

6.2. Volume, 6olatility and trading costs A final question which deserves our attention concerns the relationship between the price volatility, the volume of trading and the cost of trading. According to Admati and Pfleiderer (1988) and Foster and Viswanathan (1990) trading costs should be small when volatility and volume are high. Their models predict that, in the presence of information asymmetries, strategic liquidity traders concentrate their activity when trading costs are low. In Table 8 we report some estimates of the effective spread for different periods of the day. These values have been calculated for the median of the distribution of the order size, q tr , using models (4) and (5) as in Table 7. Table 8 is suggestive that spreads in the gilt market are higher in the morning than in the rest of the day. Notice that a similar pattern of the spread has been found by Chan et al. for the NASDAQ, another decentralised market. Comparing Table 8 with Fig. 2 of Section 2, we conclude that trading costs and trading volume are not negatively correlated, as suggested by the theory. However the slight decline of the spread during the day is in line with other empirical investigations (Hsieh and Kleidon, 1992; Mc Inish and Wood, 1993 and Foster and Viswanathan, 1993) and may indicate that as new information is processed over time its adverse selection effect reduces.

7. Conclusion This paper has provided an empirical analysis of the UK gilt market based on the study of the activity of several market makers during October to November 1994. Our analysis suggests the following results.

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1. The UK gilt market is very large and deep. Furthermore, trading activity is concentrated early in the morning and after lunch. Moreover, GEMMs seem to specialize as some deal mostly with other dealers, while others make the market for external customers. Clients tend to submit smaller market orders and the number of their buy orders prevails over that of their sell orders. 2. Turning to the analysis of the price process, we have considered a structural model which captures transaction and inventory carrying costs, information asymmetries and takes account of the decentralisation of the UK gilt market. The estimation of this model suggests that imbalances in inventories do not condition the transaction price set by market-makers. This result is consistent with the conclusions of other investigations and can be explained by the availability of several hedging instruments. 3. Market microstructure theory claims that trading costs may increase with order size when market orders carry an information content. While most empirical analysis of equity markets show that customer orders are informative, Proudman (1995) finds that this is not the case for gilts. Our regressions of the structural model are consistent with Proudman’s finding as long as we do not consider non-linear terms. 4. Non-linearities in the relationship between transaction price and order size may emerge for block trades. When we consider them, we find that non-linear terms in the structural model of the price process are significant and signal that block trades have a positive impact on the transaction price for those market makers who are mostly involved in transactions with external customers. This may be interpreted as indicating that only large customer trades are informative. 5. One of our more interesting results concerns the effect of inter-dealer trading on the price process of individual market-makers. As suggested by Lyons (1995), in decentralised markets transactions amongst dealers may signal information market-makers gather from customer orders and other private sources. We confirm this thesis, since we find that the signed total quantity of inter-dealer trading has a significant and positive impact on the transaction price of individual market-makers. This also suggests that access to IDBs open to all traders would increase the efficiency of the market. 6. Estimates of the effective spread can be obtained from the regressions of the structural model. They show that the cost of trading is very small in the bond market. However, substantial differences in the cost of liquidity charged by dealers are observed. In particular, GEMMs who deal mostly with non-members of the LSE charge larger transaction costs. 7. Finally, trading costs in the gilt market are larger in the morning than in the rest of the day, corresponding to periods of higher trading volume. This might indicate that adverse selection problems are less severe in the later hours of the day. 8. To complete our comments on the results of this paper, we should emphasize that they cannot be taken as conclusive and a more extensive analysis covering more gilts and a longer period should be considered. This has not been possible,

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given the limits of the database we had access to, but it provides a valuable direction for further research. This research should also extend our analysis in other directions. A long list of micro-structural phenomena which deserve consideration could be indicated here. Nevertheless, given the relative lack of work on the microstructure of bond markets, we believe our work represents a solid step forward.

Acknowledgements I wish to thank Francis Breedon, who introduced me to the study of the UK Government Securities market, Ian Twinn, for his assistance and comments, the London Stock Exchange, which provided the data and useful information. I received valuable comments by an anonymous referee and the Editor. I am responsible for all remaining errors.

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