European Financial Management, Vol. 8, No. 4, 2002, 449– 477 Yield Spread and Term to Maturity: Default vs. Liquidity Antonio Dÿ́az and Eliseo Navarro Universidad de Castilla-La Mancha, Departamento de Economı´a y Empresa, Facultad de Ciencias Económicas y Empresariales de Albacete, Plaza Universidad 1, 02071 Albacete, Spain email: Antonio.Diaz@uclm.es; Eliseo.Navarro@uclm.es Abstract The aim of this paper is the analysis of the yield spreads between Treasury and nonTreasury Spanish fixed income assets and its relationship with the term to maturity. We find a downward sloping term structure of yield spreads for investment-grade bonds that seems to be contrary to the ‘crisis at maturity’ theory. However, we claim that this outcome is caused mainly by the effect of liquidity on yield spreads. Once the effect of liquidity and other factors are removed we find that there is a positive relationship between default premiums and term to maturity. That result is now consistent with the existing literature. Keywords: corporate bonds; yield spread; default risk; liquidity; term to maturity. JEL classification: G10; E43 1. Introduction The aim of this paper is to identify and analyse the determinants of the yield spreads between Treasury and non-Treasury bonds traded in the Spanish fixed income markets. Although credit spreads have been thoroughly investigated for the US markets previously, the Spanish Treasury markets present, in our opinion, some features that make them specially suitable for isolating and measuring the liquidity premiums inherent in these markets and then to study, separately, the impact of two different sorts of risk (liquidity and default) on bond yields. As a first step in our empirical analysis, we proceed to estimate yield spreads. Ideally, the preferred way of constructing yield spreads would be to calculate the difference between the zero-coupon spot rates for the corporate bond market and the Treasury We would like to thank the anonymous referees for their helpful comments and suggestions. Also, we have received valuable comments from Alfonso Novales, Juan Nave and José Pernias. Additionally, we thank information provided by Madrid Stock Exchange, AIAF Fixed Income Market, Bank of Spain, Comisión Nacional del Mercado de Valores, Servicio de Compensación y Liquidación de Valores, Standard & Poor’s, Moody’s and Fitch-IBCA. We acknowledge the financial support provided by Ministerio de Ciencia y Tecnologÿ́a grant BEC 2001– 1599. Anyway, any error is entirely our own. Corresponding author: Antonio Dÿ́az. # Blackwell Publishers Ltd 2002, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA. 450 Antonio Dı´az and Eliseo Navarro bond market. However, this procedure requires quite a high number of different bonds with a similar rating being traded simultaneously in order to estimate the zero coupon yield curve for each rating. Because of this problem, most previous work in this field proceeds to calculate these spreads as the difference between the yield to maturity of corporate coupon bearing bonds and the yield to maturity of Treasury coupon bearing bonds with similar maturities. However, this procedure may lead to a misestimation of yield spreads due to the differences in coupon rates and tax treatment between corporate and Treasury bonds. To avoid these problems, we propose an alternative way based on the previous estimation of the Treasury term structure of interest rates. Once these spreads are estimated, it can be observed that the term structure of yield spreads is clearly downward although all rated bonds included in our sample are investment grade bonds. This is a rather surprising outcome as according to ‘crisis at maturity theory’ (Johnson, 1967; Fons, 1994) the yield spreads of this sort of bond should show an upward term structure. What we investigate in this paper is whether the shape of the term structure of yield spreads is the result, not only of credit risk, but both credit and liquidity risks. We would like to point out that the features of the organised Spanish fixed income markets make them specially appropriate for analysing the impact of liquidity on yield spreads. Particularly, we should mention that Spanish Treasury assets are traded simultaneously in two different markets characterised by distinct degrees of liquidity. This fact allows the estimation of liquidity premiums without the noise caused by default risk and so to capture the factors they depend on. The comparison of the prices at which Treasury assets are traded in these two markets give us a hint about the importance of liquidity in the fixed income markets, its determinants and the shape of the term structure of liquidity premiums. Then, we put forward that the observed downward slope of the term structure of yield spreads between Treasury and non-Treasury assets is caused, mainly, by the liquidity impact on yield spreads. To test this hypothesis we use two sets of variables that have been commonly used in the literature as factors for explaining liquidity risk and default risk. The main result we obtain is that when liquidity and other factors are taken into account, we find a positive relationship between yield spreads and term to maturity, an outcome that is consistent with previous literature. Moreover, this result is robust across different bond categories classified according to their rating. This paper is organised as follows. Section 2 explains briefly the three organised Spanish fixed income markets and the data we use in the analysis. In Section 3, we estimate and analyse the term structure of yield spreads between Treasury and corporate bonds. Section 4 proceeds to review the literature about the term structure of default premiums and the effect of liquidity on fixed income assets. Liquidity premiums in Treasury bonds are studied in Section 5, Section 6 focuses on the analysis of the yield spreads between Treasury and non-Treasury bonds proposing the variables and the model to be used for explaining liquidity and default premiums. The results of the estimation of the model are analysed in Section 7. Finally, in Section 8, the analysis is made distinguishing between different groups of bonds classifying by rating. Section 9 concludes. 2. Background to the Spanish fixed-income markets Spanish Treasury assets consist in Letras del Tesoro (Treasury Bills), which are issued # Blackwell Publishers Ltd, 2002 Yield Spread and Term to Maturity 451 at discount with 6-, 12- and 18-month maturities, and Bonos and Obligaciones (Treasury bonds) with annual coupon payments and maturity in 3-, 5-, 10- and 15-year time.1 Letras del Tesoro are free of withholding tax. Both types of securities are represented by book entries and issued via regular competitive auctions. Auctions take place on a monthly basis, except for 12- and 18-month issues, which are auctioned fortnightly. In the case of medium and long-term securities, issues are reopened over several consecutive auctions until the outstanding amount reaches a minimum level. The securities allocated at such auctions have identical nominal, coupon rates and redemption dates. In the secondary market (known as Mercado de Deuda Pública Anotada, MDPA) trades are conducted through three systems, the first two being reserved for market members, while the third is for transactions between market members and their clients. In the first system, or ‘blind market’, trading is electronically conducted without knowledge of the counterparty’s identity, while the second trading system channels all the remaining transactions between market members.2 Treasury securities are also listed on Mercado Bursátil Electrónico (Electronic Stock Exchange Market, ESEM).3 All fixed income assets traded on ESEM do so through a continuous electronic trading market, with real-time trading and dissemination of information.4 While MDPA can be considered as a wholesale market enjoying a high degree of liquidity, ESEM can be viewed as a retail-volume market where particular investors can buy and sell Treasury assets. As a consequence, the trading volume of the transactions that take place in ESEM is usually very small. During the sample period, the average daily trading volume per issue was about 76 million pesetas,5 more than the 50% of these transactions being below 10 million pesetas. In contrast, the average size of a Treasury security trade on MDPA was 11,789 million pesetas. Treasury assets are, by far, the most important fixed income securities traded in the Spanish organised markets. During the sample period covered by this paper (1993 – 97), they accounted for 78.7% of the amount outstanding of the total fixed income assets issued by Spanish institutions and corporations. Apart from the Spanish Treasury, other important issuers of fixed income assets were regional governments (4.1%), other public institutions (such as provincial institutions and town councils), public firms (4.4%) and corporate firms (7%).6 For example, as of 1993, there was 25.1 trillion pesetas ($197 billion) of Treasury debt outstanding from 52 different issues. By comparison, in the US Treasury, corporate and municipal bond markets, there were $2.3 trillion debt from 210 issues, $1.4 trillion debt from 10,000 issues and $802 billion debt from 70,000 issuers, respectively (Fabozzi, 1996). 1 Since 1999 Spanish Treasury also issues 30-year bonds. 2 The structure of the Spanish market is quite similar to the US Treasury market. See Fleming and Remolona (1997) for details about the US Treasury market. 3 US Treasury securities are also listed on NYSE. 4 The structure of ESEM is also quite similar to the NYSE market. NYSE-listed bonds trade through the Exchange’s Automated Bond System, a terminal-based system for the trading of corporate, agency and government bonds. 5 The average exchange rate peseta=US dollar during the sample period was 131.83 PTA=USD. 6 Also an additional 5.9% of the amount outstanding are Matador bonds. # Blackwell Publishers Ltd, 2002 452 Antonio Dı´az and Eliseo Navarro Non-Treasury fixed income assets can be traded in three different organised markets: Mercado Bursátil Electrónico (Electronic Stock Exchange Market, ESEM), AIAF market, and the section ‘Other Administrations and Public Corporations’ of the MDPA (which will be denoted by MDPAOP) where Public assets different from Treasury securities are traded. AIAF is the market where most Table 1 Average daily trading volumes of different equity markets. Table shows average daily trading volumes of equities in New York Stock Exchange, London Stock Exchange and Spanish Electronic Stock Exchange. Numbers are expressed in million US dollars and are calculated using annual average exchange rates. Equities New York Stock Exchange London Stock Exchange Spanish Stock Exchange 1993 1994 1995 1996 1997 9,235.8 9,832.8 12,532.2 16,189.9 23,203.2 3,627.1 3,753.6 4,147.0 4,612.6 6,659.1 204.3 274.6 257.9 403.1 743.8 Mean 14,198.8 4,559.9 376.7 Table 2 Average daily trading volumes of different fixed income markets. The first four columns depict average daily trading volumes of spot transactions in different Spanish fixed income markets: Spanish Public Debt Market (MDPA), segment of Treasury debt in Electronic Stock Exchange market (ESEM), segment of corporate debt in ESEM and AIAF market (including bonds, commercial paper, mortgage paper and Matador bonds). The last three columns show average daily trading volumes in the British fixed income markets and in the US Treasury market. Numbers are expressed in million US dollars and are calculated using annual average exchange rates. Spanish Fixed Income Markets British F.I. Markets MDPA – Treasury ESEM– Treasury ESEM– corporate AIAF – corporate British Goverment Other bondsa U.S. Treasuryb 1993 1994 1995 1996 1997 7,091.7 7,636.7 6,241.8 8,420.7 8,921.0 18.8 107.6 118.5 279.8 100.2 33.4 31.9 26.2 30.3 16.0 123.8 140.2 84.9 78.2 77.4 10,280.0 9,571.0 10,113.9 12,331.6 n=a 554.6 492.3 535.8 519.6 n=a 173,600.0 191,300.0 193,200.0 203,700.0 212,100.0 Mean 7,662.4 125.0 27.5 100.9 10,574.1 525.6 194,780.0 a UK Local Authority, Bulldogs, Convertibles, Preference, Debs&Loans and Other Bonds. US Treasury securities by primary dealers with inter-dealer brokers and primary dealers with others. Source: Federal Reserve Bank of New York. b # Blackwell Publishers Ltd, 2002 453 Yield Spread and Term to Maturity corporate bonds are issued and traded. The members of this market are mainly banks, saving houses and Sociedades y Agencias de Valores (Spanish brokers and dealers). So, there are three different markets where non-Treasury fixed income assets can be traded. It must be pointed out that settlement and clearing systems are different in each market, as well as the way prices and yields are calculated. The average daily trading volumes of each market are described in Tables 1 and 2. These trading values are compared to those observed in the stock and fixed income markets of USA and UK. Our database comprises of all spot daily transactions during the period January 1993 to December 19977 (1,054 trading days). It covers Treasury assets in MDPA and ESEM and non-Treasury bonds8 in MDPAOP, ESEM and AIAF. The database contains daily information about each reference: number of transactions, nominal and Table 3 Database description. Sample period comprises from January 1993 to December 1997 including all spot daily transactions of Spanish fixed income markets. It contains the transactions with Letras del Tesoro (Treasury Bills) and Bonos and Obligaciones del Estado (annual coupon Treasury bonds) traded in Treasury asset market (MDPA) and in Electronic Stock Exchange Market (ESEM). Moreover it includes the transactions with bonds of the three major non-Treasury fixed income markets: ESEM, AIAF market and the section of ‘Other Administrations and Public Corporations’ of the MDPA (MDPAOP). Monthly frequency per issue is the average ratio between traded days per an issue in a month and all trading days in that month. Daily volume per issue is the average trading volume per issue expressed in million pesetas (the average exchange rate peseta=US dollar during the sample period was 131.83 PTA=USD). Treasury debt: MDPA: Letras del Tesoro Bonos del Estado ESEM: Letras del Tesoro Bonos del Estado Number of issues Number of observations Monthly frequency per issue Daily volume per issue (million PTAs) (bills) (bonds) 255 48 8,539 24,177 5.06 16.72 4,467 14,369 (bills) (bonds) 147 39 7,936 2,070 2.86 1.54 9 803 129 395 176 7,696 38,747 3,382 1.69 3.09 0.92 528 289 879 Corporate bonds: AIAF ESEM MDPAOP 7 Source: Central de Anotaciones del Banco de España, Bolsa de Madrid, AIAF Mercado de Renta Fija. 8 We call these issues ‘non-Treasury bonds’ because they include corporate, regional governments, other public institutions (such as provincial institutions and town councils) and public firms bonds. All these bonds have the same tax treatment. # Blackwell Publishers Ltd, 2002 454 Antonio Dı´az and Eliseo Navarro effective trading volume as well as mean daily prices and yields. Also, information about coupon rates, issue and outstanding volumes, maturity and coupon payment dates is available. Table 3 summarises this database.9 As can be seen from the trading volume, the MDPA is, by far, the most important market. Also, Treasury bonds are much more liquid than Treasury bills. ESEM is the market where more corporate issues were traded during the sample period with the highest number of transactions and trading frequency. However, despite the fact that the number of transactions in AIAF and MPDAOP is smaller, the volume of each of them is much higher than in ESEM. 3. Term structure of yield spreads The ideal way for estimating yield spreads would be to calculate the difference between zero coupon corporate bond yields and zero coupon Treasury yields. This requires the estimation of zero coupon bond yield curves for bonds with similar credit risk or, alternatively, with the same rating. However, the number of different issues outstanding within each category is too small to allow a specific term structure estimation. Also, when the number of available observations is too small, term structure estimations may involve some errors due to liquidity and tax biases (Dÿ́az and Skinner, 2001). In the Spanish markets, these problems are especially acute and make this procedure for estimating yield spreads non-viable. Thus, most previous empirical work on corporate spreads define yield spreads simply as the difference between the yield to maturity of corporate coupon-paying bonds (or an index of coupon-paying corporate bonds) and the yield to maturity of coupon-paying Treasury bonds (or an index of Treasury bonds) with similar maturities. However, this procedure has several problems, especially, the biases caused by the differences in coupon rates and taxation that may appear between corporate and Treasury bonds even if they have a similar term to maturity. The yield to maturity of a given bond depends on the coupon size and the slope of the term structure of interest rates. In fact, two bonds with the same issuer and terms to maturity may have different yields if they bear different coupon rates.10 This difference in yields is caused by the so called ‘coupon bias’ which is defined as the difference between the yield of a zero coupon bond and the yield of a coupon bearing bond with the same term to maturity. Recall that the yield to maturity of a coupon bearing bond can be viewed as a weighted average of the yields of zero coupon bonds with maturities at the same dates coupon and principal payments are due, the weight being, approximately, the value of each payment with respect to the total value of the bond. So, if the term structure is upward sloping two bonds differing only in their coupon rates would have different yields to maturity, the smaller the coupon rate, the higher the yield. On the contrary, if the term structure of interest rates is downward 9 Floating rate notes, sinking funds bonds, callable and putable bonds, zero-coupon bonds and bonds with tax advantages are not included in the sample. Observations of bonds with term to maturity up to 2 months or over 10 years are omitted. Also transactions with a volume less than 100,000 pesetas (approximately $760) are not considered. 10 For instance a ten-year bond issued five years ago and a five-year bond recently issued have similar term to maturity but they are likely to have different coupon rates. # Blackwell Publishers Ltd, 2002 Yield Spread and Term to Maturity 455 sloping, the higher the coupon rate, the higher the yield to maturity.11 Then a non-zero yield spread may appear even if both bonds have the same default risk, the same liquidity risk and the same term to maturity. Also, calculating spreads as the difference between the yields of coupon-bearing bonds with the same maturity but different coupon rates means one is comparing bonds with different duration and convexity. Corporate bonds have higher coupons than Treasury bonds, thus a corporate bond that has the same maturity as that of a Treasury bond will have a shorter duration. Therefore an increase in the slope of the Treasury yield curve, holding the zero-coupon bond yield spread constant, raises the yields on Treasury bonds relative to yields on corporate bonds of equal maturity and hence decreases the yield spread of corporate bonds over Treasury bonds (Duffee, 1998). Unlike other countries,12 in Spain, the taxation of Treasury and non-Treasury bonds is the same. Nevertheless, high coupon bonds are considered to be at a disadvantage with respect to low coupon bonds. The latter allows taxation to be deferred until the payment of the principal because it reduces the withholding tax on coupon payments and, also, because capital gains tax rates are usually lower than ordinary income tax rates. As corporate bonds pay, on average, a higher coupon than Treasury bonds, this gives rise to a positive tax premium between corporate and Treasury bonds. This tax bias depends mainly on the difference in coupon size, the wider the difference in coupon size, the larger the difference in the tax bias. This fact may lead to tax clienteles, as investors within different tax brackets may desire bonds with different characteristics (see Schaefer, 1982), as well as to tax timing options, associated with the value of being able to time the sale of a bond to optimise the tax treatment of capital gains or losses (see Constantinides and Ingersoll, 1984). For all these reasons, we propose a different way to calculate yield spreads. In particular, we estimate yield spreads as the difference between the yield to maturity of a corporate bond and the yield to maturity of a theoretical Treasury bond with the same characteristics (coupon and term to maturity). The price of this theoretical Treasury bond is calculated by discounting all the promised cash flows generated by the corporate bond, using a previously estimated Treasury zero coupon bond yield curve. Next we describe with more detail the way yield spreads have been calculated. First, we have estimated the zero coupon bond yield curve using daily data from the MDPA where Treasury assets are traded more actively. The methodology employed is developed in Contreras et al. (1996) where the Vasicek and Fong (1982) term structure estimation method is adapted to the MDPA. Vasicek and Fong use a non-parametric method based on exponential splines to estimate the discount function. Their model is the following: Pk ¼ p X Ck; j D(tk; j )
Qk
Wk þ "k k ¼ 1; 2; :::; n j¼1 where Pk is the price of the kth bond, Ck, j are the cash flows of the kth bond expressed as a fraction of the par value, tk, j is the time these cash flows are due, D(t) is the 11 See Van Horne (2001) for more details. 12 For instance, interest payments on US corporate bonds are taxed at the state level whereas interest payments on US government bonds are not. For an analysis of the effects of state tax premiums see Elton et al. (2001). # Blackwell Publishers Ltd, 2002 456 Antonio Dı´az and Eliseo Navarro discount function, n the number of bonds used in the sample for estimating the term structure, Qk is the price discount attributed to the effect of taxes, Wk is the price discount due to call features and "k is a residual error. Vasicek and Fong also assume that: E["k ] ¼ 0 and E[! 2k ] ¼  2 !k , where !k ¼ (dPk =dYk ) 2 and Yk is the yield to maturity of kth bond Qk ¼ q  Ck =Pk  (dPk =dYk ) Wk ¼ w  Ik where Ik is a dummy variable which is equal to one for callable bonds and zero otherwise. Contreras et al. (1996) redefine Wk and Qk to adapt them to the characteristics of Treasury assets dropping Wk from the model as the Spanish Treasury does not issue callable bonds and redefining Qk according to the Spanish tax system as: Qk ¼ 0 for Letras del Tesoro (Treasury bills) Qk ¼ q  Ck p X (1 þ Yk )
tk; j for Bonos and Obligaciones (Treasury bonds) j¼1 where Ck is the coupon rate of the kth bond. A unique variable knot is used to adjust exponential splines, knot which is located to minimise the sum of squared residuals. The sample period ranges from January 1993 to December 1997. Those assets with a trading volume less than 500 million pesetas in a single day were eliminated from the sample. To obtain a good adjustment in the short end of the yield curve, we always include in the sample the one-week interest rate from the repo market. Once the MDPA term structures are estimated, we proceed to calculate the theoretical prices of each corporate bond as if it had been issued by Treasury. This is done by calculating the discounted value of each bond cash flows using the term structures previously estimated. From these prices it is straightforward to obtain the theoretical yields to maturity. Then we obtain the yield spread as the difference between the latter and the actual bond yield to maturity. These yield spreads are free of coupon and tax biases and so, they depend only on the risk features of each bond. From the initial sample of non-Treasury bonds which is described in Table 3 we eliminated those issues that do not reach a minimum degree of liquidity, particularly those assets that are not traded at least twice a month, and those data corresponding to bonds with term to maturity lower than 2 months or over 10 years. After eliminating outliers13 we obtain a sample for corporate fixed-income assets with 14,158 observations which is the sample eventually used in this paper. This sample is described in Table 4. There is a set of these yield spreads that are extremely high. They correspond mainly to the unrated issues ‘Sarrió Nv91’ and ‘Ebro Ag. A918’.14 The issuers of these bonds 13 For each issue, we eliminated those observations outside the interval consisting of the mean yield spread plus=minus 2 times its standard deviation. 14 After eliminating outliers there are 177 observations that correspond to Sarrió Nv91 with an average spread of 1,224 bp that reach to a maximum of 2,378 bp. Also there are 87 observations for Ebro Ag. A918 with an average spread of 531 bp with a maximum at 1,065 bp. # Blackwell Publishers Ltd, 2002 457 Yield Spread and Term to Maturity Table 4 Descriptive statistics of corporate bonds sample. The sample comprises the period January 1993 to December 1997 including all spot daily transactions with non-Treasury bonds of Spanish fixed income markets: ESEM, AIAF market and the section of ‘Other Administrations and Public Corporations’ of the MDPA (MDPAOP). Issues with average trading days per month less of two days are omitted. Observations with term to maturity lower than 2 months or over 10 years and observations with a yield spread outside the interval included between mean yield spread plus or less 2 times its standard deviation are deleted. Yield spread (YS) is the difference between the yield to maturity of the corporate bond and the yield to maturity that a theoretical Treasury bond with the same characteristics (coupon and term to maturity) would have. The price of this theoretical Treasury bond is calculated by discounting all the promised cash flows generated by the corporate bond, using a previously estimated zero coupon bond yield curve. The average exchange rate peseta=US dollar during the sample period was 131.83 PTA=USD. Number of issues Number of observations Trading days per month and issue Daily volume per issue (million PTAs) AIAF ESEM MDPAOP 36 39 20 5,166 7,515 1,477 4,97 8,67 4,19 697 120 834 Total corporate bonds 95 14,158 6,24 489 Intervals of trading volume per issue and day (million pesetas) ESEM (no Ebro and Sarrió issues) AIAF MDPAOP No. Obs. YS No. Obs. YS No. Obs. YS <1 1– 2 2– 5 5– 10 10– 20 20– 50 50– 100 100–200 200–500 500–1,000 1,000– 2,000 2,000– 5,000 5,000– 10,000 > 10;000 191 175 235 162 120 191 305 671 1,293 884 610 272 48 9 81.26 92.49 87.50 47.80 32.28 22.09 28.84 29.04 28.95 30.13 31.28 29.92 27.41 28.77 2,096 1,285 1,394 701 494 411 205 183 243 98 41 57 24 19 110.85 100.21 92.31 96.47 84.22 86.20 52.63 46.84 38.20 37.49 43.87 36.46 62.47 42.61 0 0 0 0 0 18 93 185 395 400 244 126 15 1 — — — — — 22.19 21.44 21.75 20.76 20.56 19.60 18.53 22.45 42.21 Global Standard deviation 5,166 36.61 57.30 7,251 92.80 110.83 1,477 20.54 10.15 suffered an important financial crisis during the sample period although they finally met all their due payments at maturity. So, we distinguish between the ‘complete sample’ that includes Ebro and Sarrió assets (with 14,158 observations) and the ‘reduced sample’ without them (with only 13,894 observations). # Blackwell Publishers Ltd, 2002 458 Antonio Dı´az and Eliseo Navarro One of the first points that can be inferred from the data is the strong negative relationship between yield spreads and term to maturity for those bonds with term to maturity up to 6 years, meanwhile term structure of yield spreads is nearly flat for bonds with the longest maturities. In Figure 1(a) we have depicted the yield spread of non-Treasury bonds (reduced sample) against the term to maturity. Observations have been divided into ten groups according to their term to maturity and then the average yield spread of each group has been calculated. As it can be seen from Figure 1 the mean yield spreads range from 90 basis points for those bonds maturing within one (a) Actual Mean Yield Spread (restricted sample) 100 90 Yield Spread (bp) 80 70 60 50 40 30 20 10 0 0 1 2 3 4 5 6 7 8 9 10 Term to maturity (years) (b) Actual Mean Yield Spread classified by rating 225 AAA 200 AA Yield Spread (bp) 175 A 150 Unrated 125 100 75 50 25 0 0 1 2 3 4 5 6 7 8 9 10 Term to maturity (years) Fig. 1. Yield spread depending on the term to maturity. Mean yield spread for ten annual groups of bonds according to their term to maturity. Figure 1(a) reduced sample (without Sarrió and Ebro issues). Figure 1(b) mean yield spreads classified by rating: AAA, AA, A (including BBB þ) and unrated bonds. # Blackwell Publishers Ltd, 2002 Yield Spread and Term to Maturity 459 year to 28 basis points for those bonds with the longest maturity. Although Figure 1(a) represents the whole sample (without Ebro and Sarrió issues), this result can be observed if we repeat the analysis classifying bonds by rating (see Figure 1(b)). 4. Default and liquidity risk and the term structure of yield spreads There are, basically, two different approaches for modelling credit risk: the structural and the reduced form15 models. Following Kao (2000), the basic difference between the two approaches is the type of input variables each uses. The former approach uses company-specific information and treats debt as a contingent claim on the firm’s value. From a specification of firm value behaviour, default risk is derived from the relationship between firm value and debt value. The latter approach works directly with market information, modelling default risk from what is implied in market prices, credit spreads, and in some cases, rating transitions. Kao also mentions other approaches that are popular among practitioners. One of them is the risk factor premium. Fisher (1959) considered credit spread a compensation for various risks in a linear relationship. Since this seminal paper many other articles have examined the effect of default risk on the yield spreads between corporate and Treasury bonds. More recently we have, for instance, Shulman et al. (1993), Fridson and Jónsson (1995), Fridson and Garman (1998) and Garman (2000). All these papers find evidence that default risk is the key factor for explaining yield spreads. The level of this risk varies according to the issuer risk exposition and the economic environment. Rating agencies consider all these elements to classify bonds into discrete categories according to issue default risk. According to Fischer and Jordan (1991) and Dialynas and Edington (1992) default risk depends too on the business cycle. When the economy enters a financial downturn period, bond issuers may have to face important problems to generate enough cash flows to pay back interest and principal. Also, investors may change their risk perception becoming more aware of risk. These variations do not imply necessarily a rating change although they can cause an increase in yield spreads. Among the variables usually employed to fetch the relationship between business cycle and default risk, the level and the slope of the yield curve can be mentioned. Benson et al. (1985), Duffee (1998) and Alessandrini (1999) suggest that yield spreads show a negative relationship with the level of interest rate and the slope of the term structure. Dialynas and Edington (1992) and Stock (1994) state that the slope of the term structure is one of the best indicators of the business cycle. Fridson and Garman (1998), Kao (2000) and Athanassakos and Carayannopoulos (2001) confirm this forecasting ability of the term structure, finding a slow response of corporate bond yields to changes in Treasury bond yields. The relationship between term to maturity and yield spreads has been widely discussed. The theory of ‘crisis at maturity’ proposed by Johnson (1967) assumes that the default risk perceived by investors varies along time depending on the bond rating. Firms that issue speculative-grade bonds bear important distress risks in the short term. On the one hand, if they overcome their initial problems, the issue may be upgraded or the firm may repurchase its bonds issuing new bonds at a lower cost. On the other hand, if the firm keeps its initial rating when maturity approaches, it may 15 See, for example, Kao (2000) or Nandi (1998) for a whole overview of both kinds of model. # Blackwell Publishers Ltd, 2002 460 Antonio Dı´az and Eliseo Navarro run into difficulties when facing the principal. So, the default probability perceived by investors may increase as the term to maturity shortens and so, the yield spread may widen for those bonds with shorter term to maturity. Investment-grade bonds face initially a low default risk as they have been issued by solid firms. However, this situation may change in the long run and so its default probability and yield spread may increase with the term to maturity. This reasoning explains an inverse relationship between spreads and term to maturity for speculative bonds and a direct relationship for investment-grade bonds. Although this theory has been brought into question by some authors,16 it has been supported by most of the empirical research, (see Sarig and Warga, 1989b; Fons, 1994; Kao, 2000),17 as well as by the structural models.18 With respect to our sample, which consists mainly of investment-grade bonds, we find evidence of a downward sloping term structure of yield spreads (see Figure 1). At first glance, this result could be understood as evidence against the ‘crisis at maturity’ theory. However, it must be pointed out that this theory only takes into account the effects of default risk on the yield spreads. So, in this paper, we test if this observed downward slope of the term structure of yield spreads is caused by factors different from default risk. 5. Liquidity premiums in the Spanish fixed-income markets In 1959, Fisher suggested that liquidity is one of the main determinants of the yield spreads between corporate bonds and Treasury securities. Since then, many authors have examined the effect of liquidity on corporate yield spreads, as Silvers (1973), Dialynas and Edington (1992), Shulman et al. (1993), Crabble and Turner (1995), Fridson and Jónsson (1995), Fridson and Garman (1998) and Garman (2000). Other recent papers analyse liquidity of corporate bonds examining trading volume (Alexander et al., 2000) or bid-ask spreads (Chakravarty and Sarkar, 1999; Hong and Warga, 2000). 16 Helwege and Turner (1999) observe a positive slope in the term structure of yield spreads for speculative-grade bonds. They claim that the negative relationships that have been documented in previous papers is due to a sample bias caused by the fact that only firms with a low default risk can issue long term bonds. So, the average yield spread decreases with the term to maturity. They find that the yield spread for the same issuer is upward-sloping. Other authors such as Silvers (1973), Fama (1986) and Stock (1994) observe a negative relationship for all ratings; Litterman and Iben (1991) and Adedeji and McCosh (1995) find that this relationship is always positive. Also Blume and Keim (1991), Blume et al. (1991) and Van Horne (1979) argue that there is time varying relationship between yield spread and term to maturity. 17 The results of Silvers (1973), Stock (1994), Altman (1989), Asquith et al. (1989), McDonald and Van de Gucht (1996) and Fridson and Garman (1998) support the existence of a downward sloping term structure of yield spreads for speculative-grade bonds. This term structure is upward sloping for investment-grade bonds according to Litterman and Iben (1991), Gehr and Martell (1992) and Adedeji and McCosh (1995). 18 These models suggest that the term structure of yield spreads is downward sloping for highleveraged firms, humped for medium-leveraged firms and upward sloping for low-leveraged firms. See for example Merton (1974), Brennan and Schwartz (1980) Kim et al. (1993), Nielsen et al. (1993), Longstaff and Schwartz (1995), Leland and Toft (1996), Bryis and de Varenne (1997), Cathcart and El-Jahel (1998) and Collin-Dufresne and Goldstein (2001). # Blackwell Publishers Ltd, 2002 Yield Spread and Term to Maturity 461 Liquidity in the US Treasury debt markets is analysed by Sarig and Warga (1989a), Amihud and Mendelson (1991), Warga (1992), Kamara (1994), Duffee (1996), Carayannopoulos (1996) and Elton and Green (1998). Elton and Green (1998) suggest that the best proxy for liquidity is trading volume. Other authors such as Fisher (1959) use the amount of bonds outstanding on the basis of the potential correlation between the existing stock of a particular bond and the flow of trade in the bond. The higher the dollar amount of bonds outstanding, the higher the liquidity of the issue and the lower its yield spread. Sarig and Warga (1989a) and Warga (1992) suggest that younger bonds are usually traded more frequently and so have lower spreads resulting from greater liquidity. Amihud and Mendelson (1991) observe that when bonds approach maturity they have already been locked away in investors’ portfolios, and a large part of each issue is not readily available for trading. As we claimed in the introduction, the features of the Spanish fixed income markets make them especially suitable for analysing the effects of liquidity on yield spreads. Particularly, the existence of two markets with different degrees of liquidity where Treasury assets are traded simultaneously, allows us to isolate the effects of liquidity on yields and so to estimate liquidity premiums without the noise caused by other sorts of risk as default risk. For doing this, we first compare the yields at which the same Treasury bond is traded, the same day, in MDPA and ESEM. Evidently, the spread between these two yields can be caused only by differences in liquidity19 as far as the bond is default free. We will refer to these differences in yields as yield spread between markets, YSBM. These yield spreads are not exactly the liquidity premiums of Treasury yields but the over-premium born by Treasury bonds when they are traded in a ‘retail’ market over those traded in the MDPA that can be considered as a wholesale market. In any case, when a bond is traded in MDPA it also bears a liquidity premium which may depend on different variables such as age, issue size, term to maturity, etc. These liquidity over-premiums can be explained not only by differences in trading volumes of the transactions that take place in these two markets but also by the fact that the trading system and agents that operate in MDPA and ESEM are different. Table 5 shows some descriptive statistics of the YSBM observed during the sample period. After removing outliers,20 there are 1,675 observations available. These observations are classified according to trading volume in ESEM. Most of ESEM transactions have a very low trading volume (nearly 60% of them do not reach 10 million pesetas). It should be noticed that transactions below 10 million pesetas present a YSBM significantly bigger than the remainder sample. Finally, in order to explain the YSBM, we use four explanatory variables that are commonly used in the literature as factors for explaining liquidity premiums. The first two variables, amount outstanding and age, affect bond yields in both markets (MDPA and ESEM) but we put forward that they have a more pronounced effect on the market with the lowest liquidity, i.e., ESEM. Additionally, we include two more variables: trading volume proxied by a dummy variable to distinguish very small or 19 Differences in a single day can be caused also by the asynchrony of the data; however on average these differences should disappear. 20 Observations with YSBM located outside the interval defined by mean YSBM plus or less 2 times its standard deviation were omitted. # Blackwell Publishers Ltd, 2002 462 Antonio Dı´az and Eliseo Navarro Table 5 Descriptive statistics of the yield spreads between markets and the explanatory variables. Sample extracted from spot daily transactions with Bonos and Obligaciones (coupon Treasury bonds) traded the same day in MDPA and in ESEM during the period January 1993 to December 1997. Yield spread between markets (YSBM) is the spread between the daily average yields at which the same bond is traded in ESEM and in MDPA. A total of 1,675 observations were selected from 1,801 available observations. Observations with YSBM outside the interval included between mean YSBM plus or less 1.3 times its standard deviation were omitted. Size is the issue amount outstanding at the end of month in trillions of pesetas. Relative age of an issue is the ratio between current age and term to maturity. Term to maturity is expressed in years. Retail transaction is a dummy variable that takes value one if the transaction is smaller than 10 million pesetas ($75,854) and zero otherwise. Issue daily trading volume in ESEM is expressed in million peseta. Mean Std. Deviation Median Maximum Minimum YSBM (bp) Size (trillion ptas) Relative age Term to maturity Retail transaction 31.01 42.33 19.87 196.98
102.74 0.8673 0.2327 0.9459 1.5617 0.1231 0.3545 0.2258 0.3124 0.9619 0 4.8436 3.5281 3.5096 15.3753 0.1315 0.5809 — — 1 0 YSBM Ln(Size) Relative age Term Retail trans. 1 — — — — 0.0383 1 — — — 0.3493 0.0787 1 — —
0.3313
0.1518
0.7606 1 0.2309
0.0610 0.2577 0.1726 1 No. Observations Correlation: YSBM Ln(Size) Relative age Term to maturity Retail transaction Intervals of daily trading volume in ESEM (mill. Pta.) <1 1–2 2–5 5 – 10 10 – 20 20 – 50 50 – 100 100– 200 200– 500 500– 1,000 1,000 – 2,000 2,000 – 5,000 5,000 – 10,000 >10;000 Global Standard Deviation # Blackwell Publishers Ltd, 2002 1,675 Trading volume in ESEM (mill. pta.) Trading volume in MDPA (mill. pta.) YSBM (bp) 332 226 251 164 82 45 32 49 80 87 127 124 43 33 0.45 1.33 3.15 6.93 12.98 29.71 70.84 131.72 357.07 678.94 1,390.26 3,170.46 6,796.01 20,699.61 14,512.85 13,007.53 11,598.18 12,192.11 9,947.30 18,341.66 12,306.53 16,395.73 19,107.46 22,267.54 29,546.96 32,073.78 33,663.24 51,622.13 54.32 38.44 29.47 25.20 17.97 3.79 18.01 18.02 17.08 25.27 25.19 20.69 18.09 14.66 1,675 — 982.77 3,789.67 17,822.93 28,699.96 31.01 42.33 No. observations 463 Yield Spread and Term to Maturity retail volume transactions (those with a trading volume less than 10 million pesetas) and the term to maturity. We use the latter variable to analyse explicitly the relationship between liquidity premium and term to maturity. However, the correlation coefficient between relative age and term to maturity is very high ( ¼
0:76). So, using these two variables simultaneously may cause severe multicollinearity problems. Auxiliary regressions of each independent variable with respect to the others, give a broad hint in this sense. To avoid these problems, we introduce the variable term to maturity indirectly.21 We regress term to maturity (Termtomaturity) against relative age (RelativeAge) for the whole sample and then, we use the residuals ui,t as the independent variable. Then, the variable Term i*; t; ¼ ui; t , represents that part of the term to maturity that cannot be explained by relative age and so Term i*; t and RelativeAgei;t are orthogonal. Termtomaturityi; t ¼ 0 1 RelativeAgei; t þ þ ui; t [1] Thus, the explanatory variables we propose to describe YSBM are the following: Issue size (Size): we use the natural log of the issue amount outstanding in trillions of pesetas. Age (RelativeAge): we consider the issue age in relative terms, to make its value comparable among issues with different terms to maturity.22 So we calculate the relative age as the ratio between current age and term to maturity when issued. Term to maturity (Term *): we use the residuals of accessory regression [1]. Small size transaction (RetailTransaction): we use a dummy variable as a proxy of the trading volume. It takes value 1 if the transaction is smaller than 10 million pesetas23 in the ESEM or zero otherwise. The model used to explain the YSBM is: YSBMit ¼ 0 þ þ 3 1 ln(Sizeit ) Term *it þ þ 4 2 RelativeAgeit RetailTransactionit þ "it [2] Table 6 shows the results of the regression YSBM against the four explanatory variables.24 Size does not add any explanatory power showing that the amount 21 Another alternative would consist of using a ridge regression. In this case biased estimators are used but with a lower variance and so a lower mean square error. However this procedure implies the substitution of independent variables by functions with little economic meaning. 22 For instance a three year old bond can be near its maturity if it was a three year bond when issued or to have its maturity in seven years time if it was a ten year bond when issued. In relative terms, the first bond has a relative age close to 100% and the second one has a relative age of 33%. 23 10 million pesetas are equivalent to $75,854 according to the average exchange rate peseta=US$ during the sample period. 24 Preliminary diagnostics indicated the presence of significant heteroskedasticity in the error term of the model [2]. To avoid the problems related with the probability distribution of the error terms we estimate the regression by the Generalized Method of Moments (GMM) technique with Newey-West correction. This procedure demands very weak assumptions about the error term. # Blackwell Publishers Ltd, 2002 464 Antonio Dı´az and Eliseo Navarro Table 6 Liquidity premium of Treasury bonds. Results of the regression between YSBM and the four explanatory variables: YSBMit ¼ 0 þ 1 ln(Sizeit ) þ 2 RelativeAgeit þ 3 Term * it þ 4 RetailTransactionit þ "it Yield spread between markets (YSBM) is the spread between the daily average yields expressed in basic points at which the same bond is traded in ESEM and in MDPA every trading day. Size is the issue amount outstanding at the end of month in trillions of pesetas. RelativeAge of an issue is the ratio between current age and term to maturity. Term * variable represents residuals of the regression of term to maturity against relative age in each sample. RetailTransaction is a dummy variable that takes value one if the transaction is smaller than 10 million pesetas ($75,854) and zero otherwise. Sample of 1,675 observations. Estimation is done using the Generalized Method of Moments (GMM) procedure with the Newey-West correction. The p-values of parameters significance are in parenthesis under the respective estimates. Independent variable Estimated coefficient Two tailed p-value Constant Ln(Size) RelativeAge Term * RetailTransaction dummy
3.2696 0.4137 57.0696
1.9809 13.8208 (0.9391) (0.8951) (0.0000) (0.0000) (0.0000) R2 Adjusted R2 Number of observations 15.44% 15.24% 1,674 outstanding does not explain the difference in liquidity premiums between both markets. Also, it can be noted that the intercept is not significantly different from zero at 95% confidence level. The value of the coefficient of the dummy variable is 13 basis points (b.p.) and statistically significant, indicating an additional liquidity premium for small size transactions. In any case, RelativeAge is the variable with the highest t-statistic value. Figure 2 depicts the relationship between the average YSBM, relative age and the bond term to maturity. Due to its strong negative relationship with term to maturity this result can help us to explain the negative slope of the term structure of yield spreads. In any case we also find a negative relationship between YSBM and the variable Term *, which captures that part of the term to maturity uncorrelated to RelativeAge. This result reinforces the idea of a downward sloping term structure of liquidity premiums. Moreover, this negative relationship between liquidity premium and term to maturity may have important implications on the shape of the whole term structure of yield spreads. 6. Term structure of yield spreads in the Spanish fixed-income markets In the previous analysis of the liquidity, we assume the existence of an additional liquidity premium for those transactions traded in ESEM. Now, the data comes from # Blackwell Publishers Ltd, 2002 465 80 90 70 80 YSBM 50 Relative Age 60 50 40 40 30 30 20 Relative Age (%) 70 60 20 15-16 14-15 13-14 12-13 11-12 10-11 9-10 8-9 7-8 6-7 5-6 4-5 0 3-4 0 2-3 10 1-2 10 0-1 Average YSBM (b.p.) Yield Spread and Term to Maturity Term to maturity (years) Fig. 2. Relationship between the average yield spread between markets (YSBM) and relative age with Treasury bonds. Average YSBM and average relative age are represented depending on the term to maturity. Each point corresponds to the average YSBM and average relative age for those bonds with a term to maturity within the corresponding annual time interval. YSBM is the spread between the daily average yields expressed in basic points at which the same asset is traded in ESEM and in MDPA every trading day. Relative age of an issue is the ratio between current age and term to maturity. Sample of 1,675 observations. the three different markets where corporate debt is traded. Two of them can be considered as whole-sale markets (AIAF and MDPAOP) and the other one as a retailvolume market (ESEM). In any case, the daily trading volume per issue and the amount outstanding of those bonds traded in these three markets is far from the level reached by Treasury securities in MDPA (see Table 3). In Table 4, data is ordered according to trading volume. Similarly to Treasury bonds, transactions with a trading volume less than 10 million pesetas have a significantly greater yield spread. These transactions account for 16% of all observations in AIAF and 66% in ESEM. To explain the liquidity of corporate bonds we are going to use three of the four proxies of liquidity considered in the previous section to analyse the yield spreads between markets: Size: we use as proxy of the size, the natural logarithm of the amount issued in billions of pesetas because the source of data of corporate bonds does not include the amount outstanding. RelativeAge: we consider the relative age as the current age divided by the original maturity. RetailTransaction: we include a dummy variable that takes value one for those observations with a trading volume less than 10 million pesetas and zero otherwise. # Blackwell Publishers Ltd, 2002 466 Antonio Dı´az and Eliseo Navarro With respect to default risk, according to Section 3, we assume that it depends on the rating and the business cycle. Thus, we use the following set of variables to describe the behaviour of default premiums. Table 7 Descriptive statistics of the sample classified by rating and market. Yield spread (YS) is the differences between the yield to maturity of corporate bonds and the yield to maturity of a theoretical Treasury bond with the same characteristics (coupon and term to maturity). Size is the amount issued in billions of pesetas. Daily trading volume per issue is expressed in millions of pesetas. Relative age of an issue is the ratio between current age and term to maturity. Sample of 19,809 observations (complete sample). The average exchange rate peseta=US dollar during the sample period was 131.83 PTA=USD. Yield spread (bp) AAA AA A Unrated Issue size (billion pesetas) AIAF ESEM MDPAOP Global AIAF ESEM MDPAOP Global 28 27 130 35 70 72 174 552 17 22 — 35 56 41 159 211 32 38 7 23 17 24 14 13 49 22 — 30 25 32 12 20 Daily trading volume per issue (million pesetas) AAA AA A Unrated Days per month and issue AIAF ESEM MDPAOP Global AIAF ESEM MDPAOP Global 822 776 280 641 68 325 27 46 822 918 — 680 389 688 139 479 6 5 4 4 11 6 7 7 4 4 — 2 8 5 6 4 Term to maturity (years) AAA AA A Unrated RelativeAge (%) AIAF ESEM MDPAOP Global AIAF ESEM MDPAOP Global 8.13 5.58 2.23 6.18 1.34 2.38 2.12 1.17 4.80 6.02 — 4.30 2.71 4.56 2.15 4.25 10.15 29.86 37.68 20.14 70.52 63.06 53.72 75.91 15.72 8.85 — 18.73 54.17 39.25 49.85 39.18 Number of issues AAA AA A Unrated Number of observations AIAF ESEM MDPAOP Global AIAF ESEM MDPAOP Global 6 19 4 7 21 9 5 4 10 7 0 3 37 50 10 14 596 3,268 451 851 3,783 1,776 1,420 536 926 381 0 170 5,305 5,425 1,871 1,557 # Blackwell Publishers Ltd, 2002 Yield Spread and Term to Maturity 467 Rating. We use four dummy variables to gather the different degree of exposure to default risk (AA, A,25 Unrated and EbroSarrió). Table 7 summarises the data according to its rating and market.26 A point that we had to investigate first was the fact that the average yield spread for AAA bonds was bigger than the average yield spread for AA bonds. Because of this surprising result, we test if there is a significant difference between the yield spreads of these two bond categories. We applied a sign test that reveled that the frequency of AA bonds having a yield spread bigger than AAA bonds is significantly over the 50%.27 The market seems to differentiate those bonds rated A, BBB or without rating, clearly. Among the observations included in the last group, we can distinguish those that correspond to ESEM with an average yield spread of 552 bp and those from the AIAF and MDPAOP with an average yield spread of 35 bp. The only assets that can be considered as speculative-grade bonds are Ebro and Sarrió issues and so we use a specific dummy for them. Business cycle. We use two different variables to introduce the business cycle in the model: * * Interest rates evolution (Evolution): the variable used to describe the evolution of interest rates is defined as the ratio between the current three month interest rate and its average value during the last seventy trading days. Results of Duffee (1998) indicate that an increase in the three-month Treasury bill yield corresponds to a decline in corporate bond yield spreads. Slope of the term structure of interest rates (Slope): we measure the yield curve slope as the difference between three year and three month spot interest rates. Finally, we include the variable term to maturity (Termtomaturity). This variable was used in Section 4 to explain liquidity premiums. Now, we assume that default premiums may depend on it, too. When only liquidity risk was taken into account, we could see that there was a negative relationship between liquidity spread and term to maturity. However, in this model the variable Termtomaturity captures the ‘net’ effect of the term to maturity on both liquidity and default risks. So, it will be important to 25 The few observations rated BBB þ are considered as A bonds. Also there are only a few observations with a rating lower than BBB but none of them fulfil the requirements to enter the sample. Thus, all the observations of rated bonds included in the sample are investment-grade bonds. 26 The rating is assigned by three different agencies: Standard & Poor’s, Fitch-IBCA and Moody’s. We use preferably the rating in local currency to the rating assigned to issues in other currencies. For those issues that were upgraded or downgraded during the sample period, we reclassified them when this change was made public. 27 All issues denominated in local currency that were rated AAA (or Aaa) were AA (or Aa2) in foreign currency. Until 2001 AA was the best rating reached by any Spanish issue denominated in a foreign currency. Also, the average yield spread for AAA bonds shows the impact of those bonds issued by ICO that are traded in ESEM until mid 1995. These bonds pay a very high coupon, have a small trading volume and a low amount outstanding and most of the observations correspond to speculative transactions since they have an exchanging option that allows the buyers to swap at maturity the old bond for a new issue with similar characteristics. The average spread for those bonds was 78 bp against 17 bp for those bonds issued by ICO but traded in MDPAOP. # Blackwell Publishers Ltd, 2002 468 Antonio Dı´az and Eliseo Navarro analyse the impact of default risk on the estimated value of the parameter associated with this variable. Table 8 shows some statistics of the variables we have just described. As in the previous analysis of liquidity, due to the high correlation between RelativeAge and Termtomaturity ( ¼
0:81) we introduce term to maturity indirectly using the residuals Term * ¼ ui; t of the accessory regression [1]. Thus, the final model used to explain yield spreads is: YSit ¼ ln(Sizei ) þ 0 þ þ 4 Term * it þ þ 9 Evolutiont þ 1 2 RelativeAgeit þ 5 AAit 10 þ 6 Ait þ 3 RetailTransactionit Unratedit þ 7 Slopet þ "it 8 EbroSarri oi i ¼ 1; 2; :::; 127; t ¼ 1; 2; :::; 1;054 7. Results Table 9 reports the results of two regressions of the model using the complete sample (which includes the dummy EbroSarrió) and the reduced sample where the data corresponding to EbroSarrió has been eliminated. Table 8 Descriptive statistics of the YS and the explanatory variables (reduced sample). Sample described in Table 4 without Ebro and Sarrió issues (reduced sample). Yield spread (YS) is the differences between the yield to maturity of the corporate bond and the yield to maturity of a theoretical Treasury bond with the same characteristics (coupon and term to maturity). Size is the amount issued in billions of pesetas. RelativeAge of an issue is the ratio between current age and term to maturity. RetailTransaction is a dummy variable that takes value one if the issue trading volume is smaller than 10 millions of pesetas ($75,854) and zero otherwise. Termtomaturity is expressed in years. Evolution of interest rates is the ratio between the current three month interest rate and its average value during the last seventy trading days. Slope is the difference between three year and three month interest rates. YS (b.p.) Size (billions psetas) Retail Transac. (dummy) 0.4588 0.2974 0.4428 0.9798 0 0.4490 — — 1 0 Term to maturity (years) 3.55 2.80 2.63 10 0.17 Evolution of interest rates 0.9692 0.0511 0.9550 1.1729 0.8135 Slope of interest rates Mean Std.Dev. Median Maximum Minimum 64.22 92.49 35.27 1,034.84
264.96 No.Obs.: 13,894 Correlat: YS Ln(Size) Rel. Age Retail Tr. Term Evolution Slope YS Ln(Size) Rel. Age RetailTr. Term Evolution Slope 1 — — — — — —
0.3153 1 — — — — — 0.2397
0.2387 1 — — — — 0.3389
0.4561 0.5492 1 — — —
0.2570 0.3092
0.8163
0.5464 1 — —
0.1086 0.0182
0.0826
0.0316 0.0217 1 —
0.1298 0.0555
0.2152
0.1684 0.1323 0.3912 1 # Blackwell Publishers Ltd, 2002 25.76 16.87 20.44 99.22 1.22 Relative Age
0.0015 0.0154
0.0008 0.0310
0.0416 469 Yield Spread and Term to Maturity Table 9 Yield spread of corporate bonds. Results of regressing yield spreads on explanatory variables: YSit ¼ 0 þ þ 5 1 ln(Sizei ) AAit þ 6 þ 2 RelativeAgeit Ait þ 7 Unratedit þ þ 3 RetailTransactionit 8 EbroSarri oi þ 9 þ 4 Term * it Evolutiont þ 10 Slopet þ "it Sample described in Tables 4 and 8 with Ebro and Sarrió issues (‘Complete Sample’) and without them (‘Reduced Sample’). Coefficient 8 is only estimated for the ‘Complete Sample’. Yield spread (YS) is the differences between the yield to maturity of the corporate bond and the yield to maturity of a theoretical Treasury bond with the same characteristics (coupon and term to maturity). Size is the issue amount in billions of pesetas. RelativeAge of an issue is the ratio between current age and term to maturity. RetailTransaction is a dummy variable that takes value one if the issue trading volume is smaller than 10 millions of pesetas ($75,854) and zero otherwise. Term * variable represents residuals of the regression of term to maturity against relative age in each sample. Evolution of interest rates is the quotient between the current three month interest rate and its average value during the last seventy trading days. Slope is the difference between three year and three month interest rates. Estimation is done using the Generalized Method of Moments (GMM) procedure with the Newey-West correction. The pvalues of parameters significance are in parenthesis under the respective estimates. Independent variable Constant Ln(Size) RelativeAge RetailTransaction, dummy Term to maturity * AA, dummy A, dummy Unrated, dummy EbroSarrió, dummy Evolution Slope R2 Adjusted R2 No. Observ. # Blackwell Publishers Ltd, 2002 Complete sample Reduced sample 168.21 (0.0000)
11.15 (0.0000) 21.83 (0.0000) 30.76 (0.0000) 0.57 (0.0599) 9.32 (0.0000) 112.08 (0.0000) 15.19 (0.0000) 866.44 (0.0000)
119.94 (0.0000)
977.01 (0.0000) 173.69 (0.0000)
4.99 (0.0000) 24.69 (0.0000) 36.49 (0.0000) 1.10 (0.0000) 7.62 (0.0000) 116.76 (0.0000) 15.12 (0.0000)
147.94 (0.0000)
761.18 (0.0000) 59.91% 59.89% 14,158 28.82% 28.78% 13,894 470 Antonio Dı´az and Eliseo Navarro The explanatory power of the model is 59.9% in the complete sample. However, when the reduced sample is used, the R2 is considerably smaller (28.8%) due to the important impact of Ebro and Sarrió on the variance of yield spreads. All estimated coefficients corresponding to the variables used to explain liquidity premiums have the expected sign and are statistically significant at 99% in both samples. Also, transactions with a trading volume less than 10 million pesetas have an additional liquidity premium of 36 bp. The estimated coefficients corresponding to the dummy variables that represent the rating, show values that are much more coherent than the average yield spreads shown in Table 7. Now the mean yield spread for AAA bonds is around 9 bp smaller than the yield spread for AA bonds, 112 bp for A and BBB bonds and 15 bp for those bonds without rating. Also the default premium for Ebro and Sarrió bonds is around 866 bp with respect to AAA bonds. The estimated parameters for the variables Evolution and Slope of the term structure do not differ from the results observed in other previous papers where a negative relationship has been found. Finally, in Figure 3, the estimated yield spreads for the reduced sample are represented depending on the term to maturity. Each point corresponds to the mean estimated yield spread for those bonds with a term to maturity within the corresponding annual time interval and it is obtained as the estimated coefficients times the mean value of the independent variables of those observations included in each time interval.28 Table 10 provides the result of regressing these estimated yield spreads against the term to maturity, showing a significant negative relationship between both variables. 100 90 Yield Spread (bp) 80 70 60 50 40 30 20 10 0 0 1 2 3 4 5 6 7 8 9 10 Term to maturity (years) Fig. 3. Average estimated yield spreads and term to maturity. Average estimated yield spreads for ten annual groups depending on term to maturity in the reduced sample. 28 For instance, the estimated yield spread for those bonds with a term to maturity less than one year is 89.50 bp. This value is obtained by adding the value of the constant term (173.69), the value of estimated 1 times the mean value of ln(Sizei ) for all observations with a term to maturity less than a year, the estimate of 2 times the mean value of RelativeAgei for the same set of observations and so on. # Blackwell Publishers Ltd, 2002 471 Yield Spread and Term to Maturity Table 10 Relationship between term to maturity and estimated yield spread. Results of regressing estimated yield spreads (Table 9) on term to maturity. Model: y^it ¼ 0 þ 1 Termtomaturityit þ "it , where y^it denotes the estimated yield spreads: y^it ¼ ^0 þ ^1 ln(Sizei ) þ ^2 RelativeAgeit þ ^3 RetailTransactionit þ ^4 Term * it þ ^5 AAit þ ^6 Ait þ ^7 Unratedit þ ^8 EbroSarri oi þ ^9 Evolutiont þ ^10 Slopet ‘Complete Sample’ includes Ebro and Sarrió issues; ‘Reduced Sample’ does not include Ebro and Sarrió issues. Termtomaturity is the term to maturity in years. Estimation is done using the Generalized Method of Moments (GMM) procedure with the Newey-West correction. The p-values of parameters significance are in parenthesis under the respective estimates. Independent variable Constant ( 0) Termtomaturity ( 1) R2 R2 adjusted No. observations Complete sample Reduced sample 118.69 (0.00)
11.84 (0.00) 94.97 (0.00)
8.58 (0.00) 7.30 7.29 14,158 22.35 22.35 13,894 As we can see in Figure 3, the term structure of yield spreads is downward sloping. However, one of the main results we have obtained is the fact that now, the estimated coefficient of the variable Term * is positive and significantly different from zero. This contradictory outcome suggests that if we remove the effects of liquidity and other explanatory variables for default risk, isolating the relationship between term to maturity and default premium, we find it to be positive. It must be pointed out that the sign of this parameter was negative when only liquidity risk was taken into account in the analysis of Treasury assets (Section 5). So, this change of sign must be due to the effect of default risk on yield spreads. Moreover, this positive relationship between default premiums and term to maturity must be stronger than the one suggested by the estimated value of the parameter of Term * as it captures the effects of both liquidity and default risk on yield spreads. Then, we have obtained a result that is now consistent with the upward sloping or almost flat term structure of the credit spreads expected by the literature for investment-grade bonds. 7. Analysis by rating In the previous section the behaviour of yield spreads was analysed considering a sample including all bonds traded between 1993 and 1997. In this section, we proceed to analyse the yield spread of those bonds within the same credit rating separately. We classify all bonds in four categories: AAA bonds, AA bonds, A bonds (including BBBþ) and bonds without rating (Unrated). Parameters of model [4] are # Blackwell Publishers Ltd, 2002 472 Antonio Dı´az and Eliseo Navarro estimated for each group of bonds and the results are shown in Table 11. These results are illustrated in Figure 4 that depicts the relationship between estimated yield spreads and term to maturity. We use the same method employed for drawing Figure 3. Table 12 shows the results of regressing the estimated yield spreads against the term to maturity for each bond group. Again, the yield spreads for all categories are downward sloping (Figure 4 and Table 12). Estimated yield spreads for AAA and AA bonds are very close although it must be pointed out that all AAA issues are rated AA when they are denominated in foreign currencies. Estimated yield spreads for AAA, AA and unrated bonds with Table 11 Yield spread of corporate bonds by ratings. Results of regressing yield spreads on explanatory variables: YSit ¼ 0 þ þ 4 1 ln(Sizei ) þ Term *it þ 9 2 RelativeAgeit þ Evolutiont þ 10 3 RetailTransactionit Slopet þ "it Samples: AAA bonds; AA bonds; A and BBBþ bonds; and bonds without rating excluding Ebro and Sarrió issues. Yield spread (YS) is the differences between the yield to maturity of the corporate bond and the yield to maturity of a theoretical Treasury bond with the same characteristics (coupon and term to maturity). Size is the issue amount in billions of pesetas. RelativeAge of an issue is the ratio between current age and term to maturity. RetailTransaction is a dummy variable that takes value one if the issue trading volume is smaller than 10 millions of pesetas ($75,854) and zero otherwise. Term * variable represents residuals of the regression of term to maturity against relative age in each sample. Evolution of interest rates is the ratio between the current three month interest rate and its average value during the last seventy trading days. Slope is the difference between three year and three month interest rates. Estimation is done using the Generalized Method of Moments (GMM) procedure with the Newey-West correction. The p-values of parameters significance are in parenthesis under the respective estimates. Independent variable Constant Ln(Size) RelativeAge RetailTransaction, dummy Term * Evolution Slope R2 Adjusted R2 No. Observations # Blackwell Publishers Ltd, 2002 AAA AA A Unrated 188.52 (0.00) 5.44 (0.01) 16.34 (0.00) 41.07 (0.00) 0.67 (0.09)
195.40 (0.00)
773.23 (0.00) 107.99 (0.00)
15.67 (0.00) 24.54 (0.00) 16.71 (0.00) 0.28 (0.33)
30.18 (0.04)
624.00 (0.00) 553.50 (0.00)
46.80 (0.00) 53.81 (0.00) 76.44 (0.00) 31.64 (0.00)
364.62 (0.00)
1426.36 (0.00) 51.98 (0.17) 8.94 (0.00) 44.49 (0.00) 38.23 (0.00)
1.19 (0.02)
57.53 (0.13)
527.83 (0.00) 14.75 14.58 1,871 34.79 34.79 1,293 12.22 12.13 5,305 18.18 18.09 5,425 473 Yield Spread and Term to Maturity 200 AAA 180 AA Yield Spread (bp) 160 A 140 Unrated 120 100 80 60 40 20 0 0 1 2 3 4 5 6 7 8 9 10 Term to maturity (years) Fig. 4. Estimated yield spreads and term to maturity by rating. Average estimated yield spreads for ten annual groups of corporate bonds depending on term to maturity for different ratings: AAA, AA, A (including BBBþ) and unrated bonds. Table 12 Relationship between term to maturity and estimated yield spread by ratings. Results of regressing estimated yield spreads (Table 11) on term to maturity by ratings. Model: y^it ¼ 0 þ 1 Termtomaturityit þ "it , where y^it denotes the estimated yield spreads: y^it ¼ ^0 þ ^1 ln(Sizei ) þ ^2 RelativeAgeit þ ^3 RetailTransactionit þ ^4 Term *it þ ^5 Evolutiont þ ^6 Slopet Samples AAA, AA, A and BBBþ, and unrated bonds. Termtomaturity is the term to maturity in years. Estimation is done using the Generalized Method of Moments (GMM) procedure with the Newey-West correction. Table shows estimated coefficient 1 corresponding to the slope of the term to maturity, the p-value parameters significance in parenthesis and the adjusted R2 of the regression. Independent variable Constant ( 0) Termtomaturity ( 1) R2 Adjusted R2 No. observations # Blackwell Publishers Ltd, 2002 AAA AA A Unrated 72.17 (0.00)
6.29 (0.00) 55.70 (0.00)
3.29 (0.00) 193.96 (0.00)
16.12 (0.00) 96.73 (0.00)
10.12 (0.00) 30.23 30.22 5,305 18.35 18.34 5,425 12.76 12.71 1,871 61.34 61.31 1,293 474 Antonio Dı´az and Eliseo Navarro maturity over 5 years are quite similar. The unrated bonds category is a heterogeneous mixture of different bonds. Most of the bonds with a term to maturity less than three years, which were traded mainly in the ESEM market, belong to issues with a low amount outstanding, low liquidity and poor credit quality. On the contrary, those bonds with longest terms to maturity (over five years) were traded in wholesale markets (AIAF and MDPAOP). They showed large amount outstanding and trading volumes and they were also issued by high quality borrowers (regional governments, utility companies, public firms, ...).29 As before, Table 11 shows that the estimated coefficient of the variable Term * is positive for the three samples of rated bonds, although it has a poor explanatory power for AA bonds. So the result we obtained in the former section seems to be robust across bonds with different ratings. This outcome is now consistent with the ‘crisis at maturity’ theory for investmentgrade bonds and similar to that obtained by Sarig and Warga (1989b) where the relationship between yield spreads and term to maturity was found positive and statistically significant for AAA bonds and nearly flat for bonds with AA, A and BBB ratings. So, we can infer that the observed downward sloping term structure of yield spreads is caused mainly by the structure of liquidity premiums and the effects of other explanatory variables of the default risk. 8. Conclusions In this paper the relationship between yield spreads and term to maturity is analysed, trying to separate the impact of two different sources of risk on these spreads: liquidity and default risk. First, the yield spreads are measured as the difference between the yield to maturity of corporate bonds and the yield to maturity of a theoretical default-free bond with the same characteristics (coupons and maturity). The price of this theoretical bond is obtained by discounting its cash flows according to the term structure of interest rate estimations from the Treasury bond market. Once these yield spreads were estimated, we could observe a downward sloping term structure of yield spreads for all bond categories (AAA, AA, A and unrated bonds). At first glance, this result seems to be contrary to former theoretical and empirical literature. A preliminary analysis of the two Spanish Treasury debt markets where the same default-free assets are traded simultaneously helps considerably to understand the effects of liquidity on yield spreads. Of particular relevance is the strongly downward sloping term structure of liquidity premiums we have obtained. This result seems to be caused by the effect of aging (which is highly correlated with the term to maturity) and an additional negative relationship between liquidity premiums and term to maturity itself. According to literature, we use different variables to explain the yield spreads between Treasury and non-Treasury yield spreads. Some of them account for the liquidity risk: amount issued, relative age, trading volume and term to maturity. Some others account for the default risk as rating, business cycle (using the evolution and 29 These issuers did not need rating qualification to issue in Spanish markets during the analysed period. # Blackwell Publishers Ltd, 2002 Yield Spread and Term to Maturity 475 the slope of the term structure of interest rates as proxies of the business cycle) and, again, the term to maturity. The analysis of these premiums shows that, when liquidity and variables usually used for explaining default risk are taken into consideration, we obtain a positive and significant relationship between yield spreads and term to maturity. As we had found before that relationship between liquidity premiums and term to maturity was negative, we can infer that the relationship between default premiums and term to maturity must be positive. This result is fully consistent with the ‘crisis at maturity’ theory and suggests that the observed downward sloping term structure of yield spreads is caused mainly by the strong effect of liquidity on the yields of the corporate bonds traded in the Spanish fixed income markets. This fact may have important consequences when applying bond pricing models to markets with a low liquidity level like the Spanish ones, especially those models that only take into account the effects of default risk on prices and yields. 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