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THE JOURNAL OF FINANCE • VOL. LVI, NO. 1 • FEBRUARY 2001 Explaining the Rate Spread on Corporate Bonds EDWIN J. ELTON, MARTIN J. GRUBER, DEEPAK AGRAWAL, and CHRISTOPHER MANN* ABSTRACT The purpose of this article is to explain the spread between rates on corporate and government bonds. We show that expected default accounts for a surprisingly small fraction of the premium in corporate rates over treasuries. While state taxes explain a substantial portion of the difference, the remaining portion of the spread is closely related to the factors that we commonly accept as explaining risk premiums for common stocks. Both our time series and cross-sectional tests support the existence of a risk premium on corporate bonds. THE PURPOSE OF THIS ARTICLE is to examine and explain the differences in the rates offered on corporate bonds and those offered on government bonds ~spreads!, and, in particular, to examine whether there is a risk premium in corporate bond spreads and, if so, why it exists. Spreads in rates between corporate and government bonds differ across rating classes and should be positive for each rating class for the following reasons: 1. Expected default loss—some corporate bonds will default and investors require a higher promised payment to compensate for the expected loss from defaults. 2. Tax premium—interest payments on corporate bonds are taxed at the state level whereas interest payments on government bonds are not. 3. Risk premium—The return on corporate bonds is riskier than the return on government bonds, and investors should require a premium for the higher risk. As we will show, this occurs because a large part of the risk on corporate bonds is systematic rather than diversifiable. The only controversial part of the above analyses is the third point. Some authors in their analyses assume that the risk premium is zero in the corporate bond market.1 * Edwin J. Elton and Martin J. Gruber are Nomura Professors of Finance, Stern School of Business, New York University. Deepak Agrawal and Christopher Mann are Doctoral Students, Stern School of Business, New York University. We would like to thank the Editor, René Stulz, and the Associate Editor for helpful comments and suggestions. 1 Many authors assume a zero risk premium. Bodie, Kane, and Marcus ~1993! assume the spread is all default premium. See also Fons ~1994! and Cumby and Evans ~1995!. On the other hand, rating-based pricing models like Jarrow, Lando, and Turnbull ~1997! and Das-Tufano ~1996! assume that any risk premium impounded in corporate spreads is captured by adjusting transition probabilities. 247 248 The Journal of Finance This paper is important because it provides the reader with explicit estimates of the size of each of the components of the spread between corporate bond rates and government bond rates.2 Although some studies have examined losses from default, to the best of our knowledge, none of these studies has examined tax effects or made the size of compensation for systematic risk explicit. Tax effects occur because the investor in corporate bonds is subject to state and local taxes on interest payments, whereas government bonds are not subject to these taxes. Thus, corporate bonds have to offer a higher pre-tax return to yield the same after-tax return. This tax effect has been ignored in the empirical literature on corporate bonds. In addition, past research has ignored or failed to measure whether corporate bond prices contain a risk premium above and beyond the expected loss from default ~we find that the risk premium is a large part of the spread!. We show that corporate bonds require a risk premium because spreads and returns vary systematically with the same factors that affect common stock returns. If investors in common stocks require compensation for this risk, so should investors in corporate bonds. The source of the risk premium in corporate bond prices has long been a puzzle to researchers and this study is the first to provide both an explanation of why it exists and an estimate of its importance. Why do we care about estimating the spread components separately for various maturities and rating classes rather than simply pricing corporate bonds off a spot yield curve or a set of estimated risk neutral probabilities? First, we want to know the factors affecting the value of assets and not simply their value. Second, for an investor thinking about purchasing a corporate bond, the size of each component for each rating class will affect the decision of whether to purchase a particular class of bonds or whether to purchase corporate bonds at all. To illustrate this last point, consider the literature that indicates that low-rated bonds produce higher average returns than bonds with higher ratings whereas the lower-rated bonds do not have a higher standard deviation of return.3 What does this evidence indicate for investment? This evidence has been used to argue that low-rated bonds are attractive investments. However, we know that this is only true if required return is no higher for low-rated debt. Our decomposition of corporate spreads shows that the risk premium increases for lower-rated debt. In addition, because promised coupon is higher for lower-rated debt, the tax burden is greater. Thus, the fact that lower-rated bonds have higher realized returns does not imply they are better investments because the higher realized return might not be sufficient compensation for taxes and risk. 2 Liquidity may play a role in the risk and pricing of corporate bonds. We, like other studies, abstract from this inf luence. 3 See, for example, Altman ~1989!, Goodman ~1989!, Blume, Keim, and Patel ~1991!, and Cornell and Green ~1991!. Explaining the Rate Spread on Corporate Bonds 249 The paper proceed as follows: in the first section we start with a description of our sample. We next discuss both the need for using spot rates ~the yield on zero-coupon bonds! to compute spreads and the methodology for estimating them. We examine the size and characteristics of the spreads. As a check on the reasonableness of the spot curves, we estimate, for government and corporate bonds, the ability of our estimated spot rates to price bonds. The next three sections ~Sections II–IV! of the paper present the heart of our analysis: the decomposition of rate spreads into that part which is due to expected loss, that part which is due to taxes, and that part which is due to the presence of systematic risk. In the first of these sections ~Sec. II!, we model and estimate that part of the corporate spread which is due to expected default loss. If we assume for the moment that there is no risk premium, then we can value corporate bonds under the assumption that investors are risk neutral using expected default losses.4 This risk neutrality assumption allows us to construct a model and estimate what the corporate spot rate spread would be if it were solely due to expected default losses. We find that the spot rate spread curves estimated by incorporating only the expected default losses are well below the observed spot spread curve and that they do not increase as we move to lower ratings as fast as actual spot spread curves. In fact, expected loss can account for no more than 25 percent of the corporate spot spreads. In Section III, we examine the impact of both the expected default loss and the tax premium on corporate spot spreads. In particular, we build both expected default loss and taxes into the risk neutral valuation model developed earlier and estimate the corporate spot rates that should be used to discount promised cash payments when both state and local taxes and expected default losses are taken into consideration. We then show that using the best estimate of tax rates, actual corporate spot spreads are still much higher than what taxes and default premiums can together account for. Section IV presents direct evidence of the existence of a risk premium and demonstrates that this risk premium is compensation for the systematic nature of risk in bond returns. We first relate the time series of that part of the spreads that is not explained by expected loss or taxes to variables that are generally considered systematic priced factors in the literature of financial economics. Then we relate cross-sectional differences in spreads to sensitivities of each spread to these variables. We have already shown that the default premium and tax premium can only partially account for the difference in corporate spreads. In this section we present direct evidence that there is a premium for systematic risk by showing that the majority of the corporate spread, not explained by defaults or taxes, is explained by factor sensitivities and their prices. Further tests suggest that the factor sensitivities are not proxies for changes in expected default risk. Conclusions are presented in Section V. 4 We also temporarily ignore the tax disadvantage of corporate bonds relative to government bonds in this section. 250 The Journal of Finance I. Corporate Yield Spreads In this section, we examine corporate yield spreads. We initially discuss the data used. Then we discuss why yield spreads should be measured as the difference in yield to maturity on zero-coupon bonds ~rather than coupon bonds! and how these rates can be estimated. Next, we examine and discuss the pattern of spreads. Finally, we compare the price of corporate bonds computed from our estimated spots with actual prices as a way of judging the reasonableness of our estimates. A. Data Our bond data are extracted from the Lehman Brothers Fixed Income Database distributed by Warga ~1998!. This database contains monthly price, accrued interest, and return data on all investment-grade corporate and government bonds. In addition, the database contains descriptive data on bonds, including coupons, ratings, and callability. A subset of the data in the Warga database is used in this study. First, all bonds that were matrix priced rather than trader priced are eliminated from the sample.5 Employing matrix prices might mean that all our analysis uncovers is the rule used to matrix-price bonds rather than the economic inf luences at work in the market. Eliminating matrix-priced bonds leaves us with a set of prices based on dealer quotes. This is the same type of data as that contained in the standard academic source of government bond data: the CRSP government bond file.6 Next, we eliminate all bonds with special features that would result in their being priced differently. This means we eliminate all bonds with options ~e.g., callable bonds or bonds with a sinking fund!, all corporate f loating rate debt, bonds with an odd frequency of coupon payments, government f lower bonds, and inf lation-indexed government bonds. In addition, we eliminate all bonds not included in the Lehman Brothers bond indexes, because researchers in charge of the database at Lehman Brothers indicate that the care in preparing the data was much less for bonds not included in their indexes. This results in eliminating data for all bonds with a maturity of less than one year. 5 For actively traded bonds, dealers quote a price based on recent trades of the bond. Bonds for which a dealer did not supply a price have prices determined by a rule of thumb relating the characteristics of the bond to dealer-priced bonds. These rules of thumb tend to change very slowly over time and to not respond to changes in market conditions. 6 The only difference in the way CRSP data is constructed and our data is constructed is that over the period of our study, CRSP uses an average of bid0ask quotes from five primary dealers called randomly by the New York Federal Reserve Board rather than a single dealer. However, comparison of a period when CRSP data came from a single dealer and also from the five dealers surveyed by the Fed showed no difference in accuracy ~Sarig and Warga ~1989!!. Also in Section II, we show that the errors in pricing government bonds when spots are extracted from the Warga data are comparable to the errors when spots are extracted from CRSP data. Thus our data should be comparable in accuracy to the CRSP data. Explaining the Rate Spread on Corporate Bonds 251 Finally, we eliminate bonds where the price data or return data was problematic. This involved examining the data on bonds that had unusually high pricing errors when priced using the spot curve. Bond pricing errors were examined by filtering on errors of different sizes and a final filter rule of $5 was selected.7 Errors of $5 or larger are unusual, and this step resulted in eliminating 2,710 bond months out of our total sample of 95,278 bond months. Examination of the bonds that are eliminated because of large differences between model prices using estimated spots and recorded prices show that large differences were caused by the following: 1. The price was radically different from both the price immediately before the large error and the price after the large error. This probably indicates a mistake in recording the data. 2. The company issuing the bonds was going through a reorganization that changed the nature of the issue ~such as interest rate or seniority of claims!, and this was not immediately ref lected in the data shown on the tape, and thus the trader was likely to have based the price on inaccurate information about the bond’s characteristics. 3. A change was occurring in the company that resulted in the rating of the company to change so that the bond was being priced as if it were in a different rating class. B. Measuring Spreads Most previous work on corporate spreads has defined corporate spread as the difference between the yield to maturity on a coupon-paying corporate bond ~or an index of coupon-paying corporate bonds! and the yield to maturity on a coupon-paying government bond ~or an index of government bonds! of the same maturity.8 We define spread as the difference between yield to maturity on a zero-coupon corporate bond ~corporate spot rate! and the yield to maturity on a zero-coupon government bond of the same maturity ~government spot rate!. In what follows we will use the name “spot rate” rather than the longer expression “yield to maturity on a zero-coupon bond” to refer to this rate. The basic reason for using spots rather than yield to maturity on coupon debt is that arbitrage arguments hold with spot rates, not with yield to maturity. Because a riskless coupon-paying bond can always be expressed as 7 The methodology used to do this is described later in this paper. We also examined $3 and $4 filters. Employing a $3 or $4 filter would have eliminated few other bonds, because there were few intermediate-size errors, and we could not find any reason for the error when we examined the few additional bonds that would be eliminated. 8 The prices in the Warga Database are bid prices as are the bond price data reported in DRI or Bloomberg. Because the difference in the bid and ask price in the government market is less than this difference in the corporate market, using bid data would result in a spread between corporate and government bonds even if the price absent the bid0ask spread were the same. However, the difference in price is small and, when translated to spot yield differences, is negligible. 252 The Journal of Finance a portfolio of zeros, spot rates are the rates that must be used to discount cash f lows on riskless coupon-paying debt to prevent arbitrage.9 The same is not true for yield to maturity. In addition, the yield to maturity depends on coupon. Thus, if yield to maturity is used to define the spread, the spread will depend on the coupon of the bond that is picked. Finally, calculating spread as difference in yield to maturity on coupon-paying bonds with the same maturity means one is comparing bonds with different duration and convexity. The disadvantage of using spots is that they need to be estimated.10 In this paper, we use the Nelson–Siegel procedure ~see Appendix A! for estimation of spots. This procedure was chosen because it performs well in comparison to other procedures.11 C. Empirical Spreads The corporate spread we examine is the difference between the spot rate on corporate bonds in a particular rating class and spot rates for Treasury bonds of the same maturity. Table I presents Treasury spot rates as well as corporate spreads for our sample for the three following rating classes: AA, A, and BBB for maturities from two to ten years. AAA bonds were excluded because for most of the 10-year period studied, the number of these bonds that existed and were dealer quoted was too small to allow for accurate estimation of a term structure of spots. Corporate bonds rated below BBB were excluded because data on these bonds was not available for most of the time period we studied.12 Initial examination of the data showed that the term structure for financials was slightly different from the term structure for industrials, and so in this section, the results for each sector are reported separately.13 In Panel A of Table I, we have presented the average difference over our 10-year sample period, 1987 to 1996. In Panels B and C we present similar results for the first and second half of our sample period. We expect these differences to vary over time. 9 Spot rates on promised payments may not be a perfect mechanism for pricing risky bonds because the law of one price will hold as an approximation when applied to promised payments rather than risk-adjusted expected payments. See Duffie and Singleton ~1999! for a description of the conditions under which using spots to discount cash f lows is consistent with no arbitrage. 10 The choice between defining spread in terms of yield to maturity on coupon-paying bonds and spot rates is independent of whether we include matrix-priced bonds in our estimation. For example, if we use matrix-priced bonds in estimating spots we will improve estimates only to the extent that the rules for matrix pricing accurately ref lect market conditions. 11 See Nelson and Siegel ~1987!. For comparisons with other procedures, see Green and Odegaard ~1997! and Dahlquist and Svensson ~1996!. We also investigated the McCulloch cubic spline procedure and found substantially similar results throughout our analysis. The Nelson and Siegel model was fit using standard Gauss–Newton nonlinear least squares methods. 12 We use both Moody’s and S&P data. To avoid confusion we will always use S&P classifications, though we will identify the sources of data. When we refer to BBB bonds as rated by Moody’s, we are referring to the equivalent Moody’s class, named Baa. 13 This difference is not surprising because industrial and financial bonds differ both in their sensitivity to systematic inf luences and to idiosyncratic shocks that occurred over the time period. Explaining the Rate Spread on Corporate Bonds 253 Table I Measured Spread from Treasury This table reports the average spread from treasuries for AA, A, and BBB bonds in the financial and industrial sectors. For each column, spot rates were derived using standard GaussNewton nonlinear least square methods as described in the text. Treasuries are reported as annualized spot rates. Corporates are reported as the difference between the derived corporate spot rates and the derived treasury spot rates. The financial sector and the industrial sector are defined by the bonds contained in the Lehman Brothers’ financial index and industrial index, respectively. Panel A contains the average spot rates and spreads over the entire 10-year period. Panel B contains the averages for the first five years and panel C contains the averages for the final five years. Financial Sector Maturity Treasuries AA A BBB Industrial Sector AA A BBB 0.414 0.419 0.455 0.493 0.526 0.552 0.573 0.589 0.603 0.621 0.680 0.715 0.738 0.753 0.764 0.773 0.779 0.785 1.167 1.205 1.210 1.205 1.199 1.193 1.188 1.184 1.180 0.436 0.441 0.504 0.572 0.629 0.675 0.711 0.740 0.764 0.707 0.780 0.824 0.853 0.872 0.886 0.897 0.905 0.912 1.312 1.339 1.347 1.349 1.348 1.347 1.346 1.345 1.344 0.392 0.396 0.406 0.415 0.423 0.429 0.434 0.438 0.441 0.536 0.580 0.606 0.623 0.634 0.642 0.649 0.653 0.657 1.022 1.070 1.072 1.062 1.049 1.039 1.030 1.022 1.016 Panel A: 1987–1996 2 3 4 5 6 7 8 9 10 6.414 6.689 6.925 7.108 7.246 7.351 7.432 7.496 7.548 0.586 0.606 0.624 0.637 0.647 0.655 0.661 0.666 0.669 0.745 0.791 0.837 0.874 0.902 0.924 0.941 0.955 0.965 1.199 1.221 1.249 1.274 1.293 1.308 1.320 1.330 1.337 Panel B: 1987–1991 2 3 4 5 6 7 8 9 10 7.562 7.763 7.934 8.066 8.165 8.241 8.299 8.345 8.382 0.705 0.711 0.736 0.762 0.783 0.800 0.813 0.824 0.833 0.907 0.943 0.997 1.047 1.086 1.118 1.142 1.161 1.177 1.541 1.543 1.570 1.599 1.624 1.644 1.659 1.672 1.682 Panel C: 1992–1996 2 3 4 5 6 7 8 9 10 5.265 5.616 5.916 6.150 6.326 6.461 6.565 6.647 6.713 0.467 0.501 0.511 0.512 0.511 0.510 0.508 0.507 0.506 0.582 0.640 0.676 0.701 0.718 0.731 0.740 0.748 0.754 0.857 0.899 0.928 0.948 0.962 0.973 0.981 0.987 0.993 There are a number of interesting results reported in this table. Note that, in general, the corporate spread for a rating category is higher for financials than it is for industrials. For both financial and industrial bonds, the corporate 254 The Journal of Finance spread is higher for lower-rated bonds for all spots across all maturities in both the 10-year sample and the 5-year subsamples. Bonds are priced as if the ratings capture real information. To see the persistence of this inf luence, Figure 1 presents the time pattern of spreads on 6-year spot payments for AA, A, and BBB industrial bonds month by month over the 10 years of our sample. Note that the curves never cross. A second aspect of interest is the relationship of corporate spread to the maturity of the spot rates. An examination of Table I shows that there is a general tendency for the spreads to increase as the maturity of the spot lengthens. However, for the 10 years from 1987 to 1996, and each 5-year subperiod, the spread on BBB industrial bonds exhibits a humped shape. The results we find can help differentiate among the corporate debt valuation models derived from option pricing theory. The upward sloping spread curve for high-rated debt is consistent with the models of Merton ~1974!, Jarrow, Lando, and Turnbull ~1997!, Longstaff and Schwartz ~1995!, and Pitts and Selby ~1983!. It is inconsistent with the humped shape derived by Kim, Ramaswamy and Sundaresan ~1987!. The humped shape for BBB industrial debt is predicted by Jarrow et al. ~1997! and Kim et al. ~1987!, and is consistent with Longstaff and Schwartz ~1995! and Merton ~1974! if BBB is considered low-rated debt.14 However, one should exercise care in interpreting these results, for, as noted by Helwege and Turner ~1999!, the tendency of less risky companies within a rating class to issue longer-maturity debt might tend to bias yield and to some extent spots on long maturity bonds in a downward direction. We will now examine the results of employing spot rates to estimate bond prices. D. Fit Error One test of our data and procedures is to see how well the spot rates extracted from coupon bond prices explain those prices. We do this by directly comparing actual prices with the model prices derived by discounting coupon and principal payments at the estimated spot rates. Model price and actual price can differ because of errors in the actual price and because bonds within the same rating class, as defined by a rating agency, are not homogenous. We calculate model prices for each bond in each rating category every month using the spot yield curves estimated for that rating class in that month. For each month, average error ~error is measured as actual minus model price! and the square root of the average squared error are calculated. These are then averaged over the full 10 years and separately for the first and last 5 years for each rating category. The average error for all 14 While the BBB industrial curve is consistent with the models that are mentioned, estimated default rates shown in Table IV are inconsistent with the assumptions these models make. Thus, the humped BBB industrial curve is inconsistent with spread being driven only by defaults. Figure 1. Empirical spreads on industrial bonds of six years maturity. Explaining the Rate Spread on Corporate Bonds 255 256 The Journal of Finance Table II Average Root Mean Squared Errors This table contains the average root mean squared error of the difference between theoretical prices computed from the spot rates derived from the Gauss–Newton procedure and the actual bond invoice prices. Root mean squared error is measured in cents per $100. For a given class of securities, the root mean squared error is calculated once per period. The number reported is the average of all the root mean squared errors within a class over the period indicated. Financial Sector Industrial Sector Period Treasuries AA A BBB AA A BBB 1987–1996 1987–1991 1992–1996 0.210 0.185 0.234 0.512 0.514 0.510 0.861 0.996 0.726 1.175 1.243 1.108 0.728 0.728 0.727 0.874 0.948 0.800 1.516 1.480 1.552 rating classes is very close to zero ~less than one cent on a $100 bond!. Root mean squared error is a measure of the variance of errors within each rating class. The average root mean squared error between actual price and estimated price is shown in Table II. The average root mean square error of 21 cents per $100 for Treasuries is comparable to the average root mean squared error found in other studies. Elton and Green ~1998! had showed average absolute errors of about 16 cents per $100 using GovPX data over the period June 1991 to September 1995. GovPX data are trade prices, yet the difference in error between the studies is quite small. Green and Odegaard ~1997! used the Cox, Ingersoll, and Ross ~1985! procedure to estimate spot rates using data from CRSP. Although their procedure and time period are different from ours, their errors again are about the same as those we find for government bonds in our data set ~our errors are smaller!. The data set and procedures we are using seem to produce errors in pricing government bonds comparable in size to those found by other authors. The average root mean squared pricing errors become larger as we examine lower grades of bonds while the average error does not change. Average root mean squared pricing errors are over twice as large for AA’s as for Treasuries. The root mean squared pricing errors for BBBs are almost twice those of AAs, with the errors in As falling in between. Thus, default risk leads not only to higher spot rates, but also to greater uncertainty as to the appropriate value of the bond. This is ref lected in a higher root mean squared error ~variance of pricing errors!. This is an added source of risk and may well be ref lected in higher risk premiums, a subject we investigate shortly.15 15 In a separate paper, we explore whether the difference in theoretical price and invoice price is random or related to bond characteristics. Bond characteristics do explain some of the differences but the characteristics and relationships do not change the results in this paper.