See Market liquidity: Research Findings and Selected Policy Implications in BIS (1999) for the various dimensions of liquidity.

Transcription

1 Estiating liquidity preia in the Spanish Governent securities arket 1 Francisco Alonso, Roberto Blanco, Ana del Río, Alicia Sanchís, Banco de España Abstract This paper investigates the presence of liquidity preia in the relative pricing of assets traded on the Spanish governent securities arket. Firstly we propose a classification of bonds consisting on four categories that identify groups of bonds with a different degree of liquidity. Secondly we estiate liquidity preia, including liquidity paraeters in the estiation of the zero-coupon yield curve. The results suggest the existence of a significantly higher yield (adjusted for differences in cash flows) for non-strippable bonds that ostly reflects their lower degree of liquidity. Secondly, post-benchark bonds display a positive liquidity preiu over benchark issues. Thirdly, the lack of liquidity of prebenchark bonds does not see to be priced. We also show that these pricing discrepancies are robust to the ipact of taxes on bonds. The size of relative liquidity preia sees relatively sall. 1. Introduction The liquidity of an asset is generally understood as the ease of its conversion into oney. In practice, the conversion of an asset into oney involves certain costs: searching costs, delays, broker s coissions, etc. The higher these costs the lower the degree of liquidity of the asset. In ost financial arkets there is a class of agents known as arket akers whose function is to provide liquidity. These agents are ready to buy and sell securities up to a axiu aount and ake their profit on the difference between the bid and ask prices. These latter are the prices at which the other arket participants can execute surely and iediately sell and buy transactions, respectively. As a consequence, the bid-ask spread reflects the cost incurred by a typical investor to unwind an asset position, which is part of the cost of converting an asset into oney. This is why the bid-ask spread is one of the ost widely used easures of liquidity. According to arket icrostructure odels, the bid-ask spread ay reflect three different costs faced by arket-akers: asyetric inforation costs, inventory costs, and order processing costs. However, as Gravelle (BIS, 1999) points out, asyetric inforation costs should not be very significant in the case of governent securities (GS). This iplies that liquidity in the GS arkets should be closely linked to the arket-akers inventory risk and order processing costs which ultiately depend on the level of risk of the asset (duration) and the frequency with which a transaction will be executed (turnover). Soeties, liquidity is easured by soe indicators of arket activity (turnover, turnover ratio, benchark status, age). Because investors value asset liquidity we can expect liquidity and differences in liquidity to be priced. In other words, investors ay require a liquidity preiu for holding illiquid assets in order to copensate the for bearing higher transaction costs. In the literature, there are soe papers that test for the existence of liquidity preia in securities arkets. The bulk of this literature focuses on equity arkets, 3 whereas there are only a few papers that focus on debt arkets, ost of the using US arket data. 1 3 We wish to thank Juan Ayuso, Christian Upper, Oreste Tristani, Cleente Fernández, Alfredo Martínez, Víctor García-Vaquero, Jorge Martínez and participants in the BIS Workshop on Market Liquidity for helpful coents and suggestions. See Market liquidity: Research Findings and Selected Policy Iplications in BIS (1999) for the various diensions of liquidity. See, for exaple Aihud and Mendelson (1986,1989). BIS Papers No 79

2 Papers that test for the existence of a liquidity preiu in the GS arkets have followed a nuber of approaches. For exaple, in Aihud and Mendelson (1991), Kaara (1994) and Garbade (1996) the liquidity preiu is only estiated for short-ter US Treasuries. They copare the yield of notes with that of bills with the sae ter to aturity. Since both instruents are identical, except for the fact that notes are ore actively traded, yield differences are attributed to differences in liquidity. The liquidity preia in these papers are found to be high and significant. Elton and Green (1998) use volue as a proxy for liquidity and introduce it as an explanatory variable when fitting a zero-coupon curve to the US arket. They find that the coefficient of this variable is significant for ost of the days considered, although the iplied liquidity preiu is very sall. Warga (199) proxies liquidity by indicating whether or not an issue is on-the-run (the ost recently issued security of a particular aturity). He copares the ex-post onthly excess return over the 30-day Treasury bill rate for two series of constant duration portfolios ade up of securities traded on the US arket, one containing on-the-run bonds and the other containing the other available bonds. Warga (199) finds that the portfolios having the on-the-run bonds exhibit a lower return and interprets this as evidence of a liquidity preiu. In other papers, like Shen and Starr (1998), liquidity is proxied by the bid-ask spread. In that paper the ter preiu, proxied by the excess ex-post returns of the six-onth US T-bill over the 3-onth bill, is estiated and it is found that the bid-ask spread accounts for a substantial portion of this preiu. The estiation of liquidity preia in GS arkets is iportant because aong other reasons, it ight iprove the inforation content of prices. For exaple, the existence of liquidity preia ay distort the inforation extracted fro the estiated ter structure or the estiates of iplied inflation expectations obtained by coparing fixed-coupon and inflation linked bonds. Against this background, the ain goal of this paper is to investigate whether there is a liquidity preiu in the relative pricing of assets traded on the Spanish GS arket. To do this, we first characterise the relative liquidity of bonds. The strippability of the asset and its benchark status appear to be two relevant deterinants of securities liquidity within each aturity zone. Given this property, we consider four categories of bonds that take into account these eleents. The categories are non-strippable bonds and pre-benchark (bonds that will have the benchark status in the future), benchark and post-benchark (bonds that had the benchark status in the past) strippable bonds. We find that there are iportant liquidity differences aong these categories of bonds according to different easures of liquidity based on activity easures and bid-ask spread. Benchark bonds are the ost liquid, followed by strippable non-benchark bonds. And finally non-strippable bonds appear to be very illiquid. In the second part of the paper we estiate relative liquidity preia. A traditional approach consists on calculating yield spread between non-benchark and benchark bonds. However, this estiation of the liquidity preia do not control for risk and tax factors derived fro different cash flow structures of bonds. Our ethodology follows that of Elton and Green (1998) which is based on the estiation of the ter structure of interest rate. This approach allows us a better control of effects related to the cash flow structure of bonds. Concretely, we incorporate liquidity effects in the estiation of zero-coupon yield curve introducing duy variables for the different categories of bonds. The results suggest the existence of a significantly higher yield, adjusted for differences in cash flows, for nonstrippable bonds that sees to ostly reflect their lower degree of liquidity. Second, post-benchark bonds display a positive liquidity preiu over benchark issues. Third, the lack of liquidity of pre-benchark bonds does not see to be priced. Even, in soe periods, we find evidence of a negative preiu over benchark issues for pre-benchark bonds. We also show that these pricing discrepancies are robust to the ipact of taxes on bonds. Thus, these results point to the existence of a liquidity preiu in the relative pricing of bonds traded on the Spanish GS arket, although its size sees relatively sall. The reainder of the paper is organised as follows. Section describes the structure of the Spanish GS arket. Section 3 describes the data. Section 4 proposes a classification of bonds which tries to identify bonds with a different degree of liquidity. Section 5 estiates liquidity preia. And, finally Section 6 suarises the ain conclusions.. Structure of the Spanish governent securities arket Two types of instruents are issued by the Spanish Treasury: Letras del Tesoro (Treasury bills), which are short-ter securities issued at a discount, and Bonos y Obligaciones del Estado (State bonds) which are ediu and long-ter securities with annual coupon payents. Both types of 80 BIS Papers No

3 instruents are represented by book entries and issued via regular copetitive auctions. Bills are issued at 6-, 1- and 18-onth aturities, whereas bonds are issued at 3-, 5-, 10-, 15- and 30-year aturities. Auctions take place on a onthly basis, except for 30-year issues, which are auctioned every two onths, and 1- and 18-onth issues, which are auctioned fortnightly. In the case of ediu and long-ter securities issues are reopened over several consecutive auctions until the outstanding aount reaches a iniu level.the securities allocated at such auctions have identical noinal coupon and interest payent and redeption dates. Since July 1997, the Spanish Treasury has been issuing strippable bonds. They enjoy a ore favourable tax treatent for payers of the corporate incoe tax because the latter are not subject to withholding tax on coupon payents. These securities can be stripped during their life into n+1 zero -coupon assets, where n stands for the nuber of reaining coupon payents, arising fro the cash flow generated by the bond s coupons and principal. The stripping process is conducted by a type of arket participant, known as arket akers, who assue a nuber of coitents subject to annual review. They are also allowed to conduct the reverse process (reconstitution). All outstanding bonds issued before July 1997 are non-strippable and do not enjoy the favourable tax treatent of strippable bonds. Secondary arket trades are conducted through three systes, the first two being reserved for arket ebers, while the third is for transactions between arket ebers and their clients. In the first syste (known as a blind arket) trading is electronically conducted without knowledge of the counterparty s identity. Only those arket ebers who coply with certain requireents and assue a nuber of coitents can participate in this arket segent. For instance, they are obliged to quote during at least 60% of the tie of each session the five references of bonds with benchark status subject to a axiu bid-ask spread. Blind arket trades can only be outright transactions, whether spot or forward. The second trading syste (known as second tier) channels all the reaining transactions between arket ebers. Trading is conducted directly between traders or through brokers. Soe brokers post indicative bid and ask prices on electronic arket inforation systes such as Reuters and Blooberg. In this arket segent, participants can trade outright (in spot or forward transactions) or enter into repos. Two types of repo transactions are allowed: ordinary repos and blocked repos, the difference being the fact that under the second type the buyer cannot transact freely with the securities purchased, regardless of the buy-back date set. Clearing and settleent of GS transactions is carried by the Central de Anotaciones en Cuenta (Book-Entry Syste). Each arket eber holds an account in this syste. Individuals or institutions who are not ebers have to channel transactions through a Managing Institution. The procedure used is one of cash on delivery and transactions are settled three business days later. In addition to the secondary arket, there is a futures and options arket (MEFF RF) where the underlying assets are Spanish GS. At present traded contracts include 5- and 10-year futures and options and 30-year futures. Table 1 provides turnover figures for 1999 for the different arket segents and for the different types of transactions on the Spanish GS arket. Repos are the type of transaction with the highest activity, which is ainly concentrated in the very short-ter (ainly overnight), followed by outright spot purchases. By contrast, trading activity through forward, futures, and options transactions, is ore liited. Table gives a breakdown of the holders of Spanish GS at end Financial institutions own a very large proportion of the outstanding aount (61.% for bonds and 91.3% for bills). Non-residents also have a significant share of the arket in the case of bonds (3%). By contrast, the share of non-financial copanies and households is very low. 3. Data In this paper we use daily data of prices (quoted and traded), outstanding aounts, and trading activity (trading volue and nuber of trades) for the Spanish GS arket fro January 1999 to BIS Papers No 81

4 April 000. This inforation is collected for 34 bonds, 4 4 of the being outstanding through out the saple period (see Table 3 for a description of the issues). For the short-ter, the data refer to Treasury bills and repo transactions. The price data include the following: (i) Daily ean prices traded in the blind and second tier arkets. This inforation was provided by the Central de Anotaciones del Banco de España. (ii) Daily quoted bid and ask prices collected fro two sources: (a) Reuters-BDE: since August 1998 the Banco de España Research Departent has been building a database fro prices posted by Reuters at p.. It includes best quoted bid and ask prices for long and short-ter issues; and bid and ask rates for repo transactions. Bid and ask daily prices are calculated using the quotations of four brokers: three 5 of the are pre-deterined and the fourth is the one who traded ost recently. Fro these quotations, the highest bid and the lowest ask prices are selected for each issue. If the bid price is higher than the ask, 6 then prices are sequentially reoved until a non-negative spread is obtained. (b) Blooberg: this agency provides daily quoted prices calculated as the average bid and ask quotations at the close (deterined by Blooberg to be about 5 p..). In this case, by construction, the bid-ask spread is always positive. Blooberg also provides bid and ask rates for a wide range of repo transactions. It is worth noting that these databases of quoted prices use different ethodologies to calculate daily bid-ask spreads for each instruent. The Reuters-BDE spread is the best proxy for arket spread, but it eploys non-conteporaneous quotations that ay introduce noise and ay bias downwards the size of the spread. On the other hand, the Blooberg spread cannot be interpreted as the arket spread, but its ain advantage is that it reduces non-conteporaneity probles due to the fact that quotes are averaged. Both the Reuters-BDE and Blooberg databases suffer fro the shortcoing that quotations are indicative, not fir, and therefore ay not reflect actual prices. This proble arises fro the specific icrostructure of this arket and eans that it is desirable to use traded prices as copleentary inforation. Trading activity (nuber of trades and trading volue) is provided by Central de Anotaciones del Banco de España and refers only to transactions between arket ebers, in both, the blind and the second tier arket. 4. Classifying bonds by their relative degree of liquidity 4.1. A classification of bonds according to their life cycle and tax treatent In this section we propose a classification of bonds that tries to identify a nuber of bonds groups with a different degree of liquidity. It is iportant to stress that the approach we follow in this paper of classifying bonds by their relative liquidity is not intended to copare liquidity across different aturity zones but within the. This decision is justified by the ethodology we use in the next section to estiate liquidity preia, which consists of fitting a zero-coupon yield curve. With this ethodology it would be very difficult to separate ter and liquidity effects if we used a classification of liquidity across different aturities. Our classification takes into account two eleents of an issue: its stage of the life cycle and its strippability (whether or not the issue is strippable). We consider the stage of the life because, in general, trading activity and, consequently, liquidity is related to this. It is well-known that in GS arkets trading activity tends to be concentrated in a sall group of securities known as benchark Strips are not included. The percentage of stripped bonds is very low in the Spanish arket. Four in the case of short-ter instruents. In the inforation provided by Reuters it is not uncoon to find negative bid-ask spreads, possibly due to the lack of conteporaneity in quotations. 8 BIS Papers No

5 issues. The prices of these instruents are used for extracting inforation for acroeconoic analysis and pricing purposes. In the Spanish GS arket there are five benchark issues corresponding to 3-, 5-, 10-, 15- and 30-year aturities. Since all issued bonds becoe benchark issues, the life cycle of bonds consists of three stages. In the first stage, the bond is initially issued and its outstanding volue is relatively sall, and henceforth, its trading activity is very low and does not have benchark status. Henceforth bonds in this stage will be referred to as pre-benchark issues. New fungible auctions increase the outstanding aount, and trading activity also increases until benchark status is achieved and the issue becoes the ost liquid one for a particular aturity. Finally, in the third stage, the bond is replaced by a new benchark and its activity begins to decrease. Bonds in this stage will be referred to as post-benchark issues. More specifically, our classification consists on four categories, naely: pre-benchark, benchark, post-benchark and non-strippable issues. The first three categories are only ade up of strippable bonds, whereas the last category includes all non-strippable bonds. We have decided to group all non-strippable bonds in one specific category for the following two reasons. Firstly, in our saple, all non-strippable bonds are at a very advanced third stage of their life cycle, therefore they are very illiquid. And, secondly they are subject to a less favourable tax treatent that could be reflected in a tax preiu. Over our saple period there was no official classification of benchark issues in Spain. As a consequence, the identification of the benchark issue ay be difficult during transition periods. The criterion we use in this paper considers that a new bond becoes the benchark issue when it has been traded ore than the old benchark for at least three consecutive days. Table 4 gives the dates on which a benchark bond changes according to this criterion, and copares the with those reported by Reuters and Blooberg. It can be observed that dates do not coincide for the different criteria, but differences between the rarely exceed one onth. Figure 1 shows the life cycle for all the strippable 10-year bonds of our saple. Over this period two replaceents take place, one in February 1999 when the 5.15% bond becoes the new benchark. The other takes place in October 1999, where the ost recently issued bond (4% with aturity at 31/1/10) acquires the benchark status. This figure displays the evolution of trading activity, outstanding volue and bid-ask spread. It can be seen that the life cycle in trading activity appears also to be incorporated in the evolution of bid-ask spreads, suggesting a very different degree of liquidity of bonds depending on the stage of life they are at. Table 5 gives a descriptive analysis of previously defined bond categories over our saple period. It can be seen that benchark issues account, on average, for alost 53% of the daily trading volue (see panel c). Regarding non-strippable bonds, despite the high nuber of issues (0 issues at the beginning of the period and 16 at the end), they account for just 7% of daily trading volue (see panel c). Finally, the reaining 40% of the trading volue corresponds to strippable non-benchark bonds - of which pre-benchark issues account for a 15% and post-benchark issues for a 5%. There are 4 such bonds at the beginning of the period increasing to 9 by April 000. Looking at trading activity by aturity, a high concentration around the 10-year zone is observed, with approxiately 33% of the total arket activity. The 3- and 5-year aturities account for approxiately 5% and 3% respectively. And finally, the zones of 15- and 30-year residual aturity have the lowest activity, with approxiately 5% and 3% of total arket activity respectively. Regarding outstanding volue, panel b of Table 5 shows a very different distribution. In particular, a high concentration (ore than 50%) is observed in the 0-6 years zone. 4.. Is this classification useful to identify groups of bonds with a different degree of liquidity? We now show to what extent the four categories we propose are useful to identify groups of bonds with a different degree of liquidity. To do this we copute soe liquidity easures for the different categories of bonds. Table 6 reports various easures of liquidity, all based on trading activity, with a breakdown by bond category and aturity. These easures are the nuber of trades, trading volue and turnover ratio. All these indicators are coputed per bond and, therefore, can be interpreted as liquidity easures. A feature shared by all the liquidity easures of Table 6 is the rearkable differences in liquidity between the various categories considered. BIS Papers No 83

6 When coparing liquidity within each aturity zone benchark issues are the bonds with the greatest liquidity, followed by strippable non-benchark bonds (for both pre-benchark 7 and post-benchark). Finally, non-strippable bonds are notable for their very scarce trading activity. When coparing liquidity aong aturity zones the ost liquid bonds are those with a residual aturity between 3 and 10 years. In this regard, it is worth noting that strippable non-benchark bonds are soeties even ore liquid than 15 and 30-year benchark issues. Figure displays the bid-ask spread 8 as a function of the duration for the different categories of bonds. This indicator is used as an additional easure of liquidity. A siilar pattern to that reported for trading activity also appears here when coparing the liquidity of bonds within each aturity zone (proxied by duration), although now pre-benchark issues appear to be ore siilar, in ters of liquidity, to non-strippable bonds than to post-benchark strippable issues. However, note that trading activity and the bid-ask spread would provide a very different ranking of bonds by liquidity if we did not control for tie to aturity or duration. As Figure illustrates, the bid-ask spread is positively correlated with tie to aturity. This effect clearly doinates the previously reported pattern (benchark status of the bond). This relationship between spread and tie to aturity, which has also been identified in other GS arkets, 9 can theoretically be explained by the arket-akers inventory risk and order processing costs which ultiately depend on the level of risk of the asset proxied by tie to aturity. Accordingly, a ranking of bonds using the bid-ask spread would classify short-ter securities as the ost liquid and long-ter issues as relatively illiquid. Conversely, a ranking of bonds by the liquidity easures of Table 6 would classify the 10-year bonds as the ost liquid issues. It is worth noting that our classification of bonds can be justified either by the bid-ask spread or by the trading activity easures because, as was entioned before, we do not intend to copare liquidity across different aturity zones but within the. Three conclusions ay be drawn fro the previous analysis. Firstly, the benchark status and strippability of bonds are two relevant deterinants of the liquidity differences within a aturity zone for the bonds in our saple. Secondly, the four categories we consider see useful to identify groups of bonds with a different degree of liquidity. And, finally there sees to be strong differences in liquidity between bonds, so that it akes sense to test for the existence of a liquidity preiu. This is the ai of the next section of the paper. 5. Estiating liquidity preia 5.1 Preliinary analysis Our ai in this second part of the paper is to find out if differences in liquidity are priced in the Spanish GS arket. One siple approach is to approxiate the liquidity preiu by the yield spread between non-benchark and benchark bonds. Applying this easure to the 3,5, 10 and 15-year bonds of our saple always gives a negative figure suggesting the existence of negative liquidity preia. However, it has to be taken into account that soe factors ay bias this easure. Differences in coupons between bonds iply different risk and tax burdens that ay ake the investor to deand different yields to aturity for other reasons not related to liquidity effects. The ain difficulty when identifying the liquidity preiu is the separation of the factors explaining differences in yields to aturity. With this in ind, our proposal is based on the estiation of the ter structure of interest rate, because this allows us to control any effect associated with differences in aturity and cash flows. This approach is siilar to that followed by Elton and Green (1998) Although in the case of the turnover ratio no significant differences are observed between pre-benchark and benchark issues. For this analysis we use Reuters-BDE database because it provides a spread easure ore closely linked to the concept of arket spread (see Section 3 for a description of this database and a coparison with the Blooberg data). BIS (1999) copares bid-ask spreads for on-the-run and off-the-run issues for Canada, Italy, Japan, UK and US. In all cases they find the sae results as ours, except for Japan, where the liquidity of on-the-run 10-year bonds akes their spread narrower than the one for on-the-run 5-year bonds. (See Table 3 of the docuent Market Liquidity: Research Findings and Selected Policy Iplications) 84 BIS Papers No

7 According to the analysis developed in Section 4, we distinguish four types of bonds in relation to their life cycle and tax-treatent: non-strippable bonds, pre-benchark, post-benchark, and benchark strippable bonds. As a preliinary analysis of the existence of liquidity preia we estiate a zero-coupon yield curve using the Svensson odel 10 and analyse yield errors for bonds. We find a very interesting pattern. Figure 3 shows the estiation for a representative day of the saple, (9/3/99) and Table 7 reports average yield errors for each bond in our saple distinguishing its classification over the saple. The first thing we observe is that ost non-strippable bonds appear to have on average positive yield errors, i.e. they are located above the estiated yield curve. The second point to be stressed is the tendency of pre-benchark bonds to exhibit a lower yield error than benchark bonds. Finally, the yield error of post-benchark bonds lies between yield errors of benchark and non-strippable bonds. These results suggest a preliinary evidence of a positive preiu for post-benchark and non-strippable bonds over benchark issues. Next section tries to estiate the using a ore foral approach. 5. Estiating the yield curve incorporating liquidity effects Previous results indicate that the estiation of the yield curve for the Spanish GS arket ay be iproved if we introduce liquidity and withholding tax affects. Our proposal consists of estiating the ter structure of interest rates using the Svensson odel, and introducing additional paraeters to capture these effects. Elton and Green (1998) follow a siilar procedure 11 introducing volue as a easure of liquidity. Given that the relationship between traded volue and liquidity ay not be linear, we prefer using duy variables to classify securities according to their degree of liquidity and tax treatent. The instantaneous forward rate of ter is odelled in the following way: ϕ τ = β0 + β1e 1 1 τ1 τ + β e + β3 e + γ 0PREBENCH + γ 1POSTBENCH + γ NONSTRIP τ τ where PREBENCH, POSTBENCH and NONSTRIP are duy variables which take value 1 respectively for pre-benchark, post-benchark and non-strippable bonds. Paraeters for duy variables ust be interpreted in relation to the reaining instruents (3, 5, 10, 15 and 30-year benchark bonds and short-run securities). Paraeters γ 0, γ 1 and γ capture the excess yield deanded on pre-benchark, post-benchark and non-strippable bonds respectively. Paraeters γ 0 and γ 1 can be directly interpreted as liquidity preia since the tax treatent is the sae for all strippable issues. Conversely, paraeter γ ay incorporate a tax preiu in addition to a liquidity preiu due to the relatively less favourable tax treatent of non-strippable bonds. The interpretation of reaining paraeters is the standard in the Svensson odel. Once we have odelled the instantaneous forward rate including withholding tax and liquidity effects, we estiate the paraeter vector β = β, β, β, τ, β, τ, γ, γ, ) for each day t as N pti pti ( β βˆ = argin pti i= 1 ) ( γ where pti is the actual price of bond i at tie t and N is the nuber of securities considered in the estiation. And p (β ) is the theoretical price obtained fro previous specification of the ti 10 See Annex 1 for a description of this odel. We use the id-point between the bid and ask price provided by Blooberg database. Bonds with a reaining life of under a year are excluded fro the estiation. For short-ter we use repo and bill rates. 11 They use non-linear least squares to fit a cubic spline to the after-tax cash flows of bonds. BIS Papers No 85

8 instantaneous forward rate. We iniise price errors instead of yield errors to obtain a better fit for the aturities we are ost interested in, i.e. ediu and long-ter. We distinguish four nested odels. The basic odel, called Model 1, does not consider any liquidity or tax effects, i.e. γ 0, γ 1 and γ are restricted to zero. In Model all these paraeters are freely estiated. Model 3 eliinates the duy variable for pre-benchark bonds. And finally, Model 4 estiates freely the paraeter of the duy variable for non-strippable bonds, and restricts to zero the paraeters of other duy variables. We estiate these four odels for the whole saple, fro January 1999 to April 000. Over the period 4/1/99 to 30/9/99 the Svensson odel does not iprove on the Nelson-Siegel odel 1 and consequently, we estiate the latter odel for this period. Table 8 13 reports a descriptive analysis of the estiated paraeters for duy variables, the root ean square error (RMSE), and the reduction in the RMSE with respect to the basic odel. When all the three duy paraeters are freely estiated (Model ) the average RMSE is 63% less than that of the basic odel. The estiated paraeter for the non-strippable bonds duy is positive and significant for alost the whole saple, indicating that these bonds incorporate a preiu over the benchark issues that ranges fro to 10 basis points in our saple. On average, the excess yield deanded on these bonds is 7 basis points. Regarding post-benchark bonds, they also appear to incorporate a preiu. It takes the value of 5 basis points on average, but in this case there are soe periods where the paraeter of this variable is not positive and statistically significant. Figure 4 shows the evolution of estiated paraeters, γ 0, γ 1, γ. Shaded areas indicate that γ is not statistically significant. These areas coincide with transition periods in benchark bonds. During January-February 1999 it occurs a change in 3, 5 and 10-year benchark bonds. During October-Deceber 1999 there is a change of all benchark bonds except for 30-year ter. Replaceents take place gradually in the arkets and during these transition periods frontiers between strippable categories are blurred given the sall nuber of bonds in each one. The approach we follow changes the category of a bond in a specific date (see table 4) generating sharp oveents in the estiations of preiu paraeters. The sensitivity of our estiations to benchark changes does not allow interpreting the evolution of the paraeters during transition periods. In any case, results when the categories of bonds are enough differentiated show that post-benchark bonds include a liquidity preiu over benchark issues. Regarding the paraeter of pre-benchark bonds, it turns out to be negative on average, suggesting the existence of a negative preiu for these bonds over benchark issues. However, soe care ust be taken in the interpretation of this paraeter. It is negatively significant just for 54% of the saple, and for soe periods there is just one bond included in this category. The conclusion drawn fro the analysis of this paraeter is that pre-benchark bonds do not see to include any positive liquidity preiu in spite of its low liquidity in ters of trading activity and bid-ask spreads. This result ay possibly be explained by the forward-looking behaviour of investors. It is costly to trade with these securities, but investors do not deand a higher yield because, in the future, these costs will be uch lower when the bond acquires benchark status. In addition, the liited supply of these issues ay contribute to sustain its price. Given that pre-benchark bonds do not appear to have a positive liquidity preiu over benchark issues, and given that there are not any pre-benchark bonds in our saple we proceed to group pre-benchark and benchark bonds into the sae category. Model 3 includes only two duy variables to capture liquidity differences, one for post-benchark and the other for non-strippable bonds. The reduction of RMSE with respect to the basic odel continues to be very high (51%). Non-strippable bonds appear to have a preiu of 8 basis points on average, ranging fro 5 to 1 basis points. This paraeter is statistically significant for the whole saple. For post-benchark bonds, paraeter γ 1, is positive and significant for 76% of the saple, showing on average a liquidity 1 This odel is a particular case of the Svensson odel, where the instantaneous forward rate is odelled with just one hup, i.e. β 3 and τ are set to zero and one respectively. 13 We concentrate on the interpretation of paraeters γ0, γ 1, γ, which will be reported in different tables. The reaining paraeters of the Svensson and Nelson-Siegel odel are presented in Table 1 for all odels estiated throughout the paper. 86 BIS Papers No

9 preiu of 5 basis points. Therefore, inclusion of pre-benchark bonds with benchark bonds increases the size of the preia. Finally, Model 4 includes just one duy variable for non-strippable bonds. It allows an average reduction of 37% in the RMSE with respect to the basic odel. In this odel the average preiu for non-strippable bonds over the reaining bonds is 6 basis points. The size of this paraeter is lower than in Model 3 because in this case the group of bonds excluded fro duy variables includes post-benchark issues. Suing up, the results of this section suggest the existence of a positive liquidity preiu for post-benchark issues over benchark bonds, although its size is very sall - siilar to that found by Elton and Green (1998) in the US arket. Conversely, the lack of liquidity of pre-benchark issues does not see to be priced and, even a negative preiu over benchark issues is found in soe periods. Finally, there is clear evidence of a positive preiu for non-strippable bonds in the whole saple. However, as noted before, this preiu could not be interpreted directly as a liquidity preiu since the excess yield deanded on non-strippable bonds ay also include a withholding tax preiu. In the next section we try to separate these two coponents. 5.3 Separation of withholding tax and liquidity effects for non-strippable bonds Previous results show strong evidence of a preiu for non-strippable bonds. This preiu ay be due to liquidity or withholding tax effects. In order to separate these two eleents we re-estiate Model 3 taking into account the withholding tax (Model 5). To do this we odify the cash flows of non-strippable bonds in the following way. We reduce the aount of coupon payents by 18% (withholding tax rate during the saple period) and include a new cash flow strea corresponding to the copensation for the withholding tax. The dates we assign to these cash flows are selected to coincide with the quarterly tax returns that Spanish corporations are obliged to ake. It has to be noted that this procedure considers the axiu cost faced by non-strippable bond holders since they can reduce it through coupon washing transactions. 14 Consequently, the estiated preiu for non-strippable bonds can be interpreted as a lower bound for the true liquidity preiu. Table 9 reports the estiated paraeters, which are coparable with those for Model 3. This odel reduces the preiu for non-strippable bonds by only 1. basis points, in coparison with Model 3, whereas the preiu for post-benchark bonds does not change significantly. These results suggest that ost of the estiated preia for non-strippable bonds in Models to 4 correspond to liquidity preia. According to the results of Table 9, the average liquidity preiu for non-strippable bonds is at least 6.8 basis points. This iniu liquidity preiu for non-strippable bonds is still higher, on average ters, than the one found for post-benchark bonds. This fact is logical given their strong differences of liquidity. 5.4 Robustness to tax effects The above results ay be sensitive to including general tax effects in the estiation of the zero-coupon yield curve. That is, they ay be affected by the estiation of a pre-tax instead of a post-tax yield curve. It is very difficult to estiate a post-tax yield curve, because tax treatent is very different across investors. In this section we estiate a post-tax yield curve considering the tax treatent for Spanish corporations, which hold two thirds of the outstanding volue of bonds (see Table ). The theoretical price is expressed as the present value of after-tax cash flows iposing a tax rate of 35% for both interest payent and capital gains. Capital gains or losses at redeption date are distributed over the life of the bond using a constant yield ethod, and assuing that the bond is held until aturity. Table 10 shows the ain results of the re-estiation of Model 3 using after-tax flows (Model 6). It can be seen that in this new odel the sign and significance of estiated preia reain unchanged, but their absolute size is reduced by around 35%. The paraeters that capture the asyptotic value of the 14 These transactions consist of selling non-strippable bonds to non-resident investors, who are not subject to withholding tax, before the date of the coupon and buying the again after that date. BIS Papers No 87

10 instantaneous forward rate ( β 0 = ϕ ) and the instantaneous forward rate for an infinitely sall ter to aturity ( β 0 + β1 = ϕ0 ) are also reduced by around 35%. Consequently, the liquidity preia expressed as a percentage of these interest rates reain alost unchanged (see Table 11). These results indicate that previously estiated relative liquidity preia are robust to tax effects. Finally, it is interesting to see that the odel with taxes further reduces the RMSE. In average the reduction over the basic odel is 77%, which copares with the 51% reduction of the odel with two duies without taxes (odel 3). This result suggests the relevance of introducing tax effects when fitting zero-coupon yield curves. 5.5 Ipact of liquidity preia on the estiated yield curve In this subsection we study the ipact of the introduction of liquidity effects on the estiated zero-coupon yield curve. To do this we copare the estiated paraeters for the different odels we have considered in subsections 5. to 5.4. Table 1 reports the ean and the standard deviation of the basic paraeters of the ter structure. 15 The ean of the paraeters estiates for the odels that introduce liquidity effects without taxes (Models to 5) are very close to those of the basic odel (Model 1). This is not a surprising result given the relatively sall liquidity preia we have found. Conversely, when taxes are introduced (Model 6) soe paraeters change significantly. β 0 and β 1 are now around 35% (the tax rate) below the estiated level for Model 3, whereas the changes in the other paraeters are less draatic. These changes iply that after-tax zero-coupon rates are around 35% below before-tax rates. Figure 5 depicts the zero-coupon yield curve at 9/3/99 for two of the odels we have estiated, using the Nelson-Siegel approach. The odels we consider in this figure are: the basic odel (Model 1), and the odel that introduces duy variables for both post-benchark and non-strippable bonds (Model 3). The yield curve of the odel that accounts for liquidity (Model 3) stands slightly above (with a axiu difference of 9 basis points) that of the basic odel for short-ter aturities and slightly below (with a axiu difference of 1 basis points) for ediu-ter horizons. For long-ter aturities both odels display very siilar rates. Figure 6 shows the estiated 1-year forward curves iplied by the yield curves depicted in Figure 5. Estiated forward rates for horizons shorter than 6 years are slightly lower for the odel that accounts for liquidity effects, whereas the opposite is the case for longer horizons. Figures 7 and 8 are the sae as Figures 5 and 6, except for the fact that they are estiated at 31/3/00 using the Svensson odel. In this case, the zero-coupon rates are lower for the odel that introduces liquidity effects in coparison with the basic odel, for all horizons. It is worth noting that for the ediu and long-ter horizons the difference between the two curves is saller than that found with Figure 5. This is not surprising given the reduction in the estiated liquidity preia in the second half of the saple. The introduction of liquidity effects has allowed us to identify liquidity preia and to reduce the error in the estiation of the zero-coupon yield curve. However, the iplications for inforation content of the estiated yield curve are not very iportant. This is an expected result given the sall size of the estiated liquidity preiu. 5.6 Biases in quoted prices The results of the previous analysis have been derived fro the quoted prices posted by brokers in Blooberg. We know that these prices are not fir, but erely inforative and, consequently, we do not know how accurate they are. The existence of a bias in quoted prices ay have an ipact on the liquidity preia we have estiated. In this subsection we study the existence of biases in quoted prices in coparison with traded prices and derive conclusions on their ipact on the estiated liquidity preia. To do this, for each day and security we copute the difference in yield between the ean traded price and the id-quoted price. Table 13 shows the average of these yield differences for 15 Fro 4/01/99 to 30/9/99 we estiate Nelson-Siegel odel, and fro 1/10/99 to 14/4/00 Svensson odel. 88 BIS Papers No

11 each security, distinguishing its classification along the saple in the four categories we have considered along this paper (pre-benchark, benchark, post-benchark and non-strippable). Three iportant features eerge fro Table 13. First, average yield differences are very sall for all securities (between 0 and.3 basis points), ost of the being not significantly different fro zero. Second, yield differences tend to be positive for ost bonds (those figures statistically different fro zero are all positive). Third, yield differences tend to be higher for pre-benchark and non-strippable bonds. These results suggest the existence of a sall negative bias in quoted prices in coparison with traded prices, which sees to be ore iportant for pre-benchark and non-strippable issues. This would ean that there is a negative bias in the estiated liquidity preia for non-strippable and pre-benchark bonds. That is, the actual liquidity preiu for non-strippable bonds is higher than the estiated, whereas the absolute value of the liquidity preiu for pre-benchark issues is lower. However, these biases in the liquidity preia should be relatively sall given the very sall size of the bias in quoted prices. Consequently, the reported results of sections 5.1 to 5.5 see to be robust to the data set we have used. 6. Conclusions The analysis developed in the first part of the paper has showed that there are iportant liquidity differences aong securities traded in the Spanish GS arket. The strippability of the asset strippable bonds are the ost liquid- and the benchark status benchark bonds are ore liquidappear to be two relevant deterinants of the securities liquidity within each aturity zone. The second part of the paper analyses the presence of liquidity preia in the relative pricing of assets traded in the Spanish GS arket. The estiation is carried out introducing liquidity paraeters in the Svensson odel of the zero-coupon yield curve. These liquidity paraeters allow us to estiate the excess yield of pre-benchark, post-benchark and non-strippable bonds over benchark issues. This ethodology iproves the traditional approach of the estiation of liquidity preiu which consists on coputing the yield spread between non-benchark and benchark bonds - because it allows an appropriate control of effects associated with differences in aturity and cash flows. The ain conclusions that can be drawn fro the estiations ade are the following. Firstly, results suggest the existence of a positive and significant preiu for post-benchark bonds (both strippable and non-strippable). However, these preia are very sall and siilar to those found by Elton and Green (1998) in the US arket. Secondly, the lack of liquidity of pre-benchark bonds does not see to be priced in the arket. Even, in soe periods, a negative preiu over benchark issues arises for these bonds. This is a soewhat surprising result that can possibly be explained by the forward-looking behaviour of arket participants. Thirdly, estiated liquidity preia see robust to tax effects and to the data set we have used (quoted prices instead of actual traded prices). Finally, regarding the iplications for the estiated zero-coupon yield curve, the introduction of liquidity effects do not have significant effects due to sall size of the estiated liquidity preia. References Aihud, Y. and H. Mendelson (1986) Asset pricing and the bid-ask spread, Journal of Financial Econoics 17, (1989) The effects of beta, bid-ask spread, residual risk and size on stock returns, Journal of Finance 44, (1991) Liquidity, aturity, and the yields on U.S. Treasury securities, Journal of Finance 46, pp Bank for International Settleent (1999) Market Liquidity: Research Findings and Selected Policy Iplications. Copeland, T.C. and Galai, G. (1983) Inforation effects on the bid-ask spread Journal of Finance, 38, pp Elton, E. J. and T. C. Green (1998) Tax and liquidity effects in pricing governent bonds, The Journal of Finance 53, BIS Papers No 89

12 Fleing, M. J. and E. M. Reolona (1996) Price foration and liquidity in the U.S. treasuries arket: evidence fro intraday patterns around announceents, Research Paper 9633, Federal Reserve Bank of New York. Garbade, K. D. (1996) Fixed Incoe Analysis (MIT Press, Cabridge, Mass.) Gravelle, T. (1999) Liquidity of the governent of Canada Securities Market: stylized facts and soe arket icrostructure coparisons to the United States Treasury Market, Bank of Canada, Working Paper Kaara, A. (1994) Liquidity, taxes, and short-ter Treasury yields, Journal of Financial and Quantitative Analysis 9, Litzenberger, R. H. and J. Rolfo (1984) An international study of tax effects on governent bonds, The Journal of Finance 39, 1-. Nelson C. R. and A. F. Siegel (1987) Parsionious Modelling of yield curves for US Treasury Bills, Journal of Business 60, Núñez, S. (1995) Estiación de la estructura teporal de los tipos de interés en España: elección entre étodos alternativos, Banco de España, Docuento de Trabajo nº 95. Sarig, O. and A. Warga (1989) Bond price data and bond arket liquidity, Journal of Financial and Quantitative Analysis 4, Shen, P. and R. M. Starr (1998) Liquidity of the Treasury bill arket and the ter structure of interest rates, Journal of Econoics and Business 50, pp Svensson, L.E.O. (1994) Estiating and interpreting forward interest rates: Sweden , Centre for Econoic Policy Research, Discussion Paper Warga, A. (199) Bond returns, liquidity, and issing data, Journal of Financial and Quantitative Analysis 7, BIS Papers No

13 Annex The Svensson odel Svensson (1994) specifies a sooth paraetric function for the yield curve. The functional for for the instantaneous forward rate of ter, ϕ, is the following: ϕ ( β ) = β + β e where 0 1 τ 1 + β e τ 1 τ 1 + β 3 e τ τ β = β, β, β, τ, β, ) is the vector of paraeters. ( τ is the ter to aturity. β 0 = ϕ is the asyptotic value of the instantaneous forward rate. (A1) β + = is the instantaneous forward rate for an infinitely sall ter to aturity. 0 β1 ϕ 0 τ 1 indicates the position of the first internal axiu or iniu. β deterines the agnitude and direction of the first hup. If β 0, there is a axiu at 1 τ, and a iniu if β 0. < > τ indicates the position of the second internal axiu or iniu. β deterines the agnitude and direction of the second hup. If β 0, there is a axiu 3 3 > at τ, and a iniu if β 3 < 0. The zero-coupon rate is the ean of integration of the instantaneous forward rate between period 0 and the ter to aturity, r 1 = 0 ϕ θ dθ : r ( β ) = β τ τ 1 τ1 τ1 τ 0 + ( β1 + β ) (1 e ) β e + β 3 (1 e ) β e 3 τ (A) The continuously copounded discount factor is d r ( ) = e : d(, β ) = e β τ1 τ1 τ 0 ( β1+ β ) τ1(1e ) + β e β3τ (1e ) + β τ 3e (A3) The theoretical price of bond i at tie t is the present value of its cash flows: M p ( β ) = d( j t, β ) it f ij j= t (A4) where date. f ij represents the coupon and principal payents of bond i at date j, and M is the redeption The paraeter vector is estiated by the iniisation of soe distance between the theoretical and actual prices of the bonds. Soeties the iniisation proble is specified in ters of yield errors instead of price errors, or soe cobination of both. Another possibility is estiation by axiu likelihood. BIS Papers No 91