bond lending and bond returns

Bond Lending and Bond Returns∗

Mike Anderson† Securities and Exchange Commission

Brian J. Henderson‡ The George Washington University

Neil D. Pearson§ University of Illinois at Urbana-Champaign

July 2, 2018

Abstract Existing literature finds that proxies for short-sale constraints do not predict bond returns. Using more comprehensive data over a longer sample period and rating and maturity-matched benchmarks we find that utilization, which proxies for short-sale constraints, predicts negative returns. Many lending fees are negative or low, suggesting many bond loans are financing transactions. The bonds with both high lending fees and high utilization, for which lending is likely associated with short sales and constraints are likely to be binding, display large negative excess returns. These results are robust to controlling for bond characteristics and information from the equity lending market.

∗

We thank Gergana Jostova, Jack Bao, seminar participants at Seoul National University, and staff of the Securities and Exchange Commission’s Division of Economic and Risk Analysis for helpful comments. The Securities and Exchange Commission disclaims responsibility for any private publication or statement of any SEC employee or Commissioner. This article expresses the authors’ views and does not necessarily reflect those of the Commission, the Commissioners, or other members of the SEC staff. † E-mail: [email protected]. Securities and Exchange Commission, 100 F Street, NE, Washington, DC 20549, Phone: (202) 551-4885 and George Mason University School of Business ‡ E-mail: [email protected]. The George Washington University, Department of Finance, Funger Hall Suite #502, 2201 G Street NW, Washington DC 20052. Phone: (202) 994-3669. § E-mail: [email protected]. University of Illinois at Urbana-Champaign, Champaign, IL 61820. Phone: (217) 244-0490.

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Introduction

Theoretical literature argues that short sale constraints restrict investors’ ability to trade based on negative information, resulting in slow incorporation of negative information into securities’ prices and low or negative future returns.1 Empirical research finds that proxies for short-sale constraints including lending fees and utilization predict negative abnormal returns, consistent with short sale constraints causing slow incorporation of negative information into securities prices.2 To date, most studies have focused on equity lending and short sales. However, in a recent paper Asquith, Au, Covert, and Pathak (2013) use proprietary data from a large securities lender to provide a first look at the market for lending and borrowing corporate bonds. Among their many results, and in contrast to both theoretical predictions and the empirical evidence on equity short selling, they find that utilization and lending fees do not predict bond returns. This result is puzzling and worth revisiting. One possibility is that the common assumption that securities loans are for the purpose of short selling does not apply to all bond loans, implying that utilization may not be a good proxy for bond short sale constraints. Another reason to revisit the previous findings is that there have been potentially important changes to the bond market after the end of the Asquith, Au, Covert, and Pathak (2013) sample period. For example, hedge fund fixed income assets under management more than tripled from 2006 to 2016, suggesting increased demand to short-sell bonds.3 Mutual fund (including ETF) holdings of corporate and foreign bonds increased from about 7% to almost 18% of the total amount of corporate and foreign bonds held in the U.S. (Adrian, Fleming, Shachar, and Vogt 2017, Figure 7). On the other hand, dealer inventories of corporate bonds declined dramatically from 2008 to 2016 (Adrian, Fleming, Shachar, and Vogt 2017, Figure 8). Mutual funds, ETFs, and dealer inventories are sources of lent bonds, so these changes in holdings suggest the possibility of changes in the supply of bonds available to be borrowed. Activity in single-name CDS also declined following the financial crisis, suggesting that some short positions that otherwise would have been 1

See Rubinstein (2004) for a review of the literature. Recent papers include Saffi and Vergara-Alert (2016), Muravyev, Pearson, and Pollet (2017), Engelberg, Reed, and Ringgenberg (2017), and Henderson, Jostova, and Philipov (2017). Older papers include Desai, Ramesh, Thiagarajan, and Balachandran (2002), Jones and Lamont (2002), Ofek, Richardson, and Whitelaw (2004), Asquith, Pathak, and Ritter (2005), Boehme, Danielsen, and Sorescu (2006), Cohen, Diether, and Malloy (2007), Diether, Lee, and Werner (2009) Boehmer, Huszar, and Jordan (2010), Saffi and Sigurdsson (2011), Engelberg, Reed, and Ringgenberg (2012), and Drechsler and Drechsler (2016). Another literature relates returns to the current level of short interest, for example Seneca (1967), MacDonald and Baron (1973), Figlewski (1981), Brent, Morse, and Stice (1990), Figlewski and Webb (1993), Asquith and Meulbroek (1996), Safieddine and Wilhelm (1996) Danielson and Sorescu (2001), and Dechow, Hutton, Meulbroek, and Sloan (2001). 3 The data underlying this claim are available at: https://www.barclayhedge.com/research/indices/ghs/mum/Fixed˙Income.html. 2

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established via CDS might instead be established in the bond market. Using a more comprehensive data set of bond loans covering a longer sample period, together with three extensions of the earlier analysis, we find that proxies for short-sale constraints predict negative abnormal returns, consistent with both theory and prior research on equities. Utilization predicts excess returns (relative to aggregate bond market benchmarks) of high-yield industrial bonds over a three-month horizon. When we compute abnormal returns relative to rating- and maturity-matched benchmarks the evidence for high-yield bonds becomes stronger, and we also find that utilization predicts three-month excess returns in the full sample of all corporate bonds. In the subset of bonds with both high lending fees and high utilization, which are the bonds for which short-sale constraints are most likely to bind, the negative abnormal returns are large and also appear at the one-month horizon. We continue to find negative abnormal returns on these bonds when we control for bond characteristics and information from the equity lending market using Fama-Macbeth regressions. The bond lending data we use cover the period from July 2006 through March 2015, inclusive, a total of eight and three-quarters years. They are from the Markit Securities Finance database, which Markit indicates covers about 85% of securities lending activity. In contrast, Asquith, Au, Covert, and Pathak (2013) use proprietary data from a single bond lender over the four-year period from January 2004 through December 2007. They assume their lender’s share of the bond lending market equals its share of the equity lending market, which Asquith, Au, and Pathak (2006) estimate to be 16.7%. Most of our data are from after the financial crisis, making it likely that our results also apply to the current (post-financial crisis) bond market. The three extensions we make to the Asquith, Au, Covert, and Pathak (2013) analysis, and the results we obtain from them, are as follows. First, we focus on a three-month return horizon and find that utilization predicts the abnormal returns of high-yield industrial bonds over that horizon. This differs from the insignificant results over the one-month horizon reported in Asquith, Au, Covert, and Pathak (2013).4 We focus on the three-month horizon because the lower trading frequency and liquidity in bonds as compared to equities suggests that information is incorporated into bond prices more slowly than into equity prices, suggesting that researchers should examine returns over horizons longer than the one-month horizon used in most empirical research on short selling. 4

Appendix B uses our data to replicate the findings in Asquith, Au, Covert, and Pathak (2013) that utilization and lending fees do not predict one-month abnormal returns computed relative to the aggregate bond market benchmarks they use. Asquith, Au, Covert, and Pathak (2013) do not present results for the three-month horizon, but do briefly indicate that untabulated results for the three-month horizon are similar to their one-month results.

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Second, we use refined benchmarks that explicitly account for credit and interest rate risk to provide a more precise view of abnormal returns than the aggregate benchmarks that reflect the entire bond market. Using these rating and maturity-matched benchmarks we find that utilization is significantly related to three-month returns in the full sample of all corporate bonds and a subsample of high-yield industrial bonds. We also find that bond lending fees are often negative. These negative lending fees at first glance might seem surprising because they imply that the bond lender pays the bond borrower a rebate (interest rate) on the cash collateral held by the bond lender that is in excess of the short-term interest rate. In the more common situation with a positive lending fee the rebate rate is less than the short term interest rate, with the difference being the lending fee. While negative lending fees are most common during the financial crisis, they also occur at other times. Even when non-negative, many lending fees were low—for example, the 25th percentile of lending fees for investment grade corporate bonds was below 5 bps per year in almost half of the sample months. Recognizing that for each bond-date the lending fee we have is the value-weighted average of the fees on outstanding loans and that there is considerable variation in the lending fees on individual bond loans (Asquith, Au, Covert, and Pathak 2013), the lending fees that are positive but close to zero suggest that many of the individual bond loans involve negative fees. Negative lending fees likely reflect financing transactions in which bond lenders pay a rebate rate greater than the short-term interest rate to obtain the cash collateral deposited by the bond borrower (See Pierce 2014, Foley-Fisher, Narajabad, and Verani 2016). Utilization may not be a good proxy for short-sale constraints when many of the loans are financing transactions. Bond lenders entered into the loans in exchange for very low or even negative fees, suggesting that bonds used in financing transactions are easy to borrow. Our third extension addresses this by examining the returns of portfolios that are double-sorted on utilization and lending fees, focusing on the set of bonds with both high utilization and high lending fees. Loans of these bonds are likely to reflect shorting demand, as bond loans with high lending fees are unlikely to be financing transactions.5 These bonds may also be difficult to locate because a large fraction of the lendable quantity has already been borrowed, making them the bonds most likely to be short-sale constrained. As expected, we find large and highly significant negative abnormal returns on the high utilization, high lending fee bonds in both the full sample and the subsample of high-yield industrial bonds. The point estimates of abnormal returns also 5

If the lending fee is high the rebate received by the bond borrower (cash lender) is well below the short-term interest rate, so a bond borrower will participate in the transaction only if the bond borrower wants the bond to execute a short sale.

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are negative for the high-utilization, high-lending fee, investment-grade industrial bonds, but not statistically significantly different from zero. Thus, the combination of the three-month horizon, more refined bond market benchmarks, and a focus on the bonds for which there is demand to short and short sales are constrained provides strong evidence of predictability. We also adjust the abnormal returns for the cost of borrowing the bonds and find that the returns net of lending fees remain large and significantly different from zero in both the full sample and the subsample of high-yield industrial bonds. The finding that the negative abnormal returns are larger in high-yield industrial bonds than in investment-grade industrial bonds, where the abnormal returns are not significant, is comforting. In the context of structural credit risk models, it is reasonable to expect that short-sale constraints predict the returns of high-yield bonds because they are exposed to the risk of changes in firm asset values. The lesser ability to predict the returns of investment-grade bonds is unsurprising because investment-grade bond values are less sensitive to changes in firms’ underlying asset values. Fama-MacBeth regressions show that the abnormal returns on the high-utilization, high-lending fee bonds are significantly negative in both the full sample and the subsample of high-yield industrial bonds when controlling for various bond characteristics. The point estimates of the negative abnormal returns are actually slightly larger when we control for bond characteristics. The result also survives controlling for information from the equity lending market, though in this case the point estimates of the negative abnormal returns are smaller. The result that the information in the bond lending market is incremental to the information in the equity lending market is consistent with investors in the two markets relying on different information, and also with the markets not being fully integrated, as concluded by Choi and Kim (2017). However, if supply conditions and short-sale constraints differ in the stock and bond lending markets then it is possible for bond lending market information to be incremental to equity lending market information even if the demands for shorting stocks and bonds are both driven by the same information about underlying firm values. Finally, we evaluate the role of single-name CDS in the context of bond short sales by investigating the CDS-bond basis. The basis provides a measure of frictions between trading in the bond versus the CDS market. Thus, it can be used to gain insight into investors’ preferred choice of trading venue to exploit private information. We find that the basis is, on average, negative for most of the double-sorted portfolios, but positive in the portfolio of high lending fee and high utilization high-yield bonds. This, combined with our result that high utilization and high lending fee high-yield bonds have negative abnormal returns, suggests that negative information is reflected 4

in the CDS market and that short-sale constraints and perhaps other limits to arbitrage prevent arbitrage activity from eliminating the positive basis in this portfolio. We also investigate the returns of bonds with and without actively traded CDS and obtain results for high-yield industrial bonds that are consistent with the hypothesis that CDS relax bond short-sale constraints. Because our results about the predictability of bond returns are consistent with the existing results for the equity market, we are left with the same puzzle that appears in the literature on equity short sales—it is not clear why measures of short-sale constraints that are available to sophisticated market participants are strong predictors of security returns. A developing literature has begun to consider explanations of the persistent predictability (see Duffie, Gˆarleanu, and Pedersen 2002, Drechsler and Drechsler 2016, Hong, Li, Ni, Scheinkman, and Yan 2016, Engelberg, Reed, and Ringgenberg 2017). Our reading of the literature is that the issue is not yet resolved. Regardless, given that our results regarding proxies for short-sale constraints and bond returns are consistent with the existing results for equities, it seems likely that the same mechanisms explain both phenomena. The next section of the paper describes the data we use, focusing on the lending fee data. Section 3 presents the main results regarding abnormal returns to bond portfolios sorted on the proxies for short-sale constraints. Section 4 examines whether the abnormal returns differ depending on whether CDS are traded on the bonds, and also shows that the information in the bond lending market is incremental to the information in the equity lending market. Section 5 briefly concludes.

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Data and summary statistics

The securities lending data come from the Markit Securities Finance database.6 The database includes daily data on securities lending activity aggregated to the security level (rather than at the loan level), including the quantity on loan, the number of loans, various measures of loan fees, the numbers of active brokers and lending agents, and other fields. Markit obtains the information from more than 100 lending market participants, including beneficial owners, hedge funds, investment banks, lending agents, and prime brokers. Markit indicates that the reporting contributors account for approximately 85% of U.S. securities loans. Our sample begins in July 2006 because the data coverage expanded significantly around that time and the data are available at daily frequency beginning June 28, 2006. Our sample ends with March 2015. The market for securities lending and its institutional arrangements are described elsewhere, 6

We originally licensed the data from Data Explorers, which was acquired by Markit shortly thereafter. We subsequently acquired an updated version of the data from Markit.

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including in D’Avolio (2002), Asquith, Au, Covert, and Pathak (2013), and Kolasinski, Reed, and Ringgenberg (2013). It includes three groups of participants: (i) lenders such as insurance companies, pension funds, and mutual funds, who often lend through agent lenders (custodians), (ii) ultimate borrowers, for example hedge funds, proprietary trading desks, and in the case of stocks, option market makers, and (iii) prime brokers. In the typical triparty agreement, for which we have data, hedge funds and other short sellers borrow the securities from their prime brokers, who in turn borrow from the insurance companies, mutual funds, pension funds, and other lenders (Kolasinski, Reed, and Ringgenberg 2013, especially Figure 1). In this process the prime brokers “mark up” the lending fee, that is they borrow from the original lender and then re-lend to the hedge fund or other short seller at a higher fee. Lending fees typically are not quoted directly but rather are derived from quoted rebate rates. The bond borrower usually provides cash collateral to the bond lender, and the bond lender pays interest (the rebate rate) on the cash collateral that it holds. The lending fee is the difference between the market short-term interest rate and the rebate rate paid on the cash collateral.7 During our data period Markit (and previously, Data Explorers) used the Federal Funds Open rate as the short-term interest rate in calculating the lending fee. The rebate rate can be negative when securities are hard to borrow and the lending fee is high. The lending fee can also be negative, which occurs when the rebate rate that the bond lender pays on cash collateral exceeds the short-term interest rate. We use the fee variable VWAF All, which is the value-weighted average lending fee received by the lenders on all currently outstanding loans reported to the data provider. This is the best populated lending fee variable in our version of the Markit database. The database also includes the value-weighted average fees received by lenders on loans originated in the previous one, three, seven, and 30 days. The literature that uses lending fees from Data Explorers or Markit (for example Drechsler and Drechsler 2016, Engelberg, Reed, and Ringgenberg 2017) generally uses one of the lender-side fee measures or a similar lender-side fee measure computed from a proprietary database (for example, D’Avolio 2002, Asquith, Au, Covert, and Pathak 2013). Our data also include a buy-side variable SAF that is the simple average fee paid by the borrowing hedge funds, and includes the prime broker markups. We do not use SAF because this variable is much less well populated, being available for fewer than 1% of the bond-date pairs for which VWAF All is available. Also for equities SAF appears to be subject to a selection bias in that this field is less 7

When the security borrower provides Treasury securities as collateral the lending fee is quoted and Markit derives the rebate rate as the difference between the short term interest rate and the lending fee.

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likely to be populated when stocks are hard to borrow (Muravyev, Pearson, and Pollet 2017), and this may also be the case for bonds. Our use of lender-side fees is relevant for one set of results in which we present abnormal returns net of fees, because the lender-side fees we use are lower bounds on the fees that would be paid by a hedge fund or other short seller. Turning to other data, we calculate bond returns using bond transaction prices from the Enhanced TRACE dataset. Bond characteristics are taken from the Mergent Fixed Income Securities Database (FISD). One analysis uses the CDS-bond basis; for this analysis the CDS spreads used to compute the basis come from Markit. The par-equivalent spread calculation of the CDS-bond basis also uses swap rates from the Federal Reserve. Table 1 presents various summary statistics describing the bond lending data. The top panel shows the statistics for all bonds, including those issued by financial and utility companies, in each year of the sample period, while the bottom two panels show for each year the statistics for the samples of investment-grade and high-yield industrial bonds that we use in most analyses. In the sample of all bonds, between about 6,400 and 10,000 unique bonds are lent each year.8 Conditional on being lent, bonds on average were lent between 13 and 19 times each year, and the annual average loan fee varied from 26 bps in 2006 to 9 bps in 2009 and back up to 22.6 bps in 2015. The financial crisis was associated with a noticeable decline in quantity on loan and utilization within the full sample of corporate bonds, which was proportionately larger for investment-grade than for high-yield industrial bonds. Berndt and Zhu (2018) document similar differences in lending activity between investment grade and high yield bonds. They argue that the reduction in lending of investment-grade bonds was driven by reduced market making while the persistence of high-yield lending likely reflected increased dispersion of opinion among investors directly following the crisis. Table 1 also shows that the average loan fee for investment-grade industrial bonds was less than that for high-yield industrial bonds in every year. The overall average fee for investment-grade industrial bonds was only 6.16 bps, well below the 30.43 bps overall average loan fee for high-yield industrial bonds. Strikingly, during 2008 the average loan fee for investment-grade industrial bonds was negative, −16.96 basis points. Figure 1 shows that negative lending fees also occurred outside the financial crisis. For example, the 5th percentile of investment-grade industrial bond lending fees, shown in the top panel, was negative from July through December 2006, February through June 2010, September through December 2010, June and August 2011, and April 2013, and went as low as −551 basis points in October 2008. It was less than 0.93 bps for half of the months. 8

The table entry indicating that 6,401 bonds were lent in 2006, and all other entries for 2006, reflect only activity starting in July 2006. The entries for 2015 reflect only activity through March of that year.

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The 25th percentile of lending fees was below 5 bps per year in almost half of the sample months and negative for the duration of the financial crisis. Even the 50th percentile of investment-grade lending fees was generally low as it exceeded 10 bps in only three months (March 2007, September 2008, and March 2015), and was negative for some months during the crisis and again in April 2013. Even when the mean lending fee is positive, a mean lending fee close to zero suggests that many of the individual bond loans involve negative fees because for each bond-date the lending fee we have is the value-weighted average of the fees on outstanding loans, and there is considerable variation in the fees on individual bond loans (Asquith, Au, Covert, and Pathak 2013). The top panel of Figure 2 displaying the 5th, 10th, 25th, and 50th percentiles of the distribution of loan fees on high-yield industrial bonds also reveals that lending fees on these bonds were negative at times during the crisis, though for high-yield bonds the lending fees were not consistently negative throughout the crisis. The bottom panels of Figures 1 and 2 show that loan fees at the high percentiles became very high during September 2008. The explanation for the often negative lending fees lies in the fact that a bond loan is not just a loan of a bond, collateralized by cash; it is also a loan of cash, collateralized by a bond. A bond loan can occur because a hedge fund wants to borrow the bond to short-sell it, with the hedge fund providing cash collateral. Or a bond loan can be a financing transaction driven by the bond lender’s (cash borrower’s) desire to obtain access to the cash collateral to use for other purposes, for example to invest in higher-yielding securities (see Pierce 2014, Foley-Fisher, Narajabad, and Verani 2016). A negative lending fee means that the bond lender (cash borrower) is paying a rate in excess of the Federal Funds Open rate on the cash collateral. This was common during the financial crisis, consistent with the funding liquidity difficulties experienced by many financial institutions during the crisis.9 The low and sometimes negative lending fees outside of the financial crisis suggest that even outside of the crisis period a non-trivial fraction of bond loans were financing transactions.10 Utilization is likely a poor proxy for short-sale constraints when many bond loans are financing 9 Pierce (2014) discusses how AIG and some other bond lenders used their bond lending programs as a source of financing in order to obtain funds to invest in long-term securities, including subprime residential mortgage-backed securities (RMBS). During the financial crisis, when bond borrowers sought to terminate the bond loans by returning the borrowed bonds and receiving back their cash collateral, AIG and other securities lenders were unwilling to liquidate their securities portfolios to meet their obligations to return cash collateral because doing so would require the recognition of losses (Pierce 2014, p. 28). As a result, they compensated the bond borrowers by paying high interest rates on the retained collateral. 10 The data used in Asquith, Au, Covert, and Pathak (2013) appear to contain fewer financing transactions, as during the period of overlap the lending fees in the Asquith, Au, Covert, and Pathak (2013) data are higher than those in our data. For example, for 2006 the 10th and 25th percentiles of the lending fee in the Asquith, Au, Covert, and Pathak (2013) data are 8 − 9 and 12 − 13 bps (see Asquith, Au, Covert, and Pathak (2013), Table 4), while in our data these percentiles are less than or equal to 0.77 and 4.3 basis points for every month between July and December, 2006.

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transactions. In this case utilization may also be a poor proxy for investors’ demand to short bonds. Thus, in many of the analyses below we focus on the bonds with both high lending fees and high utilization. For these bonds utilization reflects investors’ demand to short, as bond loans with high lending fees are unlikely to be financing transactions. They are expensive to borrow and may be difficult to locate because a large fraction of the lendable quantity has already been borrowed. Thus, these are the bonds that are most likely to be short-sale constrained. To study whether utilization and lending fees predict bond returns we must calculate a holding period return for each bond and month, which requires prices at the beginning and end of the month. We use “clean” transaction prices and volumes, cleaned as in Dick-Nielsen (2009, 2014), from Enhanced TRACE beginning in July of 2006 and align them with the bond lending data. In early years Enhanced TRACE provides better coverage than TRACE because it includes both disseminated and non-disseminated transactions. However, because our bond lending sample starts after the last major dissemination phase in February 2005, the main advantage of Enhanced TRACE is that it includes unmasked volume which we use to calculate daily bond prices as the trade volume-weighted average prices. Because the differences between TRACE and Enhanced TRACE are minor, we substitute TRACE for the three sample months January-March 2015 for which Enhanced TRACE was not yet available when we assembled the data. We combine the transaction data with bond characteristics from the Mergent FISD. These data include, among other characteristics, the coupon rate, frequency, and first interest payment date. From these we can determine the other interest payment dates for each bond and compute accrued interest for each date. The merge removes 4,492,182 unmatched transactions, many of which are not corporate bonds, from the sample. We focus on the transactions in corporate debentures, medium-term notes, retail notes, medium-term zeros, and zero coupon bonds. Floating rate notes, convertible debt, equity-linked notes, bonds denominated in foreign currency, bonds with warrants or sinking fund provisions, and bonds issued as part of a unit deal are eliminated from the sample. This leaves approximately 73 million bond transactions between 2006 and 2015. Using the remaining transactions, we estimate end-of-month prices for each bond to use in computing holding period returns. The majority of bonds do not trade every day, which complicates the return calculation. We define the end-of-month price for each bond as the trade volume-weighted price over all transactions on the last day the bond trades within the final five days of each month.11 If the bond does not trade within the five-day window we do not calculate a holding period return for that month or the next. For bonds with consecutive end-of-month prices, we calculate the 11

See Bessembinder, Kahle, Maxwell, and Xu (2009) for a more detailed discussion of bond holding period returns.

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monthly return as

Rt =

Pt − Pt−1 + AIt + Ct−1,t Pt−1 + AIt−1

where Pt and Pt−1 are clean end-of-month TRACE prices for months t and t − 1, respectively. Accrued interest between the last coupon payment date prior to time t and the date the monthly bond price was recorded (time t) is denoted by AIt . Ct−1,t is the total dollar value of coupon payments made over the month. The final database of bond returns contains 834,524 bond-month returns for 31,642 unique bonds, over 70% of which are corporate debentures, issued by 4,189 issuers. On average, bonds in our sample return 76 bps per month (42 bps median). The difference between the 76 bps mean bond return in our data and the 40 bps mean return reported by Asquith, Au, Covert, and Pathak (2013) is likely due to the differences in the sample period and composition.

3

Utilization, lending fees, and bond returns

We begin by examining excess returns to portfolios formed from univariate sorts based on utilization. For each sample month and bond, we compute the average utilization over the month. We form portfolios on the last day of the month by ranking bonds by their average utilization during the month and follow returns over the next three months. We consider both equal- and value-weighted excess returns, where the value weighting is done using the issue size, adjusted for redemptions due to partial calls and sinking funds. The excess returns are computed using two different sets of benchmarks. First, for each month we compute equal- and issue-size value-weighted aggregate benchmarks from all bonds with available prices in TRACE; following Asquith, Au, Covert, and Pathak (2013), we refer to these as the TRACE benchmarks. A limitation of the TRACE benchmarks is that they do not capture cross-sectional variation in compensation for credit and interest rate risk across the credit rating and maturity spectrum. Thus, we also compute equal- and issue-size value-weighted benchmarks constructed from bonds matched on credit rating and remaining time to maturity. Specifically, at the end of each month we sort bonds into seven credit rating categories and eight maturity categories, for a total of 56 groups of bonds. The seven credit rating categories are AaaAa3, A1-A3, Baa1-Baa3, Ba1-Ba3, B1-B3, below B3, and Not Rated (NR), and the eight maturity categories are 0 < τ ≤ 2, 2 < τ ≤ 4, 4 < τ ≤ 6, 6 < τ ≤ 8, 8 < τ ≤ 10, 10 < τ ≤ 15, 15 < τ ≤ 20, and τ > 20, where τ denotes the remaining time to maturity, in years. When we report mean equal-

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and value-weighted portfolio returns we compute the bond excess returns relative to the equal- and value-weighted benchmarks, respectively. Asquith, Au, Covert, and Pathak (2013) focus on excess returns over a one-month horizon. However, limited liquidity and trading activity in bonds may slow the incorporation of negative views into prices. For example, informed debt investors may pursue less aggressive trading strategies than equity investors in order to disguise trades and preserve their informational advantage. As a result, bond short sale strategies may span longer horizons than equity short sale strategies. The average bond loan tenure of approximately 80 days reported in Table 1 is consistent with this conjecture. Thus, we extend the return horizon to three months.12 Table 3 presents mean three-month excess returns and corresponding t-statistics to utilizationsorted quintile portfolios and portfolios formed from bonds with utilization greater than or equal to the 95th and 99th percentiles. The reported t-statistics are based on Newey-West (1987) using two lags due to the overlapping three-month return observations. Columns (1)–(4) present the results using the equal- and value-weighted TRACE benchmarks and columns (5)–(8) present the results using the equal- and value-weighted rating- and maturity-matched benchmarks. The results reported in columns (1)–(4) provide only limited evidence of a relation between utilization and excess returns relative to the TRACE market benchmarks. Although the average value-weighted return of the utilization-sorted quintile 5 minus quintile 1 long-short portfolio is marginally significant (t-statistic = −1.90), this is not corroborated by the equal-weighted return of the same portfolio. The only convincing evidence of a relation between utilization and excess returns is for the quintile 5 minus quintile 1 long-short portfolio of high-yield industrial bonds, where the t-statistics for the equal- and value-weighted long-short portfolio returns are −2.14 and −2.69, respectively. We also see that when the excess returns are computed using the aggregate TRACE benchmarks the equal-weighted excess returns are negative, statistically significant, and economically large for all five quintile portfolios in both the full sample and in the subsample of investment-grade industrial bonds. The value-weighted quintile portfolio excess returns are also negative, though insignificant. These results suggest that the aggregate TRACE benchmarks might not be adequate. Consistent with this, the evidence that utilization predicts returns is stronger using the ratingand maturity-matched benchmarks for which the results are presented in columns (5)–(8). For the full sample of corporate bonds, the point estimates of both equal- and value-weighted three12

For comparison with the results in Asquith, Au, Covert, and Pathak (2013), Table B.1 of Appendix B examines one-month excess returns relative to the equal- and value-weighted TRACE benchmarks. In line with Asquith, Au, Covert, and Pathak (2013), those results show no evidence that lending fees or utilization predict future one-month bond returns.

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month excess returns in columns (5) and (7) decrease monotonically as utilization increases, and the returns are statistically significant for quintiles 4 and 5 and for the 95th and 99th percentile portfolios. The returns of the quintile 5 minus quintile 1 long-short portfolio are negative and significant at the 1% level for both the equal- and value-weighted portfolios. Returns to quintiles of investment grade bond quintile portfolios (Panel B) do not exhibit the same patterns, which is consistent with these bonds being less informationally sensitive.13 That said, the equal- and value-weighted returns of the 99th percentile portfolio of investment grade bonds are negative, large (−2.37% and −1.78%), and statistically significant (t-statistics of −2.76 and −2.09). Thus, among investment-grade industrial bonds, return predictability is found in those bonds having the most extreme levels of utilization. Panel C of Table 3 presents the mean excess returns to the utilization-sorted portfolios of high-yield industrial bonds. For the highest utilization quintile portfolio, the equal- and valueweighted mean returns are −1.02% with a t-statistic of −2.22 and −1.15% with a t-statistic of −2.56. The equal- and value-weighted returns of the long-short quintile 5 minus quintile 1 portfolio are −1.30% and −1.56% with corresponding t-statistics of −3.13 and −3.44, respectively. Thus, there is economically meaningful and statistically significant evidence that utilization predicts the returns of high-yield industrial bonds. The main message from Table 3 is that utilization, a proxy for short-sale constraints, predicts bond returns once the holding period is extended to three-months and excess returns are computed relative to rating- and maturity-matched portfolios. We carried out a similar analysis of threemonth excess returns to portfolios formed using the bonds’ loan fees, another proxy for short-sale constraints. Those results, reported in Table C.1 of Appendix C, show no evidence of a significant relation between lending fees and excess bond returns.

3.1

Returns to portfolios double-sorted on utilization and lending fees

As discussed above, a significant fraction of bond loans appear to be financing transactions motivated by bond lender’ desire to access the cash collateral provided by the bond borrowers. As a result, utilization may be a less direct proxy for short-sale constraints in the bond lending market than in the equity lending market because high utilization may signal either that bonds are in demand for shorting or that bonds are heavily used in financing transactions. We address this dichotomy by examining portfolios that are double-sorted on lending fees and utilization. Specifically, we first sort bond loans into quintiles based on utilization and then, within each utilization 13

Since the matched benchmark approach controls for innovations to market-wide credit and interest rates, any information we identify in lending market activity is not related to those factors.

12

quintile, into quintiles based on fees. Bonds with high utilization and low fees are likely heavily used in financing transactions, while loans of bonds in the high-utilization, high-fee quintile are likely motivated by short sales, as bond loans with high lending fees are unlikely to be financing transactions. These bonds may also be difficult to locate because a large fraction of the lendable quantity has already been borrowed, making them the bonds most likely to be short-sale constrained. We begin by examining the average loan fees in the double-sorted portfolios, and then turn to examining the subsequent three-month bond returns. Table 4 reports the average fees separately for three groups of bonds: the full sample of corporate bonds (Panel A), investment-grade industrial bonds (Panel B), and high-yield industrial bonds (Panel C). The three panels show significant variation in loan fees within utilization quintiles, with the variation being greatest in the high utilization quintile. Each utilization quintile, including the highest utilization quintile, includes bonds with very low fees. For example, in the full sample (Panel A) and subsample of investmentgrade industrial bonds (Panel B) the average fees of the high-utilization, low-fee bonds are −13.83 and −19.67 basis points per year, consistent with the loans of these bonds being motivated by financing transactions and these bonds being easy to borrow. Among high-yield industrial bonds (Panel C), the average fee for high-utilization bonds ranges from 6.14 basis points per year for the high-utilization, low-fee quintile to 250.9 basis points per year for the high-utilization, high-fee quintile. Overall, Table 4 shows considerable variation in fees within utilization quintiles. These patterns are consistent with the view that fees and utilization measure different dimensions of constraints to borrowing corporate bonds, and that examining them jointly can more precisely identify the bond loans likely associated with short-sales. We next analyze the three-month excess returns of the bonds in the double-sorted portfolios to investigate two predictions that are implied by the joint hypothesis that bond investors have value-relevant information and some bonds are short-sale constrained. The first prediction is that bonds with both high lending fees and utilization should have negative excess returns, as these are the most short-sale constrained and hence likely to be the most overvalued. Second, the difference between the excess returns of high- and low-fee bonds, conditional on utilization, becomes larger in magnitude (more negative) as utilization increases. As previously discussed, expressing negative sentiment is more difficult when lending fees are high. Therefore, we expect higher fees to predict lower future excess bond returns but only when short-sale constraints bind, which is unlikely to be the case for all bonds. At high levels of utilization, the more constrained high-fee bonds likely predict more negative excess bond returns than less constrained low-fee bonds. The second prediction implies this relation is expected to be weaker or non-existent at lower levels of utilization where 13

short-sale constraints are unlikely to bind. Table 5 Panel A reports 3-month excess returns to the double-sorted portfolios formed using the full sample of all corporate bonds. As with the univariate sorts, we calculate excess returns relative to appropriate rating- and maturity-matched benchmarks. Within the sample of all corporate bonds, three-month excess returns are negative for all five of the high-utilization portfolios, and significant for three of the five high-utilization portfolios. The high-utilization and high-fee portfolio, which consists of the bonds for which the bonds loans are most likely associated with short sales, have negative excess returns of −96 basis points with a t-statistic of −2.78. A portfolio that is long the high utilization and high fee portfolio and short the high utilization low fee portfolio has statistically significant mean excess returns of −76 basis points with a t-statistic of −2.38. These results provide strong evidence that together, bond lending utilization and fees predict future bond returns. Panel B shows the average excess returns for the double-sorted portfolios formed from investmentgrade industrial bonds. In this subsample there is no evidence that lending fees and utilization predict excess returns. Excess returns are insignificant across all fee- and utilization-based portfolios, even for the portfolio of bonds with both high utilization and high fees. Further, there is no pattern in the spread between the returns of the high and low fee portfolios for the various levels of utilization. These results are unsurprising, as the values of investment-grade bonds are much less sensitive to information about firm values than the values of high-yield bonds. The results for high-yield industrial bonds in Table 5 Panel C show negative and statistically significant excess returns in the portfolios with both high utilization and high lending fees. Of the four portfolios formed from bonds that in both the two highest utilization and two highest lending fee quintiles (that is, the {4, 4}, {4, 5}, {5, 4}, and {5, 5} portfolios), three show large mean excess returns (−0.75%, −1.66%, and −2.92%) with t-statistics of −1.87, −2.44, and −3.80, respectively. The highest utilization and fee portfolio, where loans are most likely related to short sales, has a negative three-month excess return of −2.92% that is statistically significant at the 1% level (t-statistic −3.80). Within the high utilization quintile, the mean return of the long-short high-fee minus low-fee portfolio is −2.57% and significant at the 1% level (t-statistic of −3.22). Appendix Table C.2 shows that the combination of rating- and maturity-matched benchmarks and double-sorting yields point estimates of mean one-month excess bond returns that are consistent with the patterns in Table 5, though the point estimates of the mean returns are generally not statistically significant.14 14

In the full sample (Panel A), the point estimates of mean excess returns to the high-fee and high-utilization

14

To summarize, we find evidence that short-sale constraints, measured using information on both utilization and lending fees, predict negative excess returns in corporate bonds. There is some evidence of predictability in the full sample of all corporate bonds, and stronger evidence for highyield industrial bonds. This finding is consistent with the hypothesis that short sales of corporate bonds exploit private information, and is similar to the existing findings in the equity market. The different results for investment grade and high yield bonds are consistent with the implications of structural models of corporate bonds in which investment grade bonds are less sensitive to firm asset values than high-yield bonds.

3.2

Profitability of bond shorting

Results presented thus far are consistent with the joint hypothesis that bond short sellers possess value-relevant information but are short-sale constrained. However, they do not imply that shortselling is profitable, because the returns do not include the lending fees that must be paid by the short sellers. A finding that investors do not profit significantly from short positions would call into question the conclusion that bond short sellers are informed. In contrast, significant net-of-fee excess returns, particularly for the high-fee high-utilization portfolios, would provide additional support for the hypothesis that short sellers are informed. We explore this by extending the analysis to include the impact of bond lending fees on returns. We use the same portfolio formation and evaluation approach as before, but assume that the bond lender receives the lending fee (Markit variable VWAF All) over the three-month portfolio return horizon. Because our returns include bond coupons and accrued interest, simply adding the lending fee provides an estimate of the return to a long bond investor who chooses to lend a bond he or she owns. The returns to a short-seller are of course the negative of the returns to a long position, and thus reflect the cost of the lending fee. We again use over-lapping observations of three-month excess returns and report the means and t-statistics based on Newey-West (1987) standard errors using two lags. An important caveat is that the data provider Markit collects bond loan terms from triparty lending agreements in the intermediated securities lending market. These fees represent the cost to prime brokers of borrowing bonds from the bond owner and lender, for example a pension fund or mutual fund, rather than the fee paid by the ultimate bond borrower and short seller, for example portfolios are negative, similar to the results for three-month returns. Also similar to the results for the three-month horizon, fees and utilization do not predict one-month excess returns of investment-grade industrial bonds (Panel B). Then in Panel C showing results for high-yield industrial bonds, the mean excess return to the highest utilization, highest fee quintile portfolio is −0.82% and marginally statistically significant (t-statistic −1.95). Within the highest utilization quintile, the mean return of the high-fee minus low-fee long-short portfolio is −0.81% (t-statistic −2.27).

15

a hedge fund. As a result, we somewhat overestimate the net-of-fee returns to short selling, by an unknown amount. Unfortunately, this is unavoidable as we do not have data on prime broker markups or the fees paid by ultimate bond borrowers.15 Table 6 reports mean excess returns net of lending fees for portfolios formed from all corporate bonds (Panel A), investment-grade industrial bonds (Panel B), and high-yield industrial bonds (Panel C), respectively. While the results are weaker due to the inclusion of the fees, the pattern of results is consistent with that in Table 5. In Panel A, after accounting for lending fees, shorting the portfolio of high fee and high utilization bonds remains profitable, with a three-month return of −72 basis points and a t-statistic of −2.10. In the high utilization quintile, the return to the long-short high-fee minus low-fee portfolio remains negative with an average return of −47 basis points, but is statistically insignificant. Consistent with prior findings, there is no evidence of short-sale profits for investment-grade bonds reported in Panel B. The results for high-yield industrial bonds in Table 6 Panel C are robust to the inclusion of lending fees. Three of the four high fee and high utilization portfolios have mean excess returns of −71 bps, −151 bps, and −240 bps with corresponding t-statistics of −1.78, −2.25, and −3.13, respectively, after accounting for approximately 24 bps in lending fees paid over 3 months. Similar to the results in Table 5, within the high utilization quintile the mean return of the long-short high-fee minus low-fee portfolio is −2.07% and significant at the 1% level (t-statistic −2.45). These results show that the profitability of short-sale strategies remains after accounting for bond loan fees.

3.3

Controlling for bond characteristics using Fama-MacBeth regressions

Next, we use Fama and MacBeth (1973) regressions as an alternative to the portfolio sorting analysis. An advantage of this approach is that it allows us to control for bond characteristics that may impact returns, and thus allows us to examine whether the results from the portfolio sorts are robust to controlling for bond characteristics. The outcome variable is the three-month excess return for bond i subsequent to month t, Rit . The regression specifications include two indicator variables designating bonds in the high utilization or high fee quintiles, and also a third indicator variable consisting of their interaction. Specifically, the indicator variable DHighBondU til takes the value one for bonds sorted into the top utilization quintile in a given month, and zero otherwise. Similarly, DHighBondF ee is an indicator variable that takes the value one for bonds sorted into the top fee 15

The Markit data include a fee variable S AF (simple average fee) representing the fees paid by hedge funds. However, for bonds this variable is not well populated, being available for less than one percent of the observations in our sample.

16

quintile in a given month, and zero otherwise. The interaction term DHighBondU til × DHighBondF ee identifies bonds in both the highest utilization and highest fee quintile each month, and is the main variable of interest. The coefficient on DHighBondU til measures the marginal difference in threemonth returns between the average bond in the highest utilization quintile and the average bond in the other four utilization quintiles. Similarly, DHighBondF ee measures the marginal difference in three-month returns between the average bond in the highest fee quintile and the average bond in the other four fee quintiles. The coefficient estimate for the interaction term DHighBondU til × DHighBondF ee , our main variable of interest, measures the marginal difference in three-month returns for bonds in both the highest fee and highest utilization quintile relative to the return on the average bond that is in either of the high utilization or high fee quintiles but not both. We also include several variables to control for other attributes associated with bond returns. These include the natural log of time-to-maturity (TTM), coupon rate (Coupon), and bond rating (Rating) to control for cross-sectional variation in interest rate and credit risk. Our rating variable is the average quantified rating (AAA = 1, AA+ = 2, ...) over the Moodys, S&P and Fitch ratings each month, when available. For bonds with missing or NR ratings, the average is taken over the remaining agencies that provide ratings. If ratings from the three major agencies are missing or “NR” we assign the variable Rating a value of zero and include an indicator variable that takes the value one. Missing accounting data are often handled similarly (see for example Himmelberg, Hubbard, and Palia (1999)). To capture return differences related to bond liquidity, we include the natural log of the amount outstanding (AmountOut), the Amihud ratio (Amihud), and the realized bid-ask spread (RealizedSpread) (see Houweling, Mentink, and Vorst (2005), Dick-Nielsen, Feldh¨ utter, and Lando (2012), and Anderson and Stulz (2017)). We calculate the daily Amihud ratio for each bond as the average absolute return from sequential trades divided by the total principal traded in millions, Amihud =

1 |(Pu −Pu−1 )/Pu−1 | , u=2 N −1 Qu

PN

where Pu is the clean price for trade u on the date and Qu is volume. For the Amihud measure, we limit the calculation to institutional size trades (above $100,000 of principal), which reduces noise in the measure. The variable Amihud measures price impact, hence lower values of Amihud indicate higher bond liquidity. The realized spread (RealizedSpread) is the difference been the average daily prices of customerinitiated sell and buy trades. Customer-initiated buy/sell transactions are identified using the RPT SIDE CD and CNTRA MP ID tags in Enhanced TRACE (see Dick-Nielsen 2014, Adrian, 17

Fleming, Shachar, and Vogt 2017). A lower realized spread is associated with lower transaction costs (bid-ask spread) and higher liquidity. We calculate realized spread from institutional-size trades to minimize noise from small trades. The final specification for the monthly cross-sectional regressions is: Ri,t = αt + β1,t DHighBondU tili,t + β2,t DHighBondF eei,t + β3,t DHighBondU tili,t × DHighBondF eei,t + β4,t log(T T Mi,t ) + β5,t Couponi + β6,t log(AmountOuti,t ) + β7,t Amihudi,t

(1)

+ β8,t RealizedSpreadi,t + i,t . A negative and significant estimate of β3,t implies that the joint distribution of lending fees and utilization provides incremental information on short-sale constraints beyond that contained in univariate measures of fees or utilization. Because we use monthly regressions and a three-month return horizon, the t-statistics are based on Newey and West (1987) standard errors with two lags. Table 7 reports the time-series average of monthly cross-sectional regression coefficients from July 2006 to March 2015. Columns (1) and (2) present results for average regression coefficients estimated over the full sample of corporate bonds. Columns (3) and (4), and (5) and (6), present similar results for coefficients estimated from the subsamples of investment-grade and high-yield industrial bonds, respectively. Consistent with the results for the portfolio sorts, the sign of β3,t is negative across all subsamples and specifications. Within the full sample of bonds, β3,t is negative and significant at the 10% level for the specification in column (1) without controls; after controlling for other effects it is significant at the 5% level, although the magnitude of the coefficient estimate decreases somewhat. The coefficient is negative and significant at the 1% level for high-yield bonds but insignificant for investment-grade bonds in both the simple specifications (columns (3) and (5)) and after controlling for credit, interest rate, and liquidity risk (columns (4) and (6)). These results offer additional support for the view that bond short sales are informed while also emphasizing the importance of short sale constraints in the joint distribution of utilization and fees. Consistent with our prior findings from Table 3, these results suggest that utilization and fees considered in isolation do not capture short sale constraints—only the interaction term DHighBondU til × DHighBondF ee is significant. The estimated coefficient on DHighBondU til is insignificant in every sample and specification, and the coefficient on DHighBondF ee is actually positive and, somewhat surprisingly, significant in every column. Also consistent with the portfolio sorting results, the coefficient on the interaction term DHighBondU til × DHighBondF ee is large and significant in the high-yield subsample (columns (5) and (6)), small and insignificant for investment-grade industrial bonds, and is marginally significant (column (1)) or significant (column (2)) in the full sample. 18

The coefficient on the control variables provide some evidence that bonds with longer time to maturity and higher coupon have higher future returns, especially for investment-grade bonds. Rating is a positive and significant predictor of high-yield bond returns but does not predict future investment-grade bond returns, which is in line with prior work that shows credit risk is priced more in high-yield debt (see for example Elton, Gruber, Agrawal, and Mann 2001). The amount outstanding does not appear to have predictive power. Lastly, the sign on the Amihud ratio is consistent with higher expected returns for less liquid bonds, and is statistically significant. Controlling for additional variables increases the regression R2 from the range of 7.6% to 12.7% to 24.9% or more.

4

Alternative markets for informed trading

We now consider whether the relation between short-sale constraints and returns depends on the availability of alternative financial instruments to express negative opinions about firm values and the constraints on shorting via those alternative instruments.

4.1

Credit Default Swaps

The credit default swap (CDS) market offers an alternative to bond short sales for expressing negative opinions about credit risk. Buying CDS protection provides negative exposure to the reference entity’s bonds and can be interpreted as a synthetic short sale. It may be easier to short via CDS as compared to the actual bond market because CDS are unfunded instruments with lower search costs, suggesting that the availability of CDS may relax short-sale constraints. To the extent it does, then utilization and lending fees may be weaker predictors of bond returns when CDS based on the bond issuer’s credit risk are readily available. On the other hand, there potentially are limits to the extent to which CDS relax short sale constraints. First, buying protection using the most readily available and liquid CDS is not a perfect substitute for short selling a bond. The standard documentation templates provided by the International Swaps and Derivatives Association (ISDA) offer counterparties substantial flexibility to write CDS contracts to cover either a particular reference entity (for example, a firm) or a specific bond. However, the most liquid contracts, for which we have pricing information, have standard terms under the North American Convention and are based on credit events of reference entities rather than specific bonds, and settled via an auction procedure that does not involve delivery of a specific bond. Therefore, investors seeking exposure to a specific bond may prefer to borrow the bond in the securities lending market and short sell it rather than buy protection on the bond issuer 19

using CDS. Second, to the extent that protection sellers (for example, CDS dealers) borrow and short sell bonds to hedge their CDS positions, demand for buying protection via CDS gets passed through to the bond lending market. As a result, CDS dealers’ need to use bond short sales to hedge their CDS positions may limit the ability of CDS to relax short sale constraints. Before examining whether the availability of CDS alters the ability of utilization and lending fees to predict bond returns, we consider the CDS-bond basis in the joint distribution of lending fees and utilization. The CDS-bond basis is the difference between the credit spread quoted in the CDS market and the credit spread quoted in the bond market. A CDS-bond basis that is positive and large is consistent with investors using the CDS market as a substitute for bond short sales to express negative opinions about credit risk. If CDS and bonds are perfect substitutes, then absent frictions the CDS-bond basis should be zero. Of course, there are frictions, especially for bonds that are short-sale constrained. If trading shifts toward CDS for such bonds, short-sale constraints will limit arbitrage activity and the CDS spread will likely increase relative to the bond credit spread, resulting in a positive basis. In terms of the price, the synthetic bond will trade at a discount relative to the cash bond. Hence, a positive and significant CDS-bond basis for high utilization and high lending fee bonds is consistent with the view that investors find it more convenient to short in the CDS market. We calculate the basis relative to the CDS par equivalent spread (PES), following Elizalde, Doctor, and Saltuk (2009). We will focus on the 5-year PES, because the 5-year tenor is the most liquid CDS, and we limit our attention to bonds maturing in 4 to 6 years so that the spreads computed from them are comparable to the 5-year CDS spread. We compute the PES using the full term structure of CDS spreads to increase the precision in the basis estimate. Appendix A provides details of the basis calculation. Table 8 reports the average monthly (computed on the last trading date of the month) CDS-bond basis from July 2006 to March 2015 for different levels of utilization and lending fees. Following the previous analysis, we sequentially sort bonds into utilization quintiles, and then within each utilization quintile into fee-based quintiles. Panel A shows the average basis for the sorted portfolios of investment-grade industrial bonds and Panel B reports the same averages for the high-yield bonds. Interestingly, for investment-grade bonds the average basis is negative for 23 of the 25 portfolios, but tends to increase and become positive in the portfolios with higher utilization and lending fees. For the highest utilization and highest fee portfolio the average basis is positive 40 bps. While it is not statistically significant, the point estimate of a positive basis for high-utilization, high-fee bonds is consistent with the hypothesis that informed investors short synthetically via the 20

CDS market either because investment grade CDS offer comprehensive coverage or because these contracts are more liquid, and that short-sale constraints and perhaps other limits to arbitrage prevent arbitrage activity from eliminating the positive basis. The corresponding results for the portfolios of high-yield bonds reported in Panel B show stronger dependence of the basis on utilization and lending fees. Again, the basis increases with lending fees and utilization; for the highest fee and utilization portfolio the basis is 55 bps with a marginally significant t-statistic of 1.73. For the various utilization quintiles, the basis difference between the highest and lowest fee bonds increases with utilization and reaches an average spread of 155 bps with a t-statistic of 2.92. As with the investment grade bonds, these results are consistent with the hypothesis that informed investors short synthetically via the CDS market, and that shortsale constraints and perhaps other limits to arbitrage prevent arbitrage activity from eliminating the positive basis. We next turn to examining whether the relation between the proxies for short-sale constraints and returns depends on the availability of CDS. At the beginning of each month, for each of the 25 sorted portfolios, we partition the bonds on loan into those issued by companies named as the reference entity on an actively traded single-name CDS contract (HASCDS) and those issued by companies not named on an actively traded CDS contract (NOCDS).16 For this purpose, an actively traded CDS contract is a single-name CDS with an available quote in the Markit single-name CDS file. Because CDS can relax short-sale constraints, it is tempting to hypothesize that utilization and lending fees should be weaker predictors of returns for bonds that have CDS. Unfortunately, things are not so simple. Recognizing that utilization (a quantity) and the lending fee (a price) are equilibrium outcomes, if CDS relax short-sale constraints then bonds issued by firms with CDS are less likely to have high lending fees, and may be less likely to have high utilization. Thus, bonds with CDS may be less likely to be in the high utilization, high lending fee portfolios. But if a HASCDS bond is nonetheless in one of the high utilization, high lending fee portfolios this may indicate that the bond is particularly short-sale constrained, that is it is so short-sale constrained that even though CDS relax short-sale constraints it nonetheless appears in the one of the high utilization, high lending fee portfolios. Whether a CDS spread is quoted for a bond issuer also may be endogenous, as it may be that CDS are more likely to be available if there is demand to synthetically short-sell bonds via CDS. These complications imply that we need to be cautious in interpreting the results regarding how the relation between the proxies for short-sale constraints 16

We recognize that a lack of quotes in Markit does not imply that CDS on the company cannot be traded, though agreement on terms is likely more difficult for unquoted CDS contracts.

21

and returns depends on the availability of CDS. Table 9 compares average 3-month excess returns to portfolios partitioned on whether a CDS is quoted, that is portfolios partitioned into HASCDS and NOCDS subsamples. As in Table 5, we consider three-month excess returns relative to the rating- and maturity-matched benchmark portfolio returns, and examine the subsamples of investment-grade and high-yield corporate bonds. Because the ability of utilization and lending fees to predict returns is concentrated in the portfolios of bonds with both high utilization and high lending fees, for each sample we focus on two portfolios formed from such bonds rather than report results for all of the 25 sorted portfolios. The first of these two portfolios combines high-fee and high-utilization bonds; specifically, it is composed of bonds categorized into the top two utilization and fee quintiles each month, that is the bonds in portfolios {4, 4}, {4, 5}, {5, 4}, and {5, 5}, where the two elements indicate the utilization and fee quintiles, respectively. The second portfolio is the highest utilization and fee portfolio, that is portfolio {5, 5}. Each of these portfolios is then partitioned into the HASCDS and NOCDS subsamples, and Table 9 reports the average returns of the portfolios and the difference between the average returns of the NOCDS and HADCDS subsamples. The results in Table 9 are quite different for investment-grade and high-yield bonds. For the high utilization and high fee high-yield bonds (that is, the high-yield bonds in portfolios {4, 4}, {4, 5}, {5, 4}, and {5, 5}) for which results are shown in the left-hand half of the table, the NOCDS bonds have lower three-month returns than the HASCDS bonds; −2.70% versus −1.39%. The difference in the returns of NOCDS and HASCDS bonds of −1.30% is statistically significant (t-statistic −2.01), consistent with the hypothesis that the availability of CDS relaxes short-sale constraints. For the highest utilization and highest fee high-yield bonds (those in portfolio {5, 5}) for which results are shown in the right-hand half of the table, based on the point estimates the NOCDS bonds also have lower returns than the HASCDS bonds. This is similar to the results for the high utilization and high fee bonds, but in this case the difference in average returns is only −0.60% and is not statistically significant. Perhaps surprisingly, the results are different for the investment-grade industrial bonds. For both the high utilization, high fee and the highest utilization, highest fee portfolios the average returns on the HASCDS bonds are significantly negative and the average returns on the NOCDS bonds are not, and the differences in the average returns are significant. This finding does not support the hypothesis that the availability of CDS relaxes short-sale constraints, because that hypothesis implies that the average returns on the NOCDS bonds should be less than those of the HASCDS bonds. Recognizing that utilization and lending fees are imperfect proxies for short-sale 22

constraints, one possibility is that the availability of CDS is correlated with the dimensions of short sale constraints that are not captured by utilization and lending fees.17 Unfortunately we do not see any way to overcome the lack of identification and distinguish among the different possible explanations for the investment grade bond results using the data that we have.

4.2

Stock Market

High-yield bond returns share characteristics with equity returns. For example, in the context of structural credit risk models, negative information about a firm’s underlying asset value would predict negative returns on both the firm’s equity and any high-yield bonds issued by the firm. Thus, our finding that proxies for bond short sale constraints predict high-yield bond returns might be just another manifestation of the existing results that proxies for equity short sale constraints predict equity returns. Specifically, if the private information possessed by bond short sellers is the same as the information exploited by equity short sellers then the demands of bond and equity short sellers to borrow and short-sell debt and equity will be highly correlated. As a result short sale constraints in the bond and equity lending markets are likely be correlated, and may be highly correlated. If this were the case, then proxies for equity short sale constraints computed from equity lending data would likely subsume much of the explanatory power of their bond lending market counterparts, and proxies for bond short sale constraints computed from bond lending market data might not provide any incremental information about bond returns beyond that already reflected in proxies for equity short sale constraints. The hypothesis that equity lending market information subsumes the predictive power of bond lending market information is plausible because information-related trading might be concentrated in equities due to their greater sensitivity to changes in firm values as compared to high yield bonds. On the other hand, many investors specialize in either bonds or equities, and high-yield bond and equity investors might possess different information. Bond prices and returns may be impacted by factors such as funding liquidity that have less impact on equities, and supply conditions in the bond and equity lending markets might differ. These possibilities suggest the alternative hypothesis that the proxies for bond short sale constraints contain additional information about bond returns beyond that reflected in the proxies for equity short sale constraints. Showing that short sale returns 17

The different results for the investment grade and high yield bonds also may reflect fundamental differences in the availability of private information. Literature on credit risk transfer suggests that the separation of control and cash flow rights may lead to lower monitoring of firms with CDS available. Moreover, Parlour and Winton (2013) show that the problem is exacerbated in higher credit quality debt where CDS coverage is more comprehensive.

23

differ across markets would increase the importance and contribution of our finding that proxies for bond short sale constraints predict bond returns, as it indicates that bond short sellers process distinct information that impact bonds’ values in a manner that has not yet been documented in the existing literature. We explore whether proxies constructed from bond and equity lending market data contain independent information about bond returns by augmenting the Fama-MacBeth regressions presented in Table 7 with three additional explanatory variables constructed from data on equity utilization and lending fees that proxy for equity short sale constraints. The dependent variables are the same 3-month returns used in the Fama-MacBeth regressions in Table 7. For each month we use the equity lending fee data to sort the bond issuers’ stocks into utilization quintiles, and then within each utilization quintile sort the stocks into quintiles using the equity lending fee. Then for each bond-month we construct two indicator variables DHighEquityU til and DHighEquityF ee that take the value one if the bond issuer’s stock is categorized into the top utilization or top lending fee quintile, respectively, on the last day of the previous month. For each bond-month we also construct the interaction of DHighEquityU til × DHighEquityF ee which identifies bonds whose issuers had stocks in the highest stock lending fee quintile within the highest stock lending market utilization quintile on the last day of the previous month. The regressions also include the corresponding variables constructed from bond lending market data that were used in the regression specifications reported in Table 7, and some of them include the control variables used in the specifications reported in that table. As in the regressions reported in Table 7, we are particularly interested in the interaction term DHighBondU til × DHighBondF ee . If bond short sales reflect similar information to that reflected in equity short sales, then we expect the equity lending market variables to subsume the effect of DHighBondU til × DHighBondF ee in the regression estimates. In contrast, if this variable remains informative after controlling for equity lending market variables then bond short sales are likely driven by different information than equity short sales. Table 10 reports the average regression coefficients from the monthly cross-sectional regressions. Focusing first on the equity lending variables, we find only limited evidence that they predict negative bond returns. These variables are either insignificantly or positively related to returns in the full sample of all bonds (columns (1) and (2)), the subsample of investment grade industrial bonds (columns (3) and (4)), and in one of the specifications estimated using the subsample of high yield industrial bonds (column (5)). A negative relation is found only in the specification with all control variables estimated using the subsample of high yield bonds reported in column (6), where 24

the equity lending fee indicator variable DHighEquityF ee predicts negative bond returns (coefficient estimate of −0.015, t-statistic of −2.18) after controlling for the impact of the other variables. This negative coefficient on DHighEquityF ee in column (6) might be viewed as comforting, as structural credit risk models imply that the returns of both equities and high-yield bonds are sensitive to changes in firm asset values. Given this, and the existing evidence that equity lending fees predict equity returns, the finding that DHighEquityF ee predicts high-yield bond returns is unsurprising. On the other hand, this result is not found in column (5) that does not include all control variables, and untabulated results show that even for the results in column (6) the total marginal contribution from equity lending fees, that is the sum of the coefficient estimates on DHighEquityF ee and DHighEquityU til × DHighEquityF ee , is not significantly different from zero. Furthermore, the equity lending market variables do not negatively predict returns in the full sample of all bonds for which results are reported in columns (1) and (2). As a whole, these results indicate that the equity lending market variables are at best weak predictors of bond returns. The coefficients on the bond lending market interaction term DHighBondU til × DHighBondF ee remain negative and significant in both the full sample of all bonds and high-yield subsample, after controlling for equity lending fees and utilization. Comparing these results to those in Table 7 that do not include the equity lending market variables, the point estimates of the coefficient in the high-yield subsample decrease from −0.033 in Table 7 to −0.023 in Table 10 in the specifications in columns (5) without all control variables, and from −0.036 to −0.019 in the specifications in columns (6) with control variables. These results are consistent with overlapping information in debt and equity short sales. Nonetheless, the magnitudes of the point estimates of −0.023 and −0.019 in Table 10 are more than half the magnitude of the corresponding point estimates of −0.33 and −0.036 reported in Table 7 and remain highly significant (t-statistics of −3.19 and −2.93), indicating that the bond lending market provides incremental information beyond that in the equity lending market. Taken together, these results show that the equity lending market information overlaps with bond lending market information, but also provide convincing evidence that the bond short sale constraints’ ability to predict bond returns is not fully explained by equity short sale constraints. This latter result is consistent with the hypothesis that debt and equity short sellers at times exploit distinct information.

5

Conclusions

Using a new dataset of corporate bond loans by multiple security lenders covering the bulk of corporate bond loans from 2006 to 2015, we provide new evidence that proxies for short sale 25

constraints predict negative bond returns, consistent with short sale constrained corporate bonds being overvalued. This finding differs from the existing literature (Asquith, Au, Covert, and Pathak (2013)). Many bond loans involve negative lending fees, that is the rebate rate paid by the bond lender (cash borrower) to the bond borrower (cash lender) exceed the short term interest rate. The negative fees appear to reflect financing transactions that are motivated by the bond lender’s (cash borrower’s) desire to access the cash collateral provided by the bond borrower rather than by the bond borrower’s desire to short sell the bond. Bonds used in such financing transactions are likely to be easy to borrow and unlikely to be short-sale constrained. Since bond loans that are financing transactions are included in the inventory on loan that is used to compute utilization (the percent of inventory on loan), this limits utilization’s usefulness as a measure of bond short sale activity. We begin our analysis of bond returns by examining the returns of bonds sorted into quintile portfolios by utilization, but examine three-month returns rather than the one-month returns that are the focus of Asquith, Au, Covert, and Pathak (2013). We find some evidence that high yield bonds with high utilization have negative three-month excess returns. Next, we extend their approach in two additional ways. First, within each utilization quintile, we further sort loans into fee-based quintiles to better distinguish bond loans likely associated with short sales from those likely to be financing transactions. The idea is that bonds with high lending fees will not be used in financing transactions, and bonds with both high fees and high utilization are likely to be shortsale constrained. We hypothesize that such bonds will have subsequent negative excess returns. Second, we calculate excess returns relative to rating- and maturity-matched benchmarks rather than aggregate bond market benchmarks. Consistent with the hypothesis, we find significant negative excess returns to long bond portfolios (positive returns to bonds sold short) formed from bonds for which both utilization and lending fees are high, consistent with informed short selling in corporate bonds. This result is concentrated in high-yield industrial bonds where returns are likely most sensitive to firm-specific private information. We control for the possible impact of other variables on bond returns using Fama-MacBeth regressions. Indicator variables identify bonds in the top utilization quintile, top fee quintile of any utilization quintile, and the top fee quintile of the top utilization quintile. Consistent with the results for the double-sorted portfolios, we find that bonds in the top fee quintile of the top utilization quintile earn significant negative returns compared to other bonds. We also find that the CDS-bond basis is negative for almost all of the double-sorted portfolios, 26

meaning that the CDS spread is typically lower than the bond market credit spread. However, for bonds that are short-sale constrained, which are those that have both high utilization and high lending fees, the point estimate of the basis is positive. For high-yield industrial bonds with both high utilization and high lending fees the basis is (marginally) statistically significantly different from zero. This is consistent with the hypothesis that investors with negative information use CDS to execute synthetic short sales, and that short selling costs prevent arbitrage activity from eliminating the positive basis. We also find some limited evidence that short-sale constrained high-yield bonds issued by firms without CDS have lower (more negative) returns than short-sale constrained high-yield bonds issued by firms with CDS. Finally, we explore whether the information reflected in proxies for bond short-sale constraints is different from the information reflected in proxies for equity short sale constraints. We do this by augmenting the Fama-MacBeth regressions to include variables that measure, for each bond, whether the bond issuer’s equity is short-sale constrained. The bond short-sale constraint proxies become weaker predictors once the equity short-sale constraint proxies are included in the regressions, suggesting that there is overlap between the information possessed by equity and bond short sellers. However, bond short-sale constraint proxies continue to significantly predict bond returns even after controlling for the proxies for equity short sale constraints, indicating that they contain information incremental to that in the equity lending market. This is consistent with the hypothesis that bond short sellers exploit different information from that used by equity short sellers. In summary, we provide new results showing that proxies for short sale constraints predict corporate bond returns, consistent with corporate bond short sales based on private information. This extends the results in the existing literature by Asquith, Au, Covert, and Pathak (2013). Generally, the corporate bond market is dominated by institutional investors, lending credence to the notion that bonds are efficiently priced (see for example Chordia, Goyal, Nozawa, Subrahmanyam, and Tong (2017)). Our results suggest that bonds can suffer similar price inefficiencies as stocks, potentially encouraging further work in this area. Finally, our results extend the discussion of informed trading in corporate debt from transaction cost estimates (Edwards, Harris, and Piwowar (2007), Bessembinder, Maxwell, and Venkataraman (2006), Chen, Lesmond, and Wei (2007), and Han and Zhou (2014)) and CDS trading (see Acharya and Johnson (2007)) to bond short sales via securities lending.

27

Appendix A

CDS-Bond Basis

We measure the CDS-bond basis using the Par Equivalent Spread (PES) due to Elizalde, Doctor, and Saltuk (2009). This procedure finds a CDS spread, the PES, that is consistent with a bond price. It then computes the CDS-bond basis as the difference between the quoted CDS spread and the calculated PES. The procedure begins by extracting the term structure of risk-neutral survival probabilities from the term structure of CDS spreads. The survival probabilities are then used to calculate the bond price, where they are shifted up or down by a constant (parallel shift) to make the calculated bond price match the market price. The shifted probabilities that match the bond price are then used in the standard CDS spread formula to compute the CDS spread implied by the shifted probabilities, which is the PES. The estimated CDS-bond basis for bond j on day t is then the difference between the quoted CDS spread and the calculated PES. We compute the CDS-bond basis at the five year tenor, using bonds with maturities of between four and six years. Further details are provided below. Let ti , for i = 1, . . . , N , be the CDS payment dates, let hN be the CDS premium (spread) for a CDS with termination date tN , and let Q(ti ) be the risk neutral probability, called the survival probability, that the reference entity defaults after ti . Also let D(ti ) be the discount factor for date ti , that is the current value of a zero-coupon bond that pays $1 at date ti , let R be the recovery rate, and let δt be the fraction of a year between the quarterly CDS payment dates. Following Duffie (1999), the values of the premium and contingent (default) legs of a CDS are given by Vpremium = hN

N X

D(ti ) × Q(ti ) × δt

i=1 N X

Vcontingent

(A.1)



 ti + ti−t δt +hN D × [Q(ti−1 ) − Q(ti )] × , 2 2 i=1   N X ti + ti−t = (1 − R) D × [Q(ti−1 ) − Q(ti )]. 2

(A.2)

i=1

The equations reflect an assumption that, if a credit event occurs, it occurs midway between payment dates. In this event, the premium leg receives the premium for half of a payment period. Thus, the second term in the value of the premium leg is the present value of the premium received conditional on the occurrence of a credit event. Given the survival probabilities, the fair CDS spread or premium hN is obtained by equating the values of the premium and contingent legs and solving for hN . Alternatively, given hN and the survival probabilities ti , for i < N , one can solve for the survival probability Q(tN ). Thus, if one knows the CDS premia for CDS terminating on every payment date one can “bootstrap” the term structure of survival probabilities from the term 28

structure of CDS spreads. A preliminary step is to compute the discount factors D(ti ) from the interest rate swap spreads available in the Federal Reserve Boards H-15 Release, interpolating the swap spreads as necessary. We then interpolate from the available CDS spreads to estimate a CDS spread for every payment date ti and then “bootstrap” the term structure of survival probabilities. Starting with the first payment date t1 and CDS spread C1 , we pick the first survival probability Q(t1 ) to make the value of a CDS terminating on this date equal zero. We then successively consider payment dates t2 , t3 , . . . , tN and corresponding spreads C2 , C3 , . . . , CN , and for each payment date ti pick the survival probability Q(ti ) to make the value of a CDS with termination date ti equal zero, using the previously computed survival probabilities. We continue this process until we have computed the survival probability for the termination date of the longest tenor CDS available on the date. Because we are interested in the five-year CDS-bond basis, we require a spread quote for at least one CDS contract with maturity of five or more years. The iterative procedure described above yields a vector of risk-neutral survival probabilities Q for the CDS payment dates. Using these, the value of a bond with annual coupon rate C is Vbond (Q) =

N X

D(ti ) × Q(ti ) × C × ∆t + D(tN ) × Q(tN ) +

i=1

N X

D(ti ) × [1 − Q(ti )] × R,

(A.3)

i=1

where ∆t (typically six months) is the fraction of a year between bond payment dates. For each bond the coupon rate, coupon frequency, principal amount, and maturity date are obtained from FISD for each bond. We use the recovery rate supplied by Markit or 40% when the Markit rate is missing. For simplicity, we assume that coupon payments are made at the fraction, implied by the coupon frequency, of a 365 day year. For example, semiannual coupons are paid at day 182.5 and again on day 365. Next, we adjust these probabilities by a constant to match the model bond price to the market price reported in TRACE. Specifically, we adjust Q by adding a constant  to each element so that the vector of probabilities becomes Q + , and then pick  to equate the model bond price Vbond (Q + ) to the price reported in TRACE. Given the adjusted survival probabilities Q +  the values of the premium and contingent legs can be computed using equations (A.1) and (A.2). The PES is the CDS spread computed from these adjusted survival probabilities. It is obtained by equating the values of the premium and contingent legs and solving for the resulting premium:

29

(1 − R) P ES =

N P i=1

N P i=1

D( ti +t2i−1 ) × [Q(ti−t ) − Q(ti )]

D(ti ) × (Q(ti ) + ) × δt +

N P i=1

30

. D( ti +t2i−1 )

× [Q(ti−t ) − Q(ti )] ×

δt 2

(A.4)

Appendix B

Replication of Portfolio Return Results in Asquith, Au, Covert, and Pathak (2013)

Table 9 of Asquith, Au, Covert, and Pathak (2013) reports the average equal-weighted and issuesize value-weighted raw and excess returns for quintile portfolios sorted on utilization and lending fees, as well as for portfolios formed from bonds with utilization or fees above the 95th and 99th percentiles. The excess returns are relative to the equal- and issue-size value-weighted aggregate TRACE market benchmarks. None of the mean portfolio returns in Asquith, Au, Covert, and Pathak (2013) Table 9 are statistically significant, and Asquith, Au, Covert, and Pathak (2013) conclude that their “Table 9 indicates that shorting portfolios of bonds with high on-loan percentage or high borrowing costs are not strategies that yield abnormal returns to short sellers” (p. 177). Table B.1 replicates Asquith, Au, Covert, and Pathak (2013) Table 9 but using our bond lending data, and also presents results for subsamples of investment-grade and high-yield industrial bonds that are not considered in Asquith, Au, Covert, and Pathak (2013) Table 9. Panel A presents the results for portfolios sorted by average daily utilization during the month up through the portfolio formation date. The top one-third uses the full sample of corporate bonds, and corresponds to Panel A of Asquith, Au, Covert, and Pathak (2013) Table 9. The bottom two-thirds of the table presents the additional sorted portfolio returns for subsamples of investment-grade and high-yield industrial bonds. Following Asquith, Au, Covert, and Pathak (2013), the results include average equal-weighted and issue-size value-weighted raw and excess returns, where the excess returns are relative to equal- and issue-size value-weighted aggregate TRACE market benchmarks. Consistent with Asquith, Au, Covert, and Pathak (2013) Table 9 Panel A, Table B.1 Panel A provides no evidence that utilization predicts bond returns. There is little variation in the returns across the different portfolios in both the full sample and the subsample of investmentgrade industrial bonds, and the long-short quintile five minus quintile one mean portfolio returns are small and insignificant. In the subsample of high-yield industrial bonds the point estimates of the mean returns decline with utilization, though not monotonically. The means of the longshort quintile five minus quintile one equal- and issue-size value-weighted portfolio returns are only −0.26% and −0.32%, and insignificant. Thus, consistent with Asquith, Au, Covert, and Pathak (2013) Table 9 Panel A, these results provide no statistically significant evidence that utilization predicts bond returns. One difference between the results in Table B.1 Panel A and the corresponding results in Asquith, Au, Covert, and Pathak (2013) Table 9 Panel A is that the mean equal-weighted and issue-

31

size value-weighted excess returns to the quintile portfolios in Table B.1 Panel A are relatively large, between −0.18% and −0.32%, and not strongly related to utilization. This differs from the results in Asquith, Au, Covert, and Pathak (2013) Table 9 Panel A, where the returns are closer to zero. The mean equal-weighted and issue-size value-weighted excess returns to the quintile portfolios in the subsample of investment grade bonds in the bottom third of Table B.1 Panel A are also relatively large, between −0.27% and −0.33%, and again not strongly related to utilization. Table C.1 Panel A in Appendix C shows that these patterns are not found once the excess returns are computed relative to rating- and maturity-matched benchmarks. Using these better benchmarks the excess returns of the investment-grade industrial bonds are closer to zero, and the excess returns in the full sample are related to utilization and on average much closer to zero. This suggests that the somewhat surprising patterns of consistently large returns in B.1 Panel A are due to the aggregate benchmarks that do not reflect the credit and interest rate risk of the bonds. Panel B presents the corresponding set of results for portfolios sorted by the average daily lending fee during the month up through the portfolio formation date. Consistent with Asquith, Au, Covert, and Pathak (2013) Table 9 Panel B, it provides no evidence that utilization predicts bond returns.

32

Appendix C

Supplemental results

Several secondary results are omitted from the main text to save space. For completeness, we briefly present those results here. Table C.1 presents additional estimates of excess returns to quintile portfolios sorted by utilization (Panel A) and lending fees (Panel B). Each panel reports average equal- and value-weighted one- and three-month excess returns to the quintile portfolios as well as portfolios formed from bonds in the 95th and 99th percentiles. Columns (1)-(4) of each panel present results for onemonth excess returns relative to the rating- and maturity-matched benchmarks; they compare to those in Table B.1 computed relative to the aggregate TRACE benchmarks. Columns (5)-(8) present results for three-month excess returns computed relative to the aggregate TRACE market benchmarks, and columns (9)-(12) include results for three-month excess returns relative to ratingand maturity-matched benchmarks. The results for the one-month returns relative to the rating- and maturity-matched benchmarks in Panel A provide some suggestive, but very limited, evidence that utilization might predict returns. For the high-yield industrial bonds in the lower part of the table the point estimates decline as utilization increases, and the value-weighted return for the 95th percentile portfolio is marginally significant (t-statistic −1.83). These results contrast with the results in Table C.1 where there is a similar but less pronounced pattern in the one-month returns of high-yield bonds relative to the aggregate TRACE benchmarks, and none of the returns were significant, and with the results in Table 3 showing that utilization can predict three-month excess returns. For the full sample in the top part of the table the point estimates decline monotonically starting with quintile 3, and the value- (equal-)weighted returns for the 95th percentile portfolio is significant (marginally significant). The results for excess returns relative to the aggregate TRACE benchmarks in Table B.1 have the puzzling feature that for both the full sample and the subsample of investment grade industrial bonds the average excess returns are negative and about the same magnitude for all of the utilization-sorted quintile portfolios. The results for the excess returns relative to the rating- and maturity-matched benchmarks in Table C.1 do not have this puzzling feature. Rather, in Table C.1 the excess returns for quintile portfolios in both the full sample and the subsample of investment grade bonds are much closer to zero, with magnitudes that are typically only a few basis points. This is consistent with the view that the larger negative average excess returns in Table B.1 stem from imprecise matching of interest rate and credit risk when using the aggregate TRACE

33

benchmarks. The results for three-month excess returns relative to the rating and maturity-matched benchmarks in columns 5-12 of Panel A repeat the results presented in Table 3 and are included only for comparison. As discussed in the main text, the results for the quintile 5 portfolio provide statistically significant evidence that utilization predicts three-month excess returns relative to the rating and maturity-matched benchmarks. Table C.1 Panel B presents the corresponding set of results for portfolios sorted by lending fees. None of the mean portfolio returns in this panel are statistically significant at conventional levels. Thus, this panel provides no evidence that bond lending fees by themselves predict one-month excess returns. Table C.2 shows the mean one-month excess returns relative to rating- and maturity-matched benchmarks of portfolios formed by double sorting on utilization and then lending fees. Panels A, B and C present the results for the full sample of corporate bonds, the subsample of investmentgrade industrial bonds, and the subsample of high-yield bonds, respectively. Consistent with the three-month average portfolio excess returns in Table 5, the results for high-yields bonds in Panel C provide some evidence that constraints to short selling predict excess returns. Specifically, the average one-month excess return to the high-utilization, high-fee portfolio is −0.82% with a tstatistic of −1.95. Within the high-utilization portfolio, the average return to the long-short highfee minus low-fee portfolio is −0.81% and significant at the 5% level. In Panels A and B showing the results for the full sample and the subsample of investment-grade industrial bonds the point estimates are negative for the high-utilization, high-fee portfolios, but these point estimates are not statistically significant. Table C.3 presents the average net-of-fee one-month excess returns for the double-sorted portfolios. It compares to Table 6 that presents the average net-of-fee three-month excess returns to the double-sorted portfolios and to Table C.2 that presents the average one-month excess returns gross of fees to the same portfolios. The net-of-fee excess returns are from the perspective of the long position, and are computed by adding the lending fee back to the excess return because this provides an estimate of the return to a holder of the bond who lends it and receives the lending fee. This fee adjustment reduces the magnitude of negative excess returns to a short position. Unsurprisingly, the mean net-of-fee returns in Table C.3 differ slightly from the gross-of-fee returns in Table C.2, because of the fees. A specific difference is that the average return to the high-utilization, high-fee portfolio of high-yield industrial bonds is now −0.65% per month rather than −0.82% per month and is no longer statistically significant.

34

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Figure 1: Investment-grade industrial bond loan fees The figure presents the time series of several percentiles of the distribution of monthly loan fees for loans of investmentgrade bonds issued by industrial companies (Mergent industry code 1) from July 2006 to March 2015. Each month we compute the 95th, 90th, 75th, 50th, 25th, 10th and 5th percentiles of the distribution of bond loan fees from all open loans of investment-grade industrial bonds in the MARKIT Securities Finance file. The time series of low and high fee percentiles are shown in the top and bottom panels, respectively.

IG Lending fees at 5th, 10th, 25th, and 50th percentiles 50 0 -50 -100 -150 -200 -250

50th percentile 25th percentile

-300

10th percentile 5th percentile

-350 -400 -450 -500

Mar-15

Jul-14

Nov-14

Mar-14

Jul-13

Nov-13

Mar-13

Jul-12

Nov-12

Mar-12

Jul-11

Nov-11

Mar-11

Jul-10

Nov-10

Mar-10

Jul-09

Nov-09

Mar-09

Jul-08

Nov-08

Mar-08

Jul-07

Nov-07

Mar-07

Jul-06

Nov-06

-550

IG Lending fees at 50th, 75th, 90th, and 95th percentiles 350 300 50th percentile

250

75th percentile 90th percentile

200

95th percentile

150 100 50 0

39

Mar-15

Nov-14

Jul-14

Mar-14

Nov-13

Jul-13

Mar-13

Nov-12

Jul-12

Mar-12

Nov-11

Jul-11

Mar-11

Nov-10

Jul-10

Mar-10

Nov-09

Jul-09

Mar-09

Nov-08

Jul-08

Mar-08

Nov-07

Jul-07

Mar-07

Jul-06

Nov-06

-50

Figure 2: High-yield industrial bond loan fees The figure presents the time series of several percentiles of the distribution of monthly loan fees for loans of high-yield bonds issued by industrial companies (Mergent industry code 1) from July 2006 to March 2015. Each month we compute the 95th, 90th, 75th, 50th, 25th, 10th and 5th percentiles of the distribution of bond loan fees from all open loans of below investment-grade industrial bonds in the MARKIT Securities Finance file. The time series of low and high fee percentiles are shown in the top and bottom panels, respectively.

HY Lending fees at 5th, 10th, 25th, and 50th percentiles 20 10 0 -10 -20 -30

50th percentile 25th percentile

-40

10th percentile 5th percentile

-50 -60 -70

Mar-15

Jul-14

Nov-14

Mar-14

Jul-13

Nov-13

Mar-13

Jul-12

Nov-12

Mar-12

Jul-11

Nov-11

Mar-11

Jul-10

Nov-10

Mar-10

Jul-09

Nov-09

Mar-09

Jul-08

Nov-08

Mar-08

Jul-07

Nov-07

Mar-07

Jul-06

Nov-06

-80

HY Lending fees at 50th, 75th, 90th, and 95th percentiles 600 550 500 450 50th percentile 400

75th percentile

350

90th percentile 95th percentile

300 250 200 150 100 50 0

40

Mar-15

Nov-14

Jul-14

Mar-14

Nov-13

Jul-13

Mar-13

Nov-12

Jul-12

Mar-12

Nov-11

Jul-11

Mar-11

Nov-10

Jul-10

Mar-10

Nov-09

Jul-09

Mar-09

Nov-08

Jul-08

Mar-08

Nov-07

Jul-07

Mar-07

Jul-06

Nov-06

-50

41

Table 1: Corporate bond lending market descriptive statistics

6,401 13.23 26.01 4.36 14.71 2.45 3.08 129.11

2006

Number of unique bonds lent Average loans per bond Loan Fee Quantity on loan (% outstanding) Utilization Number brokers Number agents Loan tenure (days)

High-yield industrial bonds

Number of unique bonds lent Average loans per bond Loan fee Quantity on loan (% outstanding) Utilization Number brokers Number agents Loan tenure (days)

1,108 23.99 46.24 4.66 19.06 2.83 3.84 91.19

1,408 13.00 12.88 4.14 10.17 2.71 3.54 119.22

Investment-grade industrial bonds

Number of unique bonds lent Average loans per bond Loan fee Quantity on loan (% outstanding) Utilization Number brokers Number agents Loan Tenure (days)

All corporate bonds

Year

1,302 35.47 35.45 5.36 20.35 3.69 4.40 101.28

1,760 17.44 5.41 4.37 9.91 3.41 4.08 133.60

7,886 17.08 16.17 4.92 14.49 2.86 3.36 147.72

2007

1,096 35.91 36.27 5.17 19.61 3.65 4.55 90.74

1,747 14.99 −16.96 3.43 7.95 3.19 3.99 117.18

7,323 15.25 11.35 4.14 12.10 2.70 3.30 139.48

2008

1,149 31.06 18.61 2.90 13.29 3.09 4.03 73.97

1,971 16.99 0.10 1.47 4.87 3.17 4.03 76.93

7,392 16.81 9.01 1.67 8.11 2.90 3.33 98.42

2009

1,242 28.90 22.70 2.82 14.82 3.20 4.37 71.59

2,184 19.46 6.46 1.55 5.39 3.37 4.34 81.53

8,222 18.52 14.06 1.64 8.67 2.86 3.61 95.65

2010

Annual descriptive statistics

1,262 25.57 24.15 2.44 14.01 3.37 4.29 76.81

2,472 18.16 7.04 1.37 5.06 3.66 4.34 73.00

8,746 17.08 14.24 1.48 8.53 3.15 3.65 88.68

2011

1,321 29.98 34.04 2.54 15.33 3.71 4.79 82.05

2,744 15.22 10.35 1.04 4.58 3.41 3.74 72.30

9,357 15.56 20.01 1.25 7.94 3.03 3.40 91.12

2012

1,348 22.53 32.22 1.89 12.99 3.50 4.21 79.53

3,009 15.38 9.70 1.13 5.22 3.40 3.68 67.46

9,886 14.04 18.83 1.15 7.63 2.96 3.22 85.82

2013

1,257 23.33 29.07 1.98 13.79 3.83 4.32 80.10

3,089 16.97 10.01 1.19 5.41 3.45 3.90 79.27

9,914 14.49 18.30 1.19 7.57 3.06 3.31 95.01

2014

1,013 25.73 36.97 2.14 15.05 3.97 4.20 76.78

2,525 17.01 13.99 1.17 5.31 3.43 3.70 75.49

8,058 14.82 22.60 1.18 7.81 3.09 3.21 94.08

2015

3,320 28.39 30.43 3.12 15.61 3.49 4.34 82.23

5,071 16.65 6.16 1.76 5.86 3.38 3.96 83.87

20,352 15.83 16.38 2.13 9.44 2.95 3.37 104.45

All

This table describes the sample of corporate bond loans from July 2006 to March 2015. The sample comes from the Markit Securities Finance files. The table presents descriptive statistics for three samples: “All corporate bonds” consists of the full sample of corporate bond loans, including loans of bonds issued by financial institutions and utilities; “Investment-grade industrial bonds” consists of loans of bonds issued by industrial companies (Mergent industry group 1) with investmentgrade credit ratings; “High-yield industrial bonds” consists of loans of bonds issued by industrial companies rated below investment grade. Each column presents average characteristics for the year given in the column heading. The column labeled “All” is the pooled average over all years. Loan fee is the value-weighted average fee of outstanding loans (Markit variable VWAF All, in basis points. Quantity on loan is the total principal amount on loan divided by the total principal amount outstanding, in percent. Utilization is the total principal amount on loan divided by the total principal amount available to be loaned, in percent. Number brokers is the number of prime brokers that contribute lending market information. Number agents is the number of lending agents that contribute lending market information. Loan tenure records the average number of days existing bond loans have been open.

42

Table 2: Quintile portfolio characteristics

7.83 6.05 5.35 0.23 0.17 17.10

8.30 5.90 4.47 1.42 0.51 8.53

9.01 5.85 3.97 3.98 1.36 5.30

8.97 5.89 3.64 9.13 2.89 4.77

8.16 6.45 3.63 32.17 6.92 30.92

9.67 5.86 4.58 7.57 2.72 −12.47

Low Fees

8.57 5.81 5.66 0.21 0.15 13.15

9.07 5.59 4.69 1.18 0.45 6.90

10.34 5.50 4.11 3.05 1.14 2.84

10.67 5.41 3.74 6.57 2.36 0.88

10.94 5.38 3.43 21.20 6.14 7.82

Time-to-maturity (years) Coupon rate Seasoning Utilization Quantity lent (percentage) Fee

Variable

5.56 7.02 5.21 0.38 0.25 26.00

5.23 7.04 4.78 2.14 0.61 16.89

5.43 7.02 4.35 5.71 1.41 16.84

5.38 6.90 4.20 13.66 2.71 22.64

5.43 7.12 4.57 46.40 5.67 60.66

Portfolios Sorted on Utilization Low High 2 3 4 Utilization Utilization

Panel C: Quintile portfolio characteristics, high-yield industrial bonds

Time-to-maturity (years) Coupon rate Seasoning Utilization Quantity lent (percentage) Fee

Variable

Portfolios sorted on utilization Low High 2 3 4 Utilization Utilization

5.73 7.02 4.14 6.80 1.67 1.86

Low Fees

11.24 5.77 4.74 6.81 2.62 −15.97

Low Fees

Panel B: Quintile portfolio characteristics, investment-grade industrial bonds

Time-to-maturity (years) Coupon rate Seasoning Utilization Quantity lent (percentage) Fee

Variable

Portfolios Sorted on Utilization Low High 2 3 4 Utilization Utilization

Panel A: Quintile portfolio characteristics, all corporate bonds

8.61 5.88 3.74 7.26 1.99 7.82

3

7.79 5.97 4.35 5.85 1.42 10.10

4

10.41 5.41 3.71 6.41 2.11 6.62

3

9.10 5.44 4.17 4.85 1.41 9.15

4

5.65 6.85 3.93 9.94 2.03 6.98

2

5.18 6.92 4.24 9.90 1.82 9.30

3

5.06 6.93 5.09 12.21 1.86 16.76

4

Portfolios Sorted on Fees

10.79 5.53 3.90 7.03 2.48 1.23

2

Portfolios sorted on Fees

9.25 5.83 3.80 7.65 2.37 3.15

2

Portfolios Sorted on Fees

5.36 7.38 5.61 30.12 3.41 108.63

High Fees

8.35 5.52 4.82 7.37 1.74 28.57

High Fees

6.75 6.60 4.57 18.12 3.30 57.55

High Fees

Average bond loan characteristics for quintile portfolios formed by sorting on utilization using data from the Markit Securities Finance file between July 2006 and March 2015. Each month bonds are sorted into quintile portfolios based on either the average daily utilization or average daily loan fee during the previous month. The table reports the equal-weighted average characteristics of the portfolio bonds or loans of the portfolio bonds for the various portfolios. Panel A reports the average characteristics for quintile portfolios formed from the full sample of corporate bonds, including bonds issued by financial institutions and utilities. Panel B reports the average characteristics of quintile portfolios formed from investment-grade industrial bonds (Mergent industry group 1). Panel C reports the average characteristics of quintile portfolios formed from high-yield industrial bonds. Time-to-Maturity is the number of years remaining until a bond matures. Coupon is the annual interest rate paid to bond holders. Seasoning is the number of years elapsed since the issuance date. Utilization is the ratio of the total principal amount currently on loan to the total principal amount available to be loaned, in percent. Quantity Lent is the ratio of the total principal amount currently on loan to the total principal amount outstanding, in percent. Fee is the (annual) loan fee, in basis points, paid by the bond borrower.

Table 3: Three-month returns to bond portfolios sorted on utilization Equal- and value-weighted average three-month excess returns to utilization-sorted bond portfolios. Each month we sort bonds into quintile portfolios based on daily average utilization over the month, and then follow the returns for the next three months. Results are reported for three samples: (a) all available corporate bonds, (b) investmentgrade industrial bonds, and (c) high-yield industrial bonds, in that order. In each group of results, the first five rows report the results for the quintile portfolios. The next two rows report results for portfolios formed from bonds with utilization greater than the 95th and 99th percentiles, respectively. The last row of each group of result shows the average return difference between the the quintile 5 (highest) and quintile 1 (lowest) utilization-sorted portfolios. Columns (1)-(4) present average three-month equal-weighted (columns (1) and (2) and value-weighted (columns (3) and (4) excess returns relative to the TRACE market benchmark portfolio return and associated t-statistics. The TRACE benchmarks are the equal- or value- weighted average cumulative three-month return over all bonds with nonmissing returns. Columns (5)-(8) report the average equal- and value-weighted three-month excess returns relative to rating and time-to-maturity matched benchmark portfolio returns. To form these benchmarks, each month we independently sort TRACE bonds into seven rating categories (Aaa-Aa3, A1-A3, Baa1-Baa3, Ba1-Ba3, B1-B3, 20 years). The rating and maturity assignments result in 56 benchmark portfolios for which we construct rolling 3-month return series. Value-weights are based on the last observed price and amount outstanding in the last 5 days of the formation month. We compute t-statistics using Newey-West (1987) standard errors using two lags. *,**,*** indicate significance at the 10%, 5%, and 1% levels, respectively. Aggregate TRACE benchmark Portfolio

Equal-weighted Mean t-stat. (1) (2)

Rating- and maturity-matched benchmark

Value-weighted Mean t-stat. (3) (4)

Equal-weighted Mean t-stat. (5) (6)

Value-weighted Mean t-stat. (7) (8)

Full sample of corporate bonds Q1 (lowest) Q2 Q3 Q4 Q5 (highest) 95th %-tile 99th %-tile Q5 − Q1

−0.53% −0.92%** −0.85%** −0.81%** −0.71%** −0.72% −1.44% −0.18%

−1.60 −2.53 −2.34 −2.26 −1.98 −1.23 −1.62 −0.67

−0.07% −0.46% −0.40% −0.34% −0.48% −0.49% −1.21% −0.41%*

−0.22 −1.45 −1.29 −1.08 −1.56 −0.78 −1.30 −1.90

0.12%** −0.07% −0.09% −0.19%** −0.45%** −1.09%*** −2.48%*** −0.57%***

2.02 −1.63 −1.38 −2.55 −2.56 −2.89 −3.24 −3.46

0.14%*** −0.07% −0.08% −0.12%** −0.35%*** −1.06%*** −2.22%*** −0.50%***

3.03 −1.33 −1.38 −2.09 −2.95 −3.11 −3.78 −3.82

−0.42% −0.48% −0.46% −0.45% −0.35% −0.09% −1.46% 0.07%

−1.38 −1.55 −1.40 −1.35 −1.06 −0.24 −1.12 0.57

−0.07% −0.13% −0.11% −0.11% −0.15% −0.32% −2.37%*** −0.08%

−0.60 −1.19 −0.97 −1.08 −1.29 −1.41 −2.76 −1.06

−0.07% −0.07% −0.07% −0.10% −0.05% −0.14% −1.78%** 0.02%

−0.76 −0.73 −0.71 −1.02 −0.51 −0.62 −2.09 0.29

1.35%** 0.62% 0.07% 0.24% −0.07% −0.41% −1.39% −1.42%***

2.11 1.03 0.16 0.36 −0.09 −0.45 −0.92 −2.69

0.28% 0.09% −0.42% −0.57% −1.02%** −1.58%*** −2.48% −1.30%***

1.21 0.46 −1.55 −1.54 −2.22 −2.74 −1.62 −3.13

0.41%* 0.12% −0.46%* −0.49% −1.15%** −1.60%*** −3.41%** −1.56%***

1.73 0.49 −1.90 −1.39 −2.56 −3.41 −2.51 −3.44

Investment-grade industrial bonds Q1 (lowest) Q2 Q3 Q4 Q5 (highest) 95th %-tile 99th %-tile Q5 − Q1

−0.85%** −1.02%*** −0.99%** −0.96%** −0.94%** −0.91%*** −2.50%*** −0.09%

−2.22 −2.60 −2.42 −2.33 −2.39 −2.62 −2.61 −0.77

High-yield industrial bonds Q1 (lowest) Q2 Q3 Q4 Q5 (highest) 95th %-tile 99th %-tile Q5 − Q1

0.65% 0.07% −0.34% −0.25% −0.26% −0.73% −0.92% −0.91%**

1.19 0.16 −0.82 −0.44 −0.35 −0.86 −0.60 −2.14

43

Table 4: Bond lending fees Average bond lending fees, in basis points, for 25 bond portfolios from July 2006 to March 2015. Lending fees are from Markit’s Securities Finance files and are the value-weighted average fee across all open loans for each bond (Markit variable VWAF All ). Each month we sort bonds sequentially into quintiles based on average utilization during the prior month and then, within each utilization quintile, into quintiles based on average lending fees during the prior month. For each portfolio and month, we then compute the average lending fee. The table reports the time-series averages of the monthly portfolio lending fees for each of the double-sorted portfolios. Utilization is the ratio of the total principal amount currently out on loan to the total principal amount available to be lent, and fee is the annual lending fee. The average loan fees of the double-sorted portfolios are reported for three samples of bonds: Panel A uses the full sample of all corporate bonds, Panel B uses the subsample of investment-grade industrial bonds, and Panel C uses the subsample of high-yield industrial bonds, where an industrial bond is one issued by a company assigned Mergent industry code 1. The last row in each panel reports for each lending fee quintile the difference in the average lending fees between the high and low utilization quintile portfolios. Similarly, the last column of each panel reports for each utilization quintile the difference in average lending fees between the high and low fee quintile portfolios.

Panel A: Lending fees (basis points), full sample of corporate bonds Portfolios sorted on lending fees Low High Fees 2 Fees 3 Fees 4 Fees Fees Low utilization Portfolios sorted by utilization

−1.76

7.88

9.74

11.68

47.56

−5.53

5.91

8.24

9.58

25.34

30.84

Utilization 3

−14.54

1.33

6.27

8.91

26.39

40.93

Utilization 4

−19.95

−2.74

3.64

8.59

31.86

51.81

High utilization

−13.83

0.38

7.62

17.71

131.82

145.65

High−Low

−12.07

−7.50

−2.12

6.02

84.26

High−Low

Low utilization

−0.50

7.64

9.35

11.10

32.09

32.59

Utilization 2

−8.32

5.44

7.89

9.27

20.13

28.45

Utilization 3

−17.66

−0.52

5.14

8.36

18.41

36.07

Utilization 4

−21.60

−4.09

2.65

7.23

19.40

41.00

High utilization

−19.67

−4.64

2.28

7.61

52.10

71.78

High−Low

−19.17

−12.27

−7.07

−3.49

20.02

Panel C: Lending fees (basis points), high-yield industrial bonds Portfolios sorted on lending fees Low High Fees 2 Fees 3 Fees 4 Fees Fees

Portfolios sorted by utilization

49.32

Utilization 2

Panel B: Lending fees (basis points), investment-grade industrial bonds Portfolios sorted on lending fees Low High Fees 2 Fees 3 Fees 4 Fees Fees

Portfolios sorted by utilization

High−Low

High−Low

Low utilization

1.08

7.91

9.28

11.85

99.28

98.20

Utilization 2

2.27

6.55

8.32

10.42

41.00

38.73

Utilization 3

1.78

6.36

8.22

10.81

49.97

48.18

Utilization 4

2.70

6.81

8.72

13.58

79.45

76.74

High utilization

6.14

13.70

33.80

80.41

250.94

244.80

High−Low

5.06

5.79

24.53

68.56

151.66

44

Table 5: Returns to bond portfolios sorted on utilization and lending fees Equal-weighted average three-month excess returns, in percentage points, for 25 bond portfolios from July 2006 to March 2015. We sort bonds sequentially into quintiles based on average utilization during the portfolio formation month and then, within each utilization quintile, into quintiles based on average lending fees, and then follow the returns for three months. The three-month excess bond return is the cumulative monthly return less the cumulative return on the credit rating and maturity-matched benchmark portfolio. The portfolio excess return is the equalweighted average excess return over bonds in the portfolio. Panel A reports results for the full sample all available corporate bonds, Panel B for the subsample of investment-grade industrial bonds, and Panel C for the subsample of high-yield industrial bonds, where an industrial bond is one issued by a company assigned Mergent industry code 1. Utilization is the ratio of the total principal amount currently on loan to the total principal amount available to be loaned, and fee is the annual lending rate. The last column of each panel reports the difference in the three-month excess returns between the highest and lowest fee quintile portfolios within each utilization quintile. t-statistics based on Newey-West (1987) standard errors using two lags are in parentheses below the average returns. *,**,*** indicate significance at the 10%, 5%, and 1% levels, respectively. Panel A: All corporate bonds

Low Fees

Portfolios sorted on utilization

Portfolios sorted on lending fees High Fees 2 Fees 3 Fees 4 Fees

High−Low (5)−(1)

Low utilization

−0.08 (−0.73)

0.01 (0.13)

0.01 (0.09)

0.06 (0.34)

0.13 (0.82)

0.20 (1.24)

Utilization 2

−0.07 (−1.35)

−0.16* (−1.71)

−0.11 (−1.12)

−0.13 (−1.49)

0.58*** (2.62)

0.65** (2.05)

Utilization 3

−0.15** (−2.07)

−0.20** (−2.51)

−0.11 (−1.02)

−0.08 (−0.84)

0.16 (0.84)

0.30* (1.65)

Utilization 4

−0.11* (−1.87)

−0.19** (−2.31)

−0.30*** (−2.99)

−0.27** (−2.35)

−0.22 (−1.04)

−0.10 (−0.52)

High utilization

−0.19** (−2.12)

−0.14 (−1.34)

−0.29** (−2.54)

−0.24 (−1.60)

−0.96*** (−2.78)

−0.76** (−2.38)

Panel B: Investment-grade industrial bonds

Low Fees

Portfolios sorted on utilization

Portfolios sorted on lending fees High Fees 2 Fees 3 Fees 4 Fees

High−Low (5)−(1)

Low utilization

−0.21* (−1.71)

−0.07 (−0.56)

0.06 (0.43)

−0.12 (−0.51)

−0.07 (−0.72)

0.14 (1.51)

Utilization 2

−0.09 (−0.83)

−0.17 (−1.29)

−0.19* (−1.66)

−0.21* (−1.82)

0.05 (0.24)

0.14 (1.02)

Utilization 3

−0.07 (−0.60)

−0.09 (−0.74)

−0.18 (−1.38)

−0.12 (−0.98)

−0.16 (−0.71)

−0.09 (−0.63)

Utilization 4

−0.13 (−1.21)

−0.13 (−1.05)

0.00 (−0.04)

−0.09 (−0.89)

−0.07 (−0.57)

0.06 (0.32)

High utilization

−0.25* (−1.72)

−0.12 (−0.82)

0.10 (0.69)

−0.01 (−0.11)

−0.24 (−1.27)

0.01 (0.07)

45

Table 5 Continued: Returns to portfolios sorted on utilization and lending fees Panel C: High-yield industrial bonds

Low Fees

High−Low (5)−(1)

0.54 (1.27)

0.19 (0.42)

0.04 (0.07)

−0.58* (−1.69)

0.95 (1.37)

0.41 (0.99)

Utilization 2

−0.21 (−0.68)

−0.16 (−0.52)

−0.39 (−1.20)

0.28 (0.59)

1.55* (1.91)

1.76* (1.86)

Utilization 3

−0.26 (−0.87)

−0.45* (−1.66)

−0.68** (−2.02)

−0.75* (−1.80)

0.14 (0.18)

0.40 (0.64)

Utilization 4

−0.21 (−0.70)

−0.33 (−1.31)

−0.71 (−1.40)

−0.75* (−1.87)

−0.21 (−0.28)

0.00 (0.00)

High utilization

−0.35 (−1.09)

−0.89** (−2.40)

−0.76* (−1.78)

−1.66** (−2.44)

−2.92*** (−3.80)

−2.57*** (−3.22)

Low utilization Portfolios sorted on utilization

Portfolios Sorted on lending Fees High Fees 2 Fees 3 Fees 4 Fees

46

Table 6: Fee-adjusted returns to bond portfolios sorted on utilization and lending fees Equal-weighted average three-month excess returns, in percentage points, for 25 bond portfolios from July 2006 to March 2015, inclusive of bond lending fees. The methodology and presentation are identical to Table 5 except that the bond-level returns are adjusted to include the lending fees received by a bond owner who lends their holdings. Panel A: All corporate bonds

Low Fees

Portfolios sorted on utilization

Portfolios sorted on lending fees High Fees 2 Fees 3 Fees 4 Fees

(5)−(1)

Low utilization

−0.07 (−0.66)

0.04 (0.30)

0.03 (0.40)

0.09 (0.52)

0.21** (1.96)

0.28* (1.75)

Utilization 2

−0.08 (−1.46)

−0.14 (−1.54)

−0.09 (−0.91)

−0.11 (−1.21)

0.68*** (3.07)

0.76** (2.11)

Utilization 3

−0.18*** (−3.50)

−0.19** (−2.41)

−0.10 (−0.86)

−0.06 (−0.60)

0.26 (1.41)

0.44* (1.83)

Utilization 4

−0.16** (−2.56)

−0.20** (−2.36)

−0.29*** (−2.88)

−0.25** (−2.15)

−0.10 (−0.45)

0.06 (0.28)

High utilization

−0.25*** (−2.60)

−0.15 (−1.47)

−0.28** (−2.50)

−0.21 (−1.43)

−0.72** (−2.10)

−0.47 (−1.42)

Panel B: Investment-grade industrial bonds

Low Fees

Portfolios sorted on utilization

Portfolios sorted on lending fees High Fees 2 Fees 3 Fees 4 Fees

(5)−(1)

Low utilization

−0.20* (−1.65)

−0.05 (−0.41)

0.08 (0.61)

−0.10 (−0.40)

−0.02 (−0.16)

0.18** (1.97)

Utilization 2

−0.10 (−0.96)

−0.15 (−1.18)

−0.17 (−1.49)

−0.19 (−1.63)

0.10 (0.52)

0.20 (1.42)

Utilization 3

−0.10 (−0.95)

−0.09 (−0.75)

−0.16 (−1.27)

−0.10 (−0.81)

−0.10 (−0.44)

0.01 (0.04)

Utilization 4

−0.19* (−1.69)

−0.14 (−1.15)

0.00 (0.02)

−0.07 (−0.71)

−0.01 (−0.10)

0.18 (0.85)

High utilization

−0.31** (−2.10)

−0.13 (−0.94)

0.10 (0.72)

0.00 (0.02)

−0.13 (−0.71)

0.17 (0.98)

Panel C: High-yield industrial bonds

Low Fees

(5)−(1)

0.54 (1.29)

0.21 (0.46)

0.06 (0.11)

−0.55 (−1.60)

1.14* (1.66)

0.60 (1.35)

Utilization 2

−0.21 (−0.66)

−0.15 (−0.47)

−0.37 (−1.14)

0.31 (0.65)

1.73** (2.14)

1.94 (1.35)

Utilization 3

−0.25 (−0.85)

−0.44 (−1.60)

−0.66** (−1.96)

−0.73* (−1.73)

0.31 (0.39)

0.56 (0.84)

Utilization 4

−0.20 (−0.68)

−0.32 (−1.24)

−0.68 (−1.36)

−0.71* (−1.78)

0.03 (0.05)

0.24 (0.35)

High utilization

−0.34 (−1.05)

−0.86** (−2.34)

−0.71* (−1.67)

−1.51** (−2.25)

−2.40*** (−3.13)

−2.07** (−2.45)

Low utilization Portfolios sorted on utilization

Portfolios sorted on lending fees High Fees 2 Fees 3 Fees 4 Fees

47

Table 7: Cross-sectional regressions explaining bond returns Results of monthly Fama-MacBeth regressions explaining three-month bond returns from July 2006 to March 2015. In each monthly regression the unit of observation is a bond and the dependent variable is the holding period return over the subsequent three months. Each month we sort bonds sequentially into quintiles based on average utilization during the month and then, within each utilization quintile, into quintiles based on the average lending fee during the month. The key variable of interest is the interaction term DHighBondU til × DHighBondF ee , where DHighBondU til and DHighBondF ee are indicator variables that take the value one for bonds in the highest utilization or fee quintiles, respectively. Results are reported for three samples of bonds: the full sample of all corporate bonds, a subsample of investment-grade industrial bonds, and a subsample of high-yield industrial bonds. The baseline specification, presented in columns (1), (3), and (5) includes as covariates only the bond lending market variables. Columns (2), (4), and (6) present results of specifications that control for bond and bond loan characteristics. These characteristics are the log of years remaining to maturity (ln(T T M )), the coupon rate in percentage points (Coupon), the log of the principal amount outstanding in thousands (ln(AmountOut)), the average quantified credit rating (NR or missing = 0, AAA = 1, AA+ = 2 ) over ratings from Moodys, S&P and Fitch (Rating), an indicator variable that equals one if Rating = 0 (N otRated), the Amihud illiquidity ratio (AmihudRatio), and the realized spread (RealizedSpread). The monthly AmihudRatio and RealizedSpread used in the regression are the medians of the daily measures during the month, where the daily Amihud ratio is the average of absolute returns between sequential trades normalized by trade size in millions and the daily realized spread is the difference between the average customer sell price and the average customer buy price each day. The table reports the time-series averages of the coefficient estimates from the monthly cross-sectional regressions. t-statistics based on Newey-West (1987) standard errors using two lags are in parentheses below the average coefficient estimates. *,**,*** indicate significance at the 10%, 5%, and 1% levels, respectively. Full sample of all bonds Variable

Investment-grade industrial bonds

High-yield, industrial bonds

(1)

(2)

(3)

(4)

(5)

(6)

DHighBondU til

−0.001 (−0.71)

−0.001 (−0.29)

−0.001 (−1.09)

−0.001 (−1.33)

−0.005 (−0.76)

−0.001 (−0.39)

DHighBondF ee

0.013*** (3.06)

0.012*** (2.95)

0.003** (2.46)

0.003*** (2.80)

0.021*** (2.62)

0.026*** (2.71)

DHighBondU til × DHighBondF ee

−0.015* (−1.90)

−0.011** (−2.12)

−0.008 (−1.11)

−0.006 (−1.17)

−0.033*** (−3.79)

−0.036*** (−3.56)

ln(T T M )

0.004** (2.12)

0.005** (2.23)

0.001 (0.33)

0.001 (1.35)

0.002** (2.06)

0.002 (1.34)

ln(AmountOut)

0.001 ( −0.49)

−0.001 (−0.85)

0.001 (0.39)

Rating

0.003 (−0.95)

0.002 (−0.99)

0.005** (−2.22)

N otRated

0.010 (−1.44)

0.002 (−0.87)

0.008 (−1.59)

AmihudRatio

0.204*** ( 3.15)

0.136*** (3.41)

0.190 (1.59)

RealizedSpread

−0.016 ( −1.57)

−0.002 ( −0.35)

−0.021 ( −1.13)

Coupon

Constant R2

0.008*** (2.93)

−0.008 (−0.48)

0.007*** (3.20)

0.024 (1.60)

0.013*** (2.74)

−0.029 (−0.99)

0.083

0.268

0.076

0.331

0.127

0.249

48

Table 8: CDS-Bond basis Equal-weighted average CDS-bond basis, in percentage points, for double-sorted bond portfolios from July 2006 to March 2013. Each month we sort bonds sequentially into quintiles based on average utilization and then, within each utilization quintile, into quintiles based on average lending fees. For each portfolio, the table reports the equal-weighted average CDS-bond basis, defined as the difference between the CDS spread and the par equivalent spread, over the portfolio bonds for which we have an estimate of the CDS-bond basis. t-statistics are in parentheses below the estimates of the average CDS-bond basis. Appendix A describes the computation of the par equivalent spread and the CDS-bond basis. Due to the availability of the CDS data, the sample period ends March 2013, two years earlier than the sample periods for most other analyses. Panels A and B present the monthly average CDS-bond basis for investment-grade and high-yield industrial bonds, respectively. *,**,*** indicating significance at the 10%, 5%, and 1% level respectively.

Portfolios sorted on utilization

Panel A: Average basis (percent), investment-grade industrial bonds Portfolios sorted on lending fees Low fees

Fees 2

Fees 3

Fees 4

High Fees

Unconditional utilization

(5)−(1)

Low utilization

−0.55** (−2.25)

−0.57*** (−2.85)

−0.53** (−2.38)

−0.47** (−2.45)

−0.59*** (−2.66)

−0.54*** (−3.38)

−0.04 (−0.21)

Utilization 2

−0.49** (−2.55)

−0.63*** (−3.49)

−0.55*** (−2.88)

−0.53** (−2.53)

−0.53** (−2.30)

−0.55*** (−3.37)

−0.04 (−0.14)

Utilization 3

−0.40 (−1.34)

−0.26 (−1.16)

−0.26 (−1.22)

−0.24 (−1.37)

−0.28 (−1.18)

−0.29 (−0.56)

0.12 (0.31)

Utilization 4

−0.32 (−1.05)

−0.42 (−1.56)

−0.43* (−1.67)

−0.22 (−0.85)

−0.04 (−0.12)

−0.29 (−0.63)

0.28 (0.56)

High Utilization

−0.42 (−1.36)

−0.44 (−1.19)

−0.36 (−1.02)

0.06 (0.18)

0.40 (1.39)

−0.15 (−0.42)

0.82 (1.21)

Unconditional fees

−0.44***

−0.46**

−0.43**

−0.28

−0.21

(−2.75)

(−2.19)

(−1.97)

(−1.41)

(−1.06)

Portfolios Sorted on utilization

Panel B: Average basis (percent), high-yield industrial bonds Portfolios sorted on lending fees Low fees

Fees 2

Fees 3

Fees 4

High fees

Unconditional utilization

(5)−(1)

Low utilization

−1.40** (−2.03)

−0.67 (−1.45)

−0.88 (−1.57)

−1.32** (−2.28)

−0.88** (−1.98)

−1.06*** (−2.81)

0.52 (0.72)

Utilization 2

−1.02** (−1.97)

−0.71 (−1.08)

−0.75* (−1.83)

−0.85* (−1.95)

−0.98** (−2.03)

−0.83* (−1.85)

0.04 (0.13)

Utilization 3

−1.46*** (−2.82)

−1.63*** (−2.90)

−1.55** (−2.17)

−1.94*** (−3.33)

−0.91 (−1.39)

−1.65*** (−2.97)

0.55 (0.85)

Utilization 4

−1.64*** (−3.57)

−1.25*** (−2.93)

−1.29** (−2.15)

−1.19** (−2.45)

−1.08 (−0.27)

−1.34*** (−2.73)

0.56 (1.15)

High Utilization

−1.00 (−1.39)

−0.98 (−1.51)

−0.61 (−0.25)

0.49 (1.56)

0.55* (1.73)

−0.53 (−0.93)

1.55*** (2.92)

Unconditional fees

−1.30**

−1.04***

−1.02***

−0.96**

−0.66

(−2.35)

(−2.93)

(−2.85)

(−2.31)

(−1.48)

49

Table 9: Bond returns by CDS coverage Average three-month excess returns for portfolios formed from bonds issued by industrial companies (Mergent industry group 1) with and without traded CDS, where a traded CDS is one for which a quote is available in the Markit CDS data. Each month we sort bonds sequentially into quintiles based on average utilization during the prior month and then, within each utilization quintile, into quintiles based on average lending fees during the prior month; we then follow the returns for three months. The three-month excess bond return is the cumulative monthly return less the cumulative return on the credit rating and maturity-matched benchmark portfolio. The portfolio excess return is the equal-weighted average excess return over bonds in the portfolio. Columns (1) and (2) report the average portfolio three-month excess returns and associated t-statistics for portfolios formed from high fee and high utilization bonds issued by companies with and without traded CDS, respectively. For this table, we define high fee and high utilization bonds to be those in the top two fee quintiles within the top utilization quintiles, that is the bonds in {4, 4}, {4, 5}, {5, 4}, and {5, 5} portfolios. Column (3) reports the difference in excess returns between the bonds with and without traded CDS. Columns (4) and (5) report the average portfolio three-month excess returns for portfolios formed from bonds in the top fee quintile within the top utilization quintile (portfolio {5, 5}) for issuers with and without traded CDS. The first two rows report the average returns and t-statistics for investment-grade industrial bonds and the last two rows report the results for high-yield industrial bonds portfolios. t-statistics are based on Newey-West (1987) standard errors using two lags. *,**,*** indicate significance at the 10%, 5%, and 1% level respectively.

High utilization and fee bonds Has CDS No CDS Difference (2) − (1) (1) (2) (3)

Highest utilization and fee bonds Has CDS No CDS Difference (5) − (4) (4) (5) (6)

Investment-grade industrial bonds

−1.82%** (−2.07)

0.04% (0.11)

1.86%* (1.95)

−2.02%** (−2.06)

−0.17% (−0.32)

1.85%** (2.22)

High-yield industrial bonds

−1.39% (−1.28)

−2.70%*** (−3.07)

−1.30%** (−2.01)

−2.45%** (−2.37)

−3.05%*** (−3.06)

−0.60% (−0.71)

50

Table 10: Cross-sectional regressions explaining bond returns augmented with equity lending market variables Results of monthly Fama-MacBeth regressions explaining three-month future bond returns from July 2006 to March 2015. The regressions are similar to those reported in Table 7, except that they include additional covariates computed from equity lending market fees and utilization. DHighEquityU til takes the value one for bonds issued by companies with equity lending utilization in the top quintile, and zero otherwise; DHighEquityF ee takes the value one for bonds issued by companies with equity lending fees in the top quintile, and zero otherwise; and DHighEquityU til × DHighEquityF ee is the interaction between the two. The other variables are described in the legend of Table 7. This table reports the time-series averages of the coefficient estimates from the monthly cross-sectional regressions. t-statistics based on Newey-West (1987) standard errors using two lags are in parentheses below the average coefficient estimates. *,**,*** indicate significance at the 10%, 5%, and 1% levels, respectively. Full sample of all bonds Variable

Investment-grade industrial bonds

High-yield, Industrial bonds

(1)

(2)

(3)

(4)

(5)

(6)

DHighBondU til

0.000 (0.07)

−0.001 (−0.47)

0.000 (0.24)

−0.001 (−0.70)

−0.001 (−0.36)

−0.006** (−1.98)

DHighBondF ee

0.004*** (2.88)

0.004** (2.29)

0.000 (−0.36)

0.000 (−0.20)

0.013** (2.53)

0.006** (1.99)

DHighBondU til × DHighBondF ee

−0.006** (−2.43)

−0.007** (−2.27)

−0.001 (−0.94)

0.000 (−0.32)

−0.023*** (−3.19)

−0.019*** (−2.93)

DHighEquityU til

−0.001 (−0.23)

−0.005 (−1.07)

0.000 (−0.08)

0.000 (−0.02)

−0.004 (−0.98)

−0.001 (−0.32)

DHighEquityF ee

0.005*** (2.86)

0.002 (1.51)

0.002** (2.01)

0.001 (1.22)

−0.008 (−1.25)

−0.015** (−2.18)

DHighEquityU til × DHighEquityF ee

−0.003 (−0.57)

−0.004 (−0.65)

−0.001 (−0.44)

−0.001 (−0.35)

0.008 (1.08)

0.015 (1.40)

ln(T T M )

0.005** (2.51)

0.006** (2.54)

0.005 (1.24)

Coupon

0.000*** (2.62)

0.001 (0.88)

0.002*** (3.26)

ln(AmountOut)

−0.001 (−0.50)

0.000 (1.41)

−0.004** (−2.43)

Rating

0.002** (−2.26)

0.001 (−0.90)

0.004 (1.58)

N otRated

0.009 (−1.36)

0.003 (−0.46)

0.010* (1.66)

AmihudRatio

0.049 ( 1.06)

0.045* (1.90)

0.143* (1.65)

RealizedSpread

0.001 (0.02)

−0.005 (−1.03)

0.015 (0.43)

Constant R2

0.009*** (2.89)

−0.050 (−0.30)

0.009*** (2.78)

−0.006 (−0.47)

0.015** (2.22)

0.110 (0.55)

0.094

0.262

0.05

0.33

0.129

0.286

51

Table B.1: Monthly returns to bond portfolios sorted by utilization and lending fees Asquith, Au, Covert, and Pathak (2013) Table 9 presents average raw and excess monthly returns of bond portfolios sorted on utilization and lending fees, using data from a single securities lender. This table presents the same analyses using the Markit bond lending data, together with analyses of subsamples that are not included in Asquith, Au, Covert, and Pathak (2013) Table 9. Each month we sort bonds into quintile portfolios based on average daily utilization (percent of inventory on loan) or lending fee during the month, and also into portfolios formed from bonds with utilization or lending fees above the 95th and 99th percentiles. Then for each portfolio we compute the equal-weighted and issue-size value-weighted raw and excess returns over the next month, where the excess return is the portfolio return less the equal- or issue-size value-weighted TRACE benchmark return formed from all bonds with available prices in TRACE. Panels A and B report the results for the utilization and lending fee sorts, respectively. Each panel presents results for three samples of bonds: (i) all available corporate bonds, (ii) investment-grade industrial bonds, and (iii) high-yield industrial bonds, in this order. The monthly return for each bond is (Pt − Pt−1 + AIt + Ct−1,t )/(Pt−1 + AIt−1 ), where Pt is the last observed price during the last five days of month t, AI is accrued interest, and Ct−1,t is the coupon paid during the holding period from t − 1 to t. The TRACE benchmark return is the equal- or issue-size value-weighted monthly return for a portfolio of all corporate bonds that pass our filters and have non-missing returns. t-statistics are based on Newey-West (1987) standard errors using two lags. *,**,*** indicate significance at the 10%, 5%, and 1% levels, respectively. Panel A: Bond portfolios formed by sorting on utilization (percent of inventory on loan)

Portfolio

Number of bonds

Equal-weighted

Value-weighted

Excess returns relative to TRACE market benchmark Equal-weighted Value-weighted

Mean

t−stat

Mean

t−stat

Mean

t−stat

Mean

t−stat

bonds 0.68%*** 0.59%*** 0.63%*** 0.64%*** 0.63%** 0.64%* 0.29% −0.06%

3.97 3.34 3.51 3.48 2.41 1.65 0.58 −0.44

0.66%*** 0.56%*** 0.62%*** 0.61%*** 0.55%** 0.55% 0.27% −0.11%

3.61 2.92 3.31 3.24 2.29 1.46 0.53 −0.95

−0.18% −0.28% −0.24% −0.23% −0.24% −0.23% −0.58% −0.06%

−0.73 −1.04 −0.89 −0.82 −0.86 −0.65 −1.25 −0.44

−0.20% −0.31% −0.25% −0.26% −0.32% −0.31% −0.60% −0.11%

−0.90 −1.29 −1.04 −1.04 −1.28 −0.91 −1.30 −0.95

Investment-grade industrial bonds Q1 (lowest) 290 0.57%*** Q2 289 0.55%*** Q3 289 0.56%*** Q4 289 0.59%*** Q5 (highest) 289 0.58%*** 95th %-tile 72 0.66%*** 99th %-tile 15 0.40% Q5 − Q1 0.00%

4.15 3.56 3.52 3.55 3.21 2.75 0.70 0.03

0.53%*** 0.56%*** 0.57%*** 0.59%*** 0.60%*** 0.79%*** 0.55% 0.06%

3.77 3.42 3.36 3.35 3.20 2.88 0.80 0.91

−0.29% −0.32% −0.30% −0.28% −0.29% −0.21% −0.46% 0.00%

−1.15 −1.12 −1.06 −0.96 −1.04 −0.76 −0.89 0.03

−0.33% −0.31% −0.30% −0.28% −0.27% −0.08% −0.32% 0.06%

−1.60 −1.32 −1.24 −1.14 −1.12 −0.30 −0.49 0.91

High-yield industrial bonds Q1 (lowest) 142 0.96%*** Q2 142 0.86%*** Q3 141 0.73%** Q4 141 0.65%* Q5 (highest) 141 0.70% 95th %-tile 35 0.58% 99th %-tile 7 0.19% Q5 − Q1 −0.26%

3.05 2.96 2.42 1.71 1.54 1.15 0.25 −1.23

0.98%*** 0.91%*** 0.64%** 0.63% 0.66% 0.51% −0.08% −0.32%

2.87 2.59 1.98 1.62 1.42 0.95 −0.10 −1.35

0.09% −0.01% −0.13% −0.22% −0.17% −0.28% −0.68% −0.26%

0.30 −0.03 −0.45 −0.67 −0.41 −0.61 −0.94 −1.23

0.11% 0.04% −0.23% −0.23% −0.21% −0.36% −0.95% −0.32%

0.36 0.13 −0.79 −0.70 −0.51 −0.75 −1.26 −1.35

Mean Full sample of corporate Q1 (lowest) 750 Q2 749 Q3 749 Q4 749 Q5 (highest) 748 95th %-tile 182 99th %-tile 37 Q5 − Q1

Raw returns

52

Table B.1 Continued: Monthly returns to bond portfolios

Panel B: Bond portfolios formed by sorting on loan fees Portfolio

Number Bonds

Equal-weighted

Value-weighted

Excess returns relative to TRACE market benchmark Equal-weighted Value-weighted

Mean

t−stat

Mean

t−stat

Mean

t−stat

Mean

t−stat

bonds 0.60%*** 0.58%*** 0.52%*** 0.55%*** 0.89%*** 1.33%*** 1.70%** 0.29%

3.46 3.02 2.90 3.22 3.20 2.77 2.45 1.48

0.57%*** 0.57%*** 0.46%** 0.53%*** 0.90%*** 1.41%*** 1.79%** 0.33%*

3.20 2.82 2.42 3.18 3.31 2.84 2.39 1.69

−0.27% −0.29% −0.35% −0.32% 0.02% 0.47% 0.84% 0.29%

−0.92 −1.04 −1.31 −1.29 0.08 1.08 1.37 1.48

−0.30% −0.30% −0.40%* −0.33% 0.03% 0.54% 0.92% 0.33%*

−1.17 −1.17 −1.70 −1.57 0.13 1.19 1.34 1.69

Investment-grade industrial bonds Q1 (lowest) 287 0.56%*** Q2 289 0.59%*** Q3 257 0.52%*** Q4 309 0.54%*** Q5 (highest) 323 0.59%*** 95th %-tile 73 0.75%*** 99th %-tile 14 1.73%** Q5 − Q1 0.03%

3.23 3.31 3.27 3.71 3.89 2.83 2.00 0.33

0.57%*** 0.60%*** 0.53%*** 0.53%*** 0.58%*** 0.74%*** 1.26% 0.01%

3.09 3.20 3.19 3.72 3.80 2.96 1.50 0.15

−0.31% −0.28% −0.35% −0.33% −0.28% −0.12% 0.86% 0.03%

−1.02 −0.93 −1.21 −1.24 −1.13 −0.44 1.13 0.33

−0.30% −0.27% −0.34% −0.33% −0.29% −0.13% 0.39% 0.01%

−1.18 −1.07 −1.44 −1.57 −1.42 −0.48 0.49 0.15

High-yield industrial bonds Q1 (lowest) 140 0.73%** Q2 133 0.66%** Q3 139 0.71%** Q4 152 0.62%* Q5 (highest) 143 1.12%** 95th %-tile 36 1.16%* 99th %-tile 7 0.75% Q5 − Q1 0.39%

2.38 2.37 2.40 1.87 2.01 1.84 0.83 1.22

0.66%** 0.63%** 0.62%** 0.58% 1.26%** 1.30%* 0.41% 0.60%

2.04 2.23 2.02 1.61 1.99 1.72 0.41 1.47

−0.14% −0.21% −0.16% −0.25% 0.25% 0.29% −0.12% 0.39%

−0.47 −0.74 −0.59 −0.81 0.49 0.50 −0.14 1.21

−0.21% −0.24% −0.25% −0.29% 0.40% 0.43% −0.45% 0.60%

−0.71 −0.90 −0.92 −0.96 0.68 0.60 −0.45 1.47

Mean Full sample of corporate Q1 (lowest) 781 Q2 866 Q3 635 Q4 796 Q5 (highest) 706 95th %-tile 143 99th %-tile 28 Q5 − Q1

Raw returns

53

54

Table C.1: Excess returns to bond portfolios over one- and three-month horizons

Equal-weighted 1month excess returns matched benchmark Mean t−stat. (1) (2)

Full sample of corporate bonds Q1 (lowest) 0.03% 0.67 Q2 −0.01% −0.28 Q3 0.01% 0.16 Q4 −0.03% −0.58 Q5 (highest) −0.16% −1.11 95th %-tile −0.36% −1.14 99th %-tile −0.95%* −1.81 Q5 − Q1 −0.18% −1.51 Investment-grade industrial bonds Q1 (lowest) −0.04% −0.63 Q2 −0.03% −0.50 Q3 −0.03% −0.47 Q4 −0.01% −0.09 Q5 (highest) −0.05% −0.75 95th %-tile −0.07% −0.51 99th %-tile −0.53% −1.14 Q5 − Q1 −0.01% −0.23 High-yield industrial bonds Q1 (lowest) 0.01% 0.07 Q2 0.04% 0.31 Q3 −0.17% −0.74 Q4 −0.31% −1.07 Q5 (highest) −0.41% −1.05 95th %-tile −0.57% −1.40 99th %-tile −1.33% −1.37 Q5 − Q1 −0.42% −1.48

Portfolio

1.40 −0.77 0.39 −0.65 −1.25 −1.41 −2.10 −1.61 −0.84 −0.29 −0.32 −0.03 −0.38 −0.02 −0.92 0.63 0.33 0.50 −1.07 −1.11 −1.19 −1.83 −1.52 −1.53

0.04% −0.03% 0.02% −0.03% −0.12% −0.42% −0.96%** −0.16% −0.05% −0.02% −0.02% 0.00% −0.02% 0.00% −0.51% 0.03% 0.05% 0.08% −0.24% −0.31% −0.46% −0.67%* −1.60% −0.51%

Value-weighted 1month excess returns matched benchmark Mean t−stat. (3) (4)

0.65% 0.07% −0.34% −0.25% −0.26% −0.73% −0.92% −0.91%**

−0.85%** −1.02%*** −0.99%** −0.96%** −0.94%** −0.91%*** −2.50%*** −0.09%

−0.53% −0.92%** −0.85%** −0.81%** −0.71%** −0.72% −1.44% −0.18%

1.19 0.16 −0.82 −0.44 −0.35 −0.86 −0.60 −2.14

−2.22 −2.60 −2.42 −2.33 −2.39 −2.62 −2.61 −0.77

−1.60 −2.53 −2.34 −2.26 −1.98 −1.23 −1.62 −0.67

Equal-weighted 3month excess returns TRACE benchmark Mean t−stat. (5) (6)

1.35%** 0.62% 0.07% 0.24% −0.07% −0.41% −1.39% −1.42%***

−0.42% −0.48% −0.46% −0.45% −0.35% −0.09% −1.46% 0.07%

−0.07% −0.46% −0.40% −0.34% −0.48% −0.49% −1.21% −0.41%*

2.11 1.03 0.16 0.36 −0.09 −0.45 −0.92 −2.69

−1.38 −1.55 −1.40 −1.35 −1.06 −0.24 −1.12 0.57

−0.22 −1.45 −1.29 −1.08 −1.56 −0.78 −1.30 −1.90

Value-weighted 3month excess returns TRACE benchmark Mean t−stat. (7) (8)

Panel A: Bond portfolios formed by sorting on utilization (percent of inventory on loan)

0.28% 0.09% −0.42% −0.57% −1.02%** −1.58%*** −2.48% −1.30%***

−0.07% −0.13% −0.11% −0.11% −0.15% −0.32% −2.37%*** −0.08%

0.12%** −0.07% −0.09% −0.19%** −0.45%** −1.09%*** −2.48%*** −0.57%***

1.21 0.46 −1.55 −1.54 −2.22 −2.74 −1.62 −3.13

−0.60 −1.19 −0.97 −1.08 −1.29 −1.41 −2.76 −1.06

2.02 −1.63 −1.38 −2.55 −2.56 −2.89 −3.24 −3.46

Equal-weighted 3month excess returns matched benchmark Mean t−stat. (9) (10)

0.41%* 0.12% −0.46%* −0.49% −1.15%** −1.60%*** −3.41%** −1.56%***

−0.07% −0.07% −0.07% −0.10% −0.05% −0.14% −1.78%** 0.02%

0.14%*** −0.07% −0.08% −0.12%** −0.35%*** −1.06%*** −2.22%*** −0.50%***

1.73 0.49 −1.90 −1.39 −2.56 −3.41 −2.51 −3.44

−0.76 −0.73 −0.71 −1.02 −0.51 −0.62 −2.09 0.29

3.03 −1.33 −1.38 −2.09 −2.95 −3.11 −3.78 −3.82

Value-weighted 3month excess returns matched benchmark Mean t−stat. (11) (12)

Average bond portfolio excess returns for both one- and three-month horizons. Table 3 describes the portfolio sorting procedure and both the TRACE and rating- and maturity-matched benchmark portfolios used to compute excess returns. Columns (1)-(4) present average monthly equal-weighted and issue-size value-weighted excess returns relative to the rating- and maturity-matched benchmark portfolio returns, as well as the associated t-statistics. Columns (5)-(8) report the results for the equal- and valueweighted three-month excess returns relative to the three-month aggregate TRACE benchmark return, and columns (9)-(10) report the results for the equal- and value- weighted three-month excess returns relative to the three-month rating- and maturity-matched benchmark portfolio returns. t-statistics are based on Newey-West (1987) standard errors using two lags. *,**,*** indicate significance at the 10%, 5%, and 1% levels, respectively.

55

Equal-weighted 1month excess returns matched benchmark Mean t−stat (1) (2)

−0.02% −0.01% −0.01% −0.02% −0.03% −0.04% −0.27% −0.01%

−0.10% −0.14% −0.23% −0.32% −0.10% −0.16% −1.01% 0.00%

High-yield industrial bonds Q1 (lowest) −0.05% −0.35 Q2 −0.15% −0.78 Q3 −0.17% −0.82 Q4 −0.28% −1.12 Q5 (highest) −0.22% −0.51 95th %-tile −0.27% −0.56 99th %-tile −0.80% −0.98 Q5 − Q1 −0.17% −0.46

−0.02% −0.04% −0.03% −0.04% 0.00% −0.02% 0.25% 0.02%

−0.71 −0.83 −1.12 −1.10 −0.24 −0.31 −1.15 −0.01

−0.34 −0.11 −0.19 −0.37 −0.45 −0.25 −0.42 −0.14

−0.45 −0.76 −0.82 −0.71 0.04 −0.08 0.53 0.17

Value-weighted 1month excess returns matched benchmark Mean t−stat (3) (4)

Investment-grade industrial bonds Q1 (lowest) −0.03% −0.48 Q2 −0.02% −0.23 Q3 −0.02% −0.35 Q4 −0.03% −0.51 Q5 (highest) −0.04% −0.59 95th %-tile −0.08% −0.56 99th %-tile 0.15% 0.22 Q5 − Q1 −0.01% −0.10

Full sample of corporate bonds Q1 (lowest) −0.03% −0.73 Q2 −0.05% −1.05 Q3 0.00% −0.03 Q4 −0.05% −0.69 Q5 (highest) −0.03% −0.21 95th %-tile −0.13% −0.35 99th %-tile 0.12% 0.24 Q5 − Q1 0.00% −0.03

Portfolio

Panel B: Bond portfolios formed by sorting on loan fees

−0.35% −0.48% −0.41% −0.26% 1.16% 1.41% 3.56%* 1.50%*

−0.98%** −0.98%** −1.11%*** −0.95%** −0.82%** −0.36% 2.06% 0.16%

−0.88%** −0.86%** −1.09%*** −0.96%*** 0.10% 1.49% 3.54%** 0.97%**

−0.87 −1.20 −1.08 −0.55 1.02 1.17 1.92 1.73

−2.33 −2.41 −2.71 −2.31 −2.20 −0.81 1.16 0.97

−2.17 −2.43 −2.94 −2.81 0.22 1.61 2.45 2.07

Equal-weighted 3month excess returns TRACE benchmark Mean t−stat (5) (6)

0.03% −0.13% −0.15% 0.21% 1.99% 2.11% 3.04% 1.96%*

−0.47% −0.47% −0.57%* −0.44% −0.26% 0.29% 1.89% 0.21%

−0.45% −0.43% −0.67%** −0.52%* 0.64% 2.30%** 4.13%*** 1.09%**

0.08 −0.34 −0.38 0.36 1.39 1.39 1.59 1.70

−1.36 −1.43 −1.74 −1.37 −0.85 0.64 1.12 1.28

−1.31 −1.44 −2.11 −1.80 1.29 2.24 2.66 2.19

Value-weighted 3month excess returns TRACE benchmark Mean t−stat (7) (8)

−0.22% −0.38% −0.40% −0.46% −0.31% −0.51% 1.14% −0.08%

−0.12% −0.07% −0.10% −0.11% −0.13% −0.22% 0.28% −0.02%

−0.12%** −0.21%*** −0.10% −0.15%* −0.05% −0.13% 0.92% 0.07%

−1.05 −1.62 −1.48 −1.56 −0.54 −0.63 0.68 −0.16

−1.06 −0.63 −0.89 −1.02 −1.09 −0.64 0.18 −0.19

−2.42 −2.90 −1.17 −1.85 −0.32 −0.28 0.87 0.41

Equal-weighted 3month excess returns matched benchmark Mean t−stat (9) (10)

Table C.1 Continued: Excess returns to bond portfolios over 1 and 3 month horizons

−0.26% −0.36% −0.53%* −0.45% −0.02% −0.19% −0.02% 0.24%

−0.10% −0.06% −0.05% −0.07% −0.05% 0.05% 0.03% 0.05%

−0.07% −0.19%*** −0.10% −0.11%* 0.03% 0.20% 1.03% 0.10%

−1.47 −1.64 −1.90 −1.47 −0.04 −0.26 −0.02 0.41

−0.94 −0.60 −0.57 −0.76 −0.50 0.17 0.03 0.57

−1.40 −3.05 −1.41 −1.74 0.22 0.62 1.34 0.69

Value-weighted 3month excess returns matched benchmark Mean t−stat (11) (12)

Table C.2: One-month excess returns to portfolios sorted on utilization and lending fees Average one month excess returns, in percentage points, to bond portfolios sequentially sorted on average daily utilization then by average daily fees during the previous month from July 2006 to March 2015. Table 5 describes the methodology. Whereas Table 5 presents average returns over three-month holding periods, this table presents the results for one-month holding periods. Panel A: All corporate bonds

Low Fees Low Utilization Portfolios sorted on utilization

Portfolios sorted on lending fees High Fees 2 Fees 3 Fees 4 Fees

High−Low

0.00 (0.03)

0.02 (0.26)

0.02 (0.22)

-0.10 (−0.71)

0.04 (0.51)

0.04 (0.74)

Utilization 2

−0.03 (−0.75)

−0.06 (−1.19)

−0.02 (−0.38)

−0.01 (−0.21)

0.27*** (2.87)

0.30*** (4.14)

Utilization 3

−0.02 (0.58)

−0.02 (−0.51)

−0.04 (−0.52)

0.01 (0.24)

−0.04 (−0.22)

−0.01 (−0.17)

Utilization 4

−0.01 (−0.24)

0.00 (−0.05)

−0.07 (−1.23)

−0.10 (−1.30)

−0.03 (−0.14)

−0.02 (−0.12)

High utilization

−0.01 (−0.19)

−0.10* (−1.73)

−0.03 (−0.48)

−0.07 (−0.63)

−0.33 (−1.17)

−0.32 (−1.36)

Panel B: Investment-grade industrial bonds

Low Fees

Portfolios sorted on utilization

Portfolios sorted on lending fees High Fees 2 Fees 3 Fees 4 Fees

High−Low

Low utilization

−0.06 (−0.73)

−0.06 (−0.72)

0.04 (0.39)

0.06 (0.42)

−0.06 (−1.03)

0.00 (−0.09)

Utilization 2

−0.04 (−0.54)

−0.04 (−0.54)

0.00 (−0.04)

−0.07 (−0.83)

0.05 (0.53)

0.08 (1.18)

Utilization 3

−0.07 (−0.93)

−0.01 (−0.13)

−0.06 (−0.84)

−0.04 (−0.58)

−0.10 (−1.04)

−0.03 (−0.36)

Utilization 4

−0.01 (−0.17)

−0.02 (−0.19)

0.05 (0.84)

−0.04 (−0.62)

0.02 (0.20)

0.03 (0.22)

High utilization

−0.06 (−0.68)

−0.04 (−0.56)

0.02 (0.27)

0.06 (0.69)

−0.13 (−1.20)

−0.08 (−0.73)

Panel C: High-yield industrial bonds

Low Fees

Portfolios sorted on utilization

Portfolios Sorted on lending fees High Fees 2 Fees 3 Fees 4 Fees

High−Low

Low utilization

-0.04 (−0.21)

0.01 (0.06)

0.00 (0.00)

-0.42 (−1.21)

0.36 (0.97)

0.40** (2.22)

Utilization 2

−0.04 (−0.25)

−0.04 (−0.19)

−0.13 (−0.98)

−0.01 (−0.04)

0.41 (1.10)

0.45*** (3.23)

Utilization 3

0.03 (0.20)

−0.18 (−0.95)

−0.22 (−0.98)

−0.07 (−0.27)

−0.34 (−0.59)

−0.38 (−1.36)

Utilization 4

−0.12 (−0.69)

−0.15 (−0.88)

−0.39 (−0.96)

−0.40 (−1.29)

−0.34 (−0.79)

−0.22 (−0.78)

High utilization

−0.01 (−0.07)

−0.13 (−0.83)

−0.39 (−1.24)

−0.56 (−1.18)

−0.82* (−1.95)

−0.81** (−2.27)

56

Table C.3: One-month fee-adjusted returns to portfolios sorted on utilization and lending fees Average one month excess returns adjusted for lending fees, in percentage points, to bond quintile portfolios sequentially sorted on average daily utilization then by average daily lending fees in the previous month from July 2006 to March 2015. We follow the same methodology used to construct Table C.2, but add bond lending fees paid by the bond borrower to beneficial owner who lends the bond. Fee-adjusted returns are from the perspective of the bond owner/lender. Panel A: All corporate bonds

Low Fees

High−Low

0.00 (0.07)

0.02 (0.37)

0.03 (0.33)

−0.09 (−0.64)

0.07 (0.90)

0.07 (1.19)

Utilization 2

−0.03 (−0.80)

−0.06 (−1.09)

−0.02 (−0.26)

0.00 (−0.06)

0.31*** (3.22)

0.33*** (4.29)

Utilization 3

−0.03 (−0.83)

−0.02 (−0.45)

−0.03 (−0.44)

0.02 (0.39)

0.00 (−0.01)

0.03 (0.34)

Utilization 4

−0.03 (−0.63)

0.00 (−0.07)

−0.07 (−1.17)

−0.09 (−1.21)

0.02 (0.09)

0.04 (0.28)

High utilization

−0.03 (−0.53)

−0.10* (−1.79)

−0.03 (−0.45)

−0.06 (−0.56)

−0.25 (−0.88)

−0.22 (−0.89)

Low utilization Portfolios sorted on utilization

Portfolios sorted on lending fees High Fees 2 Fees 3 Fees 4 Fees

Panel B: Investment-grade industrial bonds

Low Fees

Portfolios sorted on utilization

Portfolios sorted on lending fees High Fees 2 Fees 3 Fees 4 Fees

High−Low

Low utilization

−0.06 (−0.69)

−0.05 (−0.64)

0.05 (0.47)

0.07 (0.49)

−0.04 (−0.69)

0.01 (0.22)

Utilization 2

−0.04 (−0.59)

−0.03 (−0.47)

0.00 (0.06)

−0.06 (−0.73)

0.07 (0.75)

0.11 (1.42)

Utilization 3

−0.08 (−1.10)

−0.01 (−0.13)

−0.06 (−0.78)

−0.03 (−0.47)

−0.08 (−0.82)

−0.01 (−0.06)

Utilization 4

−0.03 (−0.47)

−0.02 (−0.24)

0.05 (0.88)

−0.03 (−0.52)

0.04 (0.43)

0.07 (0.50)

High utilization

−0.07 (−0.91)

−0.05 (−0.62)

0.02 (0.28)

0.06 (0.76)

−0.10 (−0.87)

−0.02 (−0.19)

Panel C: High-yield industrial bonds

Low Fees

Portfolios sorted on utilization

Portfolios sorted on lending fees High Fees 2 Fees 3 Fees 4 Fees

High−Low

Low utilization

−0.04 (−0.20)

0.02 (0.09)

0.01 (0.02)

−0.41 (−1.18)

0.43 (1.18)

0.47** (2.45)

Utilization 2

−0.04 (−0.24)

−0.03 (−0.16)

−0.13 (−0.93)

0.00 (0.00)

0.47 (1.28)

0.51*** (3.44)

Utilization 3

0.04 (0.21)

−0.18 (−0.93)

−0.21 (−0.95)

−0.06 (−0.23)

−0.28 (−0.49)

−0.32 (−1.06)

Utilization 4

−0.12 (−0.68)

−0.15 (−0.85)

−0.38 (−0.94)

−0.38 (−1.25)

−0.25 (−0.58)

−0.13 (−0.44)

High utilization

−0.01 (−0.05)

−0.12 (−0.78) 57

−0.37 (−1.19)

−0.51 (−1.08)

−0.65 (−1.55)

−0.64* (−1.71)