Rainer Jankowitsch Vienna University of Technology and CCEFM Favoritenstrasse 11, A-1040 Vienna, Austria

Transcription

1 (67,0$7,1*=(52&28321<,(/'&859(6)25 (08*29(510(17%21'6 Rainer Jankowitsch Vienna University of Technology and CCEFM Favoritenstrasse 11, A-1040 Vienna, Austria Stefan Pichler Vienna University of Technology Favoritenstrasse 11, A-1040 Vienna, Austria 2FWREHU 7KLVZRUNLVEDVHGRQDUHVHDUFKSURMHFWIXQGHGE\WKH$XVWULDQ1DWLRQDO%DQN 2H1%±-XELOlXPVIRQGSURMHNW1U

2 ,QWURGXFWLRQ This document describes the technical process of selecting and collecting the bond market data during the research project Jubiläumsfondsprojekt Nr sponsored by the Austrian National Bank (OeNB). The aim of the project is to develop models to explain and to quantify credit spreads in the European Government Bond Market. The survey is restricted to the Euro-countries to concentrate on a market in a single currency. In the data collection process only those government bonds are chosen, which are used afterwards in the project. For results of the research project see Geyer et al. (2001), Jankowitsch and Pichler (2002), and Jankowitsch et al. (2002). In general, only EUR-denominated government bonds with a fixed coupon, fixed redemption and without option features are taken into account. The first step is to evaluate the possible data providers to know which information is available and where it has optimal quality. In the next step all data are downloaded from the chosen provider using different tools. A database is built which has to contain a certain data structure, that facilitates the actual use of the data. The last step is to fill the database with the downloaded data. The result is a database, which provides the necessary data for all purposes of the research project in an efficient way. The last section describes the estimation of zero-coupon yield curves using the government bond data. These zero-coupon yield curves are a starting point of nearly all other estimations and their calculation together with their representation in the database is therefore presented in this document. 6HOHFWLRQ3URFHVV 'DWD3URYLGHU The aim of the research project is to estimate credit spreads from government bonds. In the first step a data provider has to be chosen. There are two providers, that offer all the necessary information: Reuters and Bloomberg. These two providers have been evaluated at this stage of the project. 2

3 The most important information is the price history of the government bonds. We want a price history starting on 1. January 1999 (the start of the EMU) and ending on the day when we first downloaded the data (31. March 2001). The database will be updated on a yearly basis. Reuters and Bloomberg offer this history based on closing prices for all the traded government bonds from various price sources (e.g. Deutsche Bank, Paribas,...). The first analysis of the quality of price information shows that the closing price for a bond is not identical across the different prices sources. Table 1 contains the closing prices from three financial institutions for a German government benchmark bond for four days: 'HXWVFKH%DQN +\SR9HUHLQVEDQN0 QFKHQ &6)LUVW%RVWRQ 0D[LPDO'LIIHUHQFH basis points basis points basis points basis points 7DEOH±&ORVLQJSULFHVIRUWKH*HUPDQ%XQGHVDQOHLKH We see that there is a difference in the closing prices up to 14 basis points. To avoid a bias in the price history it is necessary to construct an average closing price from the best price sources for each government bond. Still this can be done with Reuters or Bloomberg data. Bloomberg offers such an average of closing pricing. It is called Bloomberg Generic (BGN) and is constructed by eliminating the highest and the lowest closing prices and calculating an average based on the remaining prices. Since this method avoids the bias in the data and is constructed in a reasonable way, we choose Bloomberg as the data provider for our research project. *RYHUQPHQW%RQGV The next step after selecting the data provider is to identify all the government bonds, which are necessary as input for the subsequent studies. As described in the introduction only government bonds of Euro-countries denominated in Euro, with fixed coupon, fixed redemption and without option features are chosen. 3

4 Bloomberg offers a suitable tool (SRCH <Go> in the Bloomberg Terminal), which searches for these bonds. In the tool all features of the instruments can be chosen and a list is returned, which contains the CUSIP-Code of all bonds, which satisfy the selected criteria. This tool returns information about nearly 700 government bonds. In the next step each of this bonds has to be checked by hand, because it is still possible due to data inconsistencies to find some bonds with e.g. option features in this list. Bloomberg offers a page for each bond with a description of its features. There each bond can be inspected. All bonds that have option features, floating or index-linked payments or that are denominated in a non-euro currency or are only traded in specialised markets, are eliminated. Figure 1 shows this description page for one bond: )LJ±6HFXULW\GHVFULSWLRQSDJH After this step we have 638 bonds remaining on the list. Table 2 shows the number of government bonds for each country. For these bonds all necessary information has to be downloaded from Bloomberg and filled in a suitable database. 4

5 1XPEHU RIERQGV *HUPDQ\ )UDQFH,WDO\ $XVWULD 1HWKHUODQGV %HOJLXP 3RUWXJDO 6SDLQ )LQODQG,UHODQG DEOH±1XPEHURIJRYHUQPHQWERQGVIRUHDFKFRXQWU\ Luxembourg is excluded because no quotes for its bonds can be found. To our information these bonds exist but are not publicly traded. Greece is also excluded because it did not take part in the starting phase of the Euro in 'DWD'RZQORDG For each government bond we need the following information: œ basic features, e.g. maturity, coupon rate œ exact cashflow schedule œ price history œ benchmark history, i.e. on which days the bond is regarded as a benchmark bond Each of these four categories has to be treated separately. The next sections explain how to download the data for each of this categories. %DVLF)HDWXUHV The basic features can be downloaded using the standard Bloomberg add-in for MS-Excel (Bloomberg Table Wizard). This category contains the following information for each bond: œ maturity œ coupon œ ticker œ collateral type œ redemption value œ amount issued œ starting day of the accrued interest 5

6 œ Isin-number œ country of issuer Figure 2 shows the Bloomberg Table Wizard, which is used to download the data to Excel: )LJ±%ORRPEHUJ7DEOH:L]DUG The result of this step is a matrix in Excel containing the information listed above for each bond. Table 3 shows this matrix for five Austrian bonds. &XVLS 0DWXULW\ &RXSRQ 7LFNHU &ROODWBW\S 5HGHPSBYDO,QWBDFFBGW $PWBLVVXHG,VLQ &RXQWU\ GG RAGB BONDS AT AS GG RAGB BONDS AT AS AA RAGB BONDS AT AS GG RAGB BONDS AT AS GG AOBL BONDS AT AS 7DEOH±%DVLFIHDWXUHVIRUILYH$XVWULDQERQGV 6

7 &DVK)ORZ6FKHGXOH For each bond we need the exact cashflow schedule. This schedule contains the following information: œ date of cashflow œ coupon payment for this date œ redemption payment for this date It is necessary to collect this information, because even for fixed coupon government bonds there is often some unregularity in the payment structure, e.g. a longer or shorter first coupon period. Bloomberg offers the &DVK)ORZ'RZQORDG7RRO to access this information. From this tool the data can be copied in an Excel-sheet. Figure 3 shows the &DVK)ORZ'RZQORDG7RRO: )LJ±%ORRPEHUJ&DVKIORZ'RZQORDG7RRO Important to note is that the first settlement date has to be entered in the field 6HWWOH 'DWH PG\, otherwise the cashflow schedule can be incorrect. 7

8 Table 4 shows the result for a bond after copying the data to Excel: Date Cusip Coupon Redemption EC EC EC EC EC DEOH±&DVKIORZRIDERQGZLWKDORQJHUILUVWFRXSRQSHULRG For every bond such a list must be copied from the tool to Excel. The drawback of the tool is that it only allows to enter one bond at time which makes the procedure rather time consuming. 3ULFH+LVWRU\ For each government bond we need the price history. For the research project this history starts on 1. January 1999 (the start of the Euro) and ends on the downloading day, which is the 31. March For each day in this time interval the following information is collected for every bond: œ ask-price œ bid-price œ ask-yield œ bid-yield The price and yield information is based on the Bloomberg Generic (BGN) data source as described in section 2. Since we want to use the BGN price data, we must change the standard price sources for government bonds in Bloomberg to BGN (FMPS <Go> in the Bloomberg Terminal). The standard Bloomberg Add-In for Excel (Bloomberg Table Wizard) can then be used to download the price information to Excel. 8

9 After these steps the price history is downloaded to Excel. Table 5 shows the results for one bond: (& 'DWH 3[$VN 3[%LG <OG<WP$VN <OG<WP%LG DEOH±3ULFHKLVWRU\IRUDJRYHUQPHQWERQG %HQFKPDUN+LVWRU\ In the European bond markets representative bonds with a certain maturity and high outstanding volumes are declared as benchmark bonds. These bonds stay benchmark for a specific time till another bond becomes the benchmark bond. The information if a bond is a benchmark bond is very important, since there is much more trading activity in these bonds. This section explains how to download this information. Unfortunately there is no standard tool to get this data, but the Bloomberg Terminal offers a history of benchmark yield curves for every country (IYC 1 <Go> in the Bloomberg Terminal). On the same page as the yield curves there is also the information, which bonds are regarded as benchmark bonds. This list can be copied to Excel. Unfortunately this has to be done by hand. To reduce this copying to a reasonable amount of time and because the benchmark bonds do not change too frequently, we decided to download the list of benchmark bonds not for every day but for every week. Table 6 shows the results for one day: 9

10 GG GG GG GG GG GG GG GG GG GG GG GG DEOH±%HQFKPDUNERQGVLQ%HOJLXPIRUWKH-DQXDU\ 'DWDEDVH After the collection of the bond information a database has to be constructed to store the data in an efficient way. We use Microsoft Access for this purpose. The first step is to define tables. Our database consists of the following three tables: EDVLFBIHDWXUH This table contains the basic features of all government bonds. It uses the following fields: œ FXVLS: Bloomberg-ID for each bond, this field is the primary key of this table œ PDW: maturity of the bond œ FSQ: coupon of the bond in percent œ WLFNHU: ticker-symbol of the bond œ FROODWBW\S: collateral type of the bond œ FRXQWU\: country of the issuing government œ UHGHPSBYDO: redemption value of the bond in percent œ LQWBDFFBGW: starting day of the accrued interest œ DPWBLVVXHG: amount issued œ LVLQ: Isin-number of the bond 10

11 FDVKIORZ This table contains the cashflow schedule of all government bonds. It uses the following fields: œ WRGD\: date of the cashflow, primary key together with FXVLS œ FXVLS: bond to which the cashflow belongs, primary key together with WRGD\ œ FRXSRQ: coupon-payment for chosen date and bond in percent œ UHGHPSWLRQ: redemption-payment for chosen date and bond in percent GDLO\BGDWD This table contains the price and benchmark history of all government bonds. It uses following fields: œ WRGD\: date of the historic information, primary key together with FXVLS œ FXVLS: bond to which the information belongs, primary key together with WRGD\ œ S[BDVN: ask-price for chosen date and bond in percent œ S[BELG: bid-price for chosen date and bond in percent œ \WPBDVN: ask-yield for chosen date and bond in percent œ \WPBELG: bid-yield for chosen date and bond in percent œ S[BSURYLGHU: price-provider, for all data Bloomberg Generic (BGN) œ EHQFKPDUN: 1...if the bond is benchmark for the chosen date, 0...otherwise In the next step the following relationships are defined for the tables. The relationships help to keep the database consistent: 1. one-to-many relationship between œ the field FXVLS of the table EDVLFBIHDWXUHV œ the field FXVLS of the table FDVKIORZ 2. one-to-many relationship between œ the field FXVLS of the table EDVLFBIHDWXUHV œ the field FXVLS of the table GDLO\BGDWD In the last step all the data that are contained in Excel-sheets, has to be transferred to the database. We develop a Visual Basic Macro for every Excel-sheet, which automatically 11

12 copies the data in the tables. After this procedure the database is ready to be used by all calculation of the research project. =HUR&RXSRQ<LHOG&XUYHV After the collection of the government bond data the most valuable information we can gain are zero-coupon yield curves for every country. These curves show the relationship between the yield and the maturity of synthetic zero-coupon bonds and are used to estimate the credit spread in the subsequent studies. Since the zero-coupon yield curves are basic data for our research project we explain their estimation in this document. (VWLPDWLRQ0HWKRG We use cubic splines as introduced by McCulloch (1975) to estimate zero-coupon yield curves for each country. This approach divides the zero-coupon yield curve in a defineable number of intervals and for each of these intervals a cubic spline is used to build the curve. If the curve is divided by N knots, we need N parameters to describe the entire zero-coupon yield curve. The parameters can be found by performing a OLS regression using the government bond data as input. The result is a zero-coupon yield curve, which minimises the pricing error between the model price and the market price of the government bonds. The model price is estimated by taking the parameters from the regression and use them to get the discount factors for the maturities when a bond has cashflows. Then the present values of these cashflows are calculated and the sum of these present values is the model price. The market price is the observed clean price, which is stored in the database, plus the accrued interest. The following paragraphs explain how the optimal N parameters can be found using OLS regression: a = (X X) 1 X Y where D is the k 1 matrix of the parameters 12

13 0DWUL[;: is n k matrix, where n is the number of bonds and k the number of parameters x ij R Ê = Z (h) *f (w (h)) " i = 1... n and j = 1... k h i 1 i j i where R i... is the number of future cashflows for bond L Z i (h)... is the future cashflow K of bond L w i (h)... is the maturity of the future cashflow K of bond L in years f j (t)... is a function of time W explained below 0DWUL[<: is a n 1 matrix, where n is the number of bonds y R i = P - Z (h) " i = 1... n i i Ê h 1 i where P i... is the market price of bond i P i = clean price from the database + accrued interest time passed since last coupon payment accrued interest = next cashflow * time between the coupon payments )XQFWLRQI W: is a function of time W and uses the user-defined knots d j, where j is the number of the knot ( j = 1... k-1) if t < d j-1 : f j (t) = 0 if d j-1 t < d j : (t - d j 1) f j (t) = 6*(d - d j 3 j 1 ) if d j t < d j+1 : 2 c c * e e e f j(t) = *(d 2 3 j 1 - d j ) where c = d j - d j-1 and e = t - d j 13

14 if d j+1 t: f (t) = (d j j 1 - d j 1 Î2 *d j 1 - d j - d j 1 t - d ) * Ï + Ð 6 2 j 1 ß à Þ Two special conditions have to be considered, when calculating f j (t): 1. if j = 1, then d j = d j-1 = 0 2. if j = k, then f j (t) = t The result of this procedure is the matrix D, which contains the optimal parameters. These parameters can now be used to calculate the discount factor for a certain maturity W: D(t) = 1 + Ê k j 1 f j(t) * a j From the discount function we can calculate the zero-coupon yield curve using the following formula: r(t) Ë = Ì Í 1 D(t) Û Ü Ý 1 t -1 In our calculations we decide to use three equidistant knots, which makes it necessary to estimate four parameters in the regression. We also calculate models using more knots, but this leads to no improvement in terms of goodness-of-fit and so the final zero-coupon yield curve is based on three knots. The first knot is always set to zero and the last knot is at least equal to the longest maturity of all included bonds. In order to avoid long time spans between the final payment dates of individual bonds at the long end of the yield curve we restrict our analysis to bonds with a time to maturity equal or shorter than ten years. The database, however, can easily be used to obtain zero-coupon yield curves using bonds with longer maturities and/or a different number of parameters. 14

15 'DWD&OHDQLQJ After the first calculation of the zero-coupon yield curves we have to undertake a data cleaning process, where we identify certain bonds or dates, that should be excluded from the sample, because they lead to obviously wrong results. As a result of the estimation procedure we obtain the pricing errors of each bond. These errors should be in an reasonable range. For some bonds, however, we find very high pricing errors (over 1 percent) for all days. For these bonds there seem to exist a problem concerning the quality of the price information. Maybe the bonds are illiquid and the prices quoted are stale and far away from market prices. This kind of bonds are marked after the first calculation of the zero-coupon yield curves and then the curves are estimated again excluding these bonds. Table 7 shows the bonds for each country, which are not used in the estimation of the zerocoupon yield curves: *HUPDQ\ )UDQFH,WDO\ $XVWULD 1HWKHUODQGV %HOJLXP 3RUWXJDO 6SDLQ )LQODQG,UHODQG - - GG GG CP EC EC DEOH±([FOXGHGJRYHUQPHQWERQGV After the elimination of these bonds still for a few days the estimated zero-coupon yield curves are obviously wrong. The major problem is that for these days only quotes for a few bonds are delivered Bloomberg. The resulting number of bonds is not sufficient to estimate a useful zero-coupon yield curve. These days are eliminated from the sample. Table 8 shows which days are excluded for each country: *HUPDQ\ )UDQFH,WDO\ $XVWULD 1HWKHUODQGV %HOJLXP 3RUWXJDO 6SDLQ )LQODQG,UHODQG DEOH±([FOXGHGGD\V After this cleaning process the zero-coupon yield curve estimation produces excellent results for all countries except for Ireland. As we can see in table 2 Ireland has 23 government bonds outstanding. After the introduction of the Euro the Irish National Treasury Management 15

16 Agency (NTMA) started a programme to introduce more liquidity in the Irish bond market. For this reason five new government bonds with large volume were issued in May 1999 and were used to buy back or exchange 91% of the outstanding volume of the old government bonds. After May 1999 the old Irish government bonds still exist and Bloomberg still delivers quotes, but their outstanding volume is negligible compared to the new issued bonds. Table 9 shows the outstanding volumes since May The five new issued bonds are marked with bold letters.,ulvk*ryhuqphqw%rqgv 2XWVWDQGLQJ9ROXPHLQ(XURP 0DWXULW\ 9% Government Bond % Capital Loan UHDVXU\%RQG 14 ¾% Development Stock UHDVXU\%RQG 9 1/4% Capital Stock /4% Exchequer Bond /4% Treasury Bond UHDVXU\%RQG 12 ½% Capital Stock % Treasury Bond % Capital Stock /4% Capital Stock % Treasury Bond UHDVXU\%RQG 8 1/2% Capital Stock , /4% Capital Stock /4% Treasury Bond UHDVXU\%RQG 7DEOH±2XWVWDQGLQJYROXPHRI,ULVK*RYHUQPHQW%RQGV 1 Source, 16

17 ) ( Since only the five newly issued bonds are actively traded on the Irish bond market and the quotes for the remaining bonds are not representative we decide to use only these five bonds to estimate the zero-coupon yield curve between May 1999 and March From January 1999 to April 1999 we use all Irish bonds to calculate the zero-coupon yield curve. After all these adjustments we now obtain reasonable and representative zero-coupon yield curves for all countries. 5HVXOWV After the data cleaning procedure we can estimate zero-coupon yield curves for all countries in our sample. Figure 4 shows the resulting zero-coupon yield curve for Germany for January 28, 2000: =HUR&RXSRQ<LHOG *+ ), &' *HUPDQ,QWHUHVW5DWH&XUYH =HUR&RXSRQ<LHOG&XUYHIRU*HUPDQ\ "! #%$ 0DWXULW\ )LJ±*HUPDQ]HURFRXSRQ\LHOGFXUYHIRUWKH-DQXDU\ The results of the zero-coupon yield curve estimation are all stored in the database table VSRWBFXUYHBVSOLQHV. There the parameters from the regression and the chosen knots are stored for all days and all countries in our sample. So this information can then easily be used for subsequent studies. Beside the zero-coupon yield curves we also obtain pricing errors for all bonds, as explained in section 5.1. Table 10 shows these pricing errors for six bonds using the zero-coupon yield curve from figure 4: 17

18 %RQG 'DWH 3ULFLQJ(UURULQ%S GG GG EC GG GG GG DEOH±3ULFLQJHUURUIRUVL[*HUPDQERQGV This information is stored in the database table SULFLQJBHUURUBVSOLQHV. After these estimations our database is filled with all the information which is necessary to start with the intended research projects using EMU government bond market information. 18

19 5HIHUHQFHV Geyer, A., Kossmeier, S., Pichler, S., 2001, Empirical Analysis of European Government Yield Spreads, Working Paper, University of Economics and Business Administration, Vienna, and Vienna University of Technology Jankowitsch, R., Mösenbacher, H., Pichler, S., 2002, Measuring the Liquidity Impact on EMU Government Bond Prices, Working Paper, Vienna University of Technology Jankowitsch, R., Pichler, S., 2002, Parsimonious estimation of credit spreads, Working Paper, Vienna University of Technology McCulloch, J.H., 1975, The Tax-Adjusted Yield Curve, Journal of Finance 30,