Short-Term Corporate Bond Yield Spreads

Short-term corporate bond yield spreads

Peter Feldh¨utter ∗

April 19, 2012

Abstract I study yield spreads on US corporate bonds maturing within three months. For most of the sample period 2002-2011 yield spreads on bonds issued by highly-rated companies are close to zero. During the subprime crisis however, yield spreads peak much more than comparable spreads in the commercial paper and LIBOR markets. A simple liquidity measure explains virtually all of the time series variation in yield spreads of highly-rated bonds. Since 2010 AAA-rated bonds have traded at negative spreads and low transaction costs, suggesting they trade at a specialness premium.

∗ London Business School, Regent’s Park, London NW1 4SA, United Kingdom (e-mail: [email protected]). I thank Jens-Dick Nielsen for helpful comments. 1. Introduction

Merton (1974) developed structural models, one of the most widely employed frameworks of credit risk. A common criticism of structural models is that model-implied corporate bond spreads are too low compared to actual spreads, giving rise to the so-called credit spread puzzle (see Huang and Huang (2003)). Highly-rated bonds with short maturities present a particularly severe challenge to structural models, because the models predict yield spreads close to zero. To shed new light on the credit spread puzzle, I therefore examine yield spreads on US corporate bonds maturing within three months. I find that yield spreads on highly-rated bonds are close to zero for most of the sample period 2002-2011 (using General Collateral repo rates as riskfree rates). This is surprising given that the credit spread puzzle is perceived to be most severe for these bonds. However, yield spreads jumped in 2007 and did not return back to normal until 2009. Bond spreads reacted much stronger to the crisis 2007-2009 than comparable spreads in other markets. Following the Lehman Brothers’ default for example, bond spreads jumped to 670 basis points compared to a jump in the one-month LIBOR spread of 213 basis points and a jump in the one-month financial commercial paper spread of 111 basis points. The slope of the curve of yield spreads as a function of maturity is examined in a number of papers but no clear conclusion has emerged. For example, Sarig and Warga (1989b) find that the slope is negative for speculative grade issuers while Helwege and Turner (1999) reach the opposite conclusion. The main problem in estimating the slope coefficient is that one

1 needs a short- and a long-maturity bond and these two bonds might have different characteristics. In this paper, I estimate the slope at short maturities by pooling transactions-based yield spreads across time. The advantage of this approach is that the same bond is used in estimating different points on the yield spread curve. I find that the curve of yield spreads are either flat or slightly upward-sloping as a function of maturity for investment grade bonds. For speculative grade bonds, the curve is downward-sloping and increasingly so as we move down the rating ladder. Yields on short-term corporate bonds provide a clean perspective on how liquidity and credit risk affect corporate bond yields. The reason is that yields on short-term bonds reflect only the current environment while yields on long- term bonds reflect both the current and future expected environment. To understand what drives short yield spreads for credit-worthy corporations, I regress quarterly median yield spreads of bonds rated AAA, AA, or A on quarterly credit risk and liquidity proxies. As liquidity measure I use roundtrip costs as defined in Chakravarty and Sarkar (2003). A roundtrip in a bond on a given day is the average investor buy price minus average investor sell price. A univariate regression of the spread on roundtrip costs delivers a stunning R2 of 96%. Although VIX is significant in a univariate regression with an R2 of 57%, it becomes insignificant when roundtrip costs are included. These results show that liquidity to a large extent drives short corporate bond spreads. And since the R2 of roundtrip costs is 96%, virtually all of the variation in short bond spreads can be explained. This implies that there is no missing factor in explaining short spread variation as Collin- Dufresne, Goldstein, and Martin (2001) find there is for yield spreads on

2 bonds with a maturity of more than four years. I also look at yield spreads on AAA-, AA-, and A-rated bonds separately. While spreads on AA- and A-rated bonds have been increasing since the summer 2010, spreads on AAA-rated bonds have been decreasing. In fact, spreads on AAA-rated bonds have been negative in the last six quarters of the sample and in the final quarter of 2011 the median spread was -10 basis points. In this period the average number of trades in AAA-rated bonds was almost five times higher than in the rest of the sample period and median roundtrip costs in AAA-rated bonds were more than seven times lower than costs in AA- and A-rated bonds. Transaction costs in AAA-rated bonds by the end of 2011 are comparable to transaction costs in the Treasury market. This evidence suggests that since 2010 AAA-rated bonds command a specialness premium similar to the premium in US Treasuries. There is to the best of my knowledge no empirical research on yield spreads on corporate bonds with a maturity of one year or below. Covitz and Downing (2007) study short-term yield spreads in the commercial paper market. As I show, the reaction to crises in the commercial paper market is very different from the reaction in the corporate bond market, so insights from the commercial paper market cannot be extended to the corporate bond market. There is a number of papers that examine what departures from the assumptions of Merton (1974)’s structural model can generate significant yield spreads at a maturity of one year or shorter. These departures include incomplete accounting information (Duffie and Lando (2001)), jumps in asset value (Zhou (2001)), business cycles (Hackbarth, Miao, and Morel- lec (2006) and Chen, Collin-Dufresne, and Goldstein (2009)), and illiquidity

3 (Ericsson and Renault (2006) and He and Xiong (2012)). My paper empirical documents facts about short-term spreads that should help us estimate the parameters of these models and assess the relative importance of different channels contributing to short-term spreads. Papers showing that liquidity proxies are significant explanatory variables for credit spreads are Houweling, Mentink, and Vorst (2005)), Downing, Underwood, and Xing (2005), de Jong and Driessen (2006), Sarig and Warga (1989a), Lin, Wang, and Wu (2011), Bao, Pan, and Wang (2011), Dick-Nielsen, Feldhütter, and Lando (2012), Friewald, Jankowitsch, and Subrahmanyam (2011), Acharya, Amihud, and Bharath (2010), and Bongaerts, Jong, and Driessen (2012), but none of the papers focus on the impact of illiquidity on short-term bond spreads.

2. Data description

Since July 1, 2002, members of the Financial Industry Regulatory Authority have been required to report their secondary over-the-counter corporate bond transactions through the Trade Reporting and Compliance Engine (TRACE) and the transactions are disseminated to the public within 15 minutes.1 Initially, the collected trade information was publicly disseminated only for investment grade bonds with issue sizes greater than $1 billion. Grad- ually, the set of bonds subject to transaction dissemination increased and since January 9, 2006 transactions in all non-144A bonds transactions have been immediately disseminated.2 Goldstein and Hotchkiss (2008) provide a

1In the initial phase of TRACE the disseminating times were longer than 15 minutes. Since July 1, 2005 the reporting and dissemination is required to occur within 15 minutes after the trade. 2Rule 144a allows for private resale of certain restricted securities to qualiﬁed institutional buyers. According to TRACE Fact Book 2011, the percent of rule 144A transactions

4 detailed account of the dissemination stages. In the publicly disseminated data the trade size is capped at $5 million in investment grade transactions and $1 million in speculative grade transactions. Only since November 3, 2008, does the publicly available TRACE data indicate whether a transaction is an interdealer transaction or a transaction with a customer and, if a customer transaction, whether the broker-dealer is on the buy or the sell side. This publicly disseminated data is available through Wharton Research Data Services (WRDS) and is used in for example Dick-Nielsen, Feldhütter, and Lando (2012) and Bao, Pan, and Wang (2011). I use this data for the period September 15, 2010-December 31, 2011. Through FINRA it is possible to get access to historical transactions information not previously disseminated. The historical data is richer than the WRDS data in three aspects. First, the data contains all transactions in non-144A bonds since July 2002, so the data set for the first years of TRACE is significantly larger than the WRDS data set. Second, the data has buy/sell indicators for all transactions, not just after October 2008 as in the WRDS data set. Third, trade volumes are not capped. FINRA only provide access to enhanced historical data that is at least 18 months old. I use this data for the period July 1, 2002-September 14, 2010. I obtain bond information from the Mergent Fixed Income Securities Database (FISD) and limit the sample to senior fixed rate or zero coupon bonds. Furthermore, I exclude bonds that are convertible, putable, per- petual, foreign denominated, Yankee, have sinking fund provisions, or have relative to all transactions was 2.0% in investment grade bonds and 8.4% in speculative grade bonds. Also, transactions reported on or through an exchange are not included in TRACE.

5 covenants. I examine bonds maturing within three months and include callable bonds since the call option is unlikely to have any value.3 I use Moody’s rating. If this is not available Standard & Poor’s rating is used and if this is not available Fitch’s rating. I track rating changes on a bond, so the same bond can appear in several rating categories over time. Bonds for which FISD do not provide information are dropped from the sample. Erroneous trades are filtering out as described in Dick-Nielsen (2009) and transactions with a price but no yield are excluded. Furthermore, I exclude bond transactions where the price is above par 100 and yield above 100%. I also exclude transactions with a yield of 99999.9999% or 99999.99%. After filtering the data, the number of transactions in bonds maturing within three months is 214,763. For riskfree rates I use General Collateral (GC) repo rates as suggested by Longstaff (2000) and Covitz and Downing (2007). The repo rate is virtually a default-free rate: when an investor borrows money in the repo market, the investor provides liquid securities as collateral to the counterparty. Standard practice is to overcollateralize the loan and during periods of higher market volatility, dealers typically increase the amount of overcollateralization. The repo market is one of the most active fixed income markets and since repo loans are purely financial contracts, not publicly traded securities, repo rates are less likely to be affected by liquidity factors. Longstaff (2000) provides a more extensive discussion of the repo market. The lender of the collateral is said to be doing a repo whereas the lender of cash is said to be doing a reverse repo. GC repo rates for the terms one day, one week, two weeks, three weeks,

3The percentage of transactions in callable bonds is 6% for both investment grade and speculative grade bonds.

6 one month, two months, and three months are from ICAP, a large and well- known securities broker. The data is collected through Bloomberg. Repo rates on other maturities are found using linear interpolation. ICAP provide both repo and reverse repo rates and the difference can be viewed as the bid- ask spread. I use the average of the repo and reverse repo rate with agency bonds as underlying collateral4. Repo rates are quoted using money market conventions while corporate bond yields are calculated using corporate bond market conventions, so before taking yield spreads I convert repo rates to corresponding bond market yields using the appropriate market conventions. To understand the properties of GC repo rates it is helpful to compare the repo rates with other well-known rates. Figure 1 plots the one-month spreads between LIBOR and GC repo and Treasury and GC repo. We see that the GC repo rate is slightly lower than the LIBOR rate in normal times and significantly lower during the crisis 2007-2009. This is because the LIBOR rate is a rate on unsecured loans between credit-worthy banks and therefore contains some default risk. We also see that the Treasury rate is lower than the GC repo rate and the difference widens during the 2007-2009 crisis. This is consistent with the finding in Feldhütter and Lando (2008) and Krishnamurthy and Vissing-Jorgensen (2010) that Treasury securities contain a specialness premium and Treasury rates are therefore lower than riskfree rates. 4The average of the daily difference between the one-month repo rate and one-month reverse repo rate is 9 basis points. If I use repo rates where MBS securities are underlying collateral the one-month riskless rate is 3 basis points higher. If I use repo rates where Treasury securities are underlying collateral the one-month riskless rate is 9 basis points lower. Repo rates where Treasury securities are collateral will be distorted by the specialness of Treasuries and are therefore less appropriate than repo rates where Agency securities are collateral.

7 3. Results

Merton (1974) developed one of the most widely employed frameworks of credit risk, structural models. The dynamics of the value of a firm is given and corporate bonds are valued as contingent claims on the firm value. A common criticism of standard structural models is that model yield spreads are too low compared to actual spreads. This has given rise to the ”credit spread puzzle”, namely that corporate yield spreads are too high to be explained by the corporate bond issuer’s default risk. The puzzle is supposedly particularly severe for bonds with a short maturity issued by highly rated companies, because structural models predict that the yield spread in this case goes to zero as maturity shortens. For example, Huang and Huang (2003) report an actual yield spread on AAA-rated 4-year bonds of 55 basis points and a model-implied spread of one basis point. Another example is Amato and Remolona (2003) who report an actual 1-3 year AAA spread of 50 basis points while expected losses can only explain 0.1 basis point. The TRACE database allows us for the first time to examine corporate bond spreads at very short maturities and in this section I examine the size of short-term spreads for different rating categories and the time series variation of spreads.

3.1. Size of short-term spreads

Table 1 shows for diﬀerent ratings the median spread in all transactions during the sample in bonds maturing within three months. The table shows spreads in transactions where an investor sells to a dealer, an investor buys from a dealer, and where all transactions are used. Furthermore, we see

8 median spreads for different trade sizes. If we include all transactions, the spread in Table 1 is 26 bps for AAA, 79 bps for AA, and 149 bps for A. These numbers are broadly in line with reported 4-year spreads in Huang and Huang (2003) and 1-3 year spreads in Amato and Remolona (2003). These papers find that bond spreads are too large to be explained by credit risk alone, so finding similar spreads as in these two papers suggest that there is a credit spread puzzle if we look at all trades. However, when we look at only large trades - typically transactions by institutional investors - spreads become much smaller. For example, if we restrict the sample to transactions of $1 million or more, the spread for AA-rated bonds is only 14 bps compared to 79 bps when all trades are used. The decrease in yield spreads as trade size increases can be explained by higher bargaining power of institutional investors relative to retail investors (Feldhütter (2012)). Surprisingly, the spread is -1 bps for AAA-rated bonds. So for institutional investors there is no credit spread puzzle where it is thought to be most severe - at short maturities for highly rated companies. The yield spread curve is the curve of bond yield spreads as a function of maturity. The slope of this curve - particularly for speculative grade bonds - has been examined in several papers but no consensus has emerged. For example, Sarig and Warga (1989b) look at spread curves for different rating classes and find that the slope of the yield spread curve for speculative grade issuers is negative. In contrast, Helwege and Turner (1999) argue that among firms with the same credit rating the safer ones tend to issue longer- dated bonds. They control for this selection bias by looking at bonds with different maturities issued by the same firm and find that spread curves for

9 speculative grade issuers are upward-sloping. The data in this paper is well- suited to examine this question because we can follow the same bond from three-months to maturity until it matures. Looking at the same bond at different time points allows a clean view of the slope at short maturities. Within a rating category, I estimate a yield spread curve for bonds maturing within the next three months based on transactions in the sample period. For investment grade bonds transactions with a volume of at least $1million is used while for speculative grade bonds all transactions are used. I use the model of Nelson and Siegel (1987) to estimate the curve. To make estimation robust to outliers, I use quantile regression and minimize absolute errors. As Koenker and Hallock (2001) explain, the method of least absolute errors estimates the conditional median of the response variable given certain values of the predictor variables, while ordinary least squares estimates the conditional mean. Figure 2 shows the estimated yield spread curves. The graph on the left shows that for highly-rated issuers, the spread curve is flat or slightly downward-sloping. For AA- and A-rated bonds the spread curve does not go to zero. This is inconsistent with standard structural models such as Merton (1974)’s model, but is in line with investors having incomplete accounting information as in Duffie and Lando (2001). The graph on the right side shows for bonds rated BBB or below the spread curves (note the logarithmic y-axis). For BBB-rated bonds the spread curve is flat, while for speculative-grade bonds it is downward-sloping and increasingly so as we move down from BB to C. Thus, spread curves for speculative-grade bonds are clearly downward-sloping at very short maturities. The sample period includes the subprime crisis which saw massive widen-

10 ings in corporate bond spreads. It is therefore interesting to examine the time series variation in short-term spreads. Figure 3 plots for transactions with volume $1 million or more the quarterly median bond spread for AAA, AA, and A along with the actual transactions. The spread curve for AAA is incomplete because there are periods in 2009-2010 where there were no transactions in short-term AAA-rated bonds. In the ﬁgures the y-axis is set such that we cannot see what happens in the subprime crisis, but later we will focus on this period. There are four distinct periods. Focusing on AAA- rated yield spreads we see that spreads are quite stable at around 10 basis in the early part of the sample period, 2002Q3-2005Q2. In 2005Q3-2007Q2 AAA-rated spreads decrease and the average is close to zero. The end of 2006 sees particularly low spreads and in this period spreads on AA- and A-rated bonds are also slightly below zero. The subprime crisis, 2007Q3-2009Q2, saw a dramatic widening of spreads, but in 2009Q3-2011Q4 spreads are back to the levels their had before the crisis. Table 2 shows the median spread for all rating categories in the four periods. To examine short-term spreads for credit-worthy ﬁrms at a higher frequency than quarterly, I pool bonds with a rating of AAA, AA, or A maturing within three months and calculate on a monthly basis the median yield spread. This time series represents the (almost) instantaneous bond spread of high-quality corporations and Figure 4 plots the result. We see three spikes in the spread: A spike of 272 basis points when Bear Sterns is taken over in March 2008, a spike of 670 basis points in October 2008 following the default of Lehman Brothers, and a spike of 272 basis points in March 2009 when the stock market lost more than 30% in value in three months.

11 Are the spikes in short-term corporate bond spreads during the crisis unique to the corporate bond market or do they reflect disruptions present in other markets as well? Since most of the transactions are in bonds issued by financial institutions, the relevant comparison is short-term debt of financials in other markets. The LIBOR rate reflects unsecured loans between banks and the one-month LIBOR-GC repo spread is shown in the graph. The commercial paper market is another market for unsecured short- term debt and the graph also shows the one-month financial commercial paper-GC repo spread. We see that the corporate bond market reacts much stronger to crises than the LIBOR and commercial paper market. Following the Lehman Brothers’ default for example, bond spreads jumped to 670 basis points compared to a jump in the one-month LIBOR spread of 213 basis points and a jump in the one-month financial commercial paper spread of 111 basis points. In addition, the corporate bond market shows a significant reaction to the decrease in stock markets in the first months of 2009, while there is almost no reaction in the two other markets. This was a period where there was strong selling pressure in the US corporate bond market as shown in Feldhütter (2012) and the graph suggests that this selling pressure was not apparent in the LIBOR and commercial paper markets.

3.2. Determinants of short-term spreads

I next explore the extent to which credit risk or liquidity risk drives the variation in short corporate bond spreads. I regress the time series of the quarterly median short-term spread of bonds rated AAA, AA, or A on time series of credit risk and liquidity proxies. The spread series is the same as

12 the one in Figure 4 except that the time series is on a quarterly basis instead of monthly basis. In standard structural models, the key drivers of credit spreads are asset volatility and leverage. As a proxy for asset volatility the CBOE VIX index is used and quarterly values are calculated by taking the median of daily values. Leverage ratio is proxied by the aggregate debt/equity ratio of nonfinancial firms extracted from the Federal Reserve’s Flow of Funds Accounts.5 Several liquidity proxies for corporate bonds has been suggested in the literature, and Dick-Nielsen, Feldhütter, and Lando (2012) examine a number of them. They find that a linear combination of four liquidity proxies outperforms commonly used liquidity measures in terms of capturing the variation in spreads while controlling for credit risk. The number of observations in this paper does not allow me to calculate their measure in all quarters, but they show that one of the four liquidity proxies used in their measure, Feldhütter (2012)’s imputed roundtrip costs, does almost as well as the linear combination in capturing variation in spreads. The data set in this paper has buy/sell indicators for all transactions and this allows me to refine the imputed roundtrip cost measure. More specifically, if there in a given bond on a given day is at least one transaction where an investor buys from a dealer and one transaction where an investor sells to a dealer, I define a roundtrip to be the average buy price minus the average sell price. If the roundtrip is zero I discard it. The roundtrip is in dollars pr $100 par value and has the obvious interpretation as the transaction costs occurred when

5The debt/equity ratio is found in line 37 in Table B.102 at http://federalreserve.gov/releases/z1/current/z1.pdf. Quarterly data can be down- loaded via http://www.federalreserve.gov/datadownload/Choose.aspx?rel=Z.1.

13 buying and subsequently selling a bond. The measure is used in Chakravarty and Sarkar (2003) and is closely related to measures in Green, Hollifield, and Schürhoff (2007), Biais and Green (2007), and Goldstein, Hotchkiss, and Sirri (2007). To get a quarterly time series, I calculate the median roundtrip each quarter. Panel A in Table 3 shows the regression of the AAA-A yield spread on VIX, leverage ratio, and the roundtrip cost measure. Both VIX and leverage ratio are significant in univariate regressions and combined the two credit risk proxies explain 61% of the variation in spreads. Strikingly, the roundtrip measure alone explains 96% of the variation in spreads, and VIX and leverage ratio have no additional explanatory power when included alongside roundtrip costs. This result implies that the major driver of short-term corporate bond yield spreads is liquidity while credit risk plays little or no role. The top graph in Figure 5 shows the quarterly spread and roundtrip costs and the graph confirms that yield spreads and roundtrip costs move closely together. Is an R2 of 96% too good to be true? A potential explanation might be that if bid-ask spreads widen, investor sell prices are affected more than investor buy prices, and this causes a ”mechanical” relation between midprices and yield spreads. If this is the case, the relation between investor buy prices and yield spreads would be weak. Panel D in Table 3 shows that using only investor buy prices to calculate yield spreads still yields an R2 of 94%, so this potential explanation is not causing the high R2. Another potential concern is that many transactions are used both in calculating roundtrip costs and yield spreads. However, interdealer transactions are not used in calculating

14 roundtrip costs, and if only these transactions are used in calculating yield spreads, the R2 is still 92% as Panel C shows. Furthermore, if roundtrip costs are calculated using bonds rated AAA, AA, or A with a maturity between three months and one year, the R2 is still 89%. If the regression is done on a monthly basis the R2 drops to 79%, but as the bottom graph in Figure 5 shows the two time series still show the same pattern but with more noise in the roundtrip cost series. Overall, the high explanatory power of roundtrip costs in a regression of yield spreads on the left-hand side is a robust result. To get a more refined picture of the relative contributions of credit risk and liquidity to the variation in spreads, I repeat the previous regression for each rating category. The results become more imprecise for particularly the AAA rating category because there are some quarters where it is not possible to calculate the roundtrip measure. Table 4 shows the results. Bearing in mind that the results for AAA are more imprecise, the table shows that the explanatory power of roundtrip costs are very high for AAA-, AA-, and A-rated bonds. As we move down in rating, the R2’s of roundtrip costs decrease and for speculative grade bonds, there is no explanatory power. For investment grade bonds, VIX and leverage ratio are significant in univariate regressions, but become insignificant when roundtrip costs are included (except for AAA-rated bonds where leverage ratio is significant at 5% level). This evidence confirms that short-term spreads of highly rated issuers are primarily driven by illiquidity. Table 4 also shows that the explanatory power of VIX, leverage ratio, and roundtrip costs are low for speculative grade bonds. It is surprising that VIX and leverage ratio are insignificant since one would expect credit risk

15 to become an important driver of spreads for credit-risky bonds. However, trading activity in speculative bonds is to a certain extent concentrated in firms close to default. For example, the largest quarterly median spread in speculative grade bonds occurs in the fourth quarter of 2009 with a median spread of 912%. This is due to large trading activity in two CIT Group bonds shortly before November 1, 2009 where CIT Group defaulted. The bonds traded around $70 - likely close to the expected recovery value - which translates into very high short-term yields. The economy-wide proxies for credit risk do not pick firm-specific events like these up.

3.3. AAA-rated corporate bonds since 2010

If we look at the top graph in Figure 3, we see that since the second half of 2010, the pattern in AAA-rated spreads is diﬀerent from the patterns in lower rating classes. AAA-rated spreads are consistently negative and in the second half of 2011 the median spread has dropped to -10 basis points. In contrast, AA- and A-rated spreads are increasing in this period. The negative AAA-spreads are accompanied by a large trading activity: during the last six quarters there are 1,094 transactions with a volume of 1$ million or more in AAA-rated short-term bonds and this is 46% of all transactions with a volume of 1$ million or more in the sample period 2002-2011. Figure 7 shows the yields - not yield spreads - in short-term AAA-bond transactions. We see that by the end of 2011, AAA-rated bonds were mostly trading at yields between 0 and 10 basis points. It is useful to look at roundtrip costs for AAA-rated securities in order to understand their low yields in the last years of the sample. Since there are

16 periods in 2009 and 2010 where there are no transactions in AAA-rated bonds maturing within three months, we cannot define a time series of roundtrips based on those bonds only. However, correlations between roundtrip costs based on AAA-A rated bonds with different maturities are quite high. The quarterly time series of roundtrip costs based on bonds maturing 0-3m and the time series based on bonds with a maturity 3m-1y is 93%, while the correlation of roundtrip costs based on bonds maturing 0-3m and based on bonds with maturity 1-3y is 73%. I therefore define quarterly time series of roundtrip costs separately for AAA-, AA-, and A-rated bonds, where the maturity of the bonds are lower than three years. The three time series are shown in Figure 6. We see that until the end of 2008, bonds in the three rating classes had similar liquidity properties. Beginning in the final quarter of 2008, roundtrips of AAA-rated bonds show a much sharper drop than roundtrips of AA- and A-rated bonds. In the second half of 2011 we see a further drop in the roundtrip costs of AAA-rated bonds and a sharp increase in the costs of AA- and A-rated bonds. How large are transaction costs of AAA-rated corporate bonds relative to US Treasuries by the end of 2011? The median roundtrip cost was $ 0.0091 in the third quarter 2011 and $ 0.0052 in the fourth quarter 2011. So in the final quarter of 2011 it cost around $520 for institutional investors to buy and sell a AAA-rated bond with a par value of $10 million. Fleming (2003) calculates median bid-ask spreads to be $ 0.0063 in a two-year treasury note for the period 1996-2000. This size of Treasury bid-ask spreads is similar to AAA-rated bonds’ roundtrip costs in the last two quarters 6. In contrast,

6Fleming (2003) reports that the median bid-ask spread of a two-year treasury note is 0.20 32nds of a point, where one point equals 1 percent of par. This implies that the

17 median roundtrip costs for AA-rated bonds in the final quarter of 2011 was 0.096, more than ten times the roundtrip costs in Treasuries and AAA-rated bonds. Overall, the evidence for AAA-rated short-term bonds in 2010-2011 is that spreads were negative, trading frequency was high relative to previous periods, and transaction costs were low and comparable to that in the Trea- sury market. This all suggests that there is now a specialness premium at- tached to short-term AAA-rated bonds similar to the premium in Treasuries documented in for example Feldhütter and Lando (2008) and Krishnamurthy and Vissing-Jorgensen (2010). There are several explanations for the negative spreads in AAA-rated bonds. Sometimes AAA-rated bonds are used for shorting interest rate risk instead of treasuries because they are cheaper to borrow (Asquith, Au, Covert, and Pathak (2011)). Also, Standard & Poor’s downgraded the US from AAA to AA+ in August 2011. Likely, this has led some institutional investors required to hold AAA-rated securities to buy AAA-rated corporate bonds. Furthermore, some portfolio managers are required to have a minimum average rating of their managed portfolio, and in response to the downgrade of the U.S. they might be selling off lower-rated corporate bonds and buying AAA-rated bonds in order to keep their average debt rating un- changed. Consistent with this AA- and A-rated bond spreads go up and AAA-rated bond spreads go down during this period. ∗ 1 bid-ask spread in terms of dollars relative to a par value of $100 is 0.20 32 = 0.0063.

18 4. Conclusion

In this paper I empirically document a number of facts about very short-term corporate bond spreads. First, yield spreads on highly-rated bonds are close to zero in normal periods. Second, the slope of yield spreads as a function of maturity is zero or slightly positive for investment-grade bonds and negative for speculative-grade bonds. Third, corporate bond yield spreads peak much more during the 2007-2009 crisis than spreads in the LIBOR and commercial paper markets that are otherwise comparable in terms of default risk. I also ﬁnd that a measure of roundtrip costs explains practically all the time series variation in yield spreads of highly-rated bonds. Together, this suggests that illiquidity is far more important than credit risk in explaining short- term corporate bond spreads. The illiquidity component in yield spreads is insigniﬁcant in normal periods but highly important in crisis periods. Finally, AAA-rated short-term bonds have commanded a specialness premium since 2010: yield spreads are negative, transaction costs are low and comparable to the Treasury market, and trading activity is high.

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23 all ≥ 100, 000 ≥ 1M ≥ 5M spread N spread N spread N spread N AAA sell 67 7177 9 2585 −1 1048 −2 321 all 26 17560 5 5886 −1 2395 −2 787 buy 2 5522 1 2138 −2 999 −2 358 AA sell 160 13788 35 3913 17 1239 14 267 all 79 35915 25 9190 14 2928 12 602 buy 26 11216 15 3542 11 1299 10 252 A sell 279 28123 79 6401 34 2023 28 464 all 149 78766 59 16632 29 4835 27 1026 buy 67 25968 30 6293 22 2075 22 447 BBB sell 501 7993 321 1512 166 530 205 189 all 505 26848 320 4386 148 1327 234 392 buy 259 9157 120 1615 90 592 180 166 BB sell 526 7175 604 633 4149 219 475 25 all 374 18398 657 1731 4594 599 381 60 buy 223 5062 505 530 4010 230 109 25 B sell 812 4708 545 423 375 94 432 14 all 594 14841 407 1244 362 226 378 30 buy 409 3710 294 356 351 77 371 11 C sell 18989 6322 23737 695 27414 235 27349 59 all 11883 22435 22087 2416 27008 583 26657 129 buy 6153 5543 19320 591 30803 200 30196 55

Table 1 Median short-term yield spreads in basis points. This table shows median yield spreads in basis points for diﬀerent ratings and trade sizes. The yield spreads are for transactions in bonds with a remaining maturity less than three months. The yield spread is deﬁned as the bond yield minus the General Collateral repo rate at the same maturity as the bond. N is the number of observations. The data set includes US corporate bond transactions from TRACE in the period July 1, 2002 to December 31, 2011.

24 2002Q3-2005Q2 2005Q3 − 2007Q2 2007Q3 − 2009Q2 2009Q3 − 2011Q4 spread N spread N spread N spread N AAA sell 10 159 4 253 68 138 −4 498 all 9 373 1 565 51 355 −3 1102 buy 7 190 −3 217 34 150 −4 442 AA sell 14 324 8 335 78 245 20 335 all 12 733 4 801 68 549 16 845 buy 10 343 2 359 55 225 13 372 A sell 27 561 14 489 283 479 33 494 all 21 1228 11 1126 232 1216 29 1265 buy 16 563 10 499 137 490 24 523 BBB sell 60 191 27 64 1032 187 192 88 all 49 469 22 145 1044 493 176 220 buy 41 238 16 72 1040 203 107 79 BB sell 713 372 454 4642 576 1759 733 402 all 642 719 308 11297 542 5079 548 1303 buy 379 216 167 3124 376 1431 275 291 B sell 730 356 304 966 1247 1759 856 1627 all 614 724 200 2236 977 5964 565 5917 buy 434 219 77 479 632 1619 388 1393 C sell 1346 108 564 2 9048 2279 44636 3933 all 1874 227 130 3 5842 8872 25825 13332 buy 755 46 76 1 3763 2507 19154 2988

Table 2 Median short-term yield spreads in basis points. This table shows median yield spreads in basis points for diﬀerent ratings and time periods. The yield spreads are for transactions in bonds with a remaining maturity less than three months. The yield spread is deﬁned as the bond yield minus the General Collateral repo rate at the same maturity as the bond. For investment grade bonds (rated AAA, AA, A, or BBB) transactions with a size of $1M or more are used, while for speculative grade bonds (rated BB, B, or C) all transactions are used. N is the number of observations. The data set includes US corporate bond transactions from TRACE in the period July 1, 2002 to December 31, 2011.

25 Panel A: All transactions used in the yield spread calculation Constant −1.33∗ −2.89∗ −0.11∗∗∗ 0.33 −0.14 (0.55) (1.28) (0.03) (0.94) (0.37) VIX 0.0847∗∗ 0.1295∗ −0.0045 (0.0293) (0.0555) (0.0121) Leverage ratio 0.0654∗ −0.0507 0.0023 (0.0272) (0.0387) (0.0115) Roundtrip 25.63∗∗∗ 26.14∗∗∗ (0.63) (1.14) R2 57% 33% 96% 61% 96% Panel B: Only investor sell transactions used in yield spread calculation Constant −1.51∗ −3.44∗ −0.10∗ 0.00 −0.55 (0.60) (1.42) (0.04) (1.09) (0.35) VIX 0.0977∗∗ 0.1385∗ −0.0180 (0.0321) (0.0633) (0.0134) Leverage ratio 0.0780∗ −0.0461 0.0157 (0.0300) (0.0445) (0.0114) Roundtrip 29.41∗∗∗ 30.52∗∗∗ (0.52) (1.18) R2 57% 36% 95% 60% 96% Panel C: Only interdealer transactions used in yield spread calculation Constant −1.37∗∗ −3.17∗ −0.00 0.19 −0.27 (0.48) (1.22) (0.05) (0.94) (0.40) VIX 0.0932∗∗∗ 0.1354∗∗ 0.0037 (0.0255) (0.0468) (0.0158) Leverage ratio 0.0736∗∗ −0.0478 0.0043 (0.0259) (0.0349) (0.0130) Roundtrip 26.96∗∗∗ 25.68∗∗∗ (1.42) (2.08) R2 60% 37% 92% 63% 92% Panel D: Only investor buy transactions used in yield spread calculation Constant −0.97∗ −2.06∗ −0.08∗∗ 0.42 0.08 (0.42) (0.98) (0.03) (0.70) (0.33) VIX 0.0622∗∗ 0.0999∗ 0.0020 (0.0224) (0.0414) (0.0107) Leverage ratio 0.0469∗ −0.0427 −0.0040 (0.0207) (0.0288) (0.0103) Roundtrip 18.92∗∗∗ 19.10∗∗∗ (0.67) (1.04) R2 56% 31% 94% 61% 94%

Table 3 Regression of short-term AAA-A yield spreads on credit risk and liquidity proxies. For bonds rated AAA, AA, or A this table shows the quarterly median yield spread in basis points regressed on VIX, leverage ratio, and roundtrip cost. The quarterly value of VIX is the median daily value. The quarterly value of leverage ratio is the debt-equity ratio of nonfinancial corporate firms extracted from the Federal Reserve’s Flow of Funds Accounts. A roundtrip is the average investor buy price minus the average investor sell price in a given bond on a given day. The yield spreads and roundtrip costs are based on transactions in bonds with a remaining maturity less than three months. The yield spread is defined as the bond yield minus the General Collateral repo rate at the same maturity as the bond. In Panel A all transactions are used in the calculation of the yield spread, while in Panel B-D only investor sells, interdealer trades, or investor buys are used. Transactions with a size of $1M or more are used and the number of observations in each regression is 38. Standard errors are corrected for heteroscedasticity according to White (1980) and ’*’, ’**’, ’***’ indicate statistical significance at the 5%, 1%, 0.1% level. The data set includes US corporate bond transactions from TRACE in the period July 1, 2002 to December 31, 2011. 26 Panel A: AAA-rated bonds (33 observations) Constant −0.64 −2.12∗∗ −0.00 −2.81∗ −1.37∗ (0.34) (0.74) (0.05) (1.08) (0.57) VIX 0.0443∗ −0.0340 −0.0135 (0.0203) (0.0291) (0.0125) Leverage ratio 0.0473∗∗ 0.0746∗ 0.0335∗ (0.0158) (0.0319) (0.0151) Roundtrip 13.23∗∗∗ 10.41∗∗∗ (2.32) (1.29) R2 30% 45% 71% 48% 78% Panel B: AA-rated bonds (38 observations) Constant −1.76 −3.16 −0.38∗∗∗ 1.79 0.86 (0.92) (1.99) (0.09) (1.41) (0.68) VIX 0.1037∗ 0.1994∗ 0.0351 (0.0486) (0.0861) (0.0206) Leverage ratio 0.0704 −0.1084 −0.0378 (0.0422) (0.0595) (0.0205) Roundtrip 36.25∗∗∗ 34.87∗∗∗ (4.67) (4.05) R2 49% 22% 90% 61% 92% Panel C: A-rated bonds (38 observations) Constant −1.32∗∗ −3.15∗∗ 0.06 0.31 −0.83 (0.40) (1.12) (0.07) (0.81) (0.77) VIX 0.0951∗∗∗ 0.1390∗∗∗ 0.0229 (0.0213) (0.0361) (0.0287) Leverage ratio 0.0749∗∗ −0.0497 0.0103 (0.0238) (0.0285) (0.0229) Roundtrip 24.17∗∗∗ 19.01∗∗∗ (1.09) (3.33) R2 65% 39% 81% 68% 84% Panel D: BBB-rated bonds (38 observations) Constant −6.00 −25.95∗ −1.24 −27.11 −0.07 (3.86) (11.07) (1.01) (17.57) (15.72) VIX 0.5232∗ −0.0468 −0.0012 (0.2146) (0.3372) (0.2904) Leverage ratio 0.6032∗ 0.6452 −0.0249 (0.2339) (0.4885) (0.3901) Roundtrip 59.52∗∗ 60.75∗ (17.03) (26.89) R2 18% 23% 50% 23% 50% Panel E: Speculative grade bonds (36 observations) Constant 33.61 −70.75 24.17 −224.34 −329.70 (32.41) (62.86) (24.05) (146.03) (173.19) VIX 0.7439 −6.1768 −15.8094 (1.0215) (4.1178) (10.5674) Leverage ratio 2.3178 7.8573 12.7162 (1.4948) (4.8870) (7.4098) Roundtrip 170.42 446.37 (165.21) (308.59) R2 0% 2% 3% 5% 16%

Table 4 Rating-specific regression of short-term yield spreads on credit risk and liquidity proxies. For bonds rated AAA Panel A in this table shows the quarterly median yield spread in basis points regressed on VIX, leverage ratio, and roundtrip cost. The quarterly value of VIX is the median daily value. The quarterly value of leverage ratio is the debt- equity ratio of nonfinancial corporate firms extracted from the Federal Reserve’s Flow of Funds Accounts. Panel B-E shows the same regression for lower-rated bonds. A roundtrip is the average investor buy price minus the average investor sell price in a given bond on a given day. Both yield spreads and roundtrip27 costs are based on transactions in bonds with a remaining maturity less than three months. The yield spread is defined as the bond yield minus the General Collateral repo rate at the same maturity as the bond. Transactions with a size of $1M or more are used. Standard errors are corrected for heteroscedasticity according to White (1980) and ’*’, ’**’, ’***’ indicate statistical significance at the 5%, 1%, 0.1% level. The data set includes US corporate bond transactions from TRACE in the period July 1, 2002 to December 31, 2011.

300 1−month LIBOR−GC repo spread 1−month Treasury−GC repo spread

250

200

150

100

50 basis points 0

−50

−100

−150

−200

Jan03 Jan04 Jan05 Jan06 Jan07 Jan08 Jan09 Jan10 Jan11 Jan12

Fig. 1 One-month LIBOR and Treasury spread to GC repo. The graph shows the daily spread between one-month LIBOR and GC repo and the daily spread between one-month Treasury and GC repo. LIBOR rates are from Bloomberg, Treasury rates are CMT rates from the Federal Reserve, and GC repo rates are from ICAP.

28 6 40 10 AAA BBB AA BB 35 A B C

5 10

4 15 10

10 yield spread in basis points yield spread in basis points

3 10

−5

2 −10 10 0.05 0.1 0.15 0.2 0.25 0.05 0.1 0.15 0.2 0.25 maturity maturity

Fig. 2 Slope of short-term yield spreads. For each rating class a Nelson-Siegel curve is ﬁtted to yield spread observations using quantile regression. The graphs for the investment grade ratings AAA, AA, A, and BBB are based on transactions with a volume of $1million or higher, while the graphs for the speculative grade ratings BB, B, and C are based on all transactions. Note that the y-axis on the right graph is logarithmic. The data set includes US corporate bond transactions from TRACE in the period July 1, 2002 to December 31, 2011.

29 AAA 80

20 basis points 0

−20 2003 2004 2005 2006 2007 2008 2009 2010 2011

AA 80

20 basis points 0

−20 2003 2004 2005 2006 2007 2008 2009 2010 2011

A 80

20 basis points 0

−20 2003 2004 2005 2006 2007 2008 2009 2010 2011

Fig. 3 Short-term yield spreads for bonds rated AAA, AA, and A. The thick line in the top graph shows the median yield spread on a quarterly basis for transactions in AAA-rated bonds maturing within three months. The dots in the graph are the actual observations the median yield spreads are based on. The middle graph shows the same graph for AA-rated bonds while the bottom graph is for A-rated bonds. The graphs are based on transactions with a volume of $1M or higher. The data set includes US corporate bond transactions from TRACE in the period July 1, 2002 to December 31, 2011.

30 700 Short AAA/AA/A corporate bond spread 1−month LIBOR spread 1−month financial commercial paper spread 600

500

400

300 basis points

200

100

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Fig. 4 Short-term yield spreads for high-grade issuers. This graph shows the monthly median yield spread of bonds with a maturity less than three months and rated AAA, AA, or A. The yield spreads are based on transactions with a volume of $1M or higher. The graph also shows the one-month LIBOR and ﬁnancial commercial paper spread. All spreads are relative to GC repo. The data set includes US corporate bond transactions from TRACE in the period July 1, 2002 to December 31, 2011.

31 Quarterly spread and roundtrip costs for short AAA−, AA−, and A−rated bonds 600 0.2398 Spread in basis points (LHS) Roundtrip costs (RHS) 500 0.2007

400 0.1616

300 0.1225

200 0.0834

100 0.0443

0 0.0052 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Monthly spread and roundtrip costs for short AAA−, AA−, and A−rated bonds

Spread in basis points (LHS) 600 0.2888 Roundtrip costs (RHS) 500 0.241

400 0.1932

300 0.1454

200 0.0977

100 0.0499

0 0.0021

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Fig. 5 Short-term yield spreads and roundtrip costs for high-grade issuers. The top ﬁgure shows the quarterly median yield spread and roundtrip costs of bonds with a maturity less than three months and rated AAA, AA, or A. The yield spreads and roundtrip costs are based on transactions with a volume of $1M or higher. The bottom ﬁgure shows the monthly median yield spread and roundtrip costs of the same bonds. Spreads are in basis points and relative to GC repo. Roundtrip costs are in dollars for a bond with par calue of $ 100. The data set includes US corporate bond transactions from TRACE in the period July 1, 2002 to December 31, 2011.

0.5 AAA−rated bonds AA−rated bonds A−rated bonds 0.45

0.4

0.35

0.3

0.25

0.2 Roundtrip cost in dollars

0.15

0.1

0.05

0 2003 2004 2005 2006 2007 2008 2009 2010 2011

Fig. 6 Roundtrip costs for bonds rated AAA, AA, and A. The thick line in the graph shows median roundtrip costs on a quarterly basis for transactions in AAA-rated bonds maturing within three years. The two other lines are for AA- and A-rated bonds. A roundtrip is the average investor buy price minus the average investor sell price for transactions with a volume of $1M or more in a given bond on a given day. A roundtrip of for example 0.1 means that the diﬀerence between the buy and sell price is $0.1 in a bond with a par value of $100. The data set includes US corporate bond transactions from TRACE in the period July 1, 2002 to December 31, 2011.

33 50

25 basis points 20

0 Jul10 Oct10 Jan11 Apr11 Jul11 Oct11 Jan12

Fig. 7 Yields on transactions in AAA-rated bonds with a maturity less than three months. This graph shows for the period July 2010-December 2011 transactions with a volume of $1M or more in AAA-rated corporate bonds with a maturity of less than three months. The transactions are US corporate bond transactions from TRACE.